# Demo a Course Session

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## Demo Video Transcripts

Duration:"00:47:15.1170000"

00:00:30.930 --
OK guys, this is lecture
8C441.

00:00:36.670 --
I think we started problem two
last time, right?

00:00:41.780 --
And I'm not. I remember is that
we already almost done with

00:00:47.420 --
that. But let's just finalize it
again. This is problem tool in

00:00:53.060 --
hand out #2.

00:00:56.140 --
So this is the problem here.

00:00:59.010 --
I think we got. We calculated
the if we go to the most.

00:01:05.460 --
We calculated the location
of the neutral axis and

00:01:10.041 --
that was 6.78.

00:01:13.120 --
Inches and then we calculated
the tracking moment of inertia

00:01:18.570 --
or the correct moment of inertia
which is 4067.

00:01:24.740 --
And then we just applied the.

00:01:28.670 --
Basic basic equation
from the mechanics of

00:01:32.709 --
materials which has.

00:01:35.960 --
This form here F sub C = M
* X divided by the correct

00:01:42.904 --
moment of inertia and we
calculated the stresses here to

00:01:47.864 --
be about 1400 peace sign.

00:01:51.440 --
Right?

00:01:53.290 --
So the last thing that we need
to do is to calculate the

00:01:56.709 --
stress in the steel and the
stresses in the steel as well

00:01:59.865 --
or the stress of the steel F
South. This is the steel

00:02:03.021 --
stress.

00:02:06.600 --
We can still use the same
formula from the mechanics of

00:02:10.835 --
materials, but what we have to
do is we have to multiply that

00:02:15.840 --
by the model ratio and so that
should be N times the moment

00:02:20.845 --
times the distance from the
neutral axis to the centroid of

00:02:25.080 --
the steel which is.

00:02:27.430 --
Do you minus X? That should
be divided by the correct

00:02:30.862 --
moment of inertia.

00:02:33.160 --
Just to make it clear here guys.

00:02:36.820 --
We do have.

00:02:38.840 --
The assumption that at this
stage of loading.

00:02:44.390 --
The stress distribution, if you
check the handout.

00:02:48.710 --
That's the cross section
of the beam.

00:02:51.790 --
And we had, I think the width of
the beam is 12 inches.

00:02:56.030 --
And the total depth
here is 20, right?

00:03:00.290 --
So this is that's the dimension
and the first step. The first

00:03:04.250 --
step that we did last time is to
locate the neutral axis to the

00:03:08.870 --
neutral axis somewhere here like

00:03:10.520 --
that. And the distance or the
location of the neutral axis

00:03:14.940 --
which is X is measured from the
compression side, assuming that

00:03:18.625 --
the main steel is down here,

00:03:20.635 --
similar to. The figures shown
on the handout right so

00:03:27.556 --
this distance here. That's the
6.78 inches, right?

00:03:34.350 --
And based on the bending theory.

00:03:37.090 --
We assume that the stress
distribution at this stage is

00:03:42.360 --
linear like that.

00:03:51.190 --
So the dashed line below the
neutral axis means that

00:03:55.490 --
concrete. These dash line
here means that concrete is

00:03:59.360 --
ignored, so there is no
stresses in the concrete.

00:04:05.540 --
So that's here no.

00:04:08.130 --
I will just. Say no concrete
stresses, and this is the

00:04:12.816 --
stress in the concrete on the
compression side which is F

00:04:17.293 --
sub C and we calculated the FC
here from again the mechanics

00:04:22.177 --
of materials equation is 1400
PS I so this is 14 one 400 PS

00:04:27.875 --
I so the maximum the maximum
compressive stress is located

00:04:31.945 --
on the top surface of the
section, right?

00:04:36.690 --
And then the stresses or the
stresses is usually decreases

00:04:41.460 --
when we. Approach the neutral
axis till we have a zero stress

00:04:46.890 --
zero strain at this point.

00:04:49.550 --
And then stresses will be.

00:04:52.620 --
Converted from compression to
tension, so anything below the

00:04:56.607 --
neutral axis is under tension
and the maximum steel stress

00:05:01.037 --
which is F Subs. Here will be
the modular ratio, and that's

00:05:06.353 --
given as nine times the moment
which is already given as well.

00:05:14.770 --
Now at 70, so that's 70. Kept
foot again. We are working in

00:05:20.698 --
pounds and inches, so that
should be multiplied by 1000.

00:05:26.590 --
Times 12 to have it an pound

00:05:29.740 --
inch. And that should be
multiplied by the distance from

00:05:34.275 --
the neutral axis to the centroid
of the steel, which is this

00:05:38.775 --
distance. So the distance from
here to here. This is guys the

00:05:43.275 --
distance D -- X.

00:05:46.490 --
So the depth of the beam that's.

00:05:49.770 --
Given in the figure, which is 17
inches minus X, which is 6.78

00:05:56.803 --
inches and that should be
divided by the correct moment of

00:06:02.754 --
inertia, which is 4067.

00:06:06.690 --
So if we calculate that in peace
I so the steel stress here would

00:06:12.486 --
be about 19,000 peace sign.

00:06:24.240 --
Yes, So what is the again D is
the depth the depth is measured

00:06:30.988 --
from the compression side.

00:06:33.530 --
To the centroid of the
steel here.

00:06:37.550 --
So this distance here, that's D.

00:06:42.510 --
And the total height of the
section H. That's 20, but the

00:06:46.974 --
depth is 17.

00:06:50.280 --
This makes sense, so now this
is the stresses or the stress

00:06:53.712 --
distribution based on that
stage or based on that

00:06:56.286 --
applied moment. Now let me
ask you a question here.

00:07:00.180 --
What will happen if we increase
at the moment the value of the

00:07:03.911 --
moment given is about 70 Kip

00:07:05.633 --
foot. Right?

00:07:08.880 --
So if we increase this M this.

00:07:12.390 --
Moment here what would happen
to FC&F Steel will go up right

00:07:17.298 --
anwer this moment usually
increases when we increase the

00:07:20.979 --
load applied to the beam. That
makes sense. So when we

00:07:25.478 --
increase the load moments will
be increased. Stresses in

00:07:29.159 --
concrete and stress in the
steel will be increased.

00:07:34.520 --
Til the whole failure of the
beam, right. And then we so

00:07:40.427 --
based on that we will go over
the ultimate strength limit

00:07:44.794 --
state. But before going to the
ultimate strength we just solve

00:07:49.161 --
another problem here guys. And
the same handout before we move

00:07:53.528 --
on to another problem you have.
Do you have any questions here?

00:08:00.690 --
Yes and represent.

00:08:03.060 --
M and this is the modular
issue. Again, this model ratio

00:08:08.100 --
and. This represents the elastic
modulus of the steel divided by

00:08:13.560 --
the elastic modulus of concrete
and why you are doing that, or

00:08:18.780 --
why you are using NB cause this
kind of analysis in concrete

00:08:24.000 --
sections based on something
called the transformed area

00:08:27.480 --
method. So we convert or we

00:08:30.090 --
transfer everything. Into an
equivalent concrete make sense.

00:08:34.450 --
Instead of dealing with concrete
and steel, we.

00:08:39.320 --
We say that no, we will transfer
everything, convert everything

00:08:42.820 --
to an equivalent concrete
section. That's the reason that

00:08:45.970 --
if you check the.

00:08:48.850 --
If you check the hand out the
figure that is drawn on page

00:08:54.804 --
tool, I have something like
this you have.

00:09:01.840 --
Did you see the guys?

00:09:04.360 --
So this is the concrete.

00:09:07.120 --
On the compression side, and
we mentioned that the concrete

00:09:10.600 --
and attention is ignored, so
we converted all the steel on

00:09:14.428 --
the tension side to an
equivalent concrete section.

00:09:20.100 --
And you see that on the finger.
So this is the.

00:09:24.450 --
End times area steam.

00:09:29.220 --
So that's the distance X.
Again, this distance here is

00:09:32.840 --
the D -- X which is from the
neutral axis. This line here

00:09:37.546 --
represents the neutral axis
to the centroid of this team.

00:09:43.060 --
So let's go to problem. Problem
Three is a straight forward. We

00:09:47.908 --
can go over that quickly. So
again in problem 3.

00:09:53.020 --
We need to determine the
allowable bending moment

00:09:55.356 --
that may be applied to the
beam of example tool. So

00:09:58.568 --
we use these numbers here.

00:10:02.840 --
If the allowable stresses is
1350PSI for concrete in

00:10:07.367 --
compression and 20,000 piece I.

00:10:11.660 --
For that, enforcing steel in
tension so it's the same thing,

00:10:16.302 --
just problem Series A
straightforward business that.

00:10:19.256 --
Let's assume guys that I that we
have some limiting values for

00:10:24.320 --
stresses. We call it the

00:10:26.430 --
allowable stresses. So what is
the maximum? Let's say that the

00:10:30.845 --
maximum allowable stresses for
concrete in compression is.

00:10:34.110 --
1350 PS I and the maximum
allowable stresses for the

00:10:40.090 --
steel intention is about
20,000 pieces.

00:10:46.790 --
So can we use these two numbers
to find the?

00:10:52.610 --
Global moment.

00:10:56.190 --
So the allowable moment means
that the maximum moment that

00:11:00.330 --
should be applied to that beam
without exceeding this allowable

00:11:04.470 --
stresses. Right,
which is the same.

00:11:11.050 --
Same equations now if we.

00:11:16.150 --
And also, given that OK, so
the moment equation, same

00:11:19.920 --
thing it's.

00:11:21.970 --
FC. Times I sub CR which
is the correct moment of

00:11:27.980 --
inertia divided by Y. So
this is the just rearranging

00:11:32.270 --
the equation from the
previous problem. Same

00:11:35.273 --
equation. So we do have FC.
This is the allowable

00:11:39.563 --
compressive stresses which
is 1350 that's given.

00:11:44.410 --
Times the correct moment of
inertia, which already

00:11:48.234 --
calculated in problem 2 and that
was 46, four 067.

00:11:53.880 --
And that should be divided by
the value of Y.

00:11:57.840 --
Which is.

00:12:00.000 --
Distance from neutral. The
distance from the neutral axis

00:12:04.680 --
to the compression side, which
is 6.6 point in 76.7.

00:12:11.340 --
So that will bring us up tool.

00:12:17.920 --
A big number.

00:12:20.180 --
Which which is if you
divide the whole thing.

00:12:24.995 --
Let's divide the whole
thing guys by 1000 * 12

00:12:30.345 --
again to convert it to
Capen foot. I think that

00:12:35.695 --
will be 67.5 foot.

00:12:45.270 --
So.

00:12:48.010 --
To make sense so that this
is the moment this is the

00:12:51.694 --
global moment based on.

00:12:54.400 --
The allowable compressive
stresses in the concrete.

00:12:58.400 --
Now we can repeat the same
equation from problem tool

00:13:02.525 --
here for the steel. So the
moment equation based on the

00:13:06.650 --
steel stress that will be what
will be again F sub S.

00:13:11.750 --
Times the correct moment of

00:13:13.790 --
inertia. Divided by the modular
ratio times D -- X.

00:13:20.580 --
Again, this is the same
equation that we just used in

00:13:24.749 --
problem 2, but just
rearranging the equation so

00:13:27.781 --
the steel stress that's
given.

00:13:30.870 --
As 20,000, which is the level
steel stress 20,000 piece I.

00:13:36.970 --
Times the correct moment of
inertia, which is a constant

00:13:43.470 --
number 4067 inch 4.

00:13:48.550 --
Divided by the moderation
which is 9.

00:13:53.880 --
Times D -- X, which is the depth
of the beam 17.

00:13:58.980 --
Minus 6.78.

00:14:03.360 --
Anne. Again, if you divide the
whole thing by 1000.

00:14:10.600 --
By 12 that will give us a

00:14:14.597 --
hard 73. .7 keep foot.

00:14:20.830 --
So we do have two moments now to
a level moments. One is

00:14:24.613 --
calculated based on the.

00:14:26.460 --
Compressive stresses in the
concrete and the 2nd is

00:14:30.240 --
calculated based on the tensile
stress in the steel right.

00:14:35.910 --
So this is the number 67 point.

00:14:39.740 --
Five and the second moment is
73.7 and I think the allowable

00:14:44.432 --
one will be which one?

00:14:47.910 --
Smaller, right? So
that world controls.

00:14:53.760 --
Windows so that will control
67.5. That will be the

00:14:59.490 --
moment controls the.

00:15:04.980 --
Beam.

00:15:07.130 --
Makes sense, yes.

00:15:10.340 --
So the first moment equation you
said why yes, but you just use

00:15:14.786 --
the X value from the past. That
is basically the same thing. Yes

00:15:19.232 --
Simpson something so that the
genetic equation in mechanics of

00:15:22.652 --
materials says M y /, y, right
or myo over I. Sorry so M Y / I

00:15:28.466 --
so this Y the definition of this
wine. Concrete is the distance

00:15:32.570 --
from the neutral axis to the
compression side which is X OK.

00:15:38.620 --
OK questions.

00:15:44.590 --
So let's go to problem 4 then.

00:15:47.790 --
Which is.

00:15:52.550 --
That is a bit interesting
here to have it.

00:15:58.150 --
So for problem 4.

00:16:01.030 --
We have just a weird section.

00:16:07.480 --
So we have a market section
guys like this.

00:16:23.860 --
So.

00:16:25.970 --
And we do have steel bars
down here, so that's the

00:16:29.523 --
tension side.

00:16:32.580 --
Um?

00:16:35.820 --
The total width here is 18.

00:16:39.800 --
That's.

00:16:44.580 --
So.

00:16:46.920 --
6 inches each and the height of
this notch here is.

00:16:52.580 --
About 6 inches.

00:16:55.260 --
Um?

00:16:57.340 --
So the model ratio is given the
value of N is 8.

00:17:02.440 --
And the moment the applied
moment to that beam is about

00:17:06.477 --
110 kept foot.

00:17:10.830 --
So we need to find the game. The
bending stresses in the.

00:17:16.730 --
Concrete and steel.

00:17:19.490 --
So the challenge here
will be locating the

00:17:23.418 --
neutral axis, right?

00:17:26.780 --
How?

00:17:31.150 --
How, how, how, how we find the
neutral axis location here?

00:17:37.970 --
And the moment of inertia for
each square and then translating

00:17:41.919 --
it to no first week before,
before, before we find the

00:17:45.868 --
moment of inertia, we have to
find the neutral axis location.

00:17:49.817 --
We cannot find the moment of
inertia without knowing the

00:17:53.407 --
location of the neutral axis. So
we need to locate Mr. NA.

00:18:00.680 --
And to do that?

00:18:03.320 --
We have

00:18:07.520 --
two options or two scenarios
options, scenarios, right?

00:18:10.832 --
Because we don't know if the
neutral axis will be located

00:18:15.386 --
over here within the notch,
right or outside here.

00:18:21.960 --
Makes sense, so we have two
scenarios. Either the neutral

00:18:24.900 --
axis located. Over the neutral
axis will be less than the six

00:18:29.590 --
inches. The height of this
launch, or it will be greater

00:18:33.242 --
than the six inches, so that.

00:18:36.410 --
The easiest way to do that is
just assume one scenario and

00:18:39.578 --
see. If the scenario is achieved
so you are correct. If not, we

00:18:44.534 --
have to go to the other one. So
in other words, what we can do,

00:18:49.664 --
let's assume that the neutral
axis is located outside the

00:18:53.084 --
match like that. So in this case
this distance here that's our X,

00:18:57.530 --
which is, I think, drawn in the
figure. But just in case. So

00:19:01.976 --
this is the X value. Now to find
the neutral Axis location X.

00:19:07.460 --
We have to take the first moment
of area about that line to be 0.

00:19:13.550 --
So what about this? Can we
guys? You know guys that

00:19:19.182 --
this area here?

00:19:22.500 --
Has nothing right? This is void.

00:19:26.090 --
So the first moment of
area what we can do is

00:19:29.335 --
we can assume the whole.

00:19:32.010 --
The first moment of area of the
whole compression block here,

00:19:36.564 --
OK, which will be what will be B
again. B is the width here.

00:19:44.580 --
Times X. Times X /
2.

00:19:54.150 --
So B * X This is the area
of the concrete rectangle.

00:20:00.280 --
Above the neutral axis.

00:20:02.470 --
Times X / 2 because we're taking
the moment of that area about

00:20:07.514 --
the neutral axis.

00:20:09.300 --
Two more easily calculate the
area, multiply the area where

00:20:12.650 --
distance and the distance is X /
2 because we measure distances

00:20:16.670 --
from. Centroid the centroid
of that shape, which is so

00:20:21.936 --
the centroid of everything
here guys.

00:20:27.010 --
These block here are these box
here the centroid is at the

00:20:30.214 --
middle which is X at distance X

00:20:32.083 --
/ 2 right? Makes sense.

00:20:35.160 --
So this is the X / 2.

00:20:39.510 --
Minus now we need to subtract

00:20:42.258 --
the. The void.

00:20:47.650 --
OK, which will be what?

00:20:50.910 --
6 * X -- 6 So that any of
that voyante is.

00:20:56.950 --
6 by 666 by 6 right,
because this is 6

00:21:00.710 --
inches, this is 6
inches, but that should

00:21:03.718 --
be 6 * 6 times.

00:21:07.520 --
The distance from the centroid
of that void.

00:21:12.040 --
Which is here. To the neutral
axis so that distances.

00:21:19.080 --
X -- 3.

00:21:22.130 --
Three yes X -- 3 because this is

00:21:24.562 --
6 right guys? So make sense.
So this distance here I will

00:21:29.512 --
just draw an error here. So
that's X -- 3.

00:21:34.580 --
So that should be multiplied by
X -- 3.

00:21:40.660 --
And then.

00:21:43.440 --
Another negative sign.

00:21:47.210 --
Will take the first moment of
area of the steel.

00:21:51.720 --
About the neutral axis.

00:21:55.370 --
So the first moment of area of

00:21:56.980 --
this deal will be. The area of
the steel. Sorry N times the

00:22:01.523 --
area of the steel because we
need to transform this steel to

00:22:05.087 --
an equivalent concrete. So
multiply that by N so that's

00:22:08.836 --
N times a sub S which is
area of the steel.

00:22:14.170 --
Times the distance from the
centroid of the steel bars.

00:22:18.850 --
To the neutral axis, which
is this distance.

00:22:23.750 --
This is D -- X.

00:22:27.130 --
So that's times D -- X that
should be 0, so makes sense.

00:22:33.640 --
So if we do that, just let's
plug numbers here, the width B

00:22:40.062 --
is 18 * X.

00:22:42.680 --
Times X / 2 -- 36
* X -- 3.

00:22:51.550 --
Minus N, which is given as eight
times the area of the steel. And

00:22:57.192 --
if you look at the figure, the
area of the steel is given as 4

00:23:03.237 --
#10 four bars number 10 which is
5.06 square inches times D -- X

00:23:08.879 --
D is the depth.

00:23:11.500 --
What is the depth guys? Can
you see that in front of

00:23:14.224 --
you 23 -- X?

00:23:16.440 --
Yeah, so the depth is.

00:23:19.130 --
23 inches, can you see that?

00:23:22.130 --
Minus X = 0.

00:23:25.080 --
So have a nice equation
here and you know that

00:23:27.910 --
you're expert in math.

00:23:30.590 --
It was your magic Calculator to
find what is X.

00:23:36.740 --
So X here will be.

00:23:39.940 --
9.32 inches, which is a
good sign.

00:23:46.370 --
Why it's a good sign?

00:23:50.060 --
It's outside, avoid yes, because
we assumed at the beginning that

00:23:54.383 --
the neutral X is larger than the
six inches depth is away from

00:23:59.492 --
the void. Based on that

00:24:02.435 --
assumption. The exact solution
is 9.32, which is verifying what

00:24:07.570 --
we're what we have assumed to.

00:24:10.770 --
Our scenario is good
makes sense.

00:24:14.280 --
So from here guys, once we have
the neutral axis questions about

00:24:17.892 --
this, yeah, probably know if our
assumption is bad. If it's

00:24:21.203 --
negative or if it's just smaller
now this more if it's 4 inches.

00:24:25.116 --
So in this case that means that
we have to go back and repeat

00:24:29.330 --
everything. That's a good
question. Makes sense guys so

00:24:32.039 --
again. This is now
this is good, right?

00:24:38.020 --
Now if it's bad.

00:24:44.890 --
Which is again or correct.

00:24:48.270 --
FX for some reason 3 inches, so
that's bad. So what should we

00:24:54.549 --
do? We have to neglect all of
that and start over from

00:25:00.345 --
scratch, assuming that the
neutral axis whoops.

00:25:05.910 --
The neutral axis is somewhere

00:25:07.775 --
here. And then you have
to repeat the process to

00:25:10.727 --
find what is the exact X.

00:25:19.470 --
Are you following them here?

00:25:22.340 --
OK.

00:25:25.560 --
OK, so we have X which is good
9.32 Now the second stage step

00:25:30.908 --
is to find.

00:25:33.670 --
The moment of inertia. What is
the correct moment of inertia

00:25:37.784 --
and at 12?

00:25:39.660 --
Have some.

00:25:42.230 --
Computational effort
here to find it, but in

00:25:46.182 --
order to small guys so.

00:25:49.850 --
Step #2

00:25:53.020 --
why find the?

00:25:56.910 --
Cracked moment of inertia. So
the correct moment of inertia

00:25:59.780 --
Now will be a challenge. How
can we find it?

00:26:12.620 --
Let me draw this again here.

00:26:16.930 --
So.

00:26:19.940 --
This is the neutral axis, right?

00:26:25.510 --
So we need to find the moment of

00:26:27.134 --
inertia of two things. For the
concrete and the compression

00:26:30.492 --
side and for the steel and
attention side. So for the

00:26:33.979 --
concrete and the compression
side we have a very weird shape

00:26:37.466 --
because we do have a void here.
So we have many different ways

00:26:41.587 --
to do it OK.

00:26:43.870 --
We know that this
distance now is X.

00:26:47.270 --
Which is 9.32 inches.

00:26:50.720 --
We know that the width here of.

00:26:54.420 --
Of this

00:26:56.250 --
port, 6 inches. Same thing here.

00:27:01.140 --
6 inches So what we can do is
we can divide that weird shape

00:27:06.954 --
into subdivisions or some small
shapes to find the moment of

00:27:10.716 --
inertia of each.

00:27:13.220 --
OK, So what we can do guys?

00:27:17.140 --
Let's do this so that's the
fairest shape here.

00:27:21.820 --
Or the 1st part. This
is the second part.

00:27:26.080 --
And that's the third part.
So this is part one. This

00:27:30.821 --
is Part 2 and.

00:27:33.960 --
This is Part 3.

00:27:36.650 --
So whenever you have a very
weird shape like that, the

00:27:40.236 --
easiest way is to divide it into
small rectangles, because we

00:27:43.822 --
know the moment of an edge of

00:27:46.104 --
each rectangle is. BH
cubed over.

00:27:51.040 --
No. Yes, I know, but this is
about the centroid, but is for

00:27:56.600 --
our case is BH cubed over 3.

00:28:00.830 --
Do you understand why correct?

00:28:03.350 --
No.

00:28:05.830 --
Yes no.

00:28:08.040 --
Why it's over 3? Again, we
mentioned that last time.

00:28:12.780 --
Side note.

00:28:15.830 --
So the BH cubed over 12. This is
the moment of inertia when the

00:28:22.130 --
neutral axis is passing through
the centroid of the area.

00:28:27.470 --
So these BHQ over 12 is the
moment of inertia about this

00:28:32.282 --
line, which is passing through

00:28:34.287 --
the centroid. But if we.

00:28:39.560 --
If we do have the same
rectangle, if we need to find a

00:28:42.810 --
moment of inertia of a

00:28:44.060 --
rectangular section. About a
line passing through its lower

00:28:48.327 --
edge like this.

00:28:51.120 --
Note the centroid, so that
will be BH cubed over three.

00:28:55.652 --
This makes sense.

00:29:01.350 --
Wake up.

00:29:04.610 --
So here we have.

00:29:07.220 --
Oh well, here we have.

00:29:10.630 --
What is the first moment of
inertia? What is the moment of

00:29:14.122 --
inertia of the first part then?

00:29:18.210 --
Six times so B is 6 inches,
right? So six times.

00:29:24.100 --
The height which is 9.32
cubed over.

00:29:31.620 --
3.

00:29:34.200 --
Over 3 * 2.

00:29:36.700 --
Because area one or part one is
similar to Part 2 makes sense.

00:29:43.440 --
OK. Plus the moment of
inertia of the small part,

00:29:48.837 --
which is part number three,
we know that this width is.

00:29:56.280 --
That's six inches, and we know
the height as well this.

00:30:00.250 --
Height is what is 9.32 -- 6,

00:30:03.659 --
right? So that will be 3.3 two?
Yeah that will be 3.

00:30:11.390 --
That would be 3.32 inches.

00:30:15.160 --
So from here, the moment of
inertia of this small part here

00:30:20.632 --
will be the width, which is 6
times the height which is 3.32

00:30:26.560 --
^3 / 3 as well.

00:30:29.990 --
This makes sense. Again, this
tool because we have two

00:30:33.500 --
similar parts which is part
one and Part 2, and this term

00:30:37.712 --
is for part number 3.

00:30:40.990 --
Plus the moment of inertia of
their enforcing steel, which is.

00:30:47.790 --
Lying here in the lower side.

00:30:52.750 --
And that should be an N, which
is the molar ratio that's eight

00:30:58.379 --
times the steel area which is.

00:31:02.460 --
Five point 5.06.

00:31:05.880 --
So this is the in value. This is
the area of the steel times the

00:31:11.520 --
distance from the centroid of

00:31:13.400 --
the steel. Through the neutral
axis, which is.

00:31:19.470 --
9.3 Two yes D -- X
which is 23 -- 9.32.

00:31:28.660 --
So this is 23
-- 9.32 ^2.

00:31:35.970 --
Squared

00:31:38.390 --
OK. Because you know the problem
with this concrete calculations.

00:31:43.139 --
If you forget the square here,
everything down here will be

00:31:47.330 --
missed. Will be missed, right

00:31:50.074 --
so? Please be focused with her
with us. If so, this is the

00:31:55.874 --
moment of inertia that we should
have and that will be about

00:32:00.578 --
10,887 inch 4.

00:32:03.940 --
So at this stage, once you have

00:32:07.580 --
them. Moment of inertia. And
once you have the location of

00:32:12.720 --
the neutral axis, we can easily
move on to find the stresses at

00:32:17.530 --
any. Location across the section
that we have so.

00:32:26.020 --
To find the stresses again will
recall the mechanics of

00:32:30.190 --
materials equation F sub C will
be the moment.

00:32:35.310 --
Times our why?

00:32:37.790 --
Which is equivalent to X to M *
X divided by the correct moment

00:32:42.816 --
of inertia. This is the equation
to find the concrete stress, and

00:32:47.124 --
we do have the moment because

00:32:49.278 --
that's given. 110

00:32:54.900 --
kept foot, so this 110 should be
multiplied by again 1000 * 12.

00:33:03.140 --
Times the distance X which is
the neutral axis, which is 9.32.

00:33:10.700 --
Divided by the correct moment of
inertia, which we just

00:33:15.030 --
calculated the 10,800.

00:33:18.530 --
87 that will give us
like 1130 P sign.

00:33:26.550 --
So about 11130, pyside, that's
the stress in the concrete. And

00:33:31.676 --
for the steel.

00:33:34.280 --
It's the equation. It's N times

00:33:37.730 --
the moment. Times the distance D

00:33:41.562 --
-- X. Divided by the correct
moment of inertia.

00:33:47.550 --
So again, repeating that N is 8.

00:33:52.250 --
The moment is 110.

00:33:55.420 --
Times 12,000.

00:34:00.780 --
Times D -- X, which is
23 -- 9.32.

00:34:07.500 --
That's divided by 10,887. So
if you simplify that, I

00:34:14.680 --
think we'll have about 13,000.

00:34:20.180 --
269 PS I.

00:34:25.080 --
So these are the stresses
in the concrete.

00:34:29.940 --
And in the steel
at the extreme.

00:34:36.360 --
Favor so.

00:34:42.990 --
This makes sense here guys.

00:34:54.060 --
So going back to
this figure here.

00:35:02.750 --
Are you done this part?

00:35:07.540 --
So stressing concrete is about

00:35:09.730 --
11:30. Steel is 13,000.

00:35:13.790 --
So if I ask you to draw the
stress distribution here, so

00:35:17.834 --
that should be the stress
distribution. Again similar to

00:35:20.867 --
what we did last time. We do
have a triangle like this.

00:35:26.800 --
And the maximum stress in the
concrete is in the top surface

00:35:31.120 --
on the compression side, which
is 1130 P sign.

00:35:36.220 --
And concrete on the tension site

00:35:38.836 --
is ignored. And the maximum
stress on the steel level, which

00:35:44.291 --
is down here.

00:35:47.160 --
That is 1113 thousand
269 peace sign.

00:35:57.310 --
So that's the stress
distribution still.

00:36:01.540 --
Perfect linear noise.

00:36:07.200 --
We'd like just to look at this
figure and just have some

00:36:12.084 --
conclusions here so.

00:36:15.990 --
From C 357 guys, you remember
that you know the target

00:36:20.731 --
compressive strength for normal
concrete at 28 days was what?

00:36:25.860 --
Roughly.

00:36:29.650 --
4000 something like that, right?
This for normal concrete that we

00:36:33.610 --
use for bridge decks like 4000.
PS. I so.

00:36:37.970 --
F prime C
at 28 days.

00:36:43.890 --
This should be the target. This
is a very well known number

00:36:48.596 --
in the in the outside the field.
The 4000 piece sign.

00:36:53.790 --
Let's assume that this concrete
that has been used in this

00:36:58.135 --
section has a compressive
strength at 28 days equals 4000,

00:37:02.085 --
right? Now when the moment
applied when the moment.

00:37:10.620 --
When the moment
of 110 kept foot.

00:37:17.570 --
Is applied to that section. How
much concrete stress we got.

00:37:22.890 --
1130 So FC we got

00:37:26.430 --
11. 30 or 1100 thirties
makes sense.

00:37:32.440 --
So this is the
maximum compressive

00:37:34.804 --
stresses on the
concrete when the

00:37:37.168 --
moment was 110.

00:37:39.990 --
The question now is.

00:37:42.790 --
What is the relationship between
the 100 so that 1130 piece I

00:37:47.086 --
compared with the 4000 peace

00:37:48.876 --
sign? Is it like less
than half equals half

00:37:52.564 --
of their value or what?

00:37:56.960 --
It's 11:30 is less than half
of the 4000 is right, so

00:38:04.832 --
when groups when not if when?

00:38:10.580 --
When F sub C, which
is the 11:30 equals

00:38:16.691 --
oh sorry less than
.5 F prime C. The

00:38:22.802 --
target at 20 days.

00:38:26.690 --
OK.

00:38:29.770 --
Stress is for the stress
distribution.

00:38:38.130 --
As assumed to be linear.

00:38:45.390 --
So as long as.

00:38:47.360 --
The compressive stress is
less than 50% of the 28

00:38:53.230 --
days compressive strength.

00:38:57.230 --
The stress distribution
is assumed to be linear

00:39:00.110 --
over the cross section.

00:39:02.930 --
If this number, which is F sub

00:39:05.380 --
C. Exceeds
50%

00:39:11.490 --
of the 4000.

00:39:13.770 --
The stress distribution will be

00:39:16.635 --
nonlinear. Because after that
number after that, sorry after

00:39:20.806 --
that threshold value which is

00:39:22.616 --
the 50%. Concrete the concrete
section will be having major

00:39:27.764 --
cracks and this major cracks
will produce non linearity in

00:39:32.194 --
the concrete behavior.

00:39:34.660 --
And in that stage.

00:39:38.350 --
The actual stress distribution
will be not linear. It will be a

00:39:43.438 --
nonlinear system distribution,
which will be. Other would be

00:39:47.254 --
our topic here so.

00:39:49.690 --
If we go back to the screen.

00:39:52.310 --
So which? Is
showing like this?

00:40:00.050 --
So. So once.

00:40:02.740 --
FC exceeds point 5F.

00:40:06.710 --
Prime, see.

00:40:09.810 --
We now entering the ultimate
flexural strength stage of

00:40:14.697 --
the concrete section and in
that stage.

00:40:19.620 --
And that's the image we do
have the stress distribution

00:40:22.910 --
groups. Can you see that the
stress distribution now became

00:40:26.200 --
nonlinear? So this is just a
3D thing. Just to make sure to

00:40:30.477 --
visualize to make sure that
you understand this. That's

00:40:33.438 --
the width of the section.
That's the height this is the

00:40:37.057 --
C value or the.

00:40:39.930 --
The location of the neutral
axis. So in the uncorrect

00:40:43.380 --
stage we named the location
of the Neutral X as an X.

00:40:47.520 --
Once we jump into the
ultimate stage now we will

00:40:50.970 --
call it C and the strip the
stress distribution now is a

00:40:55.110 --
parabolic or has a public
shape which is not linear,

00:40:58.560 --
and in this case.

00:41:01.640 --
The analysis will be a little
bit different, but again.

00:41:06.570 --
As you know, the ACI dimeric and
concrete Institute committee

00:41:11.540 --
knows that civil engineers are

00:41:14.025 --
lazy, so. And you know, we know
that we are.

00:41:19.790 --
Very strong math, right? So they
switch it or we made the life

00:41:25.406 --
more easier for us.

00:41:27.700 --
So as long as the stresses or
the stress distribution is

00:41:32.034 --
nonlinear and has a public ****
like that we have, we can assume

00:41:37.156 --
it to be or to have an
equivalent stress equivalent

00:41:41.096 --
rectangular stress block similar
to the one that is shown here.

00:41:45.430 --
So in other words, once this is
the actual stress distribution

00:41:49.764 --
for get it, which is a public
complicated shape for get it,

00:41:54.492 --
and then we will assume that the

00:41:57.250 --
section. OPS the section. We
will have a rectangular

00:42:01.474 --
equivalent stress block like

00:42:03.326 --
that. So go back going back to
it again. Sorry this is the

00:42:08.326 --
cross section. I think you
know you're familiar with it.

00:42:11.606 --
Now this is the strain
distribution. Hope So what you

00:42:14.886 --
can conclude here that.

00:42:17.370 --
Regardless of the loading stage.

00:42:20.580 --
The strain distribution is
assumed linear.

00:42:24.850 --
On correct, correct fully
cracked ultimate stage. The

00:42:27.650 --
strain distribution is linear,
but for the stress the situation

00:42:31.150 --
is different. So for the stress
distribution as you can see this

00:42:35.350 --
is the parabolic shape and we do
have the compression force on

00:42:39.550 --
the compression side. This is
the tension force and retention

00:42:43.050 --
side that is complicated for us.
So we will replace these public

00:42:47.250 --
with an equivalent stress block.
2 main important things that you

00:42:51.100 --
must understand when we talk
about Ultimate stage ultimate

00:42:54.250 --
strength. That means that the
concrete, which is the maximum

00:42:59.592 --
maximum stresses and concrete
will start to fail. So the ACI.

00:43:05.410 --
Put a threshold of the ultimate
failure strain, so once you hear

00:43:13.258 --
that the concrete strain reaches

00:43:16.528 --
0.003. That means concrete died.

00:43:22.050 --
Recent.

00:43:24.330 --
When the steel reaches the steel
strain reaches the yield strain.

00:43:30.800 --
That means that steel is filled.

00:43:34.920 --
So in conclusion, here concrete
fails at a strain equals 0.003.

00:43:41.910 --
Steel fields at a strain equal
to the yield strain.

00:43:48.210 --
So these two failure failure
thresholds or values are.

00:43:54.260 --
Or done or made for the
design purpose, so makes sense.

00:44:01.960 --
When we talk about design.

00:44:04.030 --
You have to memorize these two
numbers. However in the lab.

00:44:09.580 --
You should remember that beam.

00:44:11.910 --
That I showed you guys in the
lab when we start pushing the

00:44:16.694 --
beam to the limit, the concrete
strain will exceed .00 three and

00:44:21.110 --
the steel strain will exceed the
yield strength at the final

00:44:25.158 --
filter stage. But we cannot do
that in design and design. We

00:44:29.574 --
have to be very conservative
right? To make sure that the

00:44:33.622 --
beam or the element the concrete
element will not reach the

00:44:37.670 --
ultimate stage, because if it if
that element reaches that, so.

00:44:41.920 --
Everything will fail
immediately, right guys? So we

00:44:44.920 --
have to have a very safety
factor here, and that's based on

00:44:49.420 --
the values that the ACI
specified. So this is the actual

00:44:53.545 --
stress distribution. This is the
equivalent stress block. We

00:44:57.472 --
assume that the actual neutral
axis has a.

00:45:01.410 --
Annotation of C. Here. Once we
transfer that to the

00:45:05.160 --
equivalence, replug the neutral
X is location will be.

00:45:09.560 --
Or will equal to a?

00:45:13.970 --
OK, so this a this is the
neutral axis location the new

00:45:18.770 --
one. What is the relationship

00:45:20.770 --
between A&C? A equals another
factor called beta 1 * C.

00:45:27.630 --
So be ready that because it will
be exposed to about 1000 factors

00:45:32.531 --
from then on. So beta one.
That's the factor that we

00:45:37.055 --
must consider this beta one
depends on the compressive

00:45:40.448 --
strength of concrete. Is normal
concrete high strength, ultra

00:45:43.841 --
high performance? All a that's
will be shown here. So based on

00:45:48.365 --
the concrete compressive
strength, you can determine what

00:45:51.381 --
is the value of beta one going
back to hear the maximum

00:45:55.905 --
concrete stress that is limited

00:45:57.790 --
for design. Is 0.85 times.

00:46:01.490 --
The FC prime don't left .8 Zero
Point 8 five times.

00:46:07.570 --
Is it if Ramsey lifsey prime?

00:46:11.950 --
FC Prime FC prime.

00:46:15.640 --
Fusion FC Prime so .5 so the FC
prime that you got from the

00:46:20.960 --
machine in the lab which is 4000
PS I we will multiply that by

00:46:26.280 --
.85 to have the maximum
compressive stress limit for

00:46:29.700 --
design. Makes sense.

00:46:33.480 --
Break so.

00:46:35.750 --
So it's you guys on Friday. I
haven't hand out here. Please

00:46:40.178 --
take a copy that will use it
next week and maybe Friday and

00:46:44.975 --
it's already posted too similar.

00:46:48.500 --
Thank you.

Duration:"01:16:32.4080000"

00:00:21.550 --
OK, a couple things as we get
started. The first one is we

00:00:26.828 --
have the last lab assignment.

00:00:31.670 --
And so this one is going to be a
bus differential protection lab

00:00:35.349 --
and so the on campus students is
pretty much going to be a

00:00:39.028 --
similar setup to what you did
before. You just need to read

00:00:42.424 --
through this and then work with
the TA. As far as if you're

00:00:46.103 --
going to, I think you all of you
have groups that you've been

00:00:49.782 --
doing the labs with the TA. If
you want to stick with those

00:00:53.461 --
groups in those times. If you
wanted to negotiate a different

00:00:56.574 --
time, then you just need to
communicate with him about that.

00:01:02.040 --
Until you have a system and
you're going to look at fault

00:01:05.628 --
at a couple of different
places, this is actually

00:01:08.319 --
should be a little bit shorter
than the last, quite a bit

00:01:11.907 --
shorter than the last lab.

00:01:14.920 --
And so you're really just
going to look at several

00:01:17.710 --
different cases.

00:01:19.710 --
Look at the behavior with this.

00:01:22.940 --
The Engineering Outreach Lab is
going to be similar.

00:01:26.730 --
So this is just the description
of the entering outreach lab.

00:01:31.580 --
And so it's a little bit more
complicated system, but it's

00:01:34.616 --
still the same basic idea.

00:01:36.980 --
And also you have some
information about the CT

00:01:40.410 --
ratio that's was used for this.

00:01:44.480 --
And then this is using that.

00:01:47.590 --
Relay model that the
differential relay model we

00:01:50.462 --
talked about. So again this
is a low impedance restrained

00:01:54.052 --
differential element, so it's
not. It's not a high

00:01:57.283 --
impedance differential
element.

00:02:01.530 --
If anyone has fair time and
wants to create their own

00:02:05.369 --
creative all the create this,
it wouldn't be that hard to

00:02:09.208 --
create a lab for the restraint
for the high impedance

00:02:12.698 --
differential elements. We just
haven't had a chance to put

00:02:16.188 --
together the simulation files.

00:02:18.800 --
So anyway, it's the same idea
you read in the data files.

00:02:24.470 --
Very similar to the handout that
we talked about with the lecture

00:02:28.310 --
last week. All of this stuff
we're reading the comtrade file,

00:02:31.830 --
and so where this really starts
to differ a little bit is

00:02:35.670 --
towards the end of it. Once
we've got the phasers, so we've

00:02:39.510 --
got the things where we're
looking at the voltages in the

00:02:43.030 --
currents, and then we have the
operating restraint current, and

00:02:46.230 --
so one thing that's different
from the hand out before is now

00:02:50.070 --
the. In this case, there's no.

00:02:53.660 --
Nothing where you put in a
multiplier to imitate

00:02:56.297 --
saturation. The simulation data
that you're using for this now

00:02:59.227 --
actually has saturation in it.

00:03:01.850 --
And the case is that you'll be
doing for the on campus

00:03:05.450 --
students in the lab. You're
actually going to be doing

00:03:08.450 --
these with an RTS simulation
instead of using the model

00:03:11.450 --
power system, and so that the
RTS will have setae. Models

00:03:14.750 --
that include saturation, but
you're still going to be

00:03:17.450 --
setting the actual physical
relay.

00:03:21.310 --
And then one of the things that
this is going to show is the

00:03:25.664 --
basically the how they operate.
Quantity changes. So basically

00:03:28.463 --
as it reads through samples,
this thing is moving and then it

00:03:32.195 --
works its way up and then it has
some final value it goes to and

00:03:36.860 --
so you can as you look at these
different cases once you enter

00:03:40.903 --
the slope setting you can
actually look at a little bit

00:03:44.324 --
how the how the value evolves
and when you look at the case

00:03:48.367 --
with the saturation you can
actually see how it.

00:03:51.300 --
Now the saturation changes
what it's what the relay

00:03:54.171 --
element is seeing too, and so
this was a case for an

00:03:57.999 --
internal fault, so it grows
quickly.

00:04:02.860 --
So any questions about that?

00:04:09.170 --
Hey are there any questions
from the last lecture?

00:04:12.680 --
Yeah, so in the last lecture
when you talk about the high

00:04:16.832 --
impedance plus differential
protection, you mentioned that

00:04:19.254 --
for an external fault. Once one
of the see T starts to saturate

00:04:23.752 --
it will dive deeper into
saturation, right? So my

00:04:26.866 --
question is how will that?

00:04:29.160 --
To how will that city begin to
saturate? Like because?

00:04:33.660 --
The currents are all balanced,
right? I mean based on the

00:04:37.972 --
culture of slow, so part of
it's too far into this into the

00:04:43.460 --
hand out so.

00:04:47.760 --
That's the internal fault. So
for the external fault part of

00:04:51.148 --
it's going to be the case that.

00:04:54.690 --
We've got this one. This is 1
heck external fault, right? So

00:04:58.338 --
this is seeing the current from
all of the other feeders or

00:05:01.986 --
other lines going through it,
and so depending on what the

00:05:05.330 --
burden is for this one.

00:05:07.800 --
Oh that 'cause there's
going to be?

00:05:12.460 --
The relay and the and some of
the winding resistance is going

00:05:16.084 --
to be dominant. Burden that
affect saturation in this one in

00:05:19.406 --
a lot of ways.

00:05:21.210 --
So if this one, if there's a
fault with a lot of DC offset,

00:05:25.088 --
especially then this one is
going to start to saturate.

00:05:27.858 --
'cause this is seeing the most
current. I thought there is only

00:05:31.182 --
one button then that's the one
at the end. Well, remember that

00:05:34.506 --
the burden and we look at ACT
when we look at burden.

00:05:40.260 --
Mr Lead wire.

00:05:48.530 --
So the first thing we're going
to have is the CT winding

00:05:51.338 --
resistance. And it's so. So
in this case the Siti

00:05:54.649 --
winding resistance is going
to be the most significant

00:05:57.088 --
one, because once we get to
the terminals of the see T.

00:06:07.470 --
We're basically connecting each
of the CTS.

00:06:12.750 --
In parallel on the secondary
side, right and then once

00:06:16.320 --
they once we have this
parallel combination, then

00:06:19.176 --
that's going. Then we have
the rest of the lead wire.

00:06:25.200 --
And we have the relay out here.

00:06:30.540 --
But there's the secondary
current on the secondary

00:06:33.404 --
winding, and the CT is still
going to see.

00:06:37.340 --
All that current, right?
The current when they sum

00:06:40.328 --
to 0 between.

00:06:44.320 --
We put in a third
CT just to kind of.

00:06:49.030 --
Illustrate this a little
bit more.

00:06:58.680 --
When I talk about connecting
them together right, this is

00:07:01.940 --
where they sum to 0, right?
So if it's if it's an

00:07:05.852 --
external fault.

00:07:12.350 --
So let's say that this is
the one with.

00:07:18.870 --
The external fault, right? So
that's going to have.

00:07:23.100 --
Let's say we have current going
this way and this one. Each of

00:07:26.948 --
these are going to have their
share feeding it right, so this

00:07:30.500 --
one is going to be the sum of
this plus this and so at this

00:07:34.940 --
point here. They're going to sum

00:07:37.224 --
to 0. But this one, each one of
these is going to have its own

00:07:42.072 --
fault current share the
fault current, it's it's

00:07:44.628 --
carrying. It's going to go

00:07:46.048 --
through this resistance. And
so basically what's going to

00:07:49.888 --
drive that start driving in
this one in the saturation is

00:07:53.936 --
going to be a combination of
the voltage drop across this

00:07:57.984 --
plus the ACE asymmetric
current due to the DC offset.

00:08:03.130 --
Remember that as we talked
about with on the BH

00:08:07.030 --
characteristic, the DC offset
is shifting you in One

00:08:10.540 --
Direction and the BH
characteristic.

00:08:17.450 --
And so when we look at this.

00:08:21.080 --
So under normal conditions.

00:08:23.650 --
It's going to be doing
something like this, right? And

00:08:26.760 --
if we have a fault with no set
without significant saturation?

00:08:31.480 --
It's going to be doing some like
this, and so if we have well

00:08:36.324 --
size CTS we may only see
behavior that looks like this.

00:08:40.730 --
But for a bus situation,
sometimes it's hard to get

00:08:44.380 --
around that, but if we add.

00:08:47.510 --
The.

00:08:52.590 --
The DC offset.

00:08:54.830 --
I did not draw that very well,
sorry. So we may start out with

00:09:00.248 --
something like this. Then the

00:09:02.183 --
next cycle. It's going to be
working like this and it's going

00:09:06.480 --
to be following that DC offset,
so it's going to push it into

00:09:10.302 --
saturation. Discuss. The flux
loops are being pushed this way

00:09:13.242 --
by the DC offset.

00:09:15.870 --
And in some cases with a
combination of the of a large

00:09:20.286 --
current and going through
this resistance in a DC

00:09:23.598 --
offset, this one may start to
go into saturation an.

00:09:29.390 --
Lessina cycle.

00:09:31.800 --
Possibly quite a bit less
in the cycle.

00:09:35.790 --
And so that's why that's why
even though you on the surface,

00:09:39.606 --
you would say that there
shouldn't be much voltage across

00:09:42.786 --
this, because these current sum
to zero and the voltage drop

00:09:46.284 --
across this should normally be
negligible. But what's going to

00:09:49.464 --
happen is that the combination
of that fault current going

00:09:52.644 --
through this winding resistance
and the DC offset starts this

00:09:55.824 --
one into saturation. And then
that mismatch current through.

00:10:00.130 --
That saturation goes through
this, and because of that

00:10:03.577 --
compensating resistor that's
going to drive this voltage up.

00:10:08.730 --
But because this is the one
that's already starting to

00:10:12.290 --
saturate and has a lower
impedance than it's, it's

00:10:15.494 --
going to tend to make this
voltage collapse and keep

00:10:19.054 --
these from rising.

00:10:28.560 --
Like I said, it's not. That's a
very good question. 'cause it's

00:10:32.280 --
there's a lot of things that are
not intuitively obvious when we

00:10:36.000 --
look at the high impedance bus

00:10:37.860 --
differential. Because we're
basically using something that's

00:10:42.662 --
inherently nonlinear to work.

00:10:57.580 --
Any other questions for my son?

00:11:06.790 --
OK, so then we're going to start
on. Next, we're going to start

00:11:11.223 --
talking bout transformer
protection and I talked to I did

00:11:14.633 --
a very quick introduction to
some of the some of the issues

00:11:18.725 --
and the difference.

00:11:20.960 --
Things were gonna talk about.

00:11:21.870 --
We're going to talk about.
Fall protection of the

00:11:25.190 --
transformer itself for faults
inside the transformer.

00:11:29.680 --
And then we're also going
to look at protecting the

00:11:32.850 --
transformer, firm
external conditions, and

00:11:34.435 --
this can include faults
external to the

00:11:36.654 --
transformer. Boy, the
transformer is carrying

00:11:38.556 --
the fault currents that
goes that go to it.

00:11:47.680 --
And then there are Transformers
introduce a number of unique

00:11:51.640 --
challenges that we'll talk about
as we go through this.

00:11:56.550 --
So in some ways it will start
out looking at a concept similar

00:12:01.308 --
to what we looked at with the
bus protection. So we're going

00:12:05.700 --
to a lot of the internal fault
protection for Transformers.

00:12:09.360 --
Starts with the idea of
restrained low impedance

00:12:12.288 --
differential element, so it's
kind of build time. We start. I

00:12:16.314 --
started with the bus protection.

00:12:29.630 --
And so one of the things that
the bear in mind as we talk

00:12:35.748 --
about transformer protection is
when we talk about bus

00:12:39.681 --
protection. Fast protection has
a bus fault or misoperation

00:12:43.614 --
where a bus gets tripped when it
shouldn't can have very severe

00:12:48.858 --
operational. Consequences for
our power system. So bus faults

00:12:52.556 --
are actually fairly rare.

00:12:54.760 --
Fat faults that cause were and
the bigger concern is as

00:12:59.028 --
generally going to be external
faults that caused the bus

00:13:02.908 --
protection to miss operate.

00:13:06.160 --
And so that's why the restrained
differential element, the high

00:13:09.640 --
impedance differential element,
have so there so much efforts

00:13:12.772 --
gone into developing and
optimizing those at the relay

00:13:15.904 --
vendors is because they are very
high consequences operationally

00:13:19.036 --
to the system in the short term.

00:13:24.130 --
Transformer failures, on
the other hand.

00:13:44.050 --
Can have longer time
consequences.

00:13:54.730 --
And that's because there are
longer replacement times.

00:13:59.700 --
And in most cases, if an
internal fault happens in a

00:14:04.560 --
transformer.

00:14:06.370 --
There is a good chance that it's
going to evolve to the point

00:14:10.348 --
where it's not something that's
very simply repaired. In some

00:14:13.408 --
cases there are still a number
of cases where they're caught

00:14:16.774 --
fast enough, or it could be
repaired simply, but if it gets

00:14:20.446 --
to severe faults and you'll have
a fire in the transformer, then

00:14:24.118 --
it can be very severe.

00:14:27.950 --
And so there are a number of
things. The number of strategies

00:14:32.750 --
that try to minimize the impact
of transformer faults.

00:14:49.760 --
So one of the big ones is
finding ways to reduce the

00:14:53.252 --
likelihood of them happening.

00:15:05.320 --
And so part of what a lot of
this comes down to is.

00:15:10.900 --
Track external events.

00:15:31.620 --
And it's really the life of
the installation. That's a

00:15:34.010 --
big issue.

00:15:35.620 --
So one of the things that I
mentioned is that we have two

00:15:39.741 --
directions. We're gonna go to,
and they actually are related to

00:15:43.228 --
each other. So one of the big
things that is a has a

00:15:47.349 --
consequence for Transformers is.

00:16:06.620 --
Meeting of the installation
will have a big impact on

00:16:09.700 --
how the life or how long
that installation is going

00:16:12.780 --
to be good.

00:16:23.030 --
Transient overvoltages is
another another issue.

00:16:44.770 --
So what are some of the
things that are going to

00:16:47.168 --
cause a transformer? Cause
heating in a transformer?

00:16:51.350 --
So let's think about a
transformer for a second

00:16:53.690 --
we have.

00:16:56.970 --
So I'm just going to draw a
single phase core.

00:17:01.570 --
So as we've talked about where
we have a single phase core

00:17:05.410 --
and have the low voltage
winding on the inside, an will

00:17:08.930 --
have a higher voltage winding
wrapped around the outside of

00:17:12.130 --
it, right? And then we'll take
those out to the bushings.

00:17:16.690 --
And as I mentioned earlier, we
don't. You don't see a

00:17:20.397 --
transformer core just sitting
out open in the air, right?

00:17:24.360 --
And so usually this is
going to be.

00:17:32.140 --
In a tank.

00:17:37.710 --
Anna's tank is going to be.

00:17:45.730 --
Filled with oil, right? So
usually it's going to be some

00:17:48.271 --
sort of a dielectric oil.

00:18:02.600 --
Is also used as a coolant.

00:18:08.650 --
And so you may look at a name
plate for a transformer, an it

00:18:13.914 --
may say that you have a
transformer that's rated at 15

00:18:18.050 --
MVA, 20 MVA.

00:18:20.300 --
25 NBA

00:18:23.920 --
so why would why would there
be 3 MVA ratings for the

00:18:27.712 --
same transformer?

00:18:34.120 --
Different cooling stages. It's
different cooling stages, so

00:18:37.424 --
this is going to be.

00:18:40.720 --
Basically, entirely
passive cooling.

00:18:45.100 --
So there is going to be there
will be radiator fins or on the

00:18:49.510 --
side of this case on the side of

00:18:52.030 --
that tank. This is going to be.

00:19:03.070 --
Going to be pumps used to
circulate oil to cool the

00:19:06.029 --
transformer or cool the oil so
it's going to circulate because

00:19:08.988 --
there are going to be.

00:19:11.010 --
Different spots in the winding
that are hot spots said certain

00:19:14.156 --
certain points are going to be

00:19:15.872 --
hotter than others. And so if
you don't circulate the coolant,

00:19:19.424 --
there will be a little bit of
natural convection, but you're

00:19:22.262 --
going to. Those hot spots are
not going to be cooled as well.

00:19:26.580 --
And then this is
going to be pumps.

00:19:31.090 --
Plus

00:19:32.920 --
running cooling fans that are
blowing error basically across

00:19:36.997 --
the radiator so that the
radiator works more efficiently.

00:19:45.810 --
So depending in some cases
people will just run these

00:19:49.220 --
all the time. In some cases
they'll based on the load

00:19:52.971 --
conditions, they'll start
and stop this equipment.

00:19:56.890 --
And if you have a transformer
that's always lightly loaded,

00:19:59.290 --
they may not. Run it as. Run to
run them very much at all.

00:20:15.100 --
So other things that could
cause heating.

00:20:23.270 --
So I want to be carrying
harmonic currents.

00:20:38.460 --
Do you know external loads?

00:20:48.380 --
So for example, if we have
a transformer that one of

00:20:52.153 --
the loads.

00:20:54.110 --
Is.

00:20:59.190 --
A dialed dialed rectifier.

00:21:04.740 --
And then we have a voltage
source converter.

00:21:09.580 --
Anyway, have an induction motor.

00:21:17.060 --
If.

00:21:19.260 --
This doesn't have any
compensation.

00:21:28.570 --
The current strong by this
drive are going to look

00:21:30.800 --
something like this.

00:21:34.920 --
And so this is going to
have 5, seven, 1113 and

00:21:39.463 --
basically multiples of
6 plus or minus one.

00:21:47.670 --
Is there going to have other
loads here? But this

00:21:50.100 --
transformer is going to be
carrying this current plus

00:21:52.287 --
whatever loads are here.

00:21:57.000 --
And carrying those harmonic
currents increases Eddy current

00:22:00.808 --
losses in the transformer core.

00:22:04.480 --
And so that the transformer is
going to run hotter.

00:22:23.280 --
And so they actually
you can actually get.

00:22:27.470 --
K factor rated.

00:22:35.920 --
So basically these K factors are
more of a derating factor.

00:22:41.170 --
And so if you have, if you know
you're going to be supplying

00:22:45.642 --
harmonic loads, you can buy a
transformer that has basically

00:22:49.082 --
an extra factor in its MVA
rating to be able to deal with

00:22:53.554 --
harmonics. If you're not, if
you don't have a transformer

00:22:58.028 --
that has any K rating an you
start supplying harmonics,

00:23:01.848 --
then usually you can. There's
there are formulas from the

00:23:05.668 --
IEEE standards that talked
about how you derate the

00:23:09.106 --
transformer, so instead of
being a 15 MVA transformer, it

00:23:12.926 --
may actually be a 12 MVA
transformer due to the extra

00:23:17.128 --
heating from the harmonics.

00:23:19.820 --
And so when someone buys a
transformer, usually you're.

00:23:24.470 --
Part of the data for when
you sign the contract with the

00:23:28.019 --
supplier and stuff like that is
saying well, this is. This has a

00:23:31.568 --
30 year design life for this as
a 25 year design life.

00:23:35.850 --
If you routinely overheat the
transformer, you may take years

00:23:39.750 --
off of that life.

00:23:41.870 --
So we had an outreach student
awhile back that worked at an

00:23:46.334 --
industrial facility that was
basically with zinc smelter.

00:23:50.010 --
And so they had a lot of very
large rectifier loads and so

00:23:54.924 --
they had Trent. They bought
Transformers that had.

00:23:59.340 --
30 year old designlife

00:24:01.880 --
Then they push them kind of
right. It may be a slightly

00:24:07.520 --
beyond their NBA ratings.

00:24:10.240 --
And then they gave this heavy
harmonic loading. So they

00:24:13.060 --
lasted about 10 years.

00:24:18.790 --
An that fit and when I say
lasted about 10 years, they had

00:24:24.237 --
a fault, and so if I did so by
heating the insulation, you end

00:24:30.103 --
up causing the you decrease the
lifespan of the installation and

00:24:34.712 --
your moral an it's more likely
to fail by having our fault. And

00:24:40.159 --
so that's why this external
event, external condition stuff

00:24:44.349 --
matters from the from the
transformer Protection POV.

00:24:52.670 --
So transformer protection will
usually track the loading on a

00:24:56.900 --
transformer an if the
transformer is overloaded, and

00:25:00.284 --
then there are formulas you can
use to figure out how much

00:25:05.360 --
that's affected the life.

00:25:10.980 --
And so some other things that
will go into this are going

00:25:13.776 --
to be over excitation.

00:25:23.720 --
So on a transformer over
excitation basically means

00:25:26.400 --
a steady state.

00:25:34.200 --
However, voltage that means
you're partially saturating.

00:25:57.850 --
Angene why the transformer is
going to produce more

00:26:01.478 --
harmonics because of this?
Because this is a steady state

00:26:05.438 --
sinusoidal condition, these
will be only odd harmonics.

00:26:11.110 --
And often the 5th harmonic is
usually going to be the one

00:26:14.674 --
that's used as sort of the main
detection detector for that.

00:26:21.140 --
But again, because you're
saturating the core.

00:26:26.070 --
What does that? What does
it mean when you saturate

00:26:28.960 --
the core more deeply?

00:26:35.050 --
More excited, you have more
expectations, well over

00:26:37.938 --
expectations. We have more
expectation right? But what

00:26:40.826 --
losses go up?

00:26:44.480 --
The winding losses go up, or
so we're going to increase

00:26:50.200 --
hysteresis losses.

00:26:54.180 --
Remember, hysteresis losses
are basically proportional to

00:26:56.672 --
the area of the hysteresis
loop it follows, so if you're

00:27:00.588 --
over exciting the transformer,
your loop has a bigger bigger

00:27:04.148 --
area, so the losses are going
to be higher.

00:27:24.780 --
Another one that's a big factor
are through faults, which means

00:27:29.345 --
that the transformer.

00:27:52.160 --
So basically, one of the things
that also gets tracked is how

00:27:56.120 --
many, how many faults is this
transformer supplied? What is

00:27:59.420 --
the magnitude of the fault

00:28:01.070 --
current bin? Because. Oh through
fault can cause very substantial

00:28:05.092 --
heating. It may not. It's not
going to last very long, but

00:28:08.764 --
it's going to take a long time.
It's going to take awhile quite

00:28:12.742 --
awhile for the transformer to
cool down from that.

00:28:37.870 --
So even frequent large motor
starting or if the transformer

00:28:42.020 --
is supplying current to
energize other Transformers.

00:28:48.500 --
So for example when.

00:28:53.020 --
I think their procedures have
changed a little bit, but at

00:28:56.771 --
Grand Coulee there's a pumped
hydro storage facility that

00:28:59.840 --
has very large synchronous
Motors. They generally only

00:29:02.568 --
start those Motors once a day
because the thermal shock on

00:29:06.319 --
the Motors every time they
start them is so much that

00:29:10.070 --
they can't start them more
often.

00:29:14.040 --
They redid that facility.

00:29:17.610 --
And within the last.

00:29:20.130 --
Eight years, so I think
they've redone it, so

00:29:23.019 --
it's not quite as harsh.

00:29:26.260 --
But so basically all of
these things get tracked.

00:29:45.910 --
They predict lifespan loss and
we're going to. We're going to

00:29:48.814 --
come back and talk about the
over some of these issues and

00:29:51.982 --
how and how this factors into
the transformer protection later

00:29:54.622 --
in the course. I want to talk
about internal faults. First,

00:29:57.526 --
we're going to come back to

00:29:59.110 --
this. That a good resource for
this. Our textbook does a pretty

00:30:03.945 --
good job with this, but also the
IEEE 30 C 3791.

00:30:08.770 --
Also another good one for
this and or there's some

00:30:11.730 --
other references. We'll talk
about a little bit later.

00:30:21.310 --
And So what I want to start
talking about is now protection.

00:30:27.370 --
For internal faults.

00:30:33.170 --
And will be going through
this over the next couple

00:30:35.320 --
of lectures.

00:30:45.020 --
And so I guess that's one
other sort of structural

00:30:47.990 --
thing. When we look at.

00:30:51.370 --
Large Transformers again.

00:31:13.460 --
I felt it evolved to
the point where there's

00:31:15.485 --
a fire can cause long.

00:31:19.490 --
As I said, long repair times.

00:31:23.550 --
And so some of the things that
you'll see in a substation, for

00:31:29.205 --
example for large transfer
transmission substations

00:31:31.815 --
especially often you'll see
single phase Transformers used,

00:31:35.295 --
and so you'll see.

00:31:40.310 --
Three single phase units, and
actually they are often going

00:31:43.810 --
to be 3 winding Transformers
as we talked about earlier in

00:31:47.660 --
the semester.

00:31:49.800 --
And so they're going to have
their own individual tanks.

00:32:00.700 --
And when you look at the
substation.

00:32:04.490 --
You'll see a wall
that's been placed.

00:32:09.980 --
Between the Transformers.

00:32:13.120 --
So what's the purpose of
that wall?

00:32:16.130 --
Prevent fire from
cleaning, so these are.

00:32:20.530 --
Firewalls raise more of the
archaic usage of the term

00:32:24.070 --
instead of the one that's now
everyone uses when they talk

00:32:27.964 --
about software.

00:32:29.990 --
And so this is basically if
this one has a fault, and as

00:32:34.072 --
a fire, the idea is that
this is that this is going

00:32:37.840 --
to basically make it less
likely for any for the heat

00:32:41.294 --
in the flames to get to this
transformer, so it fails to.

00:32:49.730 --
And a lot of utilities will

00:32:52.352 --
have. A limited number of
spare Transformers that they

00:32:56.392 --
can put in to replace a
failed transformer.

00:33:00.350 --
So.

00:33:03.620 --
This was probably almost 15
years ago. Now there was a

00:33:08.328 --
transformer fault at a 500 kva.
Think it's a 500KV substation in

00:33:13.464 --
the Southwest. An
they did not have.

00:33:18.530 --
Firewalls between the single
phase transformer, so they lost

00:33:22.364 --
all three phases. They had their
spares close enough that it

00:33:27.050 --
actually scorched the paint off
of the tanks, but they actually

00:33:31.736 --
didn't lose the spares.

00:33:36.820 --
But because they lost all three
and they only had three spares,

00:33:41.392 --
then they had to scramble to try
to get spares from other people.

00:33:46.345 --
And I know that one of the
utilities in the northwest

00:33:50.536 --
sentence pairs and they had all
sorts of issues because these

00:33:54.727 --
were 500 kva Transformers, Oran,
high MVA ratings. Just

00:33:58.156 --
transporting them was difficult.

00:34:04.410 --
And I think even
transporting the spares

00:34:06.867 --
took like several months.

00:34:17.190 --
So then actually one of the
things that the.

00:34:21.070 --
US Department of Energy in
the Department of Homeland

00:34:24.814 --
Security been working on in
the last several years, is

00:34:28.974 --
basically trying to form a
kind of a national database

00:34:33.134 --
of transformer spares and
also trying to increase the

00:34:36.878 --
inventory of spares so that
if there is something like.

00:34:42.950 --
High energy electromagnetic
pulse from a nuclear weapon or a

00:34:47.550 --
major Geo Geo magnetic.

00:34:50.070 --
A disturbance for the gym
geomagnetically induced currents

00:34:53.454 --
caused transformer failures that
they've got something that they

00:34:57.261 --
can go to restore power in some

00:35:00.222 --
areas quickly.
Relatively quickly.

00:35:05.270 --
OK, so let's now start talking
a little bit more about the

00:35:08.798 --
Internal fault protection.

00:35:16.340 --
Really, the first line for
this is going to be

00:35:19.390 --
differential protection.

00:35:27.600 --
So as I said, much like
what we were just talking

00:35:31.285 --
about with the.

00:35:33.640 --
Boss protection for the
restrained low impedance

00:35:38.078 --
differential protection.

00:35:42.100 --
So let's start out looking
at a transformer that.

00:35:47.170 --
We have a YY connection.

00:35:51.350 --
And so, let's say it's.

00:35:55.330 --
3:45 KV. 2.

00:36:00.110 --
138 KV.

00:36:07.700 --
And so for the moment,
let's just say it's a.

00:36:11.870 --
2 winding Transformers.
So we're going to have

00:36:14.102 --
three leads coming out.

00:36:34.210 --
Now I have see T is on each
phase and will just look at one

00:36:38.110 --
phase for the moment.

00:36:47.100 --
And so we start out saying,
OK, well, this looks a lot

00:36:50.436 --
like what we talked about
when we anytime we talked

00:36:53.216 --
about differential
protection. So we're going to

00:36:55.162 --
have current if we have
current going this way.

00:37:02.630 --
Then we're going to have.

00:37:06.340 --
Secondary current. That's going
to circulate like this, and.

00:37:12.870 --
I op should be about 0,
right? That would be. That's

00:37:17.666 --
what we would expect.

00:37:23.200 --
Now, unlike the virus
protection, we've got a number

00:37:27.574 --
of factors that complicate this.

00:37:44.360 --
So what do you think? Some
of the complicating factors

00:37:46.660 --
might be?

00:37:49.540 --
Configuration. Well, let's
say they will stick with the

00:37:53.020 --
YY for the moment.

00:37:56.010 --
If it's why Delta that, that
will add, that will be the next

00:37:59.195 --
challenge, will talk about
after we finish this one.

00:38:03.450 --
CD accuracy. Find CD accuracy.

00:38:07.640 --
So ciety accuracy, but
there's actually something

00:38:09.831 --
before that. One is going to
be the CT ratios.

00:38:37.200 --
So we may not get apart. We
may not get a perfect

00:38:40.284 --
cancellation of.

00:38:42.410 --
So let's say that just for
making this easier, let's say

00:38:46.172 --
that this was a 2 to one ratio.

00:38:54.770 --
So let's say that this was
500KV and this was 250KV just

00:38:58.598 --
for nice numbers. Even though
the 2:50 is not something

00:39:01.788 --
you'd run across much.

00:39:04.660 --
Then we would say OK. Well
then this. Let's say that

00:39:07.608 --
this is 1000 to one CT and
this is going to be what?

00:39:15.290 --
Or 1000 to 5C T, and
that's what would this

00:39:17.760 --
would need to be then.

00:39:24.010 --
Remember, this is.

00:39:26.200 --
Two to one is the effective
voltage transformation

00:39:28.680 --
ratio, so the current goes
the opposite, right?

00:39:32.170 --
So so this one would need to
have 500 to 5 setes.

00:39:37.110 --
So that would be one that
would be an example of a

00:39:39.894 --
good cancellation. So
let's say that this was.

00:39:44.450 --
500KV to
250KV.

00:39:50.810 --
And the cities were.

00:39:53.330 --
1000 to 5

00:39:56.690 --
in. 500 to 5 so that's something
that you could pretty easily.

00:40:00.320 --
Fine cities.

00:40:03.260 --
To cancel that right?

00:40:06.340 --
If we look at 3:45 to 138.

00:40:13.080 --
That's not going to be so
easy to find CTS that give

00:40:16.572 --
you a good cancellation on
that. So even if this was

00:40:19.773 --
even if these were still.

00:40:22.920 --
Thousands of five.

00:40:27.930 --
This would need to be
basically 1000 times.

00:40:33.640 --
38 / 345.

00:40:37.240 --
To five.

00:40:43.830 --
And chances are that's not
going to be a nice stock

00:40:47.108 --
number that you're going to
be able to buy in. SNS ET.

00:40:56.510 --
And so it's one that we're we'll
talk about a solution for that,

00:41:01.424 --
but this is basically going to

00:41:03.692 --
be. Having

00:41:06.760 --
taps on the relay.

00:41:10.600 --
So watch mechanical relays. What
they had was they had multiple

00:41:13.625 --
tap points where you could

00:41:15.000 --
connect. The inputs from the
transformer for the differential

00:41:19.010 --
and you could partly correct for
that mismatch to a degree you

00:41:23.690 --
couldn't. You could not connect
4 correct for it perfectly, but

00:41:27.980 --
you could. You could go a long
ways towards correcting it.

00:41:33.160 --
What we'll see in probably not
today. We may. I don't know if

00:41:37.697 --
we get to the example today,
what you'll see in

00:41:41.187 --
microprocessor relays now that's
just a number, so it's just a

00:41:45.026 --
scaling factor, so you can. So
basically you as you enter the

00:41:49.214 --
stuff into the relay for setting
it, you're entering the

00:41:52.704 --
information so the relay
calculates that tap and you

00:41:55.845 --
don't even have to answer.
Calculate it yourself so you say

00:41:59.684 --
OK, here is the MVA rating.
Here's the voltage rating.

00:42:03.680 --
And then at the relay says
OK and this is the rated

00:42:06.980 --
current and just basically
calculates it for you.

00:42:11.830 --
And then you also put the seat.
The actual CT ratios 'cause it

00:42:15.444 --
puts that in as a correction to.

00:42:27.670 --
Another thing you'll see in a
lot of large power Transformers

00:42:31.080 --
is they have taps, right?

00:42:34.410 --
So we may see.

00:42:37.830 --
500KV to 250KV.

00:42:42.510 --
Anne, this could be we could

00:42:46.392 --
have. Plus 2
1/2% + 5%

00:42:53.060 --

5%.

00:42:58.620 --
And these could also have
some different apps. So if

00:43:01.930 --
you start putting.

00:43:04.060 --
If you and so in some
cases, these maybe.

00:43:08.340 --
For lower power ones,
these may be on load. Tap

00:43:11.695 --
changing Transformers where they
can be changed. In other cases

00:43:14.745 --
the transformer has to be D
energized for crew to come in

00:43:18.405 --
and change that tag.

00:43:22.870 --
What what is that tap change
due to the differential current?

00:43:32.540 --
You just change the ratio of the
transformer, right? So you've

00:43:36.984 --
gone to the effort of correcting
for compensating for this, this

00:43:41.428 --
ratio and the CT ratios. Now you
just threw that off because you

00:43:46.680 --
changed the transfer. The power
transformation ratio by 2 1/2%.

00:43:59.070 --
Then another one would be.

00:44:25.660 --
The transformer is always going
to draw some magnetizing current

00:44:28.480 --
if it's energized right.

00:44:32.250 --
And this is something that's.

00:44:34.160 --
Going into the transformer
and not coming out.

00:44:44.190 --
And as we talked about last
time, this might be 2 to 4%,

00:44:48.948 --
maybe 5% of the rated current.

00:45:07.230 --
It will be higher if the
transformer is over excited.

00:45:13.210 --
So there's really two things
that you need to look at with

00:45:16.414 --
over. Excitation is going to be.

00:45:18.830 --
If the over excitation is severe
enough and last long enough you

00:45:23.114 --
want to trip the transformer.

00:45:25.910 --
But you don't want to trip it
because you think it's an

00:45:29.414 --
internal fault, so you don't
want to trip at the instant it

00:45:32.918 --
happens. So there's some
tradeoffs on that, and the

00:45:36.460 --
harmonic content of that's
going to be a factor in how

00:45:39.595 --
the relay responds to it.

00:45:44.120 --
Now there's another issue
that you have to worry about

00:45:46.480 --
with magnetizing current.

00:45:51.280 --
What would that be?

00:45:58.370 --
So we have magnetizing
inrush current.

00:46:09.250 --
So if you energize a
transformer.

00:46:23.570 --
You're going to see a
current that's going to

00:46:25.568 --
start out looking like this.

00:46:28.260 --
And it may take a second or two

00:46:31.508 --
to. One at one to two seconds
to get down to the normal

00:46:36.314 --
magnetizing current.

00:46:40.990 --
So are people familiar?
Why Transformers exhibit

00:46:43.867 --
this behavior?

00:46:52.120 --
So it goes down, it goes back to
our hysteresis characteristic.

00:46:57.400 --
So the transformer is going
to when it's operating is

00:47:00.650 --
going to be.

00:47:03.580 --
Following something that looks
like this, right? So if this is

00:47:07.507 --
B versus H.

00:47:10.670 --
This is proportional to voltage.
This is proportional to current.

00:47:15.790 --
So every time you go through a
sinusoidal cycle, it's going to

00:47:18.982 --
trace this curve, right?

00:47:22.010 --
And so when you deenergize the
transformer, you deenergize

00:47:26.042 --
nearer at a current 0, right?

00:47:29.630 --
And so when the current goes to
zero, you're going to be

00:47:32.654 --
somewhere up here. And so
there's going to be some trapped

00:47:36.706 --
flux on the core.

00:47:38.830 --
When it's deenergized and
depending on where you were in

00:47:42.030 --
that hysteresis cycle, when the
breaker contact cleared or what

00:47:45.230 --
the power factor of the current

00:47:47.150 --
was. Usually the final invoice
and normal routine operation

00:47:51.948 --
when I want to Transformers.

00:47:54.940 --
D energize you open one side,
then you open the other ones

00:47:59.476 --
you're interrupting, basically
just magnetizing current with

00:48:02.122 --
the final. The energizing of
the transformer.

00:48:06.540 --
When you re energize it.

00:48:09.140 --
How is voltage related to
flux in a transformer?

00:48:13.830 --
So V is equal to NDF DT, right?
So the flux in the voltage or 90

00:48:19.014 --
degrees out of phase with each
other. But you can so that the

00:48:23.226 --
voltage here at some point in a
sinusoidal voltage waveform you

00:48:26.790 --
can map that the flux when you
energize it. So when you're when

00:48:31.002 --
you close a circuit breaker,
there's going to be some

00:48:34.242 --
basically effective flux that
you're you're trying to impose

00:48:37.158 --
on that core. So if you're lucky
and you and you pose a circuit

00:48:41.694 --
breaker in the effective flux
for the point on waiver, you're

00:48:45.258 --
closing. It's about what you
trapped on the core.

00:48:48.680 --
Then there's not really
going to draw any current.

00:48:53.430 --
If you're unlucky and you had
trap works up here and you're

00:48:56.562 --
closed when you're somewhere
down like this, now the

00:48:58.911 --
transformer is going to draw a
lot of current to try to

00:49:02.043 --
equalize that flux. And after
magnetizing inrush current.

00:49:06.320 --
And it's very nonlinear current.

00:49:09.000 --
And so this has a lot of
harmonic content. The

00:49:12.210 --
generally it's going to be
dominated by second and

00:49:15.099 --
then 5th and so on. But
it's going to have more

00:49:18.630 --
even harmonics where the
over excitation is only

00:49:21.198 --
going to be odd.

00:49:25.610 --
How's the modern steels that
they're using in newer

00:49:29.615 --
Transformers? Do not have a
sharper second harmonic

00:49:32.839 --
characteristic. They still draw
big magnetizing currents, but

00:49:35.135 --
now there's not as clear a
second harmonic, and we'll talk

00:49:38.292 --
about some of the issues with
that later in the.

00:49:42.650 --
Not this, not later
today, but next week or

00:49:45.570 --
the week after next.

00:49:49.040 --
So you've got these very large
currents again, they're just

00:49:51.940 --
going into the transformer.

00:49:57.860 --
And so you know, if you're doing

00:49:59.764 --
a normal. Registration of the
transformer. Not something

00:50:02.364 --
following like Re closing in a
fault. You might have this side

00:50:06.312 --
open and you energize this side
and so now you're seeing current

00:50:10.260 --
San people have measured
currents as high as 15 per unit.

00:50:16.260 --
If there are a lot of lights,
limits that is partly whether

00:50:19.596 --
the surrounding power system
can supply that much current.

00:50:22.098 --
If there's too much impedance
in the power system that won't

00:50:25.156 --
supply it.

00:50:28.120 --
And so you're doing. You have a
differential element. You're

00:50:31.140 --
going to see. Let's say it's
something more normal, like 5 to

00:50:34.764 --
7 per unit for a second.

00:50:37.980 --
So in electromechanical relays.

00:50:41.570 --
One of the things that they did
initially was basically turn off

00:50:46.274 --
the differential element until
the inrush current period was

00:50:49.802 --
over. They still had issues
where if you had two

00:50:53.199 --
Transformers that were close
together and you energized one

00:50:55.638 --
when the other one was on,
sometimes you had a sympathetic

00:50:58.619 --
trip of the different of the
differential element for the one

00:51:01.600 --
that was already energized.

00:51:07.180 --
Professor, I have a
question on this one, so

00:51:09.952 --
there is no saturation
really, it's just the.

00:51:13.740 --
The core trying to reach that

00:51:15.876 --
flux level. But there's no
saturation, so as.

00:51:21.150 --
It face it, it started has sort
of a saturation effect because

00:51:24.966 --
of where it pushes the flux, but
there really isn't any true

00:51:28.782 --
saturation of the core in this.

00:51:31.560 --
So why isn't it sinusoidal?

00:51:35.990 --
So when you think about the
iron in the core right, you

00:51:40.423 --
basically have a bunch of
magnetic domains that want to be

00:51:44.174 --
in random directions, right? So
let's say that because of the

00:51:47.925 --
trap flux, they're all pointing

00:51:49.630 --
this direction. And for the
inrush you're trying to flip

00:51:53.712 --
them all to go back. Basically
you want the flux to go this

00:51:58.249 --
way, so you need to flip all

00:52:00.692 --
these domains. And.

00:52:03.920 --
They don't, simply.

00:52:06.420 --
Follow a nice thing in
sinusoidal behavior as they flip

00:52:09.250 --
on this. So there's some
resistance. I'm really

00:52:12.652 --
oversimplifying this, but
basically it's it's a

00:52:15.186 --
magnetic. The nonlinear
magnetic behavior of the core

00:52:18.082 --
that keeps it from looking
sinusoidal.

00:52:25.980 --
And this harmonic, and So what
we're going to see in a little

00:52:30.426 --
bit, is that to try to minimize

00:52:32.820 --
this effect. The second
harmonic is often used as a

00:52:37.252 --
as a signature, so if the
second harmonics above a

00:52:40.942 --
certain threshold.

00:52:43.030 --
Then it's got the relay will
block the differential

00:52:46.189 --
element, so you can either do
harmonic blocking or harmonic

00:52:49.699 --
restraint, which is basically
making the slope steeper.

00:52:53.590 --
Now, this raises an interesting
thing. From a relay point of

00:52:57.572 --
view. We talked about digital
filters, right? So here we

00:53:01.192 --
talked about second harmonic. I
talked about fifth Harmonic when

00:53:04.812 --
I talked about over excitation
detecting over excitation.

00:53:09.520 --
So remember what we talked
about with digital filters? If

00:53:12.270 --
we're using cosine filters.

00:53:14.730 --
Well, the is the what is a
cosine filter due to harmonics.

00:53:19.866 --
What's the gain about cosine
filter 0, right? So the relay

00:53:24.574 --
needs a separate.

00:53:26.820 --
Cosign filter that if you want
to measure second harmonic or

00:53:30.582 --
you want to measure 5th harmonic
or any of the others, you need

00:53:35.028 --
to have some separate
filter elements that are going

00:53:38.448 --
to calculate those.

00:53:40.160 --
Because the normal cosine filter
using for your protection

00:53:43.400 --
calculations is going to have a
gain of zero and block those.

00:53:49.450 --
And when you start getting up
to 5th or 7th, now you're

00:53:52.450 --
starting to get up to the range
where the low pass filters,

00:53:55.450 --
anti aliasing filters also
going to have an effect on

00:53:57.950 --
them.

00:54:03.460 --
So when you talk about residual
magnetism, why doesn't it die

00:54:07.387 --
out? So if I'm.

00:54:09.370 --
I'm switching off or closing
opening the breaker in front of

00:54:13.286 --
the transformer at equals to
zero. Eventually the residual

00:54:16.490 --
magnetism should die out, right?
If I'm not energizing it back in

00:54:20.762 --
let's say days or weeks. So does
it die out and not? It does

00:54:25.746 --
decay OK, so basically it's a
it's a thermal process. So

00:54:29.662 --
basically these are going to try
to randomize if the car is warm

00:54:34.290 --
when you demagnetize it, then
they tend to randomize faster

00:54:37.850 --
than if the core is cool as the
core as a transformer cools that

00:54:42.834 --
slows down the rate.

00:54:44.460 --
That randomization OK, but even
if it's gone to zero an you

00:54:48.900 --
closing your somewhere up
here still we're going to have

00:54:52.970 --
some issues on that.

00:54:57.930 --
Awhile back, well actually one
of the Masters students here who

00:55:01.989 --
works at Sweitzer. Now guy named
Doug Taylor looked at using a DC

00:55:06.786 --
source to preflex the
transformer so you could put

00:55:10.476 --
the trap flux at a known at a
known point and then if you have

00:55:16.011 --
Breakers with individual phase
control then you can control

00:55:19.332 --
when you close them.

00:55:22.220 --
They also are using variations
of that an like.

00:55:28.760 --
There's been a lot of stuff
looking at that in Europe, for

00:55:32.324 --
example, in some of the offshore
wind farms where they basically

00:55:35.591 --
are in a system that can't
supply that magnetizing current

00:55:38.561 --
to magnetize the core, because
there isn't a source strong

00:55:41.531 --
enough to provide it out there.

00:55:44.090 --
And so they want to be able to
close the Transformers with no

00:55:48.276 --
inrush. And so rather than pre
flexing the cores, they're

00:55:52.692 --
looking at trying trying to
dissipate the flux in the

00:55:56.960 --
core so that they can bring it
to zero, and then they do

00:56:02.004 --
individual phase control on the
Breakers to minimize the inrush.

00:56:07.670 --
Also the whole pre fluxing
minimize trying to get the

00:56:10.730 --
known side of inrush makes a
big difference. If you have a

00:56:14.402 --
five legged core versus the
three legged core.

00:56:18.190 --
So when you see the anticipated,
basically they figure out at

00:56:21.644 --
what time or what voltage at
what point in the voltage the

00:56:25.412 --
breaker was opened, and then
based on that they calculate the

00:56:28.866 --
residual magnetism and the
decay, and then they open

00:56:31.692 --
individual phases at different
times. Or they close them, they

00:56:34.832 --
close them at specific times.
OK, so the Breakers are always

00:56:38.286 --
going to try to open it. A
natural current 0. Sure, an

00:56:42.054 --
there are actually some big
problems if you don't open it in

00:56:45.822 --
natural current 0, because then
you can get very big.

00:56:49.350 --
Transient response if you do
a current shopping.

00:56:53.590 --
So the parasitic capacitance
of the winding will interact

00:56:56.560 --
with the magnetizing branch,
and you can see like 2 / 2

00:57:00.520 --
per unit voltage.

00:57:03.600 --
Even if you're chopped
like half an amp.

00:57:11.700 --
That's a topic more for
you. See 524 though.

00:57:20.290 --
OK, so any other questions
related to the magnetizing.

00:57:24.950 --
Current behavior.

00:57:27.630 --
So these are all things that
need to be accounted for in

00:57:31.758 --
creating the differential
element an in setting like

00:57:34.510 --
the slope and the minimum
operate current.

00:57:39.090 --
The other one to look at is
going to be the transformer

00:57:42.342 --
phase shift.

00:57:49.760 --
So I started out drawing a
YY transformer.

00:58:00.000 --
So the other thing we have to
look at is Delta Y.

00:58:04.150 --
Or why Delta Transformers?

00:58:22.310 --
And so in North America there's
an ANSI IEEE standard so that

00:58:27.926 --
the phase shift is generally
very predictable, right?

00:58:33.330 --
And what's the standard?

00:58:37.720 --
Sorry. The high side
is leading by $30.

00:58:59.020 --
So V line the neutral in
the high voltage side leads

00:59:01.902 --
vilanda neutral in the low
voltage side by 30 degrees.

00:59:06.370 --
The Power systems textbook I
used when I was an undergrad

00:59:10.055 --
gave the impression that
whenever you had a Y Delta

00:59:13.405 --
transformer or the Y side always
led the Delta side by 30 degrees

00:59:17.760 --
because the author in.

00:59:20.620 --
All the cases he had run
across the Y side was always

00:59:24.328 --
a high voltage transformer,
'cause he'd always worked in

00:59:27.109 --
transmission and never worked
in distribution.

00:59:38.430 --
And so. So one of the
effects were going to have

00:59:42.274 --
obviously is the 30 degree
phase shift this also.

00:59:58.400 --
The Delta Y connection also

00:59:59.820 --
impacts the. Turns ratios right.
So now you've got this other

01:00:03.574 --
sqrt 3 that gets put in there in
addition to having.

01:00:11.110 --
The voltage
transformation ratio.

01:00:14.910 --
That sqrt 3 shows up in the
current so that reflects

01:00:18.320 --
back to the CTS.

01:00:23.620 --
And let's say that we have a
Delta Y grounded transformer.

01:00:28.640 --
So this side.

01:00:41.830 --
When we're measuring the phase
currents, there's going to be 0

01:00:45.537 --
sequence current on this side,
but there won't be on this side.

01:00:53.200 --
And so even some Even so, one of
the things that you have to be

01:00:57.550 --
careful of his solutions to try
to fix this phase shift.

01:01:01.490 --
And fix this also after account
for this. So I said that they

01:01:05.871 --
are one of the solutions that
people did for less mechanical

01:01:09.578 --
relays. Had to have an extra
step added to it because of

01:01:14.094 --
the zero sequence kind.

01:01:26.250 --
So if we have a transformer.

01:01:47.130 --
So we can look at the CTS.

01:01:51.140 --
So for electromechanical relays.

01:02:00.880 --
The common solution in this for
this was going to.

01:02:06.860 --
To use the CT connections to
help cancel for the cancel this.

01:02:12.520 --
And so.

01:02:16.250 --
So one option.

01:02:31.830 --
Would be to connect the CTS on
the Y grounded side in Delta.

01:02:38.340 --
And the CTS and the
Delta side and Y.

01:02:57.440 --
You need to make sure you
connect the Delta properly to

01:03:01.092 --
cancel the shift. But So what
that means is that the that the.

01:03:07.110 --
Phase currents that the
Delta phase currents.

01:03:12.580 --
Well, include the zero
sequence current that's going

01:03:15.148 --
to circulate in that Delta,
but then the line currents

01:03:18.358 --
coming off the Delta which go
to the differential relay

01:03:21.568 --
will not have.

01:03:23.640 --
That current

01:03:29.600 --
morning your device is running
low on memory.

01:03:37.470 --
So one of my colleagues has a
sledgehammer. He brings the

01:03:40.737 --
class for people whose cell
phones make noise during class.

01:03:47.100 --
The new phone is trying to
shut it down.

01:03:52.290 --
And so this is so, you still
will run across substations that

01:03:57.018 --
have the CTS wired this way from
the electromechanical relays.

01:04:03.920 --
And then a second option.

01:04:16.440 --
Would be the connect.

01:04:18.660 --
This it is an Y and
this it isn't Delta.

01:04:24.240 --
So yes, there's a problem
with this one, right?

01:04:30.810 --
So now the.

01:04:35.270 --
The differential element on
this, the current that goes to

01:04:38.140 --
the differential an element from
this side, it's going to include

01:04:41.297 --
zero sequence current. The one
in this one won't, right.

01:04:45.970 --
So this one is going to need.

01:04:55.020 --
So basically this one needed
an auxiliary set of current

01:04:58.210 --
Transformers that would block
the zero sequence current by

01:05:01.081 --
basically circulating it in
the auxiliary Transformers and

01:05:03.633 --
not have a go to the
differential element.

01:05:26.570 --
So now if you go to a
substation where it's new

01:05:31.553 --
construction and it's
designed not anticipating

01:05:34.271 --
that there's going to be
microprocessor relays

01:05:37.442 --
protecting this.

01:05:47.680 --
Now the seats are going to be
why on both sides and there

01:05:51.632 --
will be a ground reference in
the seat path.

01:06:19.860 --
And it will also the CTA will
basically perform calculations.

01:06:24.340 --
To compensate for the phase
shift an it's going to

01:06:28.920 --
perform another calculation
to remove I 0.

01:06:35.480 --
And these are actually going to
be matrix multiplications.

01:06:48.380 --
So I have a handout that.

01:06:51.350 --
Maybe I will pass it
out today. You need to

01:06:53.950 --
remember to bring it.

01:06:57.250 --
Don't be sorry.

01:07:13.600 --
And so.

01:07:18.360 --
This first calculation is
basically.

01:07:23.660 --
Typical calculation
that you would see.

01:07:27.220 --
Done in the relay.

01:07:29.840 --
For the.

01:07:32.120 --
As an intermediate step
for going to the

01:07:35.264 --
differential element.

01:07:37.540 --
So you're gonna have.

01:07:40.570 --
You're going to have the primary
currents. Then they're going to

01:07:44.112 --
be divided by the current

01:07:45.722 --
transform transformation
ratio. Remember, these are

01:07:48.686 --
why connected.

01:07:54.000 --
And then there's also going to
be this tap calculation, and

01:07:57.744 --
the other hand out goes into
more detail about the how this

01:08:01.488 --
tap is calculated. And then
there's going to be a correction

01:08:06.020 --
matrix, so the correction matrix
the output is going to be the

01:08:09.920 --
secondary current with the phase
and zero sequence correction.

01:08:16.110 --
And so the current from both
windings are going to. So this

01:08:20.190 --
is actually. This would be the
primary side, and then we're

01:08:23.930 --
going to secondary sidewinding.
So this is actually.

01:08:27.470 --
The power transformer primary.

01:08:53.070 --
And then the correction matrix,
or a number of correction matrix

01:08:58.240 --
we can do. And so when I say
matrix zero, that is using the

01:09:04.820 --
IC Clock terminology. So if we
think about o'clock, we're going

01:09:09.990 --
to have 12369, etc and then 12.

01:09:13.890 --
12 is also equal to 0, right?

01:09:19.820 --
And so if we have a Y
connection with, if you say

01:09:24.212 --
that we have basically our
phase, a voltage is going to

01:09:28.238 --
be here at an angle of 90
degrees. That's our zero

01:09:32.264 --
position.

01:09:37.340 --
And so the Matrix Zero is
assuming we have a Y

01:09:40.783 --
connection and we're not
trying to do any reversal of

01:09:43.913 --
the voltages, so this will be
just the identity matrix.

01:09:53.370 --
And then where matrix one is the
one o'clock position and this is

01:09:59.129 --
one that in.

01:10:00.540 --
South America is often
referred to as the DAB and

01:10:03.490 --
this would be a Delta.

01:10:08.250 --
AV connection so that means
that the first winding of the

01:10:11.583 --
Delta is connected from A to
B. The second line will be to

01:10:15.522 --
see the third one will be see
to a. This gives you remember

01:10:19.461 --
North America. You're limited
to either plus 30 degrees or

01:10:22.491 --
minus 30 degrees when you're
going from Y to Delta. So all

01:10:26.127 --
we care about in North
America is going to be the D1

01:10:29.763 --
in the D11 connection.

01:10:33.240 --
And then we have the D11
connection, and so if we

01:10:37.398 --
compare these all it's
doing is exchanging

01:10:40.044 --
which rows are have the.

01:10:43.410 --
Then have the different
column combinations.

01:10:47.840 --
And so, well, we'll talk about
this a little bit more, applying

01:10:52.172 --
it in the other example.

01:10:54.970 --
And then, as I mentioned, we
have that we need that zero

01:10:58.054 --
sequence removal matrix too.

01:11:03.900 --
And so that's what this
one does.

01:11:08.460 --
And so this is
mathematically reproducing

01:11:10.410 --
the effect of the current
circulating in the Delta.

01:11:20.750 --
Anworth this what this is
coming from?

01:11:24.700 --
A very good reference for
summarizing this is.

01:11:31.420 --
A paper that was written by.

01:11:35.230 --
I group from Basler
Electric John Horack.

01:11:37.659 --
Actually, I have a link to
on their class links web

01:11:41.476 --
page. I have a link to
webpage it he's got put

01:11:45.293 --
together an extensive web
page was protective

01:11:47.722 --
relaying. Related links.

01:11:51.260 --
And so I did not. I gave you
copy. It's, uh, some of the

01:11:54.676 --
pages from this paper. I have
links to the whole paper on

01:11:57.604 --
the course web page. That's
the on campus students. There

01:12:00.044 --
were some of the pages that
I'm going to talk to talk

01:12:02.972 --
about today and next time.

01:12:06.810 --
So this is just showing sort
of the connection information

01:12:10.070 --
as a reference for the rest
of this paper.

01:12:16.410 --
So.

01:12:18.450 --
He has uppercase letters to
indicate the primary lowercase

01:12:22.635 --
to do the secondary.

01:12:25.520 --
And then he has the third of the
terminal ends an the.

01:12:31.060 --
So this would be the
polarity end of the wine,

01:12:33.656 --
and this is the nonpolarity
end of the winding.

01:12:40.150 --
And so. This is one of the
things that you go through.

01:12:45.030 --
You're going to find different
people in different places, use

01:12:48.580 --
somewhat different notation so
we see UV WABC.

01:12:52.070 --
And so on.

01:12:59.290 --
And so if we wanted to build a
YY transformer in a typical

01:13:05.166 --
North American connection so
when we see the W1W 2W3, those

01:13:10.138 --
are referring to the winding.

01:13:14.330 --
The windings of the six
windings that produced the

01:13:17.372 --
three phase transformer.

01:13:21.590 --
And then it's not very
obvious, but these are his

01:13:24.910 --
polarity marks for those
windings.

01:13:28.910 --
And so H1X1 this is
high voltage. This is

01:13:31.664 --
low voltage and so on.

01:13:34.330 --
And so mapping these this is how
they would map.

01:13:39.870 --
Tell the two winding sets.

01:13:47.510 --
And so winding one and
winding 4 on the same course.

01:13:50.282 --
So these two are going to be
in phase with each other.

01:13:55.700 --
And so you can use this to
build the diagram for how

01:13:59.168 --
the transformer ones relate
to how the windings relate

01:14:01.769 --
to each other.

01:14:06.900 --
And so then he goes on
to look at.

01:14:15.830 --
So the basically the Y zero
is the one that's most

01:14:19.669 --
common in North America.

01:14:24.100 --
And so we can look at things
that change polarities by so

01:14:27.556 --
the Y four is now we're
shifting things down to the

01:14:30.724 --
4:00 o'clock by putting
winding one connected to Phase

01:14:33.316 --
V.

01:14:35.850 --
White and then we can just
look at all these different

01:14:39.546 --
combinations. WHI Six is just
reversing the polarity so the

01:14:42.906 --
polarity marks reversed
unwinding one.

01:14:47.440 --
And so this is another one
that is more of an industrial

01:14:51.076 --
power systems one, but you'll
sometimes see Transformers

01:14:53.500 --
with wired opposite of the
polarity marks.

01:14:57.580 --
Then he goes through the same
thing with Delta windings.

01:15:02.450 --
So the. And so next time
we'll go back and look at

01:15:06.270 --
this in terms of a Y Delta
transformer. How we do the

01:15:09.054 --
plus 30 if the Y is a high
side, how we do the minus 30?

01:15:12.534 --
If the why is the low side?

01:15:17.010 --
And so this paper goes on to
kind of lead into deriving

01:15:21.402 --
those connection matrices.

01:15:24.560 --
And so we'll finish talking
about this paper next time, and

01:15:28.014 --
then we'll talk about the.

01:15:31.130 --
Example handout so that
we're going to apply these

01:15:34.622 --
connection matrices to
measurements for a fault.

01:15:38.450 --
We can look at an internal
fault or an external fault. We

01:15:42.458 --
can also look at what happens
if somebody accidentally left

01:15:45.798 --
ascete shorted in the
substation and how that plays

01:15:48.804 --
through these connection
matrices.

01:15:51.560 --
So with that, well, any
questions before we stop.

01:15:55.730 --
OK, and just a reminder for
the outreach students.

01:15:58.115 --
There is no class on campus
next week, so there will be

01:16:01.295 --
no new lectures for a week.

01:16:05.650 --
OK, that's all done.

Duration:"00:40:29.6340000"

00:00:29.460 --
Hi, welcome back.

00:00:33.550 --
So we're going to resume chapter
two. We are in the section on

00:00:39.738 --
project management planning
tools and the next thing I

00:00:44.022 --
wanted to talk about was sipoc
diagrams. And really, there's

00:00:48.782 --
this one and one other slide
coming up here, which probably.

00:00:54.840 --
I mean I I would characterize
them as a project management

00:00:59.405 --
planning tool, although they're
really most relevant if you're

00:01:03.140 --
doing process improvement. And
again, many of us as a part of

00:01:08.120 --
our role as a project manager
have some element of process

00:01:12.685 --
improvement that has to be done.
Anna Sipoc diagram might be

00:01:17.250 --
something you would use and this
is basically where OK, let's.

00:01:23.170 --
Um?

00:01:25.970 --
This is where you would
basically identify these

00:01:29.314 --
dimensions of your process. You
want to look at suppliers inputs

00:01:33.912 --
to the process, what the process
itself is, what are the outputs

00:01:38.928 --
and who are the customers. So in
this case this is a process for

00:01:44.780 --
making pizza, so you know it
looks at our suppliers are

00:01:49.378 --
inputs or process our outputs in
our customers. You can read

00:01:53.976 --
those you know and maybe.

00:01:56.160 --
We're doing this because our
we've been getting.

00:02:02.040 --
You know complaints about how
long it takes to make pizzas in

00:02:06.936 --
our particular business, and we
might want to take a look at how

00:02:12.240 --
can we improve that? And you
want to kind of take this broad

00:02:17.544 --
perspective so you're not
necessarily honing in on

00:02:20.808 --
something which maybe isn't
going to solve your problem? It

00:02:24.888 --
may be an issue, but it might
not be related to the particular

00:02:30.192 --
metric you're trying to solve,
so it's a good way.

00:02:34.400 --
To tackle process improvement I
you know I'll be honest in

00:02:40.516 --
research and development. We
didn't really use sipoc

00:02:44.964 --
diagrams, or I hadn't seen
amused. But when I I did a

00:02:51.636 --
about 18 month rotation into our
customer service business and

00:02:57.196 --
they they always had teams who
were doing process improvements.

00:03:04.180 --
Particularly within call
centers, and they use sipoc

00:03:08.180 --
diagrams. You know it was
amazing what they what they

00:03:13.180 --
did with these as a method
to truly understand where

00:03:18.180 --
to focus their efforts.

00:03:22.470 --
Racy, racy diagram. You
kind of look at this and

00:03:25.600 --
say, well, is that really
a project management tool?

00:03:29.530 --
We will hit on this a little
more when we talk about

00:03:35.326 --
communication, which is, I think
in the leading chapter, but a

00:03:40.639 --
raci diagram is a very important
tool to have if you work in any

00:03:47.401 --
kind of environment that has
more than one team in more than

00:03:53.197 --
a handful of people, because it
helps you identify who's

00:03:58.027 --
responsible for particular sets

00:03:59.959 --
of work. Who is accountable?

00:04:03.880 --
And by that I mean who's making
decisions and who has ultimate

00:04:08.740 --
ownership, who's consulted? So
who are stakeholders in the

00:04:12.385 --
process and who might need to be
consulted before you make a

00:04:17.245 --
decision or take some action and
who just needs to be informed

00:04:22.105 --
and? You know an example. If you
work in a team where maybe

00:04:28.100 --
you're part of a matrix
organization and we'll talk

00:04:31.880 --
about that in our next chapter
on organizing. But say you have

00:04:36.920 --
multiple teams that are a part
of a project.

00:04:41.330 --
Um? You want to make sure
you're very clear about who's

00:04:47.120 --
doing what to get pieces of the
project done, in particular for

00:04:52.184 --
a matrix. It's also very
important to understand who's

00:04:55.982 --
making the final decision,
because everyone might think

00:04:59.358 --
they're making the decision
right there. They are managing a

00:05:03.578 --
team. Why aren't they
responsible? Well, in fact, if

00:05:07.376 --
you're part of a matrix
organization, you may have a a

00:05:12.018 --
program manager or.

00:05:13.370 --
A project management
organization who does in fact

00:05:16.770 --
have the final authority on the
work that gets done. People who

00:05:21.870 --
are informed might be the
managers above you. You've taken

00:05:26.120 --
some course of action and it was
clear you had the ability to

00:05:31.645 --
make that decision, but it's
good to let other people know

00:05:36.320 --
who might. Maybe just be
interested or who may need to

00:05:42.153 --
take other action based on
something you do, and so they

00:05:47.070 --
might be in inform you can find.

00:05:51.420 --
Lots of examples on line for how
you might fill that out, but

00:05:56.685 --
it's a good tool to get clarity
and alignment within a project.

00:06:03.340 --
Risk analysis.

00:06:06.440 --
You know, again, we've probably
all done risk analysis at some

00:06:12.347 --
level. I just, you know, pulled
in this example where it's

00:06:18.254 --
basically identified 10 risks
that have been deemed to be

00:06:23.624 --
project risks. It talks about
the worst case scenario, what

00:06:28.994 --
happens in case of that coming
to bear, and then you basically

00:06:35.438 --
do a qualitative and

00:06:37.586 --
quantitative. Assessment and
ultimately come up with the risk

00:06:42.148 --
rating. You can come up with
much simpler ways of looking at.

00:06:48.040 --
You could identify your risk.
Basically make an assessment of

00:06:52.950 --
the likelihood of it happening,
and then maybe you do some

00:06:58.351 --
assessment of what's the impact
and then basically multiply

00:07:02.770 --
those together and that's your
risk assessment. You can make it

00:07:08.171 --
as complicated. Or as simple
as needed. The point here

00:07:12.574 --
though is every project that
you manage. You should at

00:07:16.754 --
least do a very high level
risk analysis, typically as a

00:07:21.352 --
part of a you know if you're
following some kind of a

00:07:26.368 --
structured project management
lifecycle.

00:07:29.290 --
When you're doing your initial
project planning, you would

00:07:33.232 --
likely do a very high level risk
analysis and then have.

00:07:38.860 --
You know, figure out what your
cadence is for going back and

00:07:44.920 --
assessing where things
are. Have new risks, come up,

00:07:49.970 --
etc. The you don't want to
just put a lot of effort into

00:07:55.670 --
doing a risk analysis and then
and then never come back

00:07:59.520 --
around to in fact evaluating
it. They can be very helpful

00:08:03.370 --
in helping you mitigate issues
that may come up.

00:08:08.990 --
A quality management plan is
another example of a project

00:08:13.070 --
management tool you might use.
If you're in the quality area or

00:08:17.966 --
if you have any responsibilities
for quality and you know this is

00:08:22.862 --
something very simple which is
looking at what's the particular

00:08:26.942 --
characteristic you're looking
at. Why is it important? How are

00:08:31.022 --
you going to test for quality?
Who's going to do it, and then

00:08:36.326 --
simply a status?

00:08:39.040 --
My guess is most businesses
probably have a you know more

00:08:43.803 --
specific template you might use
as a part of a quality

00:08:48.566 --
management plan. But again, the
point here is.

00:08:53.060 --
Always be thinking about that.

00:08:56.750 --
Even you know we all have a
need to be delivering the

00:09:02.431 --
highest quality and most value
we can of whatever we do for our

00:09:08.112 --
business. And so you want to be
thinking about how can I, you

00:09:13.793 --
know what's important for me in
my team in order to deliver on

00:09:19.474 --
that high quality. So this is an
example of that. Another quality

00:09:24.718 --
tool is a failure. Modes,

00:09:26.903 --
effects analysis. And this
again, is where you're really

00:09:32.193 --
looking at. Different in this
particular case, we're

00:09:36.585 --
looking at different process
steps and identifying

00:09:40.428 --
potential failure modes.

00:09:43.460 --
What are the effects of those
modes? Assessing severity? How

00:09:47.870 --
frequently is it likely to
occur, etc. And ultimately,

00:09:51.839 --
you're going to come up with an
overall risk priority number,

00:09:56.690 --
and I have seen these use

00:09:59.336 --
pretty. Sensibly in various
research and development type

00:10:03.988 --
teams. And there are good.

00:10:07.450 --
You know fairly simple way to do
a pretty in depth analysis and

00:10:12.845 --
get an understanding of where in
fact you might be want to. You

00:10:18.240 --
might want to be investing
effort in order to prevent some

00:10:22.805 --
issues from happening.

00:10:26.740 --
Dmax

00:10:29.110 --
define measure, analyze,
improve, control is.

00:10:33.660 --
Probably a process improvement
approach. You might be familiar

00:10:37.449 --
with if you've done that as a
part of your role and again.

00:10:44.350 --
You know, when I was working in
R&D we were doing lots of

00:10:50.122 --
process improvement. We probably
weren't as rigorous as we could

00:10:54.562 --
have been at using something
like Demac as a model for doing

00:10:59.890 --
our process improvement, but
it's a good approach to

00:11:03.886 --
methodically walk through a
process improvement approach. It

00:11:07.438 --
can be for a very simple
improvement in each of the steps

00:11:12.766 --
might be quite short.

00:11:15.670 --
But it helps you think.

00:11:19.220 --
I guess more completely about
all the elements of the

00:11:24.240 --
problem in what you're trying
to do to improvement, so

00:11:29.260 --
definitely worth looking into
if you have an element of

00:11:34.280 --
process improvement in your
job and it's something that's

00:11:38.798 --
talked about pretty
extensively in the process

00:11:42.312 --
improvement class.

00:11:47.130 --
So wrapping up the discussion on
action planning, you know just a

00:11:52.470 --
couple of comments that I
thought were worth including.

00:11:56.475 --
You know. Oftentimes when we're
managers, we think it's our job

00:12:01.370 --
to do all the planning and it
is, you know, it is the role of

00:12:08.045 --
the technology and engineering
managers to do the planning. But

00:12:12.495 --
be sure to involve the people
who do the work.

00:12:17.020 --
In the planning where you can
now you don't want to go to

00:12:22.077 --
extremes. I was talking to a
friend of mine who works at a

00:12:27.134 --
very large company who's in the
midst of, I guess a very

00:12:31.802 --
horrendous product release and
everybody is getting really

00:12:34.914 --
nervous that they're going to be
late and so every day.

00:12:40.230 --
The senior vice president calls
every single engineer into a

00:12:45.140 --
meeting at 7:00 AM to walk
through their action planning

00:12:50.050 --
for the day. Now, do you think
that's really productive? The

00:12:55.451 --
answer is no, because a it's
people are, you know, people who

00:13:01.343 --
can are quitting because they're
there. It's ridiculous, you

00:13:05.762 --
know. So that's an example where
there's people at too high of

00:13:11.654 --
levels. Involved in the planning
with the doers. That's not the

00:13:16.110 --
intent here, but the intent is
if I'm a project manager and I'm

00:13:21.193 --
planning the next project, it
would behooves me to have a

00:13:25.494 --
session with the engineers at
some point. Not that you

00:13:29.404 --
necessarily want to ask them to
sit with you for two days to do

00:13:34.878 --
all of your scheduling, but you
probably want to have a.

00:13:40.510 --
You're kind of a validation

00:13:43.590 --
that. That you're on track
because a you want them to buy

00:13:48.525 --
into that plan. If you're
expecting them to deliver it.

00:13:52.990 --
Similarly, if you're doing
strategic planning, if you're

00:13:57.110 --
more senior executive and you're
doing strategic planning, always

00:14:01.745 --
involve your staff in that you
know that's a great opportunity

00:14:07.410 --
for a. Regular, you know, a
quarterly staff offsite to not

00:14:13.952 --
only build and foster teamwork
among the team, but.

00:14:19.410 --
Drive good alignment on that
strategic plan because

00:14:22.530 --
ultimately the people in your
team are the ones who are going

00:14:27.210 --
to have to do the work, so use
those planning.

00:14:32.220 --
Opportunities as a way to
drive alignment.

00:14:36.310 --
Use computer based tools when
you have access to them, and

00:14:41.403 --
again similarly to don't go
crazy involving people. Don't go

00:14:46.033 --
crazy with it mean there's some
really incredible tools out

00:14:50.663 --
there to do scheduling and
things like that, but if you

00:14:55.756 --
have, you know 1000 or 2000
tasks in a schedule is just too

00:15:01.775 --
unwieldy to manage, so use them
when they make sense

00:15:06.405 --
Alternatively. Use simple tools
when they make sense.

00:15:10.980 --
If you're doing software
development, you know everybody

00:15:14.940 --
is familiar with Agile there is.

00:15:19.200 --
Kind of an element of agile for
very simple projects where you

00:15:23.820 --
can basically use a con Bon
bored. So if you're fixing

00:15:28.055 --
defects for example in a
product, it's very easy to use a

00:15:32.675 --
con Bon bored to show how you
know when the defect gets

00:15:37.295 --
accepted into the system, who's
working on it when it's done,

00:15:41.530 --
when it's tested, when it's been
deployed to a customer, for

00:15:45.765 --
example. That's a very visual
way. You don't need a very

00:15:50.000 --
complex. Tool to track that
work, but the visual kambam

00:15:54.290 --
board is a good way to keep
everybody up to date. So figure

00:15:59.269 --
out what you need and don't
don't apply technology where you

00:16:03.482 --
don't need to.

00:16:06.430 --
Make sure you're looking at
risks in doing contingency

00:16:10.084 --
planning where you need to, and
you might have to go back and

00:16:15.362 --
iterate on the planning process.
You may say you do your planning

00:16:20.234 --
as you know your project
manager. You do some planning,

00:16:24.294 --
you have a review, say with your
team and there were some things

00:16:29.572 --
that you missed. Well, you gotta
go back and iterate. It's not

00:16:34.444 --
you don't need to feel like.

00:16:37.040 --
Iteration is a bad thing
because it's an opportunity

00:16:40.532 --
to get things right.

00:16:43.550 --
So I think those are some things

00:16:45.496 --
that. That you can keep in mind.

00:16:49.330 --
Hey, the last couple of topics
are issuing policies and

00:16:53.990 --
basically documenting
procedures, and I think

00:16:56.786 --
typically when we hear oh gosh,
you know I have to do I have

00:17:03.310 --
to generate policies that can
take a very negative connotation

00:17:07.970 --
in really policy czar directives
intended to address repetitive

00:17:12.164 --
questions, issues of general
concern, and really to drive

00:17:16.358 --
equity across your workforce. So
here's some good examples.

00:17:21.090 --
Hiring and firing guidelines.
You want to make sure that

00:17:25.700 --
you've got strong policy's for
expectations around hiring, and

00:17:29.849 --
also around terminating people.
You know, it's your it would be

00:17:34.920 --
a very uncomfortable environment
if there were no guidelines for

00:17:39.530 --
how people were terminated.

00:17:42.120 --
Equal opportunity policies might
be an example. Performance

00:17:47.760 --
appraisals are something that.

00:17:52.420 --
You are necessary in the
workplace and you want to be

00:17:57.073 --
able to do those
consistently. You might be in

00:18:00.880 --
a business where a drug
policy or drug testing is

00:18:05.110 --
mandatory.

00:18:07.090 --
So you know, these are some
examples of things where you're

00:18:11.875 --
really trying to.

00:18:14.680 --
Make sure there's equity and
address repetitive concerns.

00:18:19.008 --
Policies are there to save
management time. No, they're

00:18:23.877 --
not intended to generate lots
more work.

00:18:29.400 --
They are intended to capture it.
You know, the experience and

00:18:35.263 --
past learning of the company and
hopefully facilitate delegation

00:18:40.060 --
if there are clear policies in
place, then for example, if I'm

00:18:46.456 --
a senior level executive and
there are clear policies around

00:18:51.786 --
travel expenses and trip
reports, I could perhaps

00:18:56.050 --
delegate the ability or delegate
the responsibility to my

00:19:00.847 --
administrative assistant. To
look at those and approve them,

00:19:05.030 --
for example. That might be, that
might be something.

00:19:10.350 --
If that's allowed in
your particular

00:19:12.636 --
business, but basically
you're trying to figure

00:19:15.303 --
out a way to be
consistent on things

00:19:18.351 --
that are going to come
up over and over again.

00:19:25.340 --
Policies will apply uniformly to
all employees. They should be

00:19:30.930 --
pretty permanent. You don't want
to be changing policy's real

00:19:36.520 --
frequently, and hopefully they
foster corporate objectives. You

00:19:40.992 --
know you don't want to have
policies that really are in

00:19:47.141 --
conflict with things.

00:19:51.100 --
Things that are valued at the
corporate level, and so I think

00:19:55.780 --
you need to think about when you
need to have policy's.

00:20:00.420 --
You might have policies about
working at home. That's probably

00:20:04.720 --
the one that has come up several
times through the course of my

00:20:10.310 --
career. I can remember when
working at home or remote, you

00:20:15.040 --
know. Being a remote worker
located in a different geography

00:20:20.542 --
just wasn't an accepted Norm,
and I can remember the first

00:20:26.020 --
time we had to address this was
we had a very Senior High

00:20:32.494 --
performing engineer. Needed to
move to Wyoming because of some

00:20:37.780 --
family things with his wife and.

00:20:41.500 --
So we you know the question was
do we let him resign or do we?

00:20:47.480 --
Basically, craft a policy about
a remote worker and so we did

00:20:54.152 --
and it was interesting because
that got tested.

00:21:01.080 --
Over and over again in terms of
people you know other people

00:21:05.064 --
wanting to take advantage of
that, and it was interesting

00:21:08.384 --
because you know what? If you
have somebody who comes in,

00:21:12.036 --
wants to be a remote worker, but
there may be some kind of middle

00:21:16.684 --
of the road performer, well, how
do you know? Then you have to

00:21:21.000 --
start thinking about. Do you
have to create a policy that so

00:21:24.984 --
regimented in terms of if you
come with the request to work at

00:21:29.300 --
home? You need to be?

00:21:31.550 --
In the you know, whatever top
two tiers of performance you

00:21:36.686 --
know etc., etc.

00:21:40.230 --
Think we tried to have a policy
that was more general.

00:21:46.710 --
Probably the biggest challenge
we had was when we started

00:21:50.680 --
working with teams in other
geographies where suddenly you

00:21:54.253 --
know we worked a lot with India
and that was not a commonplace

00:21:59.414 --
thing to have people working at
home and but then they started

00:22:04.178 --
raising that with their
management and it was

00:22:07.354 --
interesting because then when I
had my assignment in Singapore,

00:22:11.324 --
that was probably one of the
first policy things we had to

00:22:16.088 --
come up with was.

00:22:17.800 --
What are we going to do? How are
we going to create a work at

00:22:23.650 --
home policy for an environment
that historically did not permit

00:22:27.550 --
that? So again, you know.

00:22:30.060 --
That's something that came up
many years ago, and it's evolved

00:22:34.614 --
overtime. I think in general,
when I was when I retired from

00:22:39.582 --
HP, we were going back to a
policy of everyone being back on

00:22:44.964 --
site so things can swing
pretty radically and come full

00:22:49.518 --
circle based on the needs of the
business. I think that's the

00:22:54.486 --
main thing you have to keep in
mind is you may create a policy.

00:23:02.020 --
If the business needs change,
you may have to go back and

00:23:06.400 --
revisit that policy and there's
nothing wrong with doing that.

00:23:11.820 --
Procedures, it's kind of the
same, you know, we think about,

00:23:16.275 --
oh, brother, you know I have to
follow a set of procedures to

00:23:21.540 --
doing something, and it's really
you're trying to standardize

00:23:25.185 --
work that benefits from.

00:23:28.560 --
Procedures, because you're doing
it over and over again, you've

00:23:32.670 --
got or you're.

00:23:34.890 --
You have some kind of
certification, perhaps that

00:23:37.810 --
is dependent on having a
procedure to ensure that

00:23:41.095 --
work is done a certain way.
Or maybe you have a say to

00:23:45.840 --
health and safety thing
where certain types of

00:23:48.760 --
manufacturing wastes have to
be disposed in a certain way

00:23:52.410 --
and you need to follow
procedures in order to

00:23:55.695 --
ensure health and safety of.

00:23:59.040 --
The workforce and.

00:24:02.560 --
So again, depending on the type
of work you're doing, the

00:24:07.301 --
procedures you're involved with
are going to be quite different.

00:24:11.611 --
If you're in an R&D team, the
product management lifecycle is

00:24:16.352 --
a procedure that establishes and

00:24:18.507 --
standardizes how. The work is

00:24:21.446 --
going to. Or the steps if
you will. At a high level the

00:24:27.586 --
work is going to follow and what
is going to happen at each of

00:24:32.878 --
those checkpoint or handoff
process is that would be a

00:24:37.036 --
procedure if you're working in.

00:24:40.210 --
You know a part of the business
where you're installing devices

00:24:45.072 --
or you're in your field.
Engineer installing devices at

00:24:49.050 --
customer sites. It's important
you have an installation manual

00:24:53.028 --
so you can follow the
appropriate steps for ensuring

00:24:57.006 --
that things are done
appropriately. So again, it's

00:25:00.542 --
not to create a bunch of
overhead and procedures for

00:25:04.962 --
every single thing you do, but
it is important to.

00:25:10.590 --
Make sure that when you need a
procedure, you get 1 written

00:25:16.026 --
appropriately. Actually this
here we go. You want to.

00:25:20.930 --
Preserve the best way to get
the work done. So how can

00:25:24.182 --
you be efficient?

00:25:26.460 --
It can help you know.
Oftentimes, procedures are one

00:25:29.997 --
of the outcomes of a process
improvement approach. You want

00:25:33.927 --
to ensure that you have
standardized action you want to

00:25:37.857 --
simplify things, and in
particular it's a way to save

00:25:41.787 --
some of your corporate memory.
How do things get done? What's

00:25:46.110 --
the right way to do things?
What's the procedure for testing

00:25:50.433 --
your device now? It doesn't
matter if somebody leaves the

00:25:54.363 --
company, you know how things get

00:25:56.721 --
done. Because you have that
documented in the form of a

00:26:00.770 --
procedure. So again, you don't
want to overdo it, but you want

00:26:05.812 --
to have good procedures when
they make sense.

00:26:10.940 --
When you want to develop a
procedure, again, concentrate

00:26:15.251 --
on the critical work. Look at
the inputs and outputs of

00:26:20.520 --
what's happening. You might
even use a sipoc diagram as

00:26:25.310 --
input to detailing or
developing a new procedure.

00:26:29.142 --
You need to talk about or
think about the

00:26:33.453 --
characteristics.

00:26:35.620 --
Proposed the procedures and then
figure out the regular timeframe

00:26:40.290 --
that you're going to come back
and review. These probably most

00:26:45.427 --
important is making sure that
the people who are involved in

00:26:50.564 --
doing the procedure have an
opportunity to give input before

00:26:55.234 --
you go develop something in
handed off to them and inspect.

00:27:00.371 --
Expect them to do it I ideally
you'd like to have their input.

00:27:06.510 --
In the creation of the
procedure in some way,

00:27:10.164 --
certainly you want to have the
review of people who are going

00:27:15.036 --
to have to execute the
procedure before you turn them

00:27:19.096 --
loose.

00:27:24.630 --
We talked about different types
of planning. We talked, we

00:27:28.350 --
started out with some discussion
on strategic planning.

00:27:32.300 --
How do we figure out what are
the right things to do in our

00:27:36.612 --
business and then? As we
transition into operation

00:27:39.725 --
planning, what are some of the
tools to help us get things done

00:27:43.898 --
the right way? Just some things
to keep in mind.

00:27:50.730 --
Validate your assumptions.
You're going to want to go out

00:27:55.160 --
there, and even if you're
planning a project that's a

00:27:59.590 --
follow on project that you've
done five times, something will

00:28:04.020 --
be different, so be sure to make
sure you're getting appropriate

00:28:08.893 --
information. You're doing some
of that forecasting. You're

00:28:12.437 --
looking at alternatives, but
really validating that the

00:28:15.981 --
assumptions you're making are

00:28:17.753 --
correct. From a people
perspective, involve the

00:28:21.938 --
right people.

00:28:24.250 --
One of the things that.

00:28:27.140 --
You know? Is important is
consider what we used to call it

00:28:32.860 --
the with them. What's in it for
me. For all stakeholders

00:28:37.458 --
involved in your planning so
involved the people are going to

00:28:42.474 --
do the work. If you're making.
If you're planning some things

00:28:47.072 --
that are going to be done
differently, you know, introduce

00:28:51.252 --
those changes in a way that
maybe you can't avoid resistance

00:28:55.850 --
but you manage it and.

00:28:58.530 --
Will in the chapter on
leading will talk a little bit

00:29:03.054 --
about John Carter's eight step
change management approach.

00:29:06.620 --
This is a perfect opportunity
for where if you're doing some

00:29:11.504 --
planning, that's going to

00:29:13.280 --
involve. Someone elses work
being done a different way?

00:29:17.756 --
Don't discard the need to do
some active change management

00:29:21.626 --
and at a minimum this
consideration of what's in it

00:29:25.496 --
for me for all your
stakeholders will help you

00:29:28.979 --
think through that.

00:29:31.250 --
Be sure to understand the
benefit versus the cost. You may

00:29:36.398 --
come up with a great plan to do,
you know, some great product,

00:29:42.482 --
but. Is the benefit there? Is it
going to cost so much that you

00:29:49.085 --
know you're never going to
recoup what you've put into it?

00:29:53.430 --
You really have to think about
benefits versus costs. Make sure

00:29:57.775 --
when you're doing your planning

00:29:59.750 --
have. A series of small steps
along the way. This allows you

00:30:05.036 --
to get some small wins. It also
allows you to make course

00:30:09.788 --
corrections if you do a project
management plan that goes

00:30:13.748 --
basically from investigation to
and say you have one task which

00:30:18.104 --
is develop the product and then
your product is done, your

00:30:22.460 --
opportunity for making midcourse
corrections is not very good in

00:30:26.420 --
that case, so you need to figure
out what's that right level of.

00:30:31.860 --
Um?

00:30:34.160 --
What's the right level you
need to break that work

00:30:37.740 --
down such that you have
the control you need, and

00:30:41.320 --
in particular the ability
to make these corrections.

00:30:46.160 --
You want to be anticipating
changes in future conditions,

00:30:49.742 --
and again, this is where you
may be thinking about

00:30:53.722 --
contingencies, and you may
have to apply a formal change

00:30:57.702 --
management process if needed.
And Lastly, of course, make

00:31:01.284 --
sure you get the commitment of
the resources you need to

00:31:05.662 --
achieve the objectives. It's
great to have a wonderful

00:31:09.244 --
plan, but if you don't have
the ability to deliver on it,

00:31:14.020 --
then that.

00:31:16.040 --
Is very discouraging
for people overtime.

00:31:22.030 --
I think wrapping up, then, you
know, planning. I think it's

00:31:26.848 --
probably fairly obvious to all
of us we plan in every part

00:31:32.542 --
of our lives really, but it is a
very important function in

00:31:37.798 --
engineering management and
technology management and the

00:31:40.864 --
key activities we talked about
were the need to forecast action

00:31:45.682 --
planning. Of course, related to
both strategic planning and

00:31:49.624 --
tactical planning, issuing
policies and establishing

00:31:52.252 --
procedures. You know, oftentimes
we think that forecasting and in

00:31:57.313 --
particular strategic planning,
are only activities by the high

00:32:01.696 --
level executives. In my, you
know, kind of my opinion is

00:32:07.053 --
don't discount those activities
at any management level in the

00:32:11.923 --
organization, because if you're
if you understand what the

00:32:16.306 --
strategic plan is at the top
levels of your business,

00:32:21.176 --
ideally. Eat their cascaded to
each level so each level then

00:32:27.150 --
could take those objectives in
based on the work they are

00:32:32.562 --
responsible for. Create their
key objectives that link to the

00:32:37.482 --
overall objectives above them
and then ultimately if you take

00:32:42.402 --
that to the you know kind of the
final step. Each individual on

00:32:48.798 --
your team hopefully has a set of

00:32:52.242 --
performance objectives.
Ideally they can see within

00:32:55.435 --
their performance
objectives how they fit

00:32:57.889 --
within the context of the
team and how the work they

00:33:02.388 --
are doing is going to
contribute to the success

00:33:06.069 --
of the team's objectives.
The teams objectives.

00:33:10.010 --
Hopefully are linked to the
team or manager above them,

00:33:15.390 --
etc and so it really allows
clear line of sight from every

00:33:21.846 --
single person in your business
or team up to the high levels

00:33:28.302 --
of the organization and.

00:33:32.270 --
My my personal opinion is
that every single manager

00:33:36.437 --
should take the time to do
that at the level that's

00:33:41.530 --
appropriate for where their
team fits in the

00:33:45.234 --
organization.

00:33:46.850 --
And then I think, Lastly
operational planning, you know.

00:33:50.970 --
Really forms the basis for much
of what we do.

00:33:55.400 --
And so you need to figure out
what are the tools that are

00:33:58.871 --
important for you to do.

00:34:01.960 --
Here's just an example of you
know how you might have to think

00:34:06.926 --
a little bit strategically, and
this was question 2.2 at the

00:34:11.128 --
back of the textbook and it

00:34:13.420 --
says. So the company has
always been focused on the

00:34:18.105 --
high quality, high priced
end of the market.

00:34:22.500 --
Now, market intelligence
indicates that some competitors

00:34:26.399 --
are planning to enter the low
price, low quality into the

00:34:32.526 --
market. What would you do?

00:34:38.660 --
It's an interesting question
because from a strategy

00:34:44.460 --
perspective you probably
have focused on.

00:34:50.170 --
Well, you obviously have focused
on the high end element of the

00:34:55.090 --
market. Probably everything in
your company is structured

00:34:58.370 --
around that. You certainly want
to figure out how to protect

00:35:04.074 --
that Mitch if you will, but
likely if you do nothing.

00:35:09.820 --
Your business will
slowly be eroded by.

00:35:15.220 --
People who are anticipating this
kind of low, low price, low

00:35:19.972 --
quality product by the
competition and there's a number

00:35:23.860 --
of options you could explore.

00:35:26.890 --
You could really look at the
option of partnering with

00:35:32.160 --
someone and you know, importing
a low price, low quality

00:35:37.430 --
product, perhaps you.

00:35:40.640 --
Label it as you know you work
with somebody by the technology

00:35:45.416 --
and label it as your own.

00:35:49.650 --
That would certainly be a way to
quickly get a product into the

00:35:55.448 --
market with the least amount of
investment necessary. Of course,

00:35:59.908 --
you know the downside of that is
if it really is low quality and

00:36:06.152 --
your brand has been all about
high quality, what does that do

00:36:11.504 --
to your customer base? They may
not be accepting of that, so you

00:36:17.302 --
have to think through.

00:36:19.810 --
That may be a really good
thing to do, but what are

00:36:23.830 --
the implications? So there
you would probably need to

00:36:26.845 --
do some scenario planning
and think through that you

00:36:29.860 --
could certainly.

00:36:33.610 --
Follow the competition more
closely and perhaps start

00:36:37.418 --
preparing to take your product.
You know, kind of downmarket

00:36:42.178 --
some. That obviously takes a
much bigger investment and takes

00:36:46.938 --
a longer period of time.

00:36:52.620 --
That might be a way to get
started on this notion of having

00:36:58.002 --
a second brand if you will
within your business. So you

00:37:02.556 --
could still maintain that high
price, high quality brand and

00:37:06.696 --
basically Re brand of product
line that's targeted at a lower

00:37:11.250 --
end of the market.

00:37:15.260 --
Yeah, I think the point is
though, you probably can't.

00:37:18.870 --
You know doing nothing is
probably a recipe for

00:37:22.119 --
failure. So in a case like
that, you need to think

00:37:26.090 --
through.

00:37:27.600 --
From a strategic planning
process, what are your options?

00:37:32.082 --
What makes sense and they can

00:37:35.070 --
range from? Investing in new
product development for that low

00:37:39.856 --
end of the product line,
recognizing that takes a long

00:37:43.426 --
time. You can do nothing at the
other end of the spectrum, which

00:37:49.104 --
probably is going to be.

00:37:52.510 --
It's going to impact your
business overtime or you

00:37:55.876 --
come up with something in
the middle. Which is this

00:37:59.616 --
idea of partnering with
somebody. And each of those

00:38:02.982 --
will have pros and cons and
benefits and risks, and that

00:38:07.096 --
would be an assessment you
have to make.

00:38:12.090 --
So I think what you can see and
will see this probably in every

00:38:17.928 --
chapter in the textbook.

00:38:20.730 --
Engineering management or
technology management is usually

00:38:24.335 --
not very black and white.

00:38:28.130 --
There is always this kind of,
typically a Gray, you know a

00:38:33.314 --
Gray area in the middle, and
that's where we want to take

00:38:38.498 --
advantage of all the tools we
have available to us. You want

00:38:43.682 --
to certainly apply critical
thinking as you're looking at

00:38:47.570 --
homework assignments that are
case studies. There's typically

00:38:51.026 --
not going to be necessarily a
right and wrong answer.

00:38:56.730 --
So what's going to be important
is are you able to think through

00:39:02.099 --
and analyze the particular
situation and use the tools at

00:39:06.229 --
hand to come up with some
possible options? So don't get

00:39:10.772 --
hung up on.

00:39:13.250 --
So you know I have to do a case
study and it's going to be. It

00:39:16.770 --
has to be. You know, if I don't
get this right answer, I'm not

00:39:21.339 --
going to get 100%. That's not
really the case. There's going

00:39:24.518 --
to be a lot of flexibility. The
main thing is to think

00:39:27.986 --
critically and apply the tools
that you have at hand.

00:39:32.010 --
So with that next, the
next lecture we will talk

00:39:38.090 --
about Chapter 3, which is
focused on organizing and.

00:39:45.870 --
Will look at a number of
different organization

00:39:48.742 --
structures when you might
use them. Some of the pros

00:39:52.332 --
and cons, and so I think
it will be an interesting

00:39:56.281 --
discussion. So thanks bye.

Duration:"00:52:28.7600000"

00:00:30.200 --
Yes.

00:00:33.030 --
So today we will continue
discussion about the

00:00:35.870 --
modified, all the method and
Runge Kutta methods. So we

00:00:39.420 --
will talk about the formulas
and then accuracy and so on.

00:00:43.325 --
So I give you hand out and
the problem. I'll use it

00:00:47.585 --
today so that we can cover a
little bit faster. And then

00:00:51.845 --
I'll spend time on other
material. OK, so.

00:00:58.460 --
In there you remember in all
this method in order to go from

00:01:03.751 --
point X&YN to point XN plus one
1 + 1, essentially with another

00:01:09.042 --
next index, we only use
information from the previous

00:01:12.705 --
point. So in a modified or leave
use information from 2 points

00:01:17.589 --
and we use oil as step to go to
the point X N + 1 NU N +

00:01:24.915 --
1. This is predicted point.

00:01:27.950 --
And then be available slope at
the predicted point and we use a

00:01:33.059 --
slope at initial, not initial.
But the point that we start

00:01:37.382 --
start from and then we average
these slopes defined slope

00:01:41.312 --
alone, which we find essentially
construct line right tangent

00:01:44.849 --
line and then we find
approximation at the next step.

00:01:48.779 --
So I also wrote this method last

00:01:51.530 --
time. So you can either define
predictor which is the Oilers

00:01:57.000 --
step and then this is slope at.

00:02:01.370 --
.1 right and here we have slope
at .2 and then we average slopes

00:02:07.082 --
and this is how we find the
next. The next point all we can

00:02:12.794 --
write down these slopes
explicitly. So K1 is a slope at

00:02:17.282 --
point. XNYN and then we use it
to March to find point you and

00:02:22.907 --
plus one. Then we find K2 slope
at the second point and then we

00:02:27.793 --
take every to the slopes
defined. And if you don't want

00:02:31.632 --
to use K1K2 and just write this
in terms of an even without you

00:02:36.518 --
N + 1, then you just write
explicitly all the expressions

00:02:40.357 --
for for you and plus one. So
this is a first step. Predictor

00:02:44.894 --
does not change and in the
second step in the character.

00:02:48.970 --
You have your own plus one
equals UN plus H / 2, so you

00:02:53.702 --
take average. This is your slope
at point XYN. This is your point

00:02:58.096 --
and you X N + 1 right here. This
is your predicted point. U N + 1

00:03:03.842 --
essentially just written

00:03:04.856 --
explicitly. OK.

00:03:09.510 --
Modified the oldest method uses
two term approximation from the

00:03:13.990 --
Taylor series right. The
constant term and the linear

00:03:18.022 --
term. The modified Euler method
uses. Also next terms uses

00:03:22.502 --
quadratic term in the Taylor
expansion, so if we go back to

00:03:27.878 --
their tail expansion then
modified Euler will use up to

00:03:32.358 --
age squared term. So this means
that the first time that you

00:03:37.734 --
neglect will be proportional to

00:03:39.974 --
H cube. Right next will be age
to the 4th. Each of the 5th and

00:03:45.450 --
if H is small then this will be
a dominant term. So air local

00:03:50.070 --
error over one step will be
proportional to H cube.

00:03:54.290 --
And then you find cumulative
error after multiple steps right

00:03:58.000 --
after. If you're going from zero
to X final, then the error will

00:04:02.823 --
be proportional to age squared,
so similar usually you lose one

00:04:06.904 --
order when you sum the errors
you find cumulative error. So

00:04:10.985 --
since modified term all this but
it matches the 1st three terms

00:04:15.437 --
in the Taylor series up to and
including termination squared,

00:04:19.147 --
the local area is proportional
to each cube, but the cumulative

00:04:23.228 --
error is proportional to age

00:04:25.083 --
squared. So if air is
proportional to H squared

00:04:28.998 --
and instead of H, you take
H / 2, what would happen

00:04:32.910 --
with the error?

00:04:35.610 --
As will decrease by
approximately 1 force, right? So

00:04:38.265 --
if you see so, this is a way how
you can check that your method

00:04:42.690 --
is quadratic. So so this means
that your method is quadratic,

00:04:45.935 --
so your error is proportional to
each squared. Let's say you

00:04:49.180 --
write a program and how would
you verify that? Yes, the method

00:04:52.720 --
is programmed correctly. So what
you can do you take you take a

00:04:56.555 --
test problem for which you know
exact solution, so you can look

00:05:00.095 --
at the error because error would
be the difference between exact

00:05:03.340 --
solution and numerical solution.
So you go from.

00:05:06.430 --
Initial time to some final time
final point, and you compute

00:05:11.457 --
solution at the final point.

00:05:14.530 --
And you look at the error right?
And then you decrease error by

00:05:18.391 --
half and look how the error will
change. So if error bill

00:05:21.955 --
decreased by by half, this means
that you have a linear method.

00:05:26.250 --
If it decreased by quarter, than
its accuracy is quadratic.

00:05:32.310 --
OK. So this is a way to verify
that your program is is correct,

00:05:37.448 --
and then once you verify your
code then you can change

00:05:41.034 --
equation. You can change
function, then you can more or

00:05:44.294 --
less thing that your program is
reliable, computes correctly, so

00:05:47.554 --
this is what happens with the
error. Is H decreased by half

00:05:51.466 --
then the arrabelle because by by
a factor of four and just for

00:05:55.704 --
comparison. Again for all this
method it's a linear

00:05:58.638 --
convergence. So if you decrease
age by half your error will also

00:06:02.550 --
decrease approximately by half.

00:06:05.710 --
OK.

00:06:11.410 --
And so essentially we know the
methods we just. I can just

00:06:15.442 --
rewrite it may be in the way
that is more convenient for for

00:06:19.810 --
programming. So if we want to
solve initial value problem with

00:06:23.506 --
some initial condition. So what
do we need? We need initial

00:06:27.202 --
condition right? So X not, why
not? We also know we need to

00:06:31.570 --
know the step size and how many
steps we have to perform right

00:06:35.938 --
function F is known. So once you
have equation you can find

00:06:39.970 --
function F so again.

00:06:41.420 --
Then before you need to compute
'cause you have some homework

00:06:46.051 --
that you have to actually
implement by hand or using

00:06:50.261 --
Calculator. So write down the
formulas before you substitute

00:06:54.050 --
values right so?

00:06:56.320 --
You can, we can use either write
this in terms of predictor

00:07:00.256 --
corrector or we can use this
slopes K1K2 to write the method

00:07:04.192 --
so XN plus 1 = X N plus H. So
every time you increment by H

00:07:09.440 --
right and also we can write

00:07:11.408 --
that. H is X final minus X
starting divided by number of

00:07:17.326 --
steps right or number of steps
is X final minus 0 / H right?

00:07:23.150 --
So if if you know number of
steps you know initial point

00:07:28.142 --
terminal point then you can
find step size or vice versa.

00:07:32.718 --
If you know step size you can
find number of steps.

00:07:39.730 --
OK, predict this step is
just the oldest method.

00:07:43.490 --
Right and then corrector? So
predicted allows you to find

00:07:46.940 --
this predictive point you N + 1
and then corrector will find

00:07:51.080 --
slopes at both points and
average them to find exponent.

00:07:55.210 --
OK, and again Alternatively this
is using the K1K2 and but

00:07:59.687 --
essentially the same.

00:08:01.550 --
OK, so whatever way you
prefer, you can use.

00:08:08.170 --
OK, any questions here.

00:08:14.070 --
So let's look at the example.

00:08:16.890 --
So in this example you have to
implement modified order in.

00:08:23.520 --
And solve the problem in 2

00:08:24.972 --
steps. So equation is Y prime
equals X + y -- 1 squared.

00:08:30.250 --
Initial condition by 0 = 2. So
find Y at. So you start from X

00:08:35.575 --
equals. O you go to X =
0.2 in two steps means that step

00:08:42.728 --
step sizes. 0.1 right again,
it's a 0.2, so H is 0.2

00:08:49.380 --
-- 0 / / 2 zero point
1 which is written here.

00:08:56.710 --
Initial condition X00Y0 stole
from here number of steps two

00:09:02.050 --
and then H you find.

00:09:06.260 --
Their function function F
function F is the right inside

00:09:09.760 --
of your equation.

00:09:12.550 --
OK, and I know it's tempting to
write down right away their

00:09:17.230 --
solutions, but take some time.
Just write down the formulas in

00:09:21.520 --
terms of X&YN, it's easier than
to substitute. I mean, if you

00:09:26.200 --
program something then you just
program with indices and then it

00:09:30.490 --
computable repeat, write your
computations. But when you do by

00:09:34.390 --
hand then you have to keep track
of X0X1Y0Y1 and then here you

00:09:39.460 --
have you also UN to worry about.

00:09:43.700 --
So you write down the formula.
So this is your next.

00:09:46.850 --
Approximation of X. This is
your predicted value just

00:09:50.540 --
using the Euler's method,
because this is your function

00:09:54.230 --
F at X&YN and then.

00:09:57.420 --
This is your next approximation.

00:10:00.110 --
By using the previous and
the average of slopes.

00:10:04.030 --
OK.

00:10:06.520 --
So for all this method to go
from one point to another, you

00:10:11.109 --
do one is 1 stage method because
you only use one point for the

00:10:16.051 --
modified order, it is 2 stage
because you have predictor an

00:10:19.934 --
you have character. So each step
has two parts.

00:10:24.160 --
OK.

00:10:26.920 --
So if we take so here, we
have N equals.

00:10:33.010 --
Zero, so when N = 0, I have X
1 = X O plus H. We find 0.1,

00:10:40.462 --
which is what supposed to be
predicted point Yuan Yuan plus

00:10:45.016 --
one. Will you one and then it's
Y0 plus HX0Y0 and you substitute

00:10:50.398 --
values you get 2.1. So this is
your predicted value and then

00:10:55.366 --
you can use it in the next stage

00:10:58.678 --
defined. Correction, OK, so this
is your essentially. This is the

00:11:02.650 --
same as what you have here.

00:11:05.450 --
So it might be more beneficial
to use key one key two if you

00:11:10.014 --
want to reduce time on writing
because you have to rewrite

00:11:13.600 --
this. And this is your slope at
the predicted point. Again, just

00:11:17.512 --
write down X0Y0X1U one before
you substitute values, because I

00:11:20.772 --
mean you see that becomes messy.

00:11:29.940 --
OK, so then we substitute values
and we obtain approximation. So

00:11:33.845 --
so we did two stages, but this
is the first step.

00:11:38.670 --
OK, it's not 2 steps first step.
So now we use N = 1 and

00:11:45.525 --
this allows us to find X2U2 and
Y2. So X2 is exam plus H, so

00:11:52.380 --
we have you too is a prediction
using the Oilers step from Point

00:11:58.321 --
X one U-1 and then you do is
correction with average of

00:12:03.805 --
slopes. Again as you see, right
down X one U1X1X2U2 and so on.

00:12:09.880 --
And then approximate and
then substitute values.

00:12:16.130 --
So finally so this is our
approximation of a solution at

00:12:19.639 --
0.2, and again this is not exact
value, right? It's only

00:12:23.148 --
approximation because we use out
of infinitely many terms in the

00:12:26.657 --
Taylor series, we only use 3.

00:12:29.290 --
So H is finite, right? So
definitely we have an error. OK,

00:12:33.442 --
so schematically what is going
on here? You start. Your initial

00:12:37.248 --
condition was at 02 right? This
is your point.

00:12:42.180 --
Predictor brings you
to point X one U-1.

00:12:47.560 --
You find slope at this point at
X1. You want you find slope at

00:12:54.224 --
X0Y0. You average corrector
gives you point X1Y1.

00:12:59.420 --
This is your first step, but

00:13:01.412 --
still stages. Then again from
point X1 U one you find

00:13:06.648 --
predictor X2U2 right YouTube
means has index as Y two. So

00:13:11.510 --
please different letter. But
it is the same index and then

00:13:16.372 --
you've added slopes at X
11X2U2 average them and this

00:13:20.792 --
gives you correct correction
point X2Y two again two stage

00:13:25.212 --
but it's one step.

00:13:31.180 --
OK.

00:13:33.760 --
Any questions here?

00:13:36.930 --
So example have either Euler or
modified Euler method to

00:13:40.870 --
implement by hand, which means
the step size will be generously

00:13:45.204 --
large, maybe like one or
something that doesn't require

00:13:48.750 --
because you cannot use
calculators for the test there

00:13:52.296 --
'cause I don't know which device
you bring mini. Something

00:13:56.236 --
computer that has access online
and so on. So the algebra will

00:14:00.964 --
be simple enough that you can do

00:14:03.722 --
by hand. But for me, even if you
have to perform 2 steps.

00:14:08.650 --
I need to see that yes, you
know what is initial

00:14:11.411 --
condition. What is the next
point and so on. So it will

00:14:14.423 --
not be a lot of steps, but at
most Euler or modified Euler.

00:14:18.810 --
OK, your homework has more steps
to perform, so you're welcome to

00:14:23.358 --
use whatever calculators
computers to get the values, but

00:14:26.769 --
you have to write down. Then you
can probably minimize number of

00:14:31.317 --
things that you write.

00:14:33.600 --
OK, your project Modeler
project is based on

00:14:36.888 --
implementing these methods
actually not implementing.

00:14:39.354 --
Using them to solve
problems because the

00:14:42.231 --
programs functions are
available on the course

00:14:45.108 --
websites. You just have to.

00:14:49.070 --
Maybe on Monday I'll bring the
laptop so I'll show you where

00:14:52.646 --
files are and how to use them.

00:14:57.500 --
OK so next method.

00:15:00.250 --
To consider is so called 1st
order on the quota method.

00:15:06.320 --
And the idea here is the
falling. So we saw from their

00:15:10.880 --
modified all the method that if
we use information from two

00:15:15.060 --
points then we get more accurate

00:15:17.340 --
approximation. Right, so can we
use more points to get the even

00:15:22.577 --
more accuracy and the question
the answer is yes. So in this

00:15:27.101 --
case we use four points.

00:15:29.560 --
So we go from .1.

00:15:32.980 --
2.2 Essentially this is your
order step. We get point .2.

00:15:38.645 --
Then we use this slope K2 to
go to .3.

00:15:44.670 --
We use the .3 slope. Do you go
to .4 and then we take weighted

00:15:50.790 --
average of the slopes at this

00:15:53.238 --
point? OK, so OK.

00:15:57.250 --
Um?

00:16:00.400 --
So which points we use? We use

00:16:03.529 --
point X. We use point in the
middle of this interval at X N +

00:16:08.925 --
H / 2 and here we have two
points to use and we also use

00:16:13.050 --
point at X = N + 1.

00:16:16.350 --
So do we? Do we give the same
weight essentially the sum of

00:16:21.316 --
slopes over 4? No, we give
twice more weight at points

00:16:25.518 --
in the middle.

00:16:36.200 --
And this is last page that you
have an I I did not print. I

00:16:42.095 --
have a few more pages, but.

00:16:45.910 --
I'll explain what we have here.
So if you have.

00:16:51.170 --
Probably let let me use, maybe
maybe maybe this so you don't

00:16:55.094 --
have this page, but this is a
recap of the last page, so you

00:16:59.672 --
have to want to solve the 1st
order equation with some given

00:17:03.596 --
initial. So I'll bring a copy of

00:17:05.885 --
this next time. So what you do
you find the slope at .1. This

00:17:11.178 --
is where you start.

00:17:13.540 --
Then you match half step to .2
using this slope.

00:17:19.110 --
So you have you have X N + H
over to you. This is your X

00:17:25.462 --
displacement an in. Why you do
Oilless step with step size H of

00:17:30.623 --
it but slow K1.

00:17:33.320 --
So once you have this
point, you use this point

00:17:37.380 --
to evaluate slope.

00:17:39.970 --
So I compute slope K2 and I find

00:17:43.858 --
.3. By marching again from KXAN
half step and using alone Def

00:17:50.700 --
line with slope Cato.

00:17:53.650 --
OK, this gives me point X 3.3,
so from .3 then we match full

00:18:00.090 --
step to find point for using
Slope case 3.

00:18:05.020 --
Once you have all these four
slopes, you have weighted

00:18:08.630 --
average so you have you give
weight 1 to the first point and

00:18:13.323 --
to the last point, but two
weights to the .3 and two and

00:18:18.016 --
three. So overall you have for
slopes six slopes. So you divide

00:18:22.348 --
age by 6.

00:18:24.130 --
So this is your average
weighted slope.

00:18:28.090 --
OK, and then you can write this
slope like even if you don't

00:18:32.640 --
know this. So you use
information from four points. OK

00:18:36.140 --
to find, so this is a full stage

00:18:38.940 --
method. Anne.

00:18:43.250 --
In order to go from X&YN 2 X N +
1 one plus one, it is still

00:18:49.098 --
using only one previous point,
right essentially, but it does

00:18:52.538 --
it in four in four stages.

00:18:55.260 --
OK.

00:19:01.760 --
OK, So what I can say
here is there wrong accoutre

00:19:08.756 --
force order matches there?

00:19:14.230 --
The local error in their own
decoder 1st order method is of

00:19:18.406 --
order H as a power 5.

00:19:21.980 --
OK, but when you find cumulative
error then you lose one order

00:19:27.476 --
and then overall the error is.

00:19:31.300 --
Proportional to H is about four
and you can. You can appreciate

00:19:35.116 --
it if H is let's say 0.01 to 10
to the point is the power of

00:19:40.204 --
negative one right? All this
method will have error also of

00:19:43.702 --
the order of 10 to the minus

00:19:45.928 --
one. Right modified order will
have error to the order 10 to

00:19:50.999 --
the minus. Two but longer code
will have error of the order 10

00:19:56.205 --
to the minus four right? So you
see that it's occasionally.

00:20:00.180 --
Logic difference in the in the
accuracy. So all this method in

00:20:03.744 --
order to get the same accuracy.

00:20:06.480 --
You need to use smaller H. Ruby
code allows you to use larger

00:20:11.992 --
step size. Because the the error
is small and So what you save,

00:20:17.542 --
you save the number of steps.
But again, remember that one

00:20:21.634 --
step of the longer quota has

00:20:23.866 --
four stages. So at each stage
you have to evaluate function

00:20:28.565 --
and function evaluation may be
consuming, so that's so. That's

00:20:32.015 --
why it's not very cheap method
because at every step you have

00:20:36.155 --
four function evaluations.

00:20:39.020 --
OK.

00:20:40.850 --
How do we check that method is
first order accurate? If we

00:20:45.686 --
decrease H by half, their level
decreased by a factor of.

00:20:55.410 --
If H is replaced with H / 2,
so the arrabelle decreased

00:20:59.622 --
by a factor of.

00:21:03.430 --
22 to the power. 416 right so
this is, you see, is a

00:21:08.929 --
significant difference between
this method and that method OK?

00:21:14.650 --
Which method you would
like to use if you have

00:21:17.570 --
to solve your problem?

00:21:22.740 --
So you have a choice. You have
three methods and you have to

00:21:27.095 --
implement MCF thread programs,
foiler for modified or Lefranc

00:21:30.110 --
equal to which method you
would start with.

00:21:33.900 --
If you want to solve the
problem that you don't know

00:21:36.595 --
solution about anything about.

00:21:39.660 --
Probably oil it while it's easy
to implement, its lately least

00:21:43.037 --
accurate, but it's easy to
implement, and for example, if

00:21:46.107 --
you programmed at an, you see
that it doesn't work. Maybe

00:21:49.484 --
there is no point of investing
time, right? But if you know

00:21:53.168 --
that yes solution exists, an
that gives you what you need,

00:21:56.545 --
you can start with all the
method just to get a feeling of

00:22:00.536 --
what solution is going to do.
But then if you need to have

00:22:04.527 --
more accuracy, or let's say if
you have to compute for long

00:22:08.211 --
time and maybe. Many points
then you probably would use on

00:22:12.492 --
GeForce order method. Matlab
in fact has so called variable

00:22:15.782 --
Force 5th order method ricotta
which allows us to change the

00:22:19.401 --
step size depending on the
estimate of the error. So they

00:22:23.020 --
have some estimate of the
error in air is small. Then

00:22:26.639 --
you can use largest largest
step. If estimate becomes

00:22:29.600 --
large then you decrease the
time step so it's not

00:22:32.890 --
constant, is not the same
method that would be

00:22:35.851 --
considered here.

00:22:37.550 --
OK, I mean whatever Matlab
built-in function solver.

00:22:42.500 --
OK, so an example and I'll have
this available on the course

00:22:47.564 --
website and then I'll give you a
hand out next time just to show

00:22:53.472 --
you what what is going on in
this ricotta method. So if we

00:22:58.958 --
want to solve this initial value
problem starting from .12 and

00:23:03.600 --
finding oh at 1.4 in two steps
using force ordering decoder

00:23:08.242 --
method, so two steps means that.

00:23:11.460 --
What is H we go from 1 to 1.4.

00:23:15.900 --
Each is.

00:23:19.750 --
So age is 1.4 -- 1 / /
2, so this will give us.

00:23:27.190 --
Zero Point 4 / 2 will be 0.2,
right? So this is your step size

00:23:32.515 --
capital N number of steps is 2
inside of each step. How many

00:23:37.130 --
stages do you have?

00:23:39.330 --
Four stages right? So 4th
function evaluations. So for

00:23:42.480 --
each stage you have to write
K1K2K3K four and then the

00:23:46.330 --
weighted average to find next

00:23:48.080 --
approximation. So K1K2K64
will be different for

00:23:51.738 --
inside of each step.

00:23:55.390 --
OK, so H with no envy, no
initial condition. X Zero is

00:23:59.626 --
one, XY0 is 2 OK, what is a
function function is X + sqrt y.

00:24:04.921 --
This is your function F so F of
XNYN is X N + sqrt y N.

00:24:12.780 --
OK, and then you carefully
substitute these values, right?

00:24:16.263 --
I mean it's OK for demonstration
purposes, so you probably want

00:24:20.520 --
to have this done by computer
right? Unless function is simple

00:24:24.777 --
that you can, you can do it. OK,
so gave one is a slope at first

00:24:30.969 --
point. In this case at X0Y0,
right? You find Cato is you

00:24:35.613 --
March, you replace X with 0 + H
to point in between and Y zero.

00:24:41.418 --
You follow The Cave one slope.

00:24:45.130 --
Right, so this is your X value.
This is your why value once you

00:24:48.882 --
have them, you substitute them
in the function, so you replace

00:24:51.830 --
X with this. Why is that?

00:24:54.140 --
Annual value it so this gives
you slope K2 then use K2 here to

00:24:59.768 --
find .3 again. X is just half
step away while zero plus K 2 *

00:25:05.798 --
H / 2 This is your ex. This is
your Y value you put in the

00:25:12.230 --
function you evaluate. Finally K
4 you much full step.

00:25:16.890 --
Use slope case 3. This is
your X value. This is your.

00:25:20.694 --
Why will you find slope K 4?
You take weighted average.

00:25:24.181 --
You get next approximation.

00:25:31.380 --
OK, so now what you found
you found.

00:25:37.130 --
X1 is 1.2 and
Y one is 2.5201.

00:25:45.570 --
So now you use this.

00:25:47.540 --
To do another step so we have
two steps here to do.

00:25:51.350 --
Right, so we have this and then
again K1K2K3K four. But now

00:25:56.990 --
instead of X0Y0 you have X1Y1.

00:26:00.690 --
Just indexes shifted and so on,
so I'll have this online and

00:26:05.034 --
I'll bring this on Monday.

00:26:09.020 --
OK, any are there
any questions yes.

00:26:14.720 --
This is based on.

00:26:17.670 --
Next one you just. Right, you
found this one from the previous

00:26:22.220 --
right step and then you just
keep it the same, but you keep

00:26:26.640 --
adding. So what I do OK, I have
formulas dependent on X&YN

00:26:30.720 --
right? So here I had to use.

00:26:34.040 --
My end was zero.

00:26:37.050 --
So I replace end with zero
everywhere before I try to

00:26:41.285 --
compute anything. So in the next
stage I have to use N equals.

00:26:46.910 --
1.

00:26:48.560 --
OK so I replace.

00:26:51.160 --
SNV X1 Y end with Y1 and
similarly everything else but

00:26:56.011 --
K1K2K3 will be different now
from the previous case from the

00:27:00.862 --
previous step. So I have F of
X1Y1 compared to.

00:27:06.930 --
F of X0Y0 I have for K2 I have F
of X1 plus HY one plus K 1 * H

00:27:14.250 --
/ 2 I have here with HO, but
this key one and escape one of

00:27:19.740 --
the same. OK, so at every
state at every step you

00:27:24.894 --
K1K2K3K four will be
different, so he probably

00:27:28.142 --
technically we have to write
down another index an, but

00:27:32.202 --
it just will increase. It
will be very cumbersome. So

00:27:36.262 --
so all slopes are different.
So for each step you

00:27:40.322 --
recompute your slopes.

00:27:44.870 --
OK, that's why.

00:27:47.280 --
Write this before you implement
your substitute values.

00:27:52.260 --
OK, right X 0X1YY1Y2 and
so on.

00:28:00.600 --
This will not be on the test.

00:28:04.540 --
OK, but it is in the homework so
so you have to do it.

00:28:10.850 --
OK, any other questions?

00:28:16.150 --
So more about numerical
methods. So we teach a

00:28:20.236 --
course which is now taught
between three department's

00:28:23.868 --
mathematics, physics, and
engineering is typically

00:28:26.592 --
chemical genius teaching and
then so this method are

00:28:30.678 --
studied in more details, but
not only this, but also

00:28:35.218 --
root, finding methods, argon
values, eigenvectors,

00:28:37.942 --
solving linear systems. So
maybe I should write so.

00:28:47.210 --
More about.

00:28:58.720 --
Anne.

00:29:01.050 --
428 and there's also so this
physics for 28 and engineering.

00:29:07.850 --
So it is the same course. I
mean, of course the also

00:29:12.602 --
graduate version.

00:29:15.760 --
529 I think and physics.

00:29:20.070 --
528 So it's slightly dependants
who is teaching, but we cover

00:29:24.437 --
the same material, so professors
from different departments POV

00:29:28.010 --
alternate, but we have the same
syllabus to follow.

00:29:36.920 --
No, normally you choose
whatever flavor you want on

00:29:40.664 --
your transcript, but that's
the only difference.

00:29:46.810 --
OK questions.

00:29:51.800 --
So.

00:29:53.810 --
I'll start Chapter 3, which
is linear equations of

00:29:57.689 --
higher order.

00:30:16.410 --
So far we've dealt only with
first order linear equations,

00:30:20.940 --
but we will look at their
methods that will allow us to

00:30:26.376 --
solve equations of high order
and linear equations do not

00:30:30.906 --
require. Coefficients to be
constantly constant, but we will

00:30:35.444 --
for simplicity we will start
with questions of miss

00:30:39.656 --
constantly efficients. OK, so
let's just recall the definition

00:30:43.868 --
of the linear equation of ends
order so linear.

00:30:51.720 --
And order.

00:30:54.120 --
Differential equation. Has
function derivative, second

00:30:58.768 --
derivative, and so on up the
derivative order NPL linearly in

00:31:04.675 --
the equation so?

00:31:07.440 --
Hey Ann.

00:31:13.720 --
Plus a N -- 1.

00:31:21.670 --
Loss etc plus a 2X.

00:31:25.550 --
D2Y T X ^2.

00:31:29.040 --
Plus a one of X.

00:31:34.190 --
Plus a 0 times function Y

00:31:37.382 --
equals. Some function that does
not depend on why.

00:31:44.150 --
So remember.

00:31:46.460 --
How, how, how we define linear
function we defined in a

00:31:50.673 --
function is a X + B right? So
your independent variable AP is

00:31:55.652 --
linearly means raised to the
power one. So now in the linear

00:32:00.248 --
differential equation you have
the same but for the function

00:32:04.078 --
derivative, second derivative
and up to the ends of the

00:32:07.908 --
derivative. These are the
functions of X only.

00:32:11.540 --
Right then they don't
involve why dependence are

00:32:14.716 --
of X is right inside.

00:32:18.020 --
Can be 00 but linearity means
that you don't have y ^2.

00:32:22.604 --
Don't have y * Y prime and so
on so so they appear linearly

00:32:27.952 --
same way as X appears in the
linear function.

00:32:32.770 --
In this case, we multiply by
constant in the equation. In

00:32:36.268 --
the case of, the equation,
coefficients can be functions

00:32:39.130 --
of X at most.

00:32:41.960 --
OK. So if.

00:32:46.070 --
Oldest coefficients.

00:32:51.390 --
Constants.

00:32:57.190 --
Then we have equations with
constant coefficients.

00:33:00.960 --
Then differential equation is.

00:33:05.460 --
A linear.

00:33:08.260 --
Differential equation with.

00:33:13.190 --
Constant.

00:33:18.560 --
Coefficients. And these are,
these equations are

00:33:23.016 --
typically easier to solve.
Otherwise equation has

00:33:26.103 --
variable coefficients.

00:33:36.630 --
This differential equation is.

00:33:41.680 --
Linear, viz.

00:33:48.200 --
Variable coefficients.

00:33:53.330 --
OK.

00:33:55.070 --
If you have a linear
equation an if right hand

00:33:59.190 --
side is identically zero,
then we have linear

00:34:02.486 --
homogeneous equation and in
fact homogeneous equation

00:34:05.370 --
only can be introduced for
linear equations. I mean

00:34:09.078 --
sometimes can be introduced
for nonlinear, but typical

00:34:12.374 --
is for linear equations.

00:34:15.830 --
Then

00:34:19.440 --
linear differential equation.

00:34:22.060 --
Is homogeneous.

00:34:29.190 --
Otherwise.

00:34:35.270 --
Linear differential equation is.

00:34:42.490 --
Nonhomogeneous

00:34:47.710 --
let's look at some examples that
we've just trying to classify

00:34:51.593 --
and then to analyze the order if
it is linear. If it is

00:34:56.182 --
homogeneous or non homogeneous.

00:35:01.010 --
So Y double prime plus X
y = 0. So what is the

00:35:05.716 --
order of this equation?

00:35:09.740 --
2nd order.

00:35:12.000 --
Is it linear or nonlinear?

00:35:16.800 --
Linear right? Because XY is
multiplied by a function of

00:35:21.040 --
XY, double prime is multiplied
by one. So linear is a

00:35:25.704 --
sensitive linear. Is it
homogeneous or non

00:35:28.672 --
homogeneous?

00:35:32.050 --
Homogeneous because there is no
function that only depends on X

00:35:36.428 --
rated 0 so homogeneous.

00:35:42.100 --
Coefficients are constant
or variable.

00:35:46.930 --
Variable because we have X
right? So this.

00:35:55.180 --
Variable coefficients. OK.

00:35:59.730 --
What about this equation?

00:36:03.530 --
X ^2 y double prime minus two XY
prime plus Y to the XY equals

00:36:10.640 --
two X -- 1.

00:36:13.550 --
Order

00:36:15.760 --
2nd. Is it linear or nonlinear?

00:36:25.740 --
OK, so we have Y times each of
the XY prime times minus two XY

00:36:30.630 --
double prime times X squared. We
have termed it depend on on why

00:36:34.868 --
is it in this form?

00:36:38.870 --
That you have derivatives
multiplied by at most

00:36:41.350 --
functions of X.

00:36:43.760 --
Yes, so it is linear, right?

00:36:46.730 --
Is it homogeneous since it is
linear or not homogeneous?

00:36:51.860 --
None, because we have
to explain this one.

00:36:56.590 --
So, nonhomogeneous? And
coefficients are variable

00:37:00.892 --
variable right? Because we have
functions so this.

00:37:07.660 --
Variable coefficients.

00:37:12.280 --
OK, next example.

00:37:15.440 --
Is 2 Y triple prime minus three
Y prime plus seven Y equals

00:37:22.499 --
luxury four X ^2 -- 1?

00:37:26.490 --
OK, the order of the equation is
3 third order.

00:37:35.940 --
Is it linear or nonlinear?

00:37:42.440 --
Huh?

00:37:43.970 --
Linear or nonlinear?

00:37:47.530 --
Why is it nonlinear?

00:37:52.610 --
We have function multiplied by 7
derivative multiplied by

00:37:57.002 --
negative three, so the order to
multiply by two.

00:38:03.220 --
Linear.

00:38:07.420 --
What is in here an is 3.

00:38:10.950 --
Look for linear equation. You
have function multiplied by at

00:38:14.430 --
most, so this this may be

00:38:16.518 --
constant. Or maybe some function
of X. This functional effects

00:38:20.159 --
may be nonlinear, but we look at
the look at the YY prime Y

00:38:24.373 --
double prime up to the highest
order derivative, not in terms

00:38:27.684 --
of X in terms of Y.

00:38:30.880 --
OK. So equation is.

00:38:34.260 --
Linear.

00:38:36.670 --
Since it is linear, is it
homogeneous or homogeneous?

00:38:41.910 --
Non, because of the logarithm
of X ^2. So nonhomogeneous

00:38:46.250 --
and coefficients are.

00:38:48.580 --
Constant rate with
constant coefficients.

00:38:54.990 --
OK and last example.

00:38:59.640 --
White triple prime my
plus 2Y double prime

00:39:04.216 --
minus y * Y prime +7.

00:39:08.920 --
The order is.

00:39:11.750 --
So the order. 3rd order.

00:39:16.710 --
Linnaean olenia.

00:39:21.560 --
Nonlinear because we have y * y
prime right nonlinear.

00:39:28.920 --
We cannot say if it is ominous
nonhomogeneous because we don't

00:39:33.980 --
have linearity to say this.

00:39:38.200 --
OK.

00:39:40.660 --
So big chunk of this course will
be devoted on the 2nd order well

00:39:45.924 --
probably not sister going to
order, so essentially it's

00:39:49.308 --
easier probably to solve 2nd
order equations, especially when

00:39:52.692 --
you consider with variable
coefficients. But the method

00:39:55.700 --
that we will develop for
equations with constant

00:39:58.708 --
coefficients can be easy.

00:40:00.470 --
Applied to the 2nd order first
Order 5th order intense order I

00:40:06.086 --
will have 19th order example to
consider. So yes.

00:40:15.070 --
It is defined only for linear
for linear equations, so.

00:40:21.530 --
I've seen some definitions that
say if identical is zero

00:40:24.950 --
solution satisfies equation,
then you can think of this as

00:40:28.370 --
homogeneous. In this case it
won't be because if you have

00:40:32.132 --
zero then this is 0. This is non
0 but typically homogeneous is

00:40:36.578 --
only for linear equations
because you have some relation

00:40:39.656 --
to linear algebra. So linear
systems, linear equations so

00:40:42.734 --
that that's the reason. So once
you may have a question on the

00:40:47.180 --
test to classify equation
equations and then so similar

00:40:50.258 --
like like we we've done here.

00:40:52.400 --
You look at the order if it
is linear then you can think

00:40:56.716 --
it's homogeneous,
nonhomogeneous, but if it's

00:40:58.708 --
not linear then you just
stop.

00:41:01.720 --
OK.

00:41:06.820 --
OK, so let's start with
second order linear

00:41:10.396 --
homogeneous equations so.

00:41:15.190 --
So we consider 2nd.

00:41:19.420 --
Modern.

00:41:24.600 --
Linear homogeneous
differential equations.

00:41:30.280 --
We will first address the
problem when we have none of

00:41:34.031 --
them, we have homogeneous
equation. Once we know how

00:41:37.100 --
to solve homogeneous then we
will study how to solve

00:41:40.510 --
nonhomogeneous equations
because there are different

00:41:42.556 --
methods how to address this
problem. OK, so in general,

00:41:45.966 --
if you have second order
linear equation then you can

00:41:49.376 --
write it in just using some
coefficients which are

00:41:52.445 --
functions of X.

00:41:55.200 --
A1 of X.

00:41:57.440 --
Divide the X + A zero
XY homogeneous. This means very

00:42:03.776 --
inside is 0.

00:42:15.190 --
And so let's look at example and
then we will try to establish

00:42:20.546 --
some properties of solutions to
the homogeneous equations.

00:42:25.750 --
So example is.

00:42:38.500 --
Let's let's let's do 2 examples,
so example a.

00:42:43.530 --
X ^2 D two YG X
^2 -- 2 X divided X.

00:42:51.680 --
Plus plus two y = 0.

00:42:54.760 --
So you can see it is
second order, right?

00:42:58.620 --
It is linear 'cause you have y *
2 divided you exams minus 2X and

00:43:03.480 --
this is also linear term and it
is not just homogeneous because

00:43:07.368 --
there is no function that only
depends on X and not multiplied

00:43:11.256 --
by wire derivative and.

00:43:13.310 --
My first statement
is that the X ^2.

00:43:17.680 --
Is a solution of this equation.

00:43:21.770 --
How do we? How do we verify that
this function is a solution?

00:43:27.300 --
We have the substitute and check
if you get identity right. OK,

00:43:30.840 --
So what do we have? If X squared
is a solution, what is the

00:43:34.970 --
derivative of this solution?

00:43:37.500 --
2X and 2nd derivative will be 2,
so we have X ^2 * 2 -- 2

00:43:44.572 --
X times. Two X + 2 times
function. So do we have 0?

00:43:51.430 --
We have two X ^2 -- 4 X
squared plus two X squared

00:43:55.863 --
right, so cancels so 0 = 0.
So this means that X squared

00:44:00.296 --
is a solution of the
equation. What happens if we?

00:44:05.020 --
Multiply this function by
by constant.

00:44:09.370 --
By some arbitrary constant.

00:44:13.130 --
The claim is that this is
also a solution.

00:44:18.740 --
So C One is an arbitrary
constant.

00:44:25.870 --
Indeed.

00:44:27.990 --
1st Order derivative will be 2 C
1X and 2nd order derivative will

00:44:32.839 --
be 2C1, right?

00:44:35.290 --
So we have X ^2 * 2 C
1 -- 2 X times 2C. One X

00:44:43.162 --
+ 2 * y C One X ^2.

00:44:48.260 --
C1 is present in all the
terms, right and otherwise

00:44:51.760 --
you have two X ^2 -- 4 X
squared X squared, so so this

00:44:56.660 --
is also zero. So again, if
you take a solution of a

00:45:00.860 --
linear homogeneous equation
multiplied by arbitrary

00:45:02.960 --
constant, you still get the
solution, so this will be

00:45:06.460 --
still a solution.

00:45:08.850 --
So similarly.

00:45:11.370 --
And you can verify that X
is a solution.

00:45:18.240 --
The first derivative is.

00:45:20.930 --
One second derivative is 0,
right? So we have X ^2 * 0

00:45:26.819 --
plus. I'm sorry minus.

00:45:32.040 --
Minus two X * 1 + 2 times
function you can see that

00:45:37.318 --
this is 0.

00:45:40.060 --
And if I multiply this solution
by an arbitrary constant, I also

00:45:44.452 --
get a solution.

00:45:49.450 --
Let's say C 2 * X is a solution.

00:45:55.110 --
And we can verify this by
substitute and so again, second

00:45:58.883 --
derivative will be 0, so we have
X, y ^2 * 0 -- 2 X times C 2

00:46:05.057 --
+ 2 * C Two X.

00:46:07.860 --
Zero and finally, if you
consider linear combination of

00:46:12.225 --
these two functions.

00:46:14.860 --
In linear combination is you
multiply function by constant by

00:46:19.410 --
different constant and you add

00:46:21.685 --
so C1. X ^2 + C
two X is.

00:46:27.720 --
Also a solution.

00:46:33.150 --
OK, let's let's verify, because
probably those cases are easy to

00:46:36.560 --
see. This one is a little bit
tricky. OK, so we have X squared

00:46:40.900 --
times second derivative. What is
the 2nd derivative here?

00:46:45.460 --
To see one right plus zero.

00:46:48.830 --
Minus two X times first order

00:46:51.908 --
derivative 2C1X. Plus C2.

00:46:56.020 --
And plus two times functions, so
C One X ^2.

00:46:59.830 --
Plus it 2X.

00:47:02.870 --
Do we have here?

00:47:06.240 --
So if I look at terms with C1.

00:47:10.270 --
I have two X ^2 -- 4 X squared,
two X squared, they cancel.

00:47:18.040 --
In terms with C2.

00:47:21.470 --
Minus two XY2 plus to exit to

00:47:24.837 --
also cancel. Right,
and this is here.

00:47:29.070 --
So 0 = 0.

00:47:36.510 --
So what we showed here is that
if you have linear homogeneous

00:47:41.178 --
equation an if you have
solutions, you form linear

00:47:44.679 --
combination. So you multiply by
constants and you add and you

00:47:48.958 --
have you keep them arbitrary.
Then result is also a solution

00:47:53.237 --
to this equation.

00:48:01.930 --
So maybe just another
example be.

00:48:05.740 --
G2Y G X ^2 +

00:48:09.486 --
3. Divide X + 2 *
y = 0 again. This is second

00:48:17.322 --
order equation. Linear
homogeneous coefficients are.

00:48:22.880 --
Constant variable so 2nd order.

00:48:29.390 --
Linear homogeneous.

00:48:34.050 --
With constant coefficients.

00:48:39.860 --
And the claims here are that E
to the minus X is a solution. So

00:48:44.615 --
at this point I'm not saying how
we find them, we will. We will

00:48:49.053 --
know this soon, but let's just
just check. So if you have it to

00:48:53.491 --
the minus X derivative will be
minus E to the minus X second

00:48:57.612 --
derivative will be with the plus
sign, right? So you have either

00:49:01.416 --
the minus X + 3 * E to the minus
X minus sign plus two times

00:49:06.488 --
function E to the minus X.

00:49:10.010 --
You get 0 right, and similarly
if you multiply by constant.

00:49:16.900 --
Is a solution.

00:49:20.190 --
That I will not verify, but
you can see that this is also

00:49:23.284 --
straightforward to do.

00:49:27.080 --
And then another solution here
available is E to the minus, 2X

00:49:32.864 --
is a solution.

00:49:38.360 --
And if we multiply by constant,
it is a -- 2. X is a solution.

00:49:45.230 --
And finally, linear
combination is.

00:49:50.340 --
Also a solution.

00:49:53.260 --
OK.

00:49:56.540 --
So so the result is how much
time do I have left?

00:50:05.830 --
One minute. OK, so I'll
I'll write the just result

00:50:09.690 --
so theorem.

00:50:12.320 --
So principle.

00:50:15.760 --
Of linear superposition?

00:50:22.460 --
It only works for linear
homogeneous equations, so given.

00:50:28.790 --
2nd order equation.

00:50:39.160 --
2nd order.

00:50:42.280 --
Linear.

00:50:44.550 --
Homogeneous equation.

00:50:51.200 --
If. Why one
of XY2 of X?

00:50:56.650 --
Our solutions.

00:51:01.250 --
Of this differential equation.

00:51:05.810 --
Then

00:51:08.050 --
their linear combination.

00:51:15.580 --
C1Y one of X + y two
Y2FX is also solution

00:51:21.212 --
of the same equation.

00:51:37.400 --
See once you're here.

00:51:41.630 --
C1C2 are arbitrary constants.

00:51:50.360 --
And similar result holds 4th
order equations, right? So this

00:51:54.430 --
doesn't change. OK, so I guess
I'm out of time, any questions?

00:52:01.690 --
OK, thank you and drive safely.

Duration:"00:56:27.8400000"

00:00:21.260 --
Alright, good morning.

00:00:22.202 --
Welcome to class city.

00:00:23.460 --
You got your homework turned in?

00:00:25.340 --
How was the assignment? Do OK with it.

00:00:29.170 --
How was the airfoil problem the long?

00:00:34.050 --
But solvable.

00:00:34.688 --
Just kind of have to be patient

00:00:36.921 --
as you work your way through it.

00:00:39.240 --
OK, so since you're here right now,

00:00:40.970 --
I will tell you next time we

00:00:42.503 --
have a midterm next Thursday.

00:00:43.930 --
We have mentored.

00:00:45.007 --
There will be an airfoil problem on the exam.

00:00:48.200 --
So study that up.

00:00:49.276 --
We'll review it a little bit later on today,

00:00:51.830 --
OK? Alright I have.

00:00:54.616 --
I have colleagues here at the university

00:00:57.292 --
and some friends in the law school.

00:00:59.620 --
That's probably a bad sign,

00:01:01.420 --
right that I have lawyer friends.

00:01:05.130 --
And I always ask, you know,

00:01:07.130 --
do you do you bring up current

00:01:09.265 --
events in your classes?

00:01:10.790 --
You know they're always the Supreme

00:01:12.854 --
Court litigation stuff going on?

00:01:14.450 --
I hear no all the time.

00:01:16.450 --
It takes too much work.

00:01:18.120 --
We do not do that in gas tax.

00:01:20.780 --
OK, just to be clear,

00:01:22.450 --
so.

00:01:25.150 --
This is. The seven minutes of terror.

00:01:29.460 --
OK, the perseverance Lander

00:01:30.888 --
that landed on Mars last week.

00:01:33.030 --
So I thought that I would go through

00:01:35.854 --
step by step to let you know what's

00:01:38.812 --
going on and then watch a video of it.

00:01:41.950 --
Just 'cause I'm the teacher, right?

00:01:44.096 --
And I say we could watch videos,

00:01:46.590 --
we're going to watch videos, all right.

00:01:49.092 --
Let's check this out.

00:01:50.520 --
So 10 minutes before landing,

00:01:52.300 --
the shell comes off and this

00:01:54.346 --
is what the Lander looks like,

00:01:56.590 --
and you can see that it maneuvers itself.

00:01:59.850 --
OK, now it's 8 minutes to entry.

00:02:01.870 --
Gets balance right here.

00:02:02.958 --
What kind of body would we call that right

00:02:05.550 --
there that that kind of rounded surface?

00:02:09.750 --
That's a blunt body. OK,

00:02:12.520 --
that's how that's how any kind of spaceship.

00:02:18.460 --
Enters the atmosphere with a blunt body and

00:02:21.100 --
we'll see that once it starts to enter.

00:02:23.630 --
Look at this, although they

00:02:25.170 --
don't draw it as a shock.

00:02:27.180 --
We know because we are experienced

00:02:29.352 --
gas dynamicist that that is a

00:02:31.554 --
shockwave that occurs right there

00:02:33.274 --
and notice that's a peak heating.

00:02:35.290 --
OK, let's look at some of these numbers.

00:02:39.140 --
Here it is 78 miles in altitude

00:02:42.262 --
above the Martian surface.

00:02:44.430 --
Look at this velocity 13,000.

00:02:47.670 --
Mph. Let's move in.

00:02:52.573 --
That is about 5900 meters per second, OK?

00:03:00.730 --
And let's see here.

00:03:02.322 --
So I did a little bit of calculation here.

00:03:06.760 --
The Martian atmosphere temperature.

00:03:08.512 --
Obviously it ranges like

00:03:10.264 --
every other atmosphere,

00:03:11.870 --
but kind of a standard temperature

00:03:15.272 --
is 60 degrees Centigrade below 0.

00:03:18.410 --
Minus 60 pretty cold, so that is 213

00:03:22.210 --
Kelvin enters at 5900 meters per second.

00:03:25.730 --
It's Martian atmosphere is primarily

00:03:28.170 --
carbon dioxide is about 95% carbon dioxide,

00:03:31.548 --
and so it's gamma is about 1.3

00:03:34.831 --
and its molecular weight is 44.

00:03:37.930 --
So we can calculate RA 314 divided

00:03:41.038 --
by 44 and it works out 'cause you

00:03:44.993 --
know how to calculate Mach numbers.

00:03:48.430 --
This works out to be a Mach number of 25.6.

00:03:53.910 --
Entering the atmosphere.

00:03:58.570 --
That's moving. That's moving OK,

00:04:00.990 --
so one of the one of the one of the

00:04:03.975 --
primary designs for this blunt body is that

00:04:07.951 --
you're traveling on Mach number of 25.6.

00:04:10.940 --
Tell me do parachutes work

00:04:12.895 --
very well in a lot #25.6 no.

00:04:15.720 --
OK, we will talk actually a little

00:04:18.303 --
bit later on in the semester that

00:04:21.516 --
there are some supersonic parachutes.

00:04:24.050 --
OK, there are some,

00:04:25.506 --
but this is not designed to do that.

00:04:28.390 --
So what the blunt body does is

00:04:30.721 --
that it absorbs that kinetic

00:04:32.582 --
energy and slows it down.

00:04:34.550 --
OK, so it's moving that amount #25.

00:04:37.080 --
Here's where it heats up that peak

00:04:39.460 --
heating and then it starts to decelerate,

00:04:42.150 --
and then finally finally it starts

00:04:44.244 --
to slow down and what it can do

00:04:47.223 --
this hypersonic aero maneuvering

00:04:48.731 --
what it does is kind of vibrate.

00:04:51.200 --
So it goes like this and it

00:04:53.657 --
converts that kinetic energy into.

00:04:55.650 --
Thermal energy and slows down.

00:04:57.510 --
That's what this maneuvering is.

00:04:59.360 --
And then finally.

00:05:00.803 --
Begins to deploy a parachute.

00:05:03.210 --
Does that at 400 meters per second.

00:05:05.980 --
Now, if you think in air that's

00:05:08.696 --
a little over Mach one,

00:05:10.730 --
it turns out for the Martian atmosphere and

00:05:14.098 --
these times it's a little bit over Mach one,

00:05:17.470 --
so it turns out that this supersonic,

00:05:20.240 --
but not real high,

00:05:21.820 --
not like hypersonic.

00:05:23.010 --
A parachute begins to deploy,

00:05:24.990 --
then the heat shield that

00:05:26.970 --
protected the spacecraft.

00:05:28.160 --
Right here, drops off.

00:05:29.988 --
OK falls off and then over here.

00:05:33.290 --
This is kind of neat.

00:05:35.210 --
The shell drops off and then there's

00:05:37.975 --
a little radar system right there

00:05:40.454 --
in that beams down to the surface to

00:05:43.756 --
determine the best place to land.

00:05:46.150 --
So it's like an autopilot.

00:05:48.140 --
It's like it's like an auto,

00:05:50.530 --
an artificial intelligence system.

00:05:52.602 --
That search arounds figures

00:05:54.674 --
out the best place to land OK?

00:05:57.420 --
Starts to collect that data and

00:05:59.706 --
then this shell drops off right

00:06:02.030 --
here and the Lander starts to

00:06:04.190 --
descend to starts to descend.

00:06:06.280 --
Excuse me, comes down,

00:06:07.776 --
it's got 4 little rockets right here

00:06:10.480 --
and these are called cold gas thrusters.

00:06:13.210 --
That's pressurized gas there,

00:06:14.902 --
so it's not necessarily a combustion

00:06:17.507 --
process starts to descend right here and

00:06:20.020 --
then it deploys what's called a sky crane,

00:06:22.830 --
so this hovers right here with those rockets,

00:06:25.910 --
and what the sky crane does.

00:06:28.380 --
Is that it lowers the Lander CABI

00:06:30.606 --
wires so that the Lander lands,

00:06:32.790 --
and then it cuts those wires in the sky,

00:06:35.840 --
crane falls away and you have

00:06:37.730 --
soft landing on the surface?

00:06:41.890 --
First off, if you're an engineer,

00:06:43.400 --
you can't look at that and say

00:06:45.213 --
that is not absolutely awesome.

00:06:47.230 --
To see that in action OK Now is actually.

00:06:49.980 --
That's kind of a complicated process if you

00:06:52.188 --
think of everything that's going on there,

00:06:54.550 --
you know one of the few seniors here that

00:06:57.016 --
learn about the Kiss principle, right?

00:06:59.125 --
Keep your design simple so that they work.

00:07:01.570 --
This is actually a pretty

00:07:03.090 --
complicated process.

00:07:03.700 --
Past Mars Landers.

00:07:06.030 --
Past Mars Landers actually have a

00:07:08.022 --
kind of a balloon on the outside

00:07:10.452 --
number of balloons that cover this in,

00:07:12.870 --
so that when it lands,

00:07:14.580 --
it actually bounces on the

00:07:16.230 --
surface of Mars until it stops.

00:07:18.340 --
Then the balloons deflated, opens up.

00:07:20.390 --
Then you have a Lander,

00:07:22.100 --
so spirit and opportunity landed like that.

00:07:24.500 --
OK, so.

00:07:26.460 --
That the pretty complicated

00:07:27.820 --
sort of landing process.

00:07:29.180 --
Now let's watch the video.

00:07:30.880 --
They actually in fact I heard

00:07:32.896 --
this on the news is that is that

00:07:35.661 --
in part of the design process,

00:07:37.680 --
they told a couple of engineers say hey,

00:07:40.400 --
listen,

00:07:40.804 --
would it be kind of cool to take high def?

00:07:44.890 --
Pictures,

00:07:45.179 --
High resolution pictures of the

00:07:46.624 --
landing process so they actually went.

00:07:48.450 --
I want to see RadioShack that kind

00:07:50.585 --
of dates me so they went to off

00:07:53.100 --
the shelf cameras and were able to

00:07:55.232 --
put it on the Lander so that you

00:07:57.360 --
can see the landing in process.

00:08:00.400 --
Dumb question, would you like to see it?

00:08:03.570 --
I thought so, so here we go.

00:08:05.630 --
So now that you know.

00:08:07.100 --
So now that you know the landing process,

00:08:09.450 --
let's see what we got here and fly

00:08:11.482 --
right maneuver where the spacecraft

00:08:13.007 --
will jettison the entry balance

00:08:14.612 --
masses in preparation for parachute

00:08:16.198 --
deploy and to roll over to give the

00:08:18.563 --
radar a better look at the ground.

00:08:23.330 --
Public it indicates she's deployed.

00:08:26.610 --
The navigation has confirmed that

00:08:28.390 --
the parachute has deployed an.

00:08:30.170 --
We're seeing significant

00:08:31.235 --
deceleration in the velocity.

00:08:32.660 --
Our current velocity is 450 meters

00:08:34.658 --
per second at an altitude of about 12

00:08:37.545 --
kilometres from the surface of Mars.

00:08:42.310 --
He tilts up. Perseverance is now,

00:08:45.000 --
so she was dropping off these

00:08:47.010 --
and then literally on Mars.

00:08:48.750 --
Just allow both the radar and the

00:08:50.920 --
cameras to get their first look

00:08:52.991 --
at the surface current velocity

00:08:54.771 --
it 145 meters per second at an

00:08:57.263 --
altitude of about 10 Columbia 9

00:08:59.321 --
1/2 kilometers above the surface.

00:09:03.160 --
Now that's pretty cool to see that close.

00:09:06.420 --
Picture in that sort of definition of

00:09:08.667 --
the Martian surface. That's pretty neat.

00:09:14.260 --
And if you look on the bottom,

00:09:16.470 --
you can kind of see it's.

00:09:18.370 --
It gives the step filter contract about

00:09:20.540 --
players entry .3 meters that there

00:09:22.546 --
should come out altitude 7.4 kilometers

00:09:24.574 --
now has radar lock on the ground.

00:09:26.580 --
Current city is about 100 meters per second,

00:09:29.110 --
6.6 kilometres of the surface.

00:09:35.220 --
President is continuing to

00:09:36.888 --
descend on the parachute.

00:09:38.560 --
We're coming up on the initialization of

00:09:41.507 --
terrain relative navigation and subsequently

00:09:43.641 --
the priming of the landing engines.

00:09:46.060 --
Our current velocity is about 90 meters per

00:09:49.724 --
second at an altitude of 4.2 kilometers.

00:09:53.320 --
Now, whether or not your geologist,

00:09:55.090 --
you could look at that surface

00:09:56.692 --
and say that there's windblown.

00:09:58.340 --
You can see the guys mentioned

00:10:00.086 --
that the reservation system has

00:10:01.595 --
produced a valid solution here,

00:10:03.060 --
and part of strain out the navigation water

00:10:05.500 --
or liquid that was there be a nominal.

00:10:07.780 --
We have timing of the landing engine's.

00:10:15.160 --
Back Shell survival at sea is 83

00:10:17.589 --
meters per second at about 2.6

00:10:19.838 --
kilometers from the surface of Mars,

00:10:22.110 --
we have confirmation that the

00:10:23.940 --
back shell has separated.

00:10:25.410 --
We are currently performing

00:10:26.870 --
the divert maneuver.

00:10:27.970 --
Travelocity is about 75 meters per

00:10:30.256 --
second at an altitude of about a

00:10:32.874 --
kilometre off the surface of Mars.

00:10:34.920 --
Here, in safety Bravo.

00:10:38.090 --
We have completed our

00:10:39.770 --
terrain relative navigation.

00:10:41.030 --
Current speed is about 30

00:10:43.130 --
meters per second altitude,

00:10:44.810 --
about 300 meters off the surface of Mars.

00:10:50.680 --
We have started our constant

00:10:52.570 --
velocity accordion, which means

00:10:54.084 --
we are conducting the skycrane,

00:10:55.970 --
so this is where the sky Crane

00:10:58.616 --
maneuver deploys at it drops,

00:11:00.510 --
there's the Lander right there?

00:11:02.400 --
I mean, that's that is totally cool,

00:11:05.040 --
20 meters off the surface.

00:11:13.220 --
And you see that in the top view,

00:11:15.220 --
that's the that's the sky cream.

00:11:16.720 --
Rocky go delta.

00:11:18.148 --
Captain confirmed persevered

00:11:19.576 --
safely on the surface of Mars,

00:11:22.130 --
ready to begin seeking

00:11:23.930 --
the sands of past life.

00:11:29.220 --
There you go.

00:11:32.380 --
How great is that?

00:11:33.828 --
And that is pretty cool.

00:11:35.640 --
And since you are,

00:11:37.088 --
since you were all gas dynamicist's,

00:11:39.260 --
you know you could figure out the

00:11:42.186 --
aerodynamics of a good portion

00:11:44.444 --
of everything that we saw there.

00:11:47.210 --
In a couple of weeks actually,

00:11:49.100 --
starting next week,

00:11:50.528 --
we'll learn about rocket nozzles.

00:11:52.910 --
OK, and how they work good.

00:11:56.780 --
Any questions at all for get going?

00:11:58.950 --
Is it not a beautiful day

00:12:00.600 --
for gas at the office today?

00:12:02.670 --
It is awesome, OK?

00:12:05.420 --
Thursday is an exam at the end of class.

00:12:08.480 --
Today we will will have a little review

00:12:11.360 --
an what's going to be on the exam,

00:12:13.920 --
but I want to just rehash

00:12:15.780 --
expansion waves to make sure

00:12:17.462 --
you've got that down expansion,

00:12:19.360 --
which are very very important concept.

00:12:21.400 --
OK so.

00:12:23.500 --
Recall that that an expansion wave

00:12:25.810 --
occurs when you have a supersonic

00:12:28.231 --
flow that turns away from itself,

00:12:30.650 --
so it's coming down this way

00:12:32.828 --
known as the mod numbers.

00:12:35.010 --
One goes through goes through

00:12:36.995 --
a turn away from itself.

00:12:38.980 --
There are some questions

00:12:40.568 --
last time after class,

00:12:42.160 --
so I just want to clarify

00:12:44.542 --
this that this line,

00:12:46.130 --
this leading Mauchline in this

00:12:48.205 --
trailing Mauchline constitute

00:12:49.450 --
what's called an expansion fan.

00:12:51.290 --
OK, those are expansion waves that.

00:12:53.810 --
That occur when a supersonic

00:12:56.005 --
flow turns away from itself.

00:12:58.200 --
OK, this leading Mauchline,

00:12:59.992 --
then that's the front edge of that fan,

00:13:03.470 --
and it occurs at this Mach angle.

00:13:06.540 --
Musa one OK?

00:13:09.470 --
It's it's the air turns through this

00:13:11.990 --
fan once it leaves the fan then it

00:13:14.769 --
falls the wall as it comes down here OK.

00:13:17.890 --
In the turning angle Delta OK,

00:13:20.590 --
recall a number of things.

00:13:22.840 --
The flow is isentropic.

00:13:24.640 --
No losses.

00:13:25.540 --
That means the stagnation pressure

00:13:27.790 --
remains constant across that turn,

00:13:30.040 --
their model number goes up.

00:13:33.190 --
It accelerates,

00:13:33.940 --
in fact,

00:13:34.690 --
I mentioned nozzles rocket nozzles will learn

00:13:37.357 --
how expansion waves work in rocket nozzles,

00:13:39.870 --
and that's how they that's how a

00:13:42.201 --
nozzle can produce supersonic flow.

00:13:44.320 --
Since the model number goes up,

00:13:46.550 --
the pressure goes down,

00:13:48.030 --
static pressure goes down,

00:13:49.510 --
static temperature goes down,

00:13:51.350 --
so these temperature and pressure ratios

00:13:54.182 --
right here are both less than one.

00:13:56.420 --
OK, again,

00:13:57.056 --
as you're going through problems,

00:13:58.650 --
make sure that you've got that.

00:14:01.850 --
That when you calculate those numbers

00:14:03.602 --
that your pressure and temperatures are

00:14:05.476 --
all trending in the right directions.

00:14:07.450 --
OK, if you haven't seen it already

00:14:09.445 --
in your homework problems,

00:14:10.870 --
but I've seen it all the time in exams.

00:14:13.670 --
You're under the pressure.

00:14:14.878 --
You gotta get the problem solved and

00:14:17.060 --
you accidentally invert a number.

00:14:18.640 --
Or you read it wrong.

00:14:20.200 --
OK,

00:14:20.540 --
check and make sure that all those

00:14:22.920 --
pressure temperature Mach number

00:14:24.332 --
values are going in the right direction.

00:14:26.670 --
OK.

00:14:28.710 --
Good we showed then what the

00:14:31.032 --
Prandtl Meyer angle was and it is.

00:14:33.400 --
It's a fictitious angle.

00:14:34.828 --
OK so it's not like as an angle.

00:14:37.740 --
You can take your protractor

00:14:39.540 --
out and measure it in the flow.

00:14:42.070 --
It's a mathematical construct that occurs

00:14:44.590 --
for every Mach number greater than one.

00:14:47.480 --
OK,

00:14:47.824 --
and as you learn in your in your homework

00:14:51.004 --
that you could go through the book

00:14:53.573 --
or go through com prop and be able

00:14:56.444 --
to figure out what that value of

00:14:58.840 --
Theta is that parental Meyer angle.

00:15:00.970 --
And this is the big relationship right here.

00:15:04.580 --
That the turning angle.

00:15:06.292 --
Right there is related to the

00:15:08.946 --
difference in the parental Myer angles.

00:15:12.100 --
OK. Alright, and this is this is

00:15:14.564 --
the key relationship right here.

00:15:16.420 --
When you're solving expansion weight

00:15:17.885 --
problems, you know any two values.

00:15:19.650 --
If you know the downstream Mach

00:15:21.360 --
number and the turning angle,

00:15:22.870 --
you can get the upstream Mach number.

00:15:24.920 --
If you know the upstream Mach number

00:15:26.901 --
in the downstream Mach number,

00:15:28.440 --
you get the turning angle.

00:15:29.900 --
If you know the turning angle

00:15:31.562 --
in the upstream Mach number,

00:15:33.120 --
you can get announcement number.

00:15:34.590 --
OK, so you'll be able to deduce

00:15:36.522 --
two pieces of information and

00:15:38.168 --
from this relationship right here

00:15:40.043 --
you can get the third OK.

00:15:42.030 --
Straight forward there.

00:15:46.230 --
OK, shock expansion theory.

00:15:48.054 --
You use this when you solve problems, OK?

00:15:54.360 --
So again, I don't want you to use

00:15:57.120 --
the airfoil function on com prop.

00:15:59.500 --
I want you to be able to look at

00:16:01.831 --
an airfoil like this and determine

00:16:04.504 --
if you have oblique shockwaves.

00:16:06.840 --
If you have expansion ways all

00:16:09.420 --
based on the geometry of the turn

00:16:12.395 --
right here and the angle of attack.

00:16:15.120 --
OK, let's let's, let's talk about.

00:16:17.160 --
Let's talk about a problem here real

00:16:19.505 --
quickly to make sure you've got this down.

00:16:22.260 --
'cause this is, this is an issue

00:16:24.514 --
that comes up many times here.

00:16:26.680 --
Let's say you have a triangular

00:16:28.720 --
shaped airfoil.

00:16:29.400 --
OK, and then we'll just put

00:16:31.494 --
this at an angle of attack of 0.

00:16:34.160 --
So looks like this.

00:16:35.520 --
It's a symmetric airfoil.

00:16:39.930 --
Looks like this here and you have some

00:16:42.314 --
Mach number that's greater than one.

00:16:44.400 --
And let's say that we have a

00:16:46.647 --
turning angle here of 10 degrees

00:16:48.601 --
just to pick a number, OK.

00:16:50.590 --
K alpha is equal to 0,

00:16:53.290 --
so zero angle of attack there.

00:16:55.290 --
What kind of waveform do

00:16:56.955 --
you see at the bottom?

00:17:01.400 --
Nothing. What's the pressure that

00:17:03.725 --
acts on the bottom right there?

00:17:06.620 --
It's whatever your that's greater than one.

00:17:08.730 --
It's whatever your piece

00:17:09.934 --
of one is right there.

00:17:11.440 --
Whatever the atmospheric pressure is.

00:17:13.770 --
OK. Right, what do you see on

00:17:17.368 --
this top surface right up here?

00:17:21.580 --
Well, big shockwave.

00:17:22.555 --
The flow is turning into itself.

00:17:24.510 --
Changes 10 degrees,

00:17:25.740 --
so in oblique shock.

00:17:27.380 --
Forms right there and what's

00:17:29.240 --
the direction of the flow?

00:17:31.100 --
Flow follows the wall.

00:17:34.730 --
So it goes up this way.

00:17:36.790 --
OK, so here's where the here's

00:17:38.680 --
where the messed up part happens.

00:17:40.830 --
What occurs around the turn here?

00:17:44.510 --
Expansion wave.

00:17:46.340 --
OK, here's the question.

00:17:47.572 --
What is the turning angle

00:17:49.112 --
across the top there?

00:17:53.090 --
For me. 20 degrees.

00:17:59.000 --
Everybody see why that is.

00:18:01.140 --
If not, let's talk about it.

00:18:03.400 --
OK, if this is where the mistake comes in.

00:18:06.970 --
If it were 10 degrees.

00:18:09.810 --
Then what would be the direction

00:18:11.904 --
of the flow coming out here?

00:18:13.990 --
It would be horizontal.

00:18:16.970 --
If that turning angle 10 degrees

00:18:18.938 --
'cause it goes down this way goes up

00:18:21.458 --
10 degrees and so it's going to turn

00:18:23.919 --
another 10 degrees just to go horizontal.

00:18:26.330 --
OK, however the flow is not

00:18:28.772 --
horizontal on that side.

00:18:30.400 --
It goes down this way another 10 degrees.

00:18:34.230 --
OK, so this turning angle.

00:18:37.910 --
Right there. 20 degrees.

00:18:42.960 --
OK. Alright.

00:18:46.690 --
OK, you can calculate the

00:18:48.475 --
pressure in this region.

00:18:49.910 --
You can calculate the pressure

00:18:51.700 --
on this plate right here?

00:18:53.490 --
Can you calculate the pressure

00:18:55.280 --
in this region right here?

00:18:57.070 --
Absolutely OK with those three pressures.

00:18:59.910 --
Determine what the force is.

00:19:02.860 --
And then some of the forces.

00:19:05.930 --
In the vertical.

00:19:08.090 --
And the horizontal directions

00:19:09.534 --
get the lift in the draft.

00:19:11.700 --
OK.

00:19:12.160 --
Good.

00:19:12.620 --
OK, this is not so critical in

00:19:15.840 --
your calculations of lift and drag,

00:19:19.470 --
but an actually an oblique

00:19:22.250 --
shockwave forms here.

00:19:23.920 --
And the reason that is is because

00:19:26.188 --
the flow now comes down this way

00:19:28.809 --
and it's going to turn horizontally.

00:19:31.180 --
Across here.

00:19:31.922 --
So the float turns into itself,

00:19:34.150 --
and so there's going to be

00:19:35.890 --
an oblique shockwave,

00:19:36.760 --
but you don't have to worry about that

00:19:38.864 --
for to calculate the lift and drag.

00:19:41.090 --
OK, so it's this turning angle right there.

00:19:44.010 --
That causes problems.

00:19:45.102 --
I wanna make sure you got that down OK?

00:19:48.280 --
Excellent.

00:19:50.460 --
OK.

00:19:52.370 --
Overhead,

00:19:52.728 --
alright,

00:19:53.086 --
so actually all this is just a

00:19:55.592 --
review of what we talked about here

00:19:57.736 --
that the lift is equal to the sum

00:20:00.230 --
of the vertical components of all

00:20:02.150 --
the forces that act on the plate.

00:20:06.740 --
Very good. The lift coefficient

00:20:08.890 --
often used in the in determining

00:20:11.560 --
what kind of airfoil you want to

00:20:14.570 --
use and over what flight regimes.

00:20:17.590 --
OK is just the lift lift force.

00:20:21.340 --
Divided by 1/2 rho V squared,

00:20:23.660 --
this is the dynamic pressure.

00:20:26.230 --
Multiplied by the.

00:20:28.420 --
Multiplied by S here,

00:20:31.340 --
that is the area of the wing.

00:20:35.170 --
That's what S is there.

00:20:36.980 --
OK, and we showed in class in

00:20:39.101 --
the past that 1/2 rho V squared

00:20:41.245 --
is the same as one half P Mach

00:20:43.857 --
number squared right there.

00:20:47.600 --
OK.

00:20:50.040 --
So let's look at some.

00:20:51.890 --
Let's look at some things.

00:20:53.730 --
Let's let's just solve for L for

00:20:56.999 --
this relationship right here.

00:20:58.910 --
L and let's see what we can

00:21:01.101 --
do to generate lift here. OK.

00:21:03.381 --
We could have a better lift coefficient.

00:21:06.960 --
OK, so that's going to depend.

00:21:08.720 --
That's going to depend on

00:21:10.190 --
the shape of the airfoil.

00:21:11.660 --
OK, we could get better lift if you

00:21:14.212 --
have a higher freestream pressure.

00:21:16.990 --
OK, are you higher in the atmosphere,

00:21:19.430 --
lower in atmosphere that governs that?

00:21:22.880 --
But look at this right here. The lift.

00:21:26.392 --
Goes like the Mach number squared.

00:21:30.870 --
So what does that say about how fast you fly?

00:21:33.580 --
What is that going to generate?

00:21:36.120 --
More. Lift.

00:21:39.910 --
OK, so that means you can have

00:21:42.570 --
some very poorly shaped airfoils.

00:21:45.090 --
OK, so this Isabelle.

00:21:46.890 --
This lift coefficient might be bad.

00:21:49.590 --
But if your Mach number is high enough.

00:21:52.050 --
You can generate a lot of lift.

00:21:54.650 --
My number squared.

00:21:56.045 --
Also says that the that the wing

00:21:59.398 --
area S the larger the wing area,

00:22:02.320 --
the greater the lift you have.

00:22:05.290 --
OK, now this actually works well.

00:22:07.580 --
Not this relationship right here,

00:22:09.480 --
but this relationship.

00:22:10.953 --
If we wrote this is 1/2 Rho

00:22:14.496 --
v ^2 s think about a glider.

00:22:17.250 --
Moves very slow, right?

00:22:19.790 --
V is pretty small.

00:22:21.042 --
How does a glider make up for the

00:22:23.660 --
lift that it has to generate?

00:22:25.640 --
Was it have?

00:22:28.740 --
Lots of wing area.

00:22:30.344 --
Wings are very very long,

00:22:32.350 --
so as if we wrote this as rho V squared.

00:22:36.080 --
Just substituting this right here.

00:22:37.940 --
If V is small then you could have

00:22:40.428 --
a large wing area right here to

00:22:43.223 --
generate whatever list you have nice.

00:22:45.770 --
OK, so that's the balance.

00:22:47.640 --
In aerodynamic design there OK?

00:22:50.770 --
We we've seen this diagram a few times and

00:22:53.920 --
showing the difference between a subsonic

00:22:56.374 --
airfoil you seem kind of nice rounded,

00:22:59.390 --
symmetric airfoil right there.

00:23:00.958 --
This is subsonic.

00:23:02.140 --
Speeds is getting close to transonic

00:23:04.408 --
here at the transonic regime.

00:23:06.450 --
Remember we said that now all the shockwaves

00:23:10.146 --
start to form right up there in the top.

00:23:13.870 --
And then that subsonic airfoil

00:23:15.900 --
has a bow shock here when it's

00:23:19.414 --
traveling supersonically,

00:23:20.810 --
whereas whereas a supersonic airfoil

00:23:23.765 --
like we see right here very thin.

00:23:27.830 --
OK, here you can see the shaded area right

00:23:30.827 --
here is going to give you it's roughly

00:23:33.616 --
related to the amount of drag that you see.

00:23:36.700 --
OK, so this shaded area right here

00:23:39.129 --
is smaller compared to its companion

00:23:41.223 --
there at the top same Mach number,

00:23:43.520 --
but different airfoil has

00:23:45.388 --
a nice rounded shape.

00:23:47.260 --
And then Supersonically right here,

00:23:48.920 --
you see, an oblique shockwave that forms.

00:23:51.870 --
Across that very thin airfoil,

00:23:53.290 --
whereas whereas you would have a bow shock

00:23:55.714 --
if you have a subsonic airfoil there.

00:23:58.250 --
OK, so again subsonic airfoils are great.

00:24:01.640 --
Flying subsonic Lee, they're awful.

00:24:04.060 --
Supersonically supersonic airfoils

00:24:05.512 --
are awful subsonic Lee,

00:24:07.450 --
but very good supersonically OK.

00:24:09.870 --
And then we talked a little bit

00:24:12.894 --
last time about these airfoils.

00:24:15.670 --
Here you see,

00:24:17.764 --
it's very thin.

00:24:19.860 --
K very thin right across here.

00:24:21.620 --
It's got a little curve there at the

00:24:23.764 --
bottom gives a little camber little

00:24:25.599 --
curvature so that you can generate lift.

00:24:27.800 --
Subsonic Lee.

00:24:28.722 --
This is the Russian.

00:24:30.570 --
This is the Russian aircraft that didn't

00:24:33.125 --
have that that crashed really bad.

00:24:35.550 --
That's our 71 and then we talked about this

00:24:39.042 --
plane and F15 that flew with only one wing.

00:24:42.450 --
OK, Why was able to fly with one wing?

00:24:45.890 --
Well,

00:24:46.273 --
if we went back to our CISA Bell right?

00:24:49.720 --
He already went over it.

00:24:53.180 --
Right here so so it loses a wing.

00:24:55.880 --
So that means this area S decreases.

00:24:58.240 --
But as you increase the

00:24:59.920 --
Mach number right there,

00:25:01.270 --
you can generate the lift that you

00:25:03.552 --
need in order to fly in order to

00:25:06.088 --
in order to stay straight and level

00:25:08.430 --
roughly straight and level OK.

00:25:13.130 --
So actually before we get to that, here is.

00:25:19.100 --
So Mr Castle, sorry it's a Navy plane.

00:25:21.560 --
You OK with that? OK good.

00:25:24.310 --
So this is an F18 Hornet right here.

00:25:28.120 --
I want you to look. At the wings.

00:25:34.040 --
Can you get an idea for what that

00:25:36.152 --
for those wings look like right?

00:25:38.100 --
There? You see how thin those are?

00:25:40.870 --
It's got a very sharp leading edge.

00:25:44.130 --
OK, very thin all the way across there.

00:25:47.850 --
OK, now this actually has a really,

00:25:51.100 --
really cool design to fly.

00:25:53.430 --
Subsonic Lee. We saw F-14.

00:25:55.750 --
Tomcat had the swing wings.

00:25:58.080 --
Variable variable, swept wings.

00:25:59.860 --
If you look closely on

00:26:02.085 --
this airplane right here.

00:26:06.620 --
There is a hinge there and

00:26:09.608 --
the hinge right there. OK.

00:26:11.979 --
So what this plane does this is this

00:26:15.011 --
is awesome engineering as well.

00:26:17.960 --
OK, what this plane does with

00:26:20.234 --
this hinge here and the ailerons

00:26:22.601 --
here in the back. What it does?

00:26:28.420 --
OK, so as you say,

00:26:30.290 --
unhinged is probably a little bit unhinged,

00:26:32.900 --
so OK, so there's a hinge right there.

00:26:36.530 --
Flat plate for the surface of the wing

00:26:39.210 --
and then the other runs here in the back.

00:26:42.240 --
OK, so there's a kind of a classic

00:26:44.456 --
real thin supersonic airfoil.

00:26:46.270 --
What this leading edge hinge

00:26:47.965 --
does when it flies subsonic Lee.

00:26:49.970 --
Is that this actually bends down a little

00:26:52.906 --
bit and I'm just going to exaggerate

00:26:55.447 --
it so you can see what's going on.

00:26:58.450 --
So look like this.

00:27:01.320 --
Then the wing comes across here.

00:27:04.430 --
And then either on comes

00:27:05.855 --
back down there a little bit.

00:27:07.580 --
You see what that does to the wing?

00:27:11.290 --
Provides a little bit of curvature

00:27:14.170 --
little camber to the wing there so

00:27:17.438 --
that subsonic Lee you can take off and

00:27:21.124 --
land relatively relatively safely.

00:27:23.780 --
OK, that's that's pretty cool

00:27:25.880 --
design right there.

00:27:27.140 --
OK, will show some pictures a little

00:27:29.975 --
bit later on in the semester,

00:27:32.600 --
but one of the one of the research areas

00:27:35.750 --
that Aerodynamicists are working on now.

00:27:38.900 --
So let's say you're in the class,

00:27:41.840 --
which you really like materials.

00:27:43.940 --
OK, your control systems,

00:27:45.620 --
and not necessarily interested in that.

00:27:48.140 --
Fluids in the aero part they're

00:27:50.660 --
working water called smartwings.

00:27:52.340 --
OK, so smart wing.

00:27:55.400 --
So it has a surface like this cake

00:27:57.480 --
kind of a classic subsonic airfoil,

00:27:59.740 --
but this airport is actually

00:28:01.770 --
made up of a bunch of sections.

00:28:04.930 --
Right here. OK, on the wing.

00:28:08.774 --
So kind of looks like this,

00:28:11.390 --
and so those sections and

00:28:13.010 --
I'm just putting a squares.

00:28:14.630 --
I think they're hexagons.

00:28:15.926 --
I don't recall right off hand,

00:28:17.870 --
but you get the idea.

00:28:19.490 --
OK,

00:28:19.804 --
each of these little sections and

00:28:21.688 --
what they what they do depending on

00:28:24.008 --
the flight regime that you're in,

00:28:25.970 --
flying really fast or really slow,

00:28:27.920 --
it actually changes the shape

00:28:29.535 --
of the wing or your fly.

00:28:33.950 --
OK, so there are little.

00:28:37.460 --
Their little devices, little little motors,

00:28:39.530 --
little servos here on the inside that can

00:28:42.322 --
move up and down and change the shape of

00:28:45.297 --
the wing to make it the most aerodynamic

00:28:48.091 --
and the most the most efficient wing

00:28:51.070 --
for that particular flight regime.

00:28:54.050 --
That school engineering. OK.

00:28:59.040 --
Good, here's a here's another

00:29:01.895 --
little bit of supersonic design.

00:29:04.750 --
OK, I don't mean to.

00:29:06.570 --
I don't mean to brag on

00:29:08.682 --
this little guy right here.

00:29:10.570 --
Here's the X one.

00:29:11.966 --
We mentioned that that it did break.

00:29:14.580 --
The sound barrier didn't have swept wings.

00:29:17.130 --
Not not the best compressible flow design.

00:29:19.670 --
Here's another part that that Aerodynamicists

00:29:21.884 --
didn't understand at the time,

00:29:23.680 --
but is not a good design here is

00:29:27.192 --
that if you look at the tail.

00:29:30.490 --
OK, if you look at the tail right there,

00:29:33.700 --
notice it's got cut.

00:29:35.256 --
Classic tail design tail here and you see

00:29:38.286 --
you see here these tabs here in the back.

00:29:41.200 --
In the back there so that when this

00:29:43.816 --
is flying this remains flat and

00:29:45.979 --
then those back parts go up and

00:29:48.565 --
down again so that can maneuver

00:29:50.791 --
the plane going like this.

00:29:52.696 --
Turns out that Supersonically that is

00:29:55.054 --
not a very good way to maneuver in aircraft.

00:29:58.680 --
OK, so let's see why.

00:30:00.390 --
If this is flying super fast or if it's

00:30:03.261 --
flying this in the in the supersonic regime,

00:30:06.220 --
there were going to form there at the front.

00:30:12.230 --
Oblique shockwaves OK,

00:30:13.565 --
so an oblique shockwave forms there and

00:30:16.755 --
then these fins go up and down like this,

00:30:19.700 --
and so another shockwave is

00:30:21.665 --
going to format that side.

00:30:23.630 --
So you get 2 shocks that would form

00:30:26.014 --
and what aerodynamics is found is that

00:30:28.404 --
you could get a shock interaction

00:30:30.724 --
between those two shockwaves that

00:30:33.329 --
form their supersonic aircraft.

00:30:35.420 --
Nowadays will go back to

00:30:37.385 --
our F18 Hornet right here,

00:30:39.350 --
and you look at the tail.

00:30:42.720 --
Right here, OK, notice that there's no.

00:30:45.740 --
There's no part in the back there

00:30:49.408 --
that the whole tail moves up and down.

00:30:53.600 --
Like this or like this OK?

00:30:56.020 --
And it turns out that aerodynamically

00:30:58.438 --
again when this, when this turns,

00:31:01.363 --
say down like that.

00:31:03.650 --
Shockwave's going to form there at the

00:31:06.037 --
top and then you get smooth flow all

00:31:08.703 --
the way across the rest of the elevator.

00:31:11.420 --
OK, so that's another sign that you

00:31:13.583 --
could tell of what a supersonic

00:31:15.632 --
aircraft looks like if that whole

00:31:17.750 --
tail moves as opposed to just the

00:31:20.057 --
just the back portion of the tail.

00:31:24.300 --
Alright.

00:31:26.960 --
Aren't you gonna glad

00:31:27.896 --
you came to class today?

00:31:29.070 --
I'm glad that you came in class. OK.

00:31:33.690 --
Alaskan, so one of the things that now

00:31:36.554 --
that we've got this here, so let's see.

00:31:39.450 --
Did you send this to me?

00:31:41.610 --
Yes, so I got an email from Samantha.

00:31:44.490 --
He ran. She said that you should check

00:31:46.826 --
out this particular design and it's

00:31:49.187 --
called a coleopter Anna Coleoptile.

00:31:51.330 --
If you notice there that it has a,

00:31:54.210 --
it has a rounded wing on it.

00:31:57.880 --
That's that's kind of cool

00:31:59.755 --
right across there.

00:32:00.880 --
So here's the rounded wing.

00:32:02.760 --
Now it turns out that when

00:32:05.268 --
you have a finite wing.

00:32:07.520 --
Like you have here,

00:32:08.820 --
the pressure on the bottom of the

00:32:11.148 --
wing is higher than the pressure

00:32:13.014 --
on the top of the wing does.

00:32:15.150 --
That's how you generate lift.

00:32:16.740 --
But what happens is you have

00:32:18.504 --
what are called end effects.

00:32:20.240 --
So in end effect occurs when

00:32:22.052 --
the air on the bottom of the

00:32:24.311 --
wing kind of leaks out here,

00:32:26.280 --
and so you have high pressure air on the

00:32:29.133 --
bottom and low pressure air on the top.

00:32:31.690 --
And what that does is generate

00:32:33.826 --
these vertical structures go like

00:32:35.582 --
this and that causes a lot of drag.

00:32:37.730 --
It's a parasitic drag problem.

00:32:39.590 --
End effect drag problem OK in in

00:32:43.545 --
aerodynamics class you'd learn about how

00:32:46.926 --
wings can be shaped to minimize that.

00:32:50.610 --
The Spitfire that flew in World War

00:32:53.263 --
Two has elliptical shaped wings.

00:32:55.390 --
Beautiful beautiful aircraft but those

00:32:57.545 --
elliptical shapes right there minimized

00:32:59.759 --
the formation of those tip foresees.

00:33:01.750 --
OK so menace and minimizes

00:33:03.740 --
the drag flights faster.

00:33:05.340 --
OK so one of the nice things

00:33:08.028 --
about this design over here of

00:33:10.389 --
the coleopter is that it's got a

00:33:13.105 --
rounded wing so that there are no

00:33:16.024 --
tip effects that go across there.

00:33:18.489 --
Alright so you might think well.

00:33:20.910 --
How the heck does that generate

00:33:23.046 --
any kind of lift?

00:33:24.470 --
OK,

00:33:24.817 --
well it turns out that the angle

00:33:27.246 --
of attack is also related to the

00:33:29.756 --
amount of lift that you have,

00:33:31.950 --
so the higher angle of attack that you get,

00:33:35.150 --
the more lift you can generate.

00:33:37.290 --
Now for those that are paper airplane.

00:33:40.370 --
Enthusia STS

00:33:44.170 --
is it cold after I hear? Ever seen this?

00:33:48.130 --
And you can fly it. We'll see,

00:33:50.858 --
maybe we can catch this in slo-mo

00:33:53.266 --
from our from our from the cameras

00:33:55.583 --
here so you can fly this like this.

00:34:00.800 --
Not very good. Not very good.

00:34:04.260 --
But the idea is that you can generate lift.

00:34:07.500 --
Now you might think how can you

00:34:09.803 --
generate lift from something like that.

00:34:12.180 --
And again notice that in the picture

00:34:14.812 --
here it's flying at an angle of attack.

00:34:17.580 --
OK, so an airplane like this right here.

00:34:21.240 --
OK, actually has a slight angle of attack

00:34:24.008 --
built into it so that when it takes off.

00:34:26.710 --
In fact, if you if you look at it

00:34:29.374 --
straight and level right here, that Wing

00:34:31.812 --
has a little bit of an angle of attack.

00:34:34.760 --
OK, so that angle of attack is going to

00:34:37.460 --
create a small shockwave on the bottom.

00:34:39.920 --
Slight expansion wave on the top

00:34:41.852 --
so it generates lift.

00:34:43.140 --
OK, now it also answers the age old question

00:34:46.632 --
of how can a plane like this fly inverted?

00:34:50.330 --
OK, again, if this plane and you'll

00:34:52.283 --
notice it notice any aircraft when it

00:34:54.374 --
flies upside down screen level like

00:34:56.233 --
the Blue Angels and the Thunderbirds

00:34:57.871 --
when they do a flight show like that,

00:35:00.422 --
there's always a little bit of an

00:35:02.957 --
angle of attack as it goes down so

00:35:05.253 --
that it generates lift. OK, good.

00:35:10.130 --
That's your area lesson for today.

00:35:12.980 --
Alright. Got any questions?

00:35:14.924 --
Any questions? Anything we've seen so far?

00:35:18.570 --
OK.

00:35:21.500 --
So let's see here what we'd like to do now is

00:35:24.903 --
to figure out what we know for turning angle,

00:35:27.980 --
you can accelerate the flow.

00:35:29.600 --
What is the maximum turning angle?

00:35:31.540 --
How much can you turn?

00:35:33.810 --
And then what is the associated

00:35:35.670 --
Mach number associated with that?

00:35:37.230 --
OK, so here's our parental Meyer angle.

00:35:39.410 --
Theta of M is equal to this relationship,

00:35:41.900 --
right here it's got an arctangent of

00:35:43.972 --
the Mach number there and arctangent

00:35:45.881 --
of the Mach number right over here, OK.

00:35:48.439 --
So this is this will harken

00:35:50.353 --
back to your calculus days.

00:35:52.400 --
I know that was three or four years ago,

00:35:54.870 --
right so?

00:35:57.110 --
We're going to take a limit.

00:35:59.800 --
And what we're going to do is we're going

00:36:02.500 --
to take the limit as this angle as Phi.

00:36:05.330 --
We want to know what that

00:36:07.988 --
maximum turning angle is.

00:36:09.760 --
Of of our flow here.

00:36:11.500 --
So notice that in these arc

00:36:13.480 --
tangents right here we have gammas.

00:36:15.660 --
Cagamas are going to be constant for the air.

00:36:18.780 --
The only variable that we

00:36:20.515 --
have is the Mach number.

00:36:22.250 --
So we want to say if this

00:36:25.029 --
Mach number goes to Infinity.

00:36:27.460 --
What's the turning angle going to be?

00:36:30.510 --
OK, so just from mathematics right here.

00:36:33.560 --
The arctangent of Infinity is π / 2.

00:36:40.720 --
So we figure that one out.

00:36:43.170 --
Arctangent of Infinity is π / 2.

00:36:45.917 --
Let's go to the overhead here.

00:36:49.080 --
So have a triangle.

00:36:52.060 --
OK, and this is fi right here.

00:36:56.910 --
What's the tangent of Phi?

00:37:01.070 --
Say X. Why? Z what's tangent feet?

00:37:10.090 --
Tangent of Phi. The rise over the run. Y / X.

00:37:16.840 --
OK, alright, so let's let's

00:37:19.200 --
expand fi a little bit here.

00:37:26.040 --
Here is why an X.

00:37:30.280 --
10s if he's going to get bigger

00:37:32.555 --
there right? 'cause your eyes.

00:37:34.314 --
Why is large and X is small here?

00:37:37.390 --
What happens when you have

00:37:38.560 --
a triangle look like this?

00:37:46.200 --
Look at this rise divided by

00:37:48.858 --
that teeny tiny run right there.

00:37:51.840 --
And then eventually.

00:37:53.553 --
You just have a straight line.

00:37:56.980 --
This is 90 degrees right here.

00:37:59.530 --
Which is the same. Is π / 2?

00:38:05.520 --
So the arctangent.

00:38:07.371 --
A fee from our little trigonometry

00:38:11.073 --
bit right there is π / 2.

00:38:14.287 --
That's why the limit as

00:38:16.972 --
fee tends to Infinity. OK.

00:38:21.280 --
Net fee is just the rise over the run.

00:38:23.900 --
That's why are y / X here is equal to π / 2.

00:38:27.653 --
OK, so if we take that limit then

00:38:29.757 --
Theta taking the limit here as

00:38:31.596 --
N goes to Infinity here an as N

00:38:34.053 --
goes to Infinity here substituting

00:38:35.528 --
in π / 2 to both of those terms,

00:38:38.160 --
we get that Theta is equal to π /

00:38:40.780 --
2 times the square root of gamma

00:38:42.803 --
plus one divided by gamma minus one.

00:38:44.850 --
All this minus one right here.

00:38:47.720 --
So you can actually get a turning

00:38:51.066 --
angle of 130 degrees.

00:38:53.440 --
If you could turn that flow 130 degrees,

00:38:55.910 --
you would accelerate it to Infinity.

00:38:59.920 --
Obviously that's not going to happen OK,

00:39:02.030 --
Anna 130 degrees.

00:39:02.930 --
I mean, if you think about it,

00:39:05.040 --
it's got not just 90 degrees,

00:39:06.840 --
but now it's coming back

00:39:09.105 --
in the opposite direction.

00:39:10.920 --
Not an actual physical limit,

00:39:12.320 --
but a theoretical limit on what

00:39:14.474 --
the term could be in your flow.

00:39:16.940 --
OK, little bit of mathematical

00:39:20.750 --
gymnastics there OK?

00:39:23.040 --
This is the problem that was

00:39:24.912 --
cancelled in your homework assignment,

00:39:26.850 --
but I want you to make sure that

00:39:29.258 --
we've got shock tubes down so that you

00:39:32.133 --
understand how a shock tube works.

00:39:34.460 --
OK, so again,

00:39:35.264 --
this is 1/2 of it as a rehash from

00:39:38.039 --
when we did normal shocks and moving

00:39:40.909 --
normal shocks in a shock tube.

00:39:43.110 --
You have a driver section.

00:39:44.840 --
OK, high pressure gas right?

00:39:46.570 --
Over here there's a membrane that

00:39:48.856 --
separates this high pressure region

00:39:50.786 --
from a low pressure region right over here.

00:39:53.520 --
And this is what the pressure

00:39:55.986 --
profile looks like.

00:39:57.220 --
So you have a high pressure

00:39:59.542 --
region in the driver region.

00:40:01.740 --
A low pressure area right

00:40:03.795 --
here in the DRIVIN region.

00:40:05.850 --
OK then we break the membrane

00:40:08.406 --
and what that membrane does is

00:40:10.967 --
that it creates a normal shock

00:40:13.277 --
and that normal shockwave then

00:40:15.692 --
propagates down from left to right.

00:40:18.810 --
OK,

00:40:19.214 --
and so this stuff that we talked

00:40:22.042 --
about in class when we did

00:40:24.901 --
normal shops right across here.

00:40:27.350 --
Right across here,

00:40:28.307 --
we figured out what what the pressure

00:40:30.602 --
profiles the Mach number is.

00:40:32.200 --
The Mach number of the wave, and so on.

00:40:35.225 --
We figured all this stuff out and we

00:40:38.262 --
ignored the things on the left hand side OK.

00:40:41.780 --
Kate, now that we know about expansion waves.

00:40:44.930 --
What's going on here between 3:00 and

00:40:47.450 --
1:00 is an expansion wave problem.

00:40:50.330 --
Just like we talked about before.

00:40:53.610 --
OK,

00:40:54.067 --
so what's happening here is that again

00:40:57.266 --
you have a high pressure region here.

00:41:00.780 --
There is a lower pressure region

00:41:02.898 --
right across here in Region 3.

00:41:04.980 --
In fact,

00:41:05.714 --
if you look at the pressure

00:41:07.916 --
profile here it is.

00:41:09.180 --
This is the driven section

00:41:10.930 --
has a low pressure,

00:41:12.330 --
goes across the shock.

00:41:13.610 --
That's what this region is right

00:41:15.597 --
across here and then that pressure

00:41:17.727 --
remains constant to what's called

00:41:19.582 --
the contact surface right here.

00:41:21.430 --
And that's where Region 3 contacts Region 4.

00:41:24.230 --
And then there is a gradual

00:41:26.606 --
increase in the pressure right up

00:41:29.075 --
here and then the driver section.

00:41:31.480 --
OK,

00:41:32.021 --
so this gas this high pressure gas

00:41:35.808 --
begins to expand. As it goes across.

00:41:40.872 --
OK.

00:41:41.640 --
Draw that out, drawn out process out here,

00:41:44.900 --
OK?

00:41:46.430 --
So.

00:41:52.870 --
So here's the membrane.

00:41:54.442 --
Here's the high pressure section.

00:41:56.410 --
Here is the low pressure section here.

00:41:59.160 --
OK, when the membrane breaks.

00:42:03.680 --
Creates a shockwave.

00:42:06.900 --
Propagates down this direction here,

00:42:09.680 --
and an expansion wave

00:42:12.464 --
forms as this gas expands.

00:42:15.950 --
Into this region right over

00:42:18.695 --
here so that wave propagates.

00:42:21.440 --
Starts out small here,

00:42:23.416 --
gets a little bit larger.

00:42:25.890 --
And then that distance increases

00:42:27.525 --
right across there as this high

00:42:29.536 --
pressure gas region expands

00:42:30.820 --
and goes across this way.

00:42:35.040 --
As a as my kids say, you know fun

00:42:39.299 --
fact fun fact about expansion waves.

00:42:42.140 --
OK, this behaves exactly like.

00:42:46.240 --
A traffic jam or traffic

00:42:49.620 --
flow at a red light. OK.

00:42:54.940 --
But how could that be OK?

00:42:57.100 --
Think about this.

00:42:58.180 --
You have a red light right here.

00:43:04.440 --
We want to make this authentic,

00:43:06.310 --
so there's a red light right there.

00:43:08.480 --
OK? And there are cars lined up.

00:43:11.840 --
And it's all bumper to bumper, right?

00:43:13.897 --
I'm sure all of you keep a safe

00:43:16.593 --
distance right when you break.

00:43:18.520 --
In traffic, especially,

00:43:19.669 --
the traffic jams here in Moscow ID OK,

00:43:22.620 --
so looks like this and you can have a line

00:43:26.893 --
of cars that go all the way back here.

00:43:30.670 --
OK, so the red light then turns green.

00:43:35.490 --
Green light right here.

00:43:40.130 --
There's a green light OK,

00:43:42.170 --
and now the cars go do all seven of

00:43:45.050 --
these cars move at the same speed and

00:43:48.453 --
propagate through their drive-thru light?

00:43:51.150 --
No, what happens?

00:43:52.809 --
First car goes it's here.

00:43:55.580 --
And there's a larger distance

00:43:57.390 --
between that one and the next one,

00:43:59.880 --
and then that distance gets a

00:44:01.890 --
little bit smaller and smaller,

00:44:03.810 --
and the way in the back here is that,

00:44:07.040 --
and I've had this happen to me before.

00:44:09.900 --
Is that you see the green light here,

00:44:12.760 --
but the distance when I'm parked

00:44:14.710 --
way back here the distance between

00:44:16.863 --
me and that car hasn't changed.

00:44:19.210 --
Heckuva lot for 1015 seconds,

00:44:21.000 --
however long it takes to

00:44:22.790 --
propagate that through these cars.

00:44:24.580 --
Driving through here.

00:44:26.062 --
It turns out have the same

00:44:29.026 --
mathematical modeling associated

00:44:30.809 --
with expansion ways right there.

00:44:33.820 --
Same modeling process here.

00:44:35.308 --
This membrane breaks the gases expand.

00:44:37.540 --
This wave goes faster than this one,

00:44:40.140 --
which goes faster than this one and so on.

00:44:43.490 --
So as this as this pressure wave

00:44:46.381 --
propagates there through the back

00:44:48.431 --
has the same properties as cars

00:44:50.645 --
parked not part but in a in a

00:44:53.369 --
traffic line right across there.

00:44:57.160 --
There you can tell your folks

00:44:58.984 --
over the break that you learned

00:45:01.030 --
something here in gas dynamics.

00:45:02.940 --
OK, like I said, fun fact.

00:45:05.720 --
OK, shock tubes in let's go and here is

00:45:09.374 --
what happens after the membrane breaks.

00:45:13.010 --
OK, so let's look at the

00:45:15.920 --
expansion wave process.

00:45:17.380 --
OK, so here again these waves

00:45:19.840 --
propagate back and as they propagate

00:45:22.606 --
back eventually this high pressure

00:45:25.216 --
region is going to completely expand.

00:45:28.560 --
OK, so the initial state of our

00:45:32.179 --
of our shock tube right here.

00:45:35.730 --
Of this pressure difference

00:45:36.918 --
across here from one to two,

00:45:38.700 --
we have a high pressure region

00:45:40.380 --
in a low pressure region,

00:45:41.970 --
right across here,

00:45:42.858 --
that's called the diaphragm pressure ratio.

00:45:46.930 --
OK, right across there after that

00:45:49.348 --
diaphragm or the membrane breaks,

00:45:51.510 --
then the pressure in Region 3 is the

00:45:55.190 --
same as the pressure in region 4.

00:45:58.840 --
And the speed in Region 3 is the

00:46:01.216 --
same as the speed in region 4.

00:46:03.520 --
So if we go back to our

00:46:05.627 --
little drawing right here,

00:46:06.950 --
these two pressures are the same.

00:46:08.820 --
Cross this contact surface and the speed

00:46:11.004 --
of the air or the gases between those

00:46:13.570 --
two regions are the same as well. What?

00:46:16.176 --
What do you think would be different?

00:46:19.580 --
Speeds the same pressures the same.

00:46:21.010 --
What do you think would be

00:46:23.380 --
different across there?

00:46:24.570 --
What happens to the temperature

00:46:27.760 --
across a shockwave?

00:46:29.680 --
It goes up what happens to the

00:46:32.214 --
pressure downstream of this expansion

00:46:34.112 --
wave as it starts to expand.

00:46:36.320 --
Goes down. OK, so there's a.

00:46:38.530 --
There's a temperature difference between

00:46:40.365 --
3:00 and 4:00, right across there.

00:46:42.586 --
OK, T4 is going to be higher than T2,

00:46:45.890 --
and T3 is going to be higher than T1.

00:46:49.830 --
That's really what defines that difference

00:46:51.882 --
right across there is that temperature OK,

00:46:54.380 --
but the pressures in those

00:46:56.130 --
two regions are the same.

00:46:57.880 --
The speed in those two regions of the same.

00:47:01.030 --
OK, so again, across an expansion wave,

00:47:03.480 --
the flow is isentropic.

00:47:04.764 --
So we can use our isentropic relations here.

00:47:07.680 --
P3 or P1 is equal to T3 over T1 to

00:47:10.572 --
the gamma over gamma minus one power.

00:47:13.630 --
Or we could write that in terms

00:47:16.843 --
of the densities as well.

00:47:19.090 --
You know this is nice because

00:47:20.590 --
once we get it in this form,

00:47:22.390 --
we can write this in terms

00:47:24.412 --
of the speed of sound.

00:47:26.330 --
So now P3 over P11 minus gamma one.

00:47:30.120 --
Over 2 times V 2 /, 81 squared.

00:47:33.334 --
So this is the Mach number.

00:47:36.680 --
OK, in the expansion region right there to

00:47:39.272 --
the two gamma sub one over gamma minus one,

00:47:42.260 --
right across there.

00:47:43.769 --
OK if we solve for V then.

00:47:47.290 --
We can solve for V2.

00:47:48.760 --
We can solve for the speed and region 2.

00:47:52.260 --
Right across there and it is just

00:47:54.808 --
a function of the speed of sound.

00:47:57.450 --
He said one and this pressure ratio,

00:48:00.050 --
the diaphragm pressure ratio P2 over P1 OK.

00:48:04.450 --
What it gives us here is that since gamma

00:48:07.105 --
minus one this power right over here,

00:48:09.410 --
gamma minus 1 / 2 gamma is less

00:48:11.658 --
than one as PP1 tends to Infinity.

00:48:14.060 --
This term is going to go to zero,

00:48:16.540 --
and So what this does is you

00:48:18.990 --
can generate a maximum.

00:48:20.780 --
Speed in region 2.

00:48:22.528 --
From this term right there twice,

00:48:25.150 --
the speed of sound divided

00:48:26.930 --
by gamma minus one.

00:48:28.360 --
OK, enough gammas for air,

00:48:29.850 --
that's one point 4 -- 1 or that's two

00:48:32.588 --
times the speed of sound divided by .4.

00:48:34.920 --
What it tells you can do is you

00:48:37.608 --
can generate pretty high speeds.

00:48:39.820 --
With the shock tube.

00:48:42.040 --
OK, they don't last for very long.

00:48:44.230 --
OK,

00:48:44.522 --
but you can get hypersonic flows from a

00:48:46.858 --
shock tube that comes right across here,

00:48:49.240 --
OK?

00:48:51.270 --
Good,

00:48:51.614 --
so that was the problem

00:48:53.334 --
that was cancelled is

00:48:54.781 --
to figure out the expansion portions

00:48:56.983 --
of the flow. OK, any questions? Yes.

00:49:04.810 --
OK, I'm getting to that,

00:49:06.520 --
so I answer part one.

00:49:08.220 --
No shock tube questions,

00:49:09.572 --
no moving shock problems on the exam.

00:49:14.180 --
What's that? And an airfoil

00:49:18.041 --
is not a shock tube, so yes,

00:49:20.052 --
so there is an airfoil problem.

00:49:21.770 --
There is not a shock to problem.

00:49:23.780 --
OK, I just want to make sure that

00:49:26.068 --
you understood kind of the basic

00:49:27.825 --
workings of what a shock tube are.

00:49:29.810 --
OK, not answer your question here.

00:49:31.530 --
Exams are open book.

00:49:33.690 --
Open notes OK.

00:49:37.600 --
And it's also open laptops if you

00:49:40.414 --
choose that you've got a laptop to use

00:49:43.203 --
com prop that is OK to use as well,

00:49:45.950 --
but there are no no communications

00:49:48.122 --
with the outside world or the

00:49:50.278 --
inside world on your laptop.

00:49:51.870 --
So if you have a phone 'cause you

00:49:54.558 --
want to use your app, that's OK too.

00:49:59.430 --
OK, so open book, open notes, open com,

00:50:02.910 --
prop, or if you've got some other,

00:50:05.960 --
you know if you use some other device

00:50:08.848 --
for your compressible flow tables,

00:50:11.610 --
that's OK as well, yes?

00:50:17.110 --
Open Book open notes.

00:50:24.070 --
There are five problems on the exam,

00:50:25.450 --
so if you spend all your time looking

00:50:26.946 --
at your notes, you're not going to

00:50:28.408 --
have time to solve the problems.

00:50:32.510 --
OK, so be sure that your

00:50:34.682 --
your laptops are charged.

00:50:36.130 --
We don't have a whole lot of.

00:50:38.660 --
Let's see. Do you have?

00:50:40.470 --
Do you have plugs underneath?

00:50:44.200 --
Not sure what you got there. OK.

00:50:48.770 --
And you will have the hour and 15

00:50:51.746 --
minutes to solve the exam as well.

00:50:54.520 --
OK, I will talk to the greater today and we

00:50:57.548 --
will try and get this graded by tomorrow.

00:51:00.370 --
So if you want to pick him up

00:51:02.818 --
tomorrow you could come by my

00:51:04.854 --
office and pick up the exams.

00:51:06.870 --
That's fine.

00:51:07.616 --
The solutions are also will

00:51:09.481 --
be available this afternoon.

00:51:11.310 --
So even though even if you don't

00:51:12.689 --
have your homework assignment,

00:51:13.750 --
if the greater can't get it back in time.

00:51:17.120 --
Can you can always look online on TV learn?

00:51:21.160 --
OK. Good, so let's see here.

00:51:24.980 --
I would say that the exam problems

00:51:26.807 --
are going to be very similar to what

00:51:28.959 --
you see in the homework problems.

00:51:30.830 --
Let's just let's just review.

00:51:33.610 --
Write reviews 'cause then you

00:51:35.720 --
can see how intelligent you have

00:51:38.277 --
become over the last one week.

00:51:40.500 --
Six now, let's see what we've discussed here,

00:51:43.740 --
OK?

00:51:45.680 --
Just going through just going through the

00:51:49.460 --
going through the table of contents here.

00:51:53.280 --
OK, let's see here.

00:51:54.708 --
You probably won't have any problem that

00:51:57.396 --
just discusses the continuity equation.

00:51:59.780 --
You probably won't have a problem

00:52:02.222 --
that just has the ideal gas law,

00:52:05.050 --
but you could certainly use it.

00:52:08.650 --
OK,

00:52:09.065 --
some fundamental aspects

00:52:10.310 --
of compressible flow.

00:52:11.560 --
You know how to calculate the speed of sound?

00:52:16.350 --
OK, and you know how to calculate

00:52:18.380 --
Mach numbers and Mach waves.

00:52:19.950 --
I would say that's going to

00:52:21.840 --
be something to study up on.

00:52:23.550 --
Make sure that you understand what

00:52:25.224 --
a Mach wave is and how different

00:52:27.348 --
it is from an oblique shockwave.

00:52:29.250 --
What is the difference?

00:52:32.300 --
What's the difference between an

00:52:33.910 --
oblique shockwave animac wave?

00:52:37.280 --
A Mach wave is an infinitesimally

00:52:40.880 --
weak oblique shockwave.

00:52:42.680 --
OK. Good. Uh, now?

00:52:49.560 --
You probably won't have a problem.

00:52:50.820 --
It says, just calculate the speed of sound,

00:52:52.500 --
but you will likely have a problem.

00:52:53.970 --
You'll have to calculate the speed of sound.

00:52:56.440 --
OK, so this is all fundamental

00:52:59.068 --
stuff right here.

00:53:00.390 --
OK, in chapter four we learned about

00:53:02.938 --
isentropic flows and the difference

00:53:05.251 --
between stagnation conditions,

00:53:06.980 --
static conditions and critical

00:53:08.732 --
conditions right there, OK?

00:53:12.020 --
You probably won't have a problem

00:53:14.138 --
that says what is the stagnation

00:53:16.500 --
temperature of such and such.

00:53:18.680 --
You might OK, but you'll be able to.

00:53:21.820 --
You'll need to calculate what stagnation

00:53:25.144 --
temperatures are and pressures.

00:53:27.360 --
Pretty straightforward using

00:53:28.542 --
the tables using comp.

00:53:30.120 --
However you want to do it OK.

00:53:32.880 --
We learned about shockwaves.

00:53:35.072 --
OK, and you'll probably see some problems

00:53:38.584 --
that have a normal shocks in him.

00:53:41.890 --
OK, that's very important in gas dynamics.

00:53:46.210 --
OK, pitot tubes. Are also important,

00:53:51.190 --
so make sure you got those down.

00:53:54.150 --
Don't worry bout moving normal shocks.

00:53:58.200 --
OK.

00:54:00.360 --
Are oblique shock waves are important?

00:54:02.620 --
Make sure that you've got those down

00:54:05.147 --
and expansion waves are also important.

00:54:07.520 --
Make sure that you've got that down.

00:54:12.350 --
And make sure that you've got

00:54:14.702 --
the reflection part of oblique

00:54:16.895 --
shockwaves down pretty well. OK.

00:54:21.310 --
Again, as you learn in your problems,

00:54:23.570 --
a lot of it's just the geometry.

00:54:25.830 --
Make sure you've got the

00:54:27.890 --
direction of the flow right. OK.

00:54:32.670 --
Just to re clarify. We're going to

00:54:36.557 --
go back to our normal shocks here.

00:54:42.040 --
Region 1. Region 2 flow goes

00:54:44.950 --
this way comes out this way.

00:54:47.930 --
This is the region that is upstream.

00:54:53.590 --
It is also ahead. Of the shock.

00:54:59.930 --
OK, this is the supersonic flow.

00:55:03.280 --
Regime this is the subsonic flow.

00:55:07.240 --
Regime this is. Downstream.

00:55:12.700 --
Of the shock, this is also behind.

00:55:17.250 --
The shock there means the same thing.

00:55:21.530 --
OK, sometimes a problem will ask

00:55:23.396 --
what what's the temperature and

00:55:25.004 --
pressure just downstream of the shock?

00:55:26.870 --
Where does that where you where?

00:55:28.750 --
Are you looking to calculate that?

00:55:31.280 --
Right there.

00:55:34.070 --
Just downstream so you don't have to

00:55:35.876 --
worry about any of the flow anywhere else.

00:55:38.000 --
What's the temperature and pressure?

00:55:39.310 --
The Mach number just downstream of the

00:55:41.564 --
shock just in that region right there?

00:55:44.080 --
OK. Excellent. Any questions?

00:55:52.850 --
OK, have a wonderful day study

00:55:55.724 --
up for the exam and we'll see

00:55:59.529 --
Thursday bright and early.

Duration:"00:49:15.0530000"

00:00:27.640 --
Alright, for today we're going
to start in Chapter 3. We're

00:00:31.336 --
going to go over. Some were
basically kind of reviewing at

00:00:35.032 --
this point, so a couple of
things to show everybody on the

00:00:39.064 --
website. Is if we go to I have
to move this up here. Sorry I

00:00:45.806 --
forgot I have a preview in a
program one so up here the

00:00:50.928 --
lectures we have. Intro class
review so for this I have been

00:00:55.656 --
an I will continue to do so.
Uploading my intro class of

00:01:00.384 --
lectures. Hopefully most of
these links should work OK good

00:01:04.324 --
and they were working on the
right files. That's even

00:01:08.264 --
important. Super important

00:01:09.446 --
actually. So there's the.

00:01:13.100 --
And.

00:01:14.470 --
Basic Intro class review
lectures. Like I said, I'll

00:01:16.882 --
be putting up a whole bunch
more, especially as we run

00:01:19.830 --
into more stuff that's more
pertinent to the stuff we're

00:01:22.510 --
looking at and or reviewing.

00:01:25.260 --
And on today's we are going to
be in Module 3 which just from

00:01:28.550 --
correspond to chapter three. I'm
not quite sure why use the term

00:01:31.370 --
module, but I did and there it
is, so we're using it.

00:01:35.560 --
So here my links are working.
Yeah, I have a few more links

00:01:39.408 --
for other things to look at, so
my central limit theorem we're

00:01:42.960 --
going to talk about that today
review that I have two

00:01:46.216 --
different lectures for that.
One of 'em actually shows a

00:01:49.176 --
simulation which will be. I
don't know. I always enjoyed

00:01:52.136 --
this simulation. Once I finally
thought so it was kind of nice

00:01:55.688 --
to see. And we're also going to
go through this probability

00:01:58.944 --
distributions handout. I wasn't
actually going to put this up

00:02:01.904 --
and I'm going to do most of it
on the document camera, but.

00:02:07.070 --
I decided to at the last minute
and it literally is a last

00:02:10.567 --
minute hand out, so don't expect
anything gorgeous. No pretty

00:02:13.257 --
colors, sorry, no pretty colors
here. Have a couple of nice

00:02:16.216 --
looking tables or just not
sitting where I want them to,

00:02:19.175 --
but the handout itself will work
just fine, and that's actually

00:02:22.134 --
primarily we're going to go
through today and then we'll see

00:02:25.093 --
if we get a chance to look at at
least one of these central limit

00:02:29.128 --
theorem. Handouts, so today we
are going to look at this, but

00:02:33.546 --
we are going to walk through all
this, so we want to do most of

00:02:37.836 --
this on the document camera, but
I wanted to show something

00:02:40.982 --
first, because, well, this thing
can graph so much nicer than I

00:02:44.414 --
can. So alright first.

00:02:49.140 --
We need to review some
basic terms from

00:02:53.228 --
probability and we want to.

00:02:57.150 --
Zoom in just to hear will come
back to the computer in just a

00:03:02.358 --
bit. So remember, we're going
to be talking about is

00:03:06.078 --
probability distributions.

00:03:10.950 --
We'll start out with this simple
case just to work through. Now

00:03:14.826 --
that we're going to get into a
super highly complex one, but

00:03:18.702 --
will start out with a simple
case. Alright, so we have this

00:03:22.578 --
hypothesize data, and that's
what this worksheet that I made

00:03:25.808 --
is going to basically following
through it. Oh, sorry

00:03:28.715 --
hypothesis. Can you tell that to
normal term? I use hypothesized.

00:03:36.740 --
Population.

00:03:41.420 --
And it's an old example. It's
probably not extremely current

00:03:45.010 --
in terms of its probabilities.
Fitting it is OK. It will still

00:03:49.318 --
work. So here we have the number
of TV sets that are owned.

00:03:55.960 --
Per household.

00:04:01.570 --
Nowadays it might be more
more interesting to look at

00:04:05.960 --
phones or computers, but
everybody's got something

00:04:09.033 --
alright. So in this
population, well, we can

00:04:12.545 --
either have the TV's can take
on values of 0123 or four. Do

00:04:18.252 --
I have for USF 4?

00:04:21.920 --
And then we have some
probabilities associated

00:04:23.845 --
with those.

00:04:26.400 --
P of TV's.

00:04:29.250 --
So the probability of those.

00:04:31.860 --
So I'm just going to write

00:04:33.006 --
another wreath. We can make
a nice pretty table here

00:04:35.404 --
when we're done.

00:04:40.190 --
Alright.

00:04:42.870 --
OK, so this example is at least.

00:04:46.220 --
Now might be over 10 years old,
but it's at least 10 years old.

00:04:50.100 --
So the probability that probably
not quite so accurate anymore,

00:04:53.140 --
but that's OK for what we want
to do here. So this is the

00:04:57.396 --
number of TV sets owned per
household. And if you want to

00:05:01.044 --
think about it this way for
remember what this term is is

00:05:04.692 --
the number of TV's this is going
to be a random variable.

00:05:10.630 --
Which remember is kind of like a
function of valued function.

00:05:15.910 --
So a specific value of our
distribution has a specific

00:05:19.610 --
probability associated with it.

00:05:23.440 --
Alright.

00:05:25.470 --
So actually, let's make a nice
table. I should have done that

00:05:28.350 --
to begin with, but whatever.

00:05:30.770 --
I do things the hard
way sometimes, so TV's

00:05:34.991 --
probability of TV's.

00:05:43.660 --
Your attentive and you
want to redo it, go

00:05:45.928 --
for it, I understand.

00:05:48.120 --
Probably not necessary, as long
as you got all your information,

00:05:51.442 --
but nice little table.

00:05:54.160 --
I could have done it vertically,
whatever it however you want to

00:05:57.280 --
look at it. Either way, this
will get us the basic idea.

00:06:02.790 --
And that's where my graph comes
into play and I totally draw it.

00:06:06.287 --
But really, my my little my
little handout can show so much

00:06:09.515 --
better than I could ever draw
it. So if you want to look at

00:06:13.281 --
that real quick on the computer
that is distribution TV's.

00:06:17.910 --
Thought about playing with
colors, but I just left alone.

00:06:20.390 --
Figured you could get the gist
of it. So we got our 20% here at

00:06:24.110 --
zero and two 40% at one and then
our 10% at three and four.

00:06:28.490 --
Alright. So back to
our examples here.

00:06:35.110 --
So one of the things, well, we
have many things of interest

00:06:38.254 --
that we'd like to look at
about. One of the major things

00:06:41.398 --
we want to look at is to look
at some of our summary

00:06:44.804 --
statistics, and while looking
at this, it would probably be

00:06:47.424 --
nice to know on average, how
many TV's are owned per

00:06:50.306 --
household. So we want to find a
mean.

00:06:53.970 --
And we also call this here
in. With this we call this

00:06:58.134 --
an expected value.

00:07:02.070 --
Expected value alright, so an
expected value is a mean, but

00:07:06.756 --
unlike our continuous
distributions versus discrete

00:07:09.312 --
and this is more of one of those
discrete answers 'cause you

00:07:14.424 --
can't own. 1 1/2 television
sets. You could on average but

00:07:19.110 --
not. Literally.

00:07:22.380 --
You probably don't want broken
ones. I think they think they're

00:07:26.208 --
counting functional TV's not
nonfunctional TV's as well, so

00:07:29.340 --
this would be discreet.

00:07:33.200 --
So basically you want to think
about it that your your variable

00:07:36.344 --
in our book uses why a lot
versus X, but pick a letter. It

00:07:40.012 --
doesn't really matter. I'm going
to use why just because their

00:07:42.894 --
book does, but what was I going
with? This whole number values?

00:07:46.860 --
That's what these
things can take on.

00:07:50.850 --
There's an S there. There we go.

00:07:54.640 --
So this mean here the way we're
going to compute it is because

00:07:59.359 --
it's basically it's a weighted
average, so not every value of

00:08:03.352 --
our random variable TV's.

00:08:05.560 --
Takes on equal probabilities,
they don't have equal

00:08:08.240 --
probabilities, so we have a
weighted average that we're

00:08:11.255 --
going to do.

00:08:13.440 --
And.

00:08:15.690 --
Since we're dealing with the
population, this is what we

00:08:18.900 --
call deductive because we
know exactly what's going to

00:08:21.789 --
be happening in the
population versus a sample,

00:08:24.357 --
and most of our exploration
there is going to be

00:08:27.567 --
inductive, but this ones
deductive, because we can

00:08:30.135 --
actually see what's actually
happening, so we're going to

00:08:33.024 --
call this thing mu the
population mean of the

00:08:35.913 --
distribution, some other
notation E of Y, like

00:08:38.481 --
function notation.

00:08:41.180 --
And to calculate this is the

00:08:44.180 --
sum. So Sigma sum at
each Y times its

00:08:50.164 --
corresponding probability.

00:08:53.320 --
They just calculate about
products and add them all up.

00:08:59.830 --
Alright, so why not? We're here.
We should do this, for example.

00:09:05.870 --
So to calculate our expected
value of Y or mean for this

00:09:11.258 --
we would take zero times its
probability.

00:09:15.950 --
Plus one, so I was trying to
parenthese ahead of time times

00:09:19.922 --
the probability of 1.

00:09:22.890 --
Two times its probability plus
three times .1.

00:09:30.060 --
There's four times by 1.

00:09:33.490 --
There's also and then
we get a lovely 1.5.

00:09:38.590 --
Oops, sorry, papers got broken.

00:09:42.410 --
So on average, we could
expect a household to

00:09:45.830 --
have about 1 1/2 TV's.

00:09:49.290 --
It's like the 1 1/2 kids thing,
though obviously we can't have a

00:09:51.994 --
half a TV or a half a kid, but
it's an average, even if it's

00:09:55.114 --
not a part of the original

00:09:56.362 --
distribution. And that's OK.

00:09:59.780 --
So. This, unfortunately, you're
going to have to torture with my

00:10:03.740 --
drawing anyways. If I drew out
our little distribution.

00:10:09.860 --
So this will be our probability.

00:10:12.750 --
We have wide on the X axis.

00:10:16.310 --
Let's see here.

00:10:18.840 --
So I'm just kind of
guesstimating I'm not an artist

00:10:22.290 --
by any stretch of the
imagination. I can draw a decent

00:10:26.085 --
Bell curve. And occasionally
decent rectangles.

00:10:31.040 --
Pretend those are both .1 and
the other ones are point 2.4,

00:10:35.348 --
point 2.1. .1 there we go.

00:10:40.090 --
So if we imagine where we put
the mean, that would be right

00:10:43.639 --
about here. Well, this is
basically what we would consider

00:10:46.369 --
this center of mass. So if we
actually try to balance this

00:10:49.645 --
thing on, that's exactly the
point where it would balance the

00:10:52.648 --
center of mass right there. And
that's where that mean is.

00:10:59.580 --
I think I just wanted to
touch you with my drawing.

00:11:01.395 --
That's not what I think I
needed to do here.

00:11:04.750 --
Right, and of course we love
measures of location. That's

00:11:08.310 --
what the mean is. But we also
love measures of spread so we

00:11:12.938 --
can see how much variation we
actually have. So this is our

00:11:17.210 --
measure.

00:11:19.070 --
Of spread.

00:11:21.380 --
Variation.

00:11:27.190 --
It's one of 'em, but this
one in particular.

00:11:31.040 --
The variance.

00:11:34.270 --
Is the average.

00:11:40.050 --
Important work here squared.

00:11:43.820 --
Distance.

00:11:46.410 --
Each point is from its mean.

00:11:53.280 --
Remove there.

00:11:59.540 --
So we can see how much variation
we have in our data. Points were

00:12:03.670 --
in relation to the center.

00:12:05.750 --
Of the distribution.

00:12:11.170 --
At see here it's units.

00:12:14.290 --
R-squared units.

00:12:22.720 --
Measurement but yeah.

00:12:25.130 --
But it's not on the same scale
as the mean, so not all the

00:12:29.568 --
time. Is this the one we want to
directly deal with? But we still

00:12:34.006 --
have to calculate it. So to do
that it's it's Greek symbol is a

00:12:38.444 --
Sigma squared. Yeah,
my Sigma is mostly OK.

00:12:42.810 --
And one of my friends used to
draw it and it looked like a

00:12:44.896 --
Theta and I was like Theta

00:12:45.790 --
squared shoes. Now it's a Sigma.
OK, mine supposed to be a Sigma

00:12:50.030 --
at mostly kind of looks like
one. You can also use via Y. Now

00:12:54.930 --
this V here is going to denote
the actual true variance.

00:12:59.660 --
And of course, since we're
dealing with the population,

00:13:01.694 --
that's OK. 'cause that's what
we're going to be looking at.

00:13:04.180 --
But that reason I brought that
up is that will come into play

00:13:07.118 --
here in just a bit, so.

00:13:09.070 --
Keep that in the back of your

00:13:10.183 --
head, all right. So
what we're going to do

00:13:14.456 --
is look at Y minus mu.

00:13:18.550 --
Quantity squared times the
probability of Y, so we'll take

00:13:23.300 --
each squared difference of each
value between it and the mean.

00:13:29.170 --
Look at that squared distance
and multiply it by the

00:13:32.280 --
probability of that data point
and that gives us.

00:13:35.970 --
What we're looking for in terms
of the variation.

00:13:42.290 --
Alright. So of course we're
going to do that.

00:13:48.350 --
And I got a little carried away
on my hand out, which is OK and

00:13:52.910 --
carried away in a good way, sort
of. It might be a little

00:13:56.862 --
redundant for you, but I did
actually expand some of these

00:14:00.206 --
formulas a little bit more, but
I did show the actual work later

00:14:04.158 --
on, so we will actually do this.
So Sigma squared is the variance

00:14:08.110 --
of Y. So we're going to take the
first data point, which is a 0.

00:14:13.780 --
Minus the mean.

00:14:15.750 --
Squared and the probability of
zero was a .2.

00:14:21.720 --
And we get to do this for all

00:14:23.704 --
five values. So next one 1 --
1 1/2 ^2 * .4.

00:14:33.350 --
I have the right table. I'm
just making sure I have the

00:14:35.318 --
right values OK.

00:14:37.450 --
And the next one 2
-- 1 1/2 ^2 * .2.

00:14:43.550 --
I have to move it down page
or move it down the line.

00:14:47.400 --
3 minus the mean squared times
.1 and the last one 4 -- 1 1/2

00:14:53.715 --
squared times point. That's a
two up there. Sorry times .1.

00:15:01.080 --
Well, you know this stuff and
all these lovely little.

00:15:06.550 --
Squared differences in products
all add up to 1.45.

00:15:14.620 --
Ann, if at anytime you're
working through this on your own

00:15:17.887 --
and you get a different number
than I do, don't hesitate to say

00:15:21.748 --
something. It happens,
unfortunately, but it happens

00:15:23.827 --
and I won't be offended.

00:15:27.730 --
I used to wonder why I was like

00:15:29.498 --
why. How is it so easy to make
mistakes? And I think it's

00:15:33.506 --
actually really easy on this end
'cause you get caught up in what

00:15:36.665 --
you're doing. You don't think
about something that you're

00:15:38.852 --
dealing with right this moment
when you're trying to talk about

00:15:41.525 --
something 5 minutes ahead of you
know and think 5 minutes ahead.

00:15:44.441 --
Yeah, it's interesting, alright,
but if I do make a mistake,

00:15:47.114 --
don't hesitate to let me know.

00:15:49.900 --
So. Of course, the variance
leads us to the next one, which

00:15:55.212 --
is the standard deviation anisur
standard measurement of spread.

00:16:02.230 --
And.

00:16:04.320 --
So it's a again a
measure of spread.

00:16:09.480 --
Variation that's an
R in there, sorry.

00:16:12.890 --
It is the average distance.

00:16:17.670 --
Without the squared.

00:16:20.910 --
Each point is from its mean.

00:16:23.690 --
Oh, there's an end in there.

00:16:32.600 --
So.

00:16:36.450 --
It's just the square root of
the variance, and since it's

00:16:39.365 --
really what we end up wanting
to do because its units of

00:16:42.545 --
measurement are the same as the
mean, so they have single non

00:16:45.725 --
squared units of measurement.

00:16:47.830 --
It has seem.

00:16:55.120 --
Units of measurement azzameen

00:17:00.870 --
which is good? Want to keep
things on the same scale?

00:17:06.180 --
And it literally is just the
square root of the variance.

00:17:14.510 --
The positive square root,
of course.

00:17:19.220 --
Remember, standard deviations
invariances cannot be negative.

00:17:21.789 --
They can be 0.

00:17:23.810 --
Which is not very exciting, but
they can't be negative.

00:17:27.280 --
'cause if there is zero, you

00:17:28.678 --
have identical data points.
Which I suppose is not

00:17:31.805 --
necessarily that it's not
super exciting. There could be

00:17:34.550 --
a good case for it, but it
might not be that exciting to

00:17:38.515 --
look at. So Sigma without the
squared is our notation.

00:17:43.890 --
So SD of Y.

00:17:46.650 --
Probably, but as of why, but
that might mean something else

00:17:50.005 --
in a different class, so I use
SD and so we just take the

00:17:54.275 --
square root of our variance.

00:17:56.910 --
Or the square root of Sigma
squared. Either way for us in

00:18:01.962 --
this example, is sqrt 1.45.

00:18:05.720 --
Which is fire Mario 1.2?

00:18:13.770 --
Or something close.

00:18:22.100 --
Alright, this would be great if
we could always get population

00:18:25.070 --
values and we would never have
to worry about doing. You know

00:18:28.310 --
we'd always be able to know
everything about the population.

00:18:32.020 --
Not always the exact case in
life. Unfortunately, there's a

00:18:36.010 --
lot of unknown.

00:18:38.650 --
And it's a two point 1.20 that
some decimals off the end, but I

00:18:42.458 --
just found it to 1 decimal place
as far as your work goes most of

00:18:46.538 --
the time using significant
digits is not a horrible idea,

00:18:49.258 --
but I would say except in a rare
case when we get to the last

00:18:53.338 --
chapters, you probably don't
need to carry it more than two

00:18:56.330 --
to four decimal places are last
chapters or there are some

00:18:59.322 --
concepts where we're going to
have a small value, some sort of

00:19:02.586 --
density value which is very
similar to like a growth or

00:19:05.578 --
decay rate, so you'd probably
more like a decay rate, so you

00:19:08.842 --
probably want to make sure you
might want to carry those out a

00:19:12.378 --
little bit further, but.

00:19:13.640 --
The most part significant digits
or two to four decimal places

00:19:17.457 --
will be more than sufficient for
what you need.

00:19:22.630 --
But unfortunately we don't have.

00:19:26.030 --
Population values all the time.
He did. Life would be simple and

00:19:29.510 --
then we wouldn't probably need a
whole discipline called

00:19:32.120 --
statistics for all this stuff
because we wouldn't know the

00:19:35.020 --
entire population. But since we
don't, we have to use

00:19:37.920 --
statistics. So what we're going
to do is take samples and that's

00:19:41.400 --
really what you're doing. Here
is looking at the samples from

00:19:44.590 --
surveys and what have you and
trying to make estimations. Our

00:19:47.780 --
main estimations are going to be

00:19:49.520 --
a mean. A total which you may or
may not have dealt with in your

00:19:55.123 --
intro class and a proportion.
There are others, of course, but

00:19:58.764 --
those are our main.

00:20:00.180 --
Three statistics of interest
while we're here in this course

00:20:02.840 --
and those would be the main
three statistics of interest in

00:20:05.766 --
surveys as well. So.

00:20:08.360 --
And of course with that we
always want to have a variance,

00:20:12.284 --
so we getting back to
calculating this all right now.

00:20:16.590 --
You've probably seen that
there are different.

00:20:20.540 --
Calculations formulas for
population versus sample values.

00:20:25.880 --
So let's kind of take a peek at

00:20:28.336 --
the differences. Population.

00:20:33.650 --
Versus sample.

00:20:36.980 --
So population value for a mean.

00:20:40.470 --
Is mew. I'm going to write the
word meaning here so we know

00:20:44.698 --
what this is at first case. It's
been a little while since you've

00:20:47.402 --
seen some of these. So if we
knew every single value in the

00:20:51.642 --
population, we would sum all of
those up. So I'm going to use.

00:20:55.516 --
Not that you can tell the
difference, but that's supposed

00:20:58.496 --
to be a capital Y versus a small
way. Usually my capital wise are

00:21:02.668 --
straight just lines and my lower
case. Why is usually kind of got

00:21:06.542 --
a curve to it?

00:21:08.830 --
I'll usually remind you as we
get there, so we take every

00:21:12.514 --
value of the population.

00:21:14.700 --
And we divide it by. Now we have
a new symbol, big End. Big N

00:21:19.875 --
represents population size.

00:21:22.480 --
I'm actually going to write
that on my previous sheet of

00:21:25.351 --
paper that I'm going to bring
down Tuesday here, so an is

00:21:28.483 --
always your sample size.

00:21:32.560 --
And Big N is going to be
your population size.

00:21:37.320 --
Which is actually important.
In this course we need to

00:21:39.380 --
know that for the surveys and
stuff that we were analyzing.

00:21:45.350 --
Alright.

00:21:48.520 --
Before a sample.

00:21:51.400 --
Ala carte, why bar could be X
bar. Yeah, Brooke. Uses why

00:21:54.856 --
we're going to stick with guys.
We would take the sum of all of

00:21:58.888 --
our sample. Observations and
divided by the number of

00:22:03.687 --
observations in our sample.

00:22:06.980 --
Depending on how we draw a
sample, these could be

00:22:10.090 --
identical. But it's not going to
happen terribly often, except in

00:22:14.340 --
my example. Today it was
coincidence. I swear I actually

00:22:17.390 --
do a random sample, and the
thing we're going to look at

00:22:21.050 --
today, and it turned out that
the sample mean is going to end

00:22:25.015 --
up being exactly the population
mean, but that doesn't always

00:22:28.065 --
happen, but it should be most of
the time, pretty close.

00:22:33.250 --
Alright, variance.

00:22:36.060 --
So we call it Sigma squared.

00:22:40.420 --
I'm going to actually give
you two different derivations

00:22:43.183 --
of the same formula.

00:22:46.410 --
There's one you've seen before.

00:22:47.860 --
Maybe sort of. So why that
should be an eye for each

00:22:52.895 --
individual observation minus mu?

00:22:55.150 --
Quantity squared
divided by big N.

00:22:58.680 --
Or in the discrete case, what
you saw earlier?

00:23:04.730 --
That was the sum Y minus mu
quantity squared times the

00:23:09.427 --
probability of Y.

00:23:15.730 --
Alright.

00:23:19.650 --
S squared following the same
sort of formula over here.

00:23:24.040 --
It's going to be.

00:23:27.980 --
The sum why I -- Y bar quantity
squared. We divide that by

00:23:33.661 --
little N -- 1.

00:23:36.370 --
Because it came from a
sample and we're losing

00:23:38.773 --
some information. If you
look there at the formula

00:23:41.176 --
I have. Why bar versus mu,
since we don't know mu, we

00:23:44.380 --
lose. We lose our
information. A degree of

00:23:46.516 --
freedom. So that's why
we're dividing by N -- 1

00:23:49.186 --
little N -- 1.

00:23:51.980 --
But in the population case,
we wouldn't actually lose any

00:23:55.010 --
information because we have
it all. So, and we're using

00:23:58.040 --
the real mean.

00:24:01.050 --
This one here. Technically we
still use via why, but it's more

00:24:05.154 --
ha with a hat on it, so anytime
you see a hat on something

00:24:09.942 --
that's usually called an
estimator and you're actually

00:24:12.678 --
going to see a hat on a V. More
often than not. So this one

00:24:17.808 --
implies that we actually do

00:24:19.518 --
know. All the values and
population. Here we are

00:24:23.030 --
estimating the variance, so it's
the estimated variance of Y.

00:24:27.750 --
And it really isn't going to
look hugely different.

00:24:36.970 --
As well, calculate the expected

00:24:38.450 --
value of Y. Or mew hat.

00:24:42.130 --
Yeah, this book likes to use
hats on things, so if you

00:24:44.962 --
haven't seen that too much
before, we're going to have

00:24:47.322 --
hats. Lots of hats.

00:24:51.340 --
Standard deviation, well,
that's actually.

00:24:57.180 --
Not that exciting or different
than what we were used to. So

00:25:01.212 --
Sigma is the square root of
Sigma squared and over here S is

00:25:05.580 --
sqrt X ^2.

00:25:11.650 --
Alright.

00:25:15.800 --
Trying to keep my pages and
pages in line here so in our

00:25:21.065 --
statistical studies we love to
take samples and we make

00:25:25.115 --
inferences from those samples
about the larger population. So

00:25:28.760 --
we want to make.

00:25:30.980 --
Well, it's an inference is an
educated guess, but we're using

00:25:34.126 --
data and facts to back that up.
So it is an educated guess.

00:25:37.844 --
Guess sounds so. I don't
know Willy nilly versus.

00:25:42.350 --
An educated statement I don't
know, but that's what we're

00:25:45.690 --
going to do. So a lot of times
we want to make inferences about

00:25:50.366 --
unknown population parameters.
So what do we do? We use our

00:25:54.040 --
sample statistics, so we're
going to get back to our TV

00:25:57.714 --
example. 'cause it's completely
exciting an in our TV example.

00:26:04.140 --
TV simple. Let's say I took
a sample an it's not a very

00:26:09.301 --
big sample, it's only a
sample size 4.

00:26:13.970 --
An out of this sample, we knew
that we could have values that

00:26:18.169 --
were 0123 or four, but in this
particular sample my values

00:26:21.722 --
were. Those are my sorry. These
are supposed to be my curly

00:26:25.598 --
braces, but I suck at drawing
them, so that's what it is.

00:26:30.900 --
These were my data points.

00:26:34.650 --
There we go.

00:26:37.580 --
2013

00:26:42.340 --
now just for reference, our
population had a sample or

00:26:44.780 --
had a size 4 as well, but
we're going to take a sample

00:26:47.952 --
of size 4 and it could have
been any values Now notice.

00:26:52.870 --
We actually had five different
values that could happen. We

00:26:55.460 --
only chose for actually so big N
is. I have a big I have a typo

00:26:59.604 --
on my thing. I gotta fix it big
and is actually 5 here, alright?

00:27:04.520 --
So let's estimate mu. So
mu hat. We usually just

00:27:07.920 --
call that Y bar X bar.

00:27:11.360 --
Pick a letter well, minus a few
of 'em till pigsie.

00:27:17.060 --
But here it is. When we
use the sum of our values

00:27:21.296 --
divided by your sample
size. So we can do that.

00:27:27.960 --
Divided by 4, why are we doing
it this way? Well in this case.

00:27:33.280 --
We're kind of assuming that
they didn't have different

00:27:36.286 --
probabilities from our sample
when we actually went to those

00:27:39.626 --
probabilities were different
based on numbers in a

00:27:42.298 --
household, but from our
sample, each of these had an

00:27:45.638 --
equal chance of being chosen.

00:27:48.740 --
So we do this and
like I said before.

00:27:54.130 --
We actually get.

00:27:56.190 --
The same number, or pretty close
to it, 6 force. I don't know.

00:27:59.986 --
Today is one of those days.

00:28:02.510 --
One of my favorite teachers in
the math Department, so some

00:28:05.370 --
days are Calculator days, even
for the most simple things like

00:28:08.230 --
1 1/2. Which I already told you
it was the same, but all of a

00:28:12.991 --
sudden my brain said no, you
must test it again. So even

00:28:16.195 --
though I calculated it 2 hours
ago, evidently I needed to do it

00:28:19.666 --
again. Alright now your sample
mean is not always going to be

00:28:22.870 --
equal to your population mean.
It should be relatively close

00:28:25.540 --
most of the time this just
happened have been one of those

00:28:28.744 --
samples that I happened to draw
and I did actually honestly draw

00:28:31.948 --
it randomly. And it just
happened to be that this sample

00:28:35.507 --
mean was the same as a
population mean, which is OK,

00:28:38.290 --
that's not a bad thing.

00:28:41.470 --
But now we're going to get
into calculating our variance

00:28:46.070 --
and standard deviation.

00:28:49.020 --
So here's our variance. We
can call it Sigma squared

00:28:52.170 --
hat or Sigma hat squared,
probably Sigma hat squared.

00:28:56.380 --
Or you just call ask word
that works too.

00:28:59.750 --
We're going to use the other
formula, the second, well, the

00:29:02.335 --
first one I drew out, but not
the first one we actually used.

00:29:06.540 --
Why I -- Y bar quantity squared
divided by N -- 1?

00:29:12.260 --
That's the one we're
going to use.

00:29:16.480 --
Amazon to all this
lovely fun stuff.

00:29:22.350 --
And we got a zero. Remember
using the values from the sample

00:29:25.878 --
and not the actual population.

00:29:28.710 --
1 -- 1 1/2 squared and
3 -- 1 1/2 ^2.

00:29:38.620 --
Bye bye oh I was gonna say
4 -- 3. Now the answer is

00:29:42.904 --
three 4 -- 1.

00:29:47.900 --
We had five thirds or 1.67.

00:29:53.010 --
Versus what was it before 1.45?

00:29:58.000 --
So a little more variation in

00:29:59.842 --
this. Particular sample,
then there wasn't a

00:30:01.996 --
population, that's OK.

00:30:05.390 --
And then for the standard
deviation.

00:30:08.780 --
Sigma hat or S just take the
square root of your S ^2.

00:30:15.100 --
Anne will get.

00:30:17.490 --
Our standard deviation 1.29.

00:30:22.170 --
As probably.

00:30:28.010 --
Alright.

00:30:30.940 --
Not very exciting, but I thought
we do a nice little nice

00:30:34.816 --
overview. Just remind you so for
random samples from infinite

00:30:38.046 --
populations, which is what we're
kind of doing. The expected

00:30:41.276 --
value of the sample mean.

00:30:43.670 --
Is usually the true meaning that
leads us toward what we're

00:30:47.850 --
looking at next, which is not
just probability distributions,

00:30:51.270 --
but distributions of statistics.

00:31:02.590 --
Sample statistics so
distributions of sample

00:31:05.278 --
statistics, or in other
words, sampling

00:31:07.966 --
distributions. That's
usually the more common

00:31:10.654 --
terminology.

00:31:16.340 --
So just a reminder, what a
sampling distribution is is that

00:31:21.235 --
it looks it's the distribution.

00:31:28.200 --
Of all possible samples, Whoops,
there's 2 S is there?

00:31:37.310 --
Of a sample statistic.

00:31:46.050 --
We like that we have a specific
theorem that we really really

00:31:50.106 --
like. And I need to go find that
real quick here now. We probably

00:31:56.269 --
going to look through one of
these on the computer up here,

00:32:00.985 --
but it didn't want to go

00:32:03.343 --
through. Well, I wanted to show
I didn't want to necessarily go

00:32:06.891 --
through both of 'em 'cause the
other one really just kind of

00:32:09.663 --
summarizes this whole thing
together. So that's something

00:32:11.511 --
you can look at the other link
for. It's called CLT 2.

00:32:15.230 --
But we're going to do is we're
going to look at the sampling

00:32:18.961 --
distribution an. I actually
have a couple of examples to

00:32:21.831 --
show through simulation how
this actually works and why

00:32:24.414 --
we're still able to actually
use a normal model. Most of

00:32:27.571 --
the time for analysis, and
we're going to do a normal

00:32:30.728 --
model in this classroom as
well for this course.

00:32:34.600 --
Not all your surveys are going
to have variables that follow

00:32:38.131 --
normal models. OK, not all of
'em, but provided we look at we

00:32:42.304 --
have large enough samples and
what have you most of the time

00:32:46.156 --
we should be OK, but not every
time. There are exceptions to

00:32:50.008 --
that rule always. So first thing
you should always do graph your

00:32:53.860 --
data if you don't know what your
data looks like visually, then

00:32:57.712 --
you're only getting probably
about 1/3 to half of the

00:33:00.922 --
picture. So alright, so we're
gonna look at the central Limit

00:33:04.453 --
theorem. And for that one, our
sampling distribution of the

00:33:08.129 --
sample mean is approximately
normal with a mean mu and

00:33:11.539 --
standard deviation of the
sampling distribution of the

00:33:14.267 --
sample mean. Is Sigma divided
by square root of N. So since

00:33:18.359 --
we're looking at the
distribution of the sample

00:33:21.087 --
mean, we don't just use our
variance, we take the variance

00:33:24.838 --
divided by N or the standard
deviation divided by the

00:33:28.248 --
square root of N. We call that
Sigma over square root of N.

00:33:32.681 --
We used to call that a
standard error.

00:33:36.760 --
That is provided that N is
sufficiently large. This theorem

00:33:39.570 --
can also apply to other
statistics, which is really,

00:33:42.099 --
really handy because we're going
to be using those other

00:33:44.909 --
statistics as well. The sample
proportion an one of 'em I

00:33:48.000 --
didn't actually have on here.
The sample total which could be

00:33:51.091 --
used in case I don't know if you
guys have ever dealt with the

00:33:55.025 --
total before, but it could be
nice, say for an airline we need

00:33:58.678 --
to know how many passengers are
boarding the plane right? And

00:34:01.769 --
the other thing we do is we
weigh how much your bags weigh.

00:34:05.810 --
We need to know the weight of
your bags, how much junk

00:34:09.002 --
you're taking with you on the
plane, in addition to the

00:34:11.928 --
weight of everything else on
the plane, the humans on the

00:34:14.854 --
plane, everything.

00:34:16.640 --
So it might be nice to know what
the average weight per person

00:34:20.085 --
should be. The maximum average
weight per person, but that's

00:34:22.735 --
not the only thing of interest.
It could actually be of interest

00:34:25.915 --
to look at the entire plane full
of people's total weight. That's

00:34:29.095 --
just one example. It's not the
only one, but it's one of the

00:34:32.540 --
few examples that you could use
a total for, and so that's how

00:34:35.985 --
that's going to play in when we
start getting to that.

00:34:39.770 --
Alright, so for the most part,
the sample size should be

00:34:43.752 --
approximately at least 30.

00:34:46.100 --
If your distribution wasn't
already normal to quote

00:34:48.956 --
unquote, guarantee the
normality I say and kind of

00:34:52.169 --
using that term guarantee a
little. Loosely, there's no

00:34:55.382 --
guarantees, but to get us
the approximate normality,

00:34:58.238 --
we should have a sample size
of at least 30. Now, if your

00:35:02.879 --
original distribution you
already know is inherently

00:35:05.378 --
normal, that sample size
stipulation is not required.

00:35:08.234 --
You could have a sample size
is smallest 2.

00:35:12.850 --
But if you don't know anything
about your original

00:35:15.613 --
distribution, always safer to
take a sample size of at least

00:35:18.990 --
30. That being said, in surveys
we take, sample size is usually

00:35:22.674 --
of probably at least 10 or more
times than that than 30, so.

00:35:27.480 --
And we're going to sample
proportion. We usually want to

00:35:30.000 --
sample size of at least 60. Most
of your information from sample

00:35:33.024 --
surveys, alot of time, not most
or all. But a lot of times are

00:35:36.552 --
going to be percent, so that
would be of interest.

00:35:39.800 --
And again, I said here, if
you're just distribution is

00:35:42.520 --
already inherently normal, your
sample size stipulation can be

00:35:44.968 --
ignored. It's not that you're
ignoring it, but it's not. It's

00:35:47.960 --
not relevant to what you need to
worry about it, alright?

00:35:52.040 --
This one sorry. The book I was
using used pie instead of P for

00:35:56.184 --
the proportion. Now it should be
like most. I'm an intro books,

00:35:59.736 --
they always use P, but as soon
as you hit like our 431 class,

00:36:03.880 --
that book uses pie 'cause
everything else uses a Greek

00:36:06.840 --
letter. Why not? So why not
intro class? Well unfortunately

00:36:09.800 --
will never find that answer out
but we still go back to P in

00:36:13.944 --
this book. This book uses P for
that terminology just to kind of

00:36:17.792 --
let you know. But you can
interchange it with pie. It is

00:36:21.344 --
the same basic thing.

00:36:23.990 --
Alright, so in shorthand
notation. Our sample mean X bar

00:36:28.110 --
or why bar is distributed
normally with a mean mu and the

00:36:33.054 --
Sigma sub X bar is another
notation for that standard

00:36:37.174 --
error. Sigma over square then.

00:36:41.150 --
Same thing for the one for the
proportion and the total would

00:36:44.042 --
work as well. I thought this was
my updated file that showed.

00:36:47.630 --
Totals so all this is nice and
interesting in review. You'd not

00:36:51.950 --
be calculating Z scores in here.

00:36:54.890 --
So if you're hoping to see Z&T
scores in here, I'm actually

00:36:58.454 --
going to see those, but that's
OK, Alright? This is the

00:37:01.721 --
important part, so we actually
see how this distribution works

00:37:04.691 --
and how the central Limit
Theorem helps us to look at

00:37:07.958 --
normality. So we're actually
going to look at a distribution

00:37:10.928 --
that's already normal, so it's
not going to be that exciting

00:37:14.195 --
when we take the look at the
sampling distribution, it's

00:37:17.165 --
still going to be normal. There
are going to be some

00:37:20.432 --
differences, but then we're
going to look at an exponential

00:37:23.402 --
distribution, which is obviously

00:37:24.590 --
not. A normal Bell curve
distribution and a binomial

00:37:27.672 --
distribution, just so you can
see how the central Limit

00:37:31.062 --
theorem works on even the non
normal distributions.

00:37:35.200 --
You don't ever have to reproduce
this unless you want to, and

00:37:38.608 --
which case if you want to borrow
my code, just ask me, But what

00:37:42.584 --
this does is I'm basically going
to take this is in our command,

00:37:46.276 --
so our norm. And you plug in how
many values you want into that.

00:37:50.969 --
That will give you random
numbers generated from a normal

00:37:53.659 --
distribution. If you don't
specify the mean and standard

00:37:56.080 --
deviation, it will assume the
mean is 0 and the standard

00:37:59.039 --
deviation is 1, just like the Z

00:38:00.922 --
distribution. So we needed.

00:38:04.070 --
And in this case I actually gave
it a different mean in a

00:38:08.256 --
different standard deviation
than the Z distribution. So I

00:38:11.154 --
took a sample of 500.

00:38:13.810 --
Out of a normal distribution and
I set the mean at 100 and the

00:38:18.612 --
standard deviation at 10 and I
said, oh, let's look at the mean

00:38:23.071 --
so mean for that particular
sample was 100.25.

00:38:26.970 --
So close.

00:38:29.170 --
And here's our histogram. So the
spread on this one goes from

00:38:33.898 --
about 65 to 135, give or take.

00:38:39.630 --
And another random sample
just to show the mean change

00:38:42.480 --
to her. But we're still right
around that 100 mark.

00:38:46.440 --
And then. For some silly reason,
I decided I need to put a curve

00:38:51.432 --
on it. I hardly ever put curves
on my on my distributions like

00:38:54.890 --
this, but this one was like I'm
going to put that curve on

00:38:58.348 --
there. So there it is. So it is
a normal distribution still

00:39:01.540 --
spread out between 65 and 135
center right about 100.

00:39:05.510 --
Oh, rest of my code fell
off, sorry.

00:39:09.260 --
Alright, so for this simulation
process I'm setting the mean and

00:39:12.714 --
the standard deviation. I'm
going to take samples of size

00:39:16.232 --
5 and I'm going to do that 500
times. We're going to have 500

00:39:20.236 --
samples of size 5, so we can
look at the means of all of

00:39:24.240 --
those, and that's what I'm
calculating here.

00:39:28.350 --
And then we look at histogram
and there is the distribution of

00:39:32.898 --
the sampling distribution of the
sample mean. So the spread

00:39:36.688 --
changes 'cause we're dividing it
by the square root of N. So it's

00:39:41.615 --
now spread from about 85 to
maybe 115 versus 65135.

00:39:46.160 --
So the curve got skinnier and a
little bit taller and that

00:39:50.324 --
happens. But it's still a
normal distribution, but

00:39:53.151 --
this is now the distribution
of X bar versus X.

00:39:56.910 --
And they are just kind of
arbitrary values. I guess I

00:39:59.968 --
just. Grabbed grabbed a mean
in a standard deviation and

00:40:03.884 --
just used it so.

00:40:05.900 --
Normal spread change though.

00:40:08.720 --
That's important to look at.

00:40:10.480 --
Exponential distribution. I
don't know why I really like

00:40:12.919 --
this distribution. If you took
201 or 251 then chances are you

00:40:16.171 --
probably didn't see this. You
may have heard about it, but you

00:40:19.423 --
probably didn't see this. If you
take 301, they may have seen

00:40:22.675 --
this, but don't stress it if you

00:40:24.572 --
haven't seen it. I'm not going
to test you on this formula,

00:40:29.394 --
but this just shows you the
formula I'm using, so it's an

00:40:33.786 --
exponential distribution.
Exponential is really great

00:40:35.982 --
for modeling the waiting time
between events.

00:40:39.620 --
Other processes too, but that's
one of its big big draws.

00:40:43.920 --
Now let's see. Here we are going
to be looking at this with this

00:40:47.784 --
one. We're going to use a
distribution with a rate of 1.

00:40:52.180 --
Alright, so random number
again, a different

00:40:54.595 --
distribution R has told
whole bunch of different

00:40:57.355 --
distributions. You can
randomly generate numbers

00:40:59.425 --
out of which is great.

00:41:03.170 --
We need N.

00:41:05.160 --
Anna rate. So with this one
we're going to sample size 500.

00:41:10.040 --
We will find the mean.

00:41:11.880 --
That's pretty close to 1.

00:41:14.470 --
That sample #1 sample #2.

00:41:18.450 --
Actually knows same sample.
This sample number one.

00:41:21.362 --
Sorry, obviously not a
normal distribution.

00:41:25.370 --
And do it again. This time the
mean was to even just a hair

00:41:28.968 --
lower. But we're still pretty
close to the one mark.

00:41:33.720 --
There we go. Being silly had to
add that curve in again. So

00:41:37.984 --
there's our our curve or
exponential curve and the

00:41:40.936 --
regular distribution of it.

00:41:43.260 --
So now we're going to do the
same thing, except for I'm

00:41:46.776 --
going to be taking samples
of size 30 and I'm going to

00:41:50.292 --
take 500 samples of size 30
to calculate. 500 means joy.

00:41:54.530 --
It's kind of fun to do. Well,
this is the first time so.

00:41:58.840 --
This one, a sample size of 30
almost gives it the normality.

00:42:03.016 --
It's not perfect, but it's.

00:42:05.570 --
Close enough, that's the one
thing that's hard to once you

00:42:08.309 --
get out. Intro class is
looking at some of these

00:42:10.799 --
curves, and some of these they
might not look normal to. You

00:42:13.787 --
might want to go. Some of
these are going to be normal

00:42:16.775 --
enough. This one is actually
good.

00:42:19.450 --
Obviously not exponential
anymore and then binomial. So

00:42:23.266 --
remember binomial distribution
is one of those discrete

00:42:27.082 --
distributions for absence or
presence, so success or failure.

00:42:33.220 --
So this one is again 500
samples with a binomial

00:42:38.020 --
distribution. Its probability
of success was .8 an. We did

00:42:42.820 --
sample sub size 10.

00:42:46.370 --
But this person will probably do
500, though again binomial. You

00:42:49.967 --
can randomly generate, so this
first one is actually 500. Later

00:42:53.564 --
on when we do, the 500 samples
were going to take 500 samples

00:42:57.815 --
of size 30. I think or is it 10,
probably 10? I don't know. I'll

00:43:02.530 --
double check. I looked through
it today and then I forgot.

00:43:06.200 --
So the eight the mean should
be 8, so the mean for a

00:43:11.127 --
binomial is N * P, so 10 times
.8 gives us 8 and this one's

00:43:16.812 --
pretty darn close 7.98.

00:43:20.370 --
Not even a continuous
distribution.

00:43:25.820 --
There we go again, and this one
that means just a hair over

00:43:29.668 --
eight. OK, so that was our
second random sample and there's

00:43:32.924 --
our second. Histogram.

00:43:36.780 --
Same process we're doing
samples of size 10, but

00:43:39.012 --
we're taking 500 of them.

00:43:42.220 --
And look at that all of a
sudden. It's not the prettiest

00:43:46.084 --
thing I've ever seen, seen
prettier distributions, but

00:43:48.660 --
it's still approximately
normal.

00:43:51.700 --
Excuse me, centered right about
8:00, so that's what the central

00:43:54.989 --
limit Theorem does. Remember,
when I took my intro course, I

00:43:58.278 --
was just like it was just kind
of this concept. You had to just

00:44:02.464 --
think about it was like, OK, I'm
sure I'll use it, but actually

00:44:06.351 --
saying it for me it made a huge

00:44:08.743 --
difference this other. Thing
that you get Lord death right?

00:44:12.372 --
I zoomed in, sorry this other
one that you can look at is

00:44:16.090 --
just moves a nice little
handout that my 200 level class

00:44:19.236 --
professor had given to us. So I
asked him if I could steal it.

00:44:23.240 --
Well, I said I asked him if I
could borrow it so I said well

00:44:27.530 --
can I. Can I borrow it and give
it to my class and you said OK,

00:44:32.106 --
that's fine so I stole it.
There it is but I did I did put

00:44:36.396 --
his name down there so.

00:44:39.460 --
Alright. So we're looking at
this thing. We're probably not

00:44:43.222 --
gonna be able to finish this up
today, which is OK. We can

00:44:46.576 --
finish this up later, but we can
kind of set ourselves up for the

00:44:50.188 --
end of this. So what we
want to do?

00:44:54.510 --
Is we have our population
at see here.

00:44:59.810 --
I left my pen open, sorry.

00:45:03.800 --
So this is our original
population values.

00:45:08.530 --
And we're going to.

00:45:11.320 --
I think in this case just
take samples.

00:45:19.530 --
Size 2

00:45:22.310 --
just keep simple.

00:45:25.620 --
Now.

00:45:28.390 --
In this case.

00:45:31.100 --
This is this is our population
and this is the number the

00:45:35.132 --
sample size we're going to do.
We want to actually look at all

00:45:39.500 --
possible samples for this so.

00:45:49.860 --
All possible samples.

00:45:54.600 --
From in this case, what we're
doing is those were the number

00:45:58.344 --
of TV's in the House, but what
we're going to do is we're going

00:46:02.712 --
to be looking at from 4 houses.

00:46:06.240 --
So let's say we have House 1-2,
three and four.

00:46:13.590 --
So this has a population of
four different.

00:46:19.210 --
Possibility so for houses
small town. There we go

00:46:22.666 --
more than Moscow.

00:46:26.250 --
One of the things we got
excited about when I was a kid

00:46:29.396 --
we were driving. I think we
were driving to California and

00:46:32.058 --
we were driving through
southern Idaho really late

00:46:33.994 --
tonight. My dad got all excited
how to wake all of us up. It

00:46:37.382 --
was like 3:00 o'clock in the
morning. 'cause one of the

00:46:40.044 --
towns we came from California
so this was a pretty cool

00:46:42.706 --
concept to us. 'cause it was
cute, neat. One of the towns

00:46:45.610 --
actually like listed on the
animals and I can't remember

00:46:48.030 --
what town it is but listed all
the animals, the cows, the

00:46:50.934 --
humans telling my dad had to
wake us all up. Look, look at

00:46:54.080 --
this look at this.

00:46:57.060 --
Alright, so small town that was
a small town, not as small as

00:47:01.038 --
this little town we're going to
deal with, so we're going to

00:47:04.710 --
sample the houses. And then
we're going to ask them.

00:47:11.280 --
How many?

00:47:13.980 --
TV's do you own?

00:47:20.060 --
All right, we're going to look
at all possible samples.

00:47:25.100 --
So if we just line 'em up.

00:47:29.080 --
One and two can be one of
the samples 'cause we're

00:47:31.621 --
taking samples of size 2.

00:47:34.540 --
Now we're obviously going to
assume something here that's

00:47:37.528 --
going to be kind of important
for us to talk about. Kind of

00:47:41.844 --
important. That's an
understatement.

00:47:44.660 --
Is that we're doing this?

00:47:49.350 --
Without replacement.

00:47:52.210 --
So what I'm doing here is
that when I choose a house,

00:47:56.086 --
it can no longer be chosen
for the observation #2. So

00:47:59.639 --
if it's been chosen for
observation number one, it

00:48:02.546 --
can't be chosen again for
observation #2, so we

00:48:05.453 --
couldn't go to the House
number one twice or House

00:48:08.683 --
number 2 twice, etc.

00:48:12.680 --
Now two and three can be
chosen, and this is all

00:48:15.969 --
possible samples. It's not
what we actually did, but

00:48:18.660 --
we're looking at the
possibilities.

00:48:21.830 --
I don't know. I like Roman
numerals. I always have it

00:48:24.888 --
thing from when I was a kid.
I apologize, but I'm not

00:48:28.224 --
that sorry.

00:48:31.500 --
So these are all possible
samples. We had six of them.

00:48:37.480 --
And that's where we get to pick

00:48:39.545 --
up next time. Figure out what
to do with this thing.

00:48:46.780 --
And that's it, and we will
finish this tomorrow or

00:48:49.910 --
finish this next class.

Duration:"01:16:36.5220000"

00:00:21.060 --
Audi so this is the 7th lecture and

00:00:25.486 --
we're going to continue on with work

00:00:28.634 --
related musculoskeletal diseases.

00:00:30.250 --
So when I talked about anthropometry

00:00:33.778 --
couple lectures ago I talked a little bit

00:00:37.595 --
about this one commercial where Shaquille

00:00:40.120 --
O'Neal is trying to get into a small car.

00:00:43.670 --
And I have found that video and I'm waiting.

00:00:46.270 --
I'm trying to find another video that I

00:00:48.310 --
want to show from anthropometry as well,

00:00:50.610 --
and I haven't located it yet,

00:00:52.340 --
but I want to show this video really quick,

00:00:54.940 --
and again it's throwback to

00:00:56.380 --
a previous lecture,

00:00:57.250 --
but it's pretty interesting

00:00:58.430 --
how they how they set it up.

00:01:12.700 --
I may have retired from the game.

00:01:14.870 --
But not from being big. Good thing.

00:01:17.104 --
One car gives me full size luxury and

00:01:19.916 --
36 MPG which is nice because I've got

00:01:22.596 --
shoes that are bigger than most hybrids.

00:01:25.370 --
And more stylish too.

00:01:27.990 --
If you don't know the luxurious yet fuel

00:01:30.542 --
efficient across you, don't know Buick.

00:01:32.433 --
Get two years of premium services

00:01:34.359 --
with nothing to at least signing on.

00:01:36.520 --
The EPA estimated 36 Hwy MPG

00:01:38.416 --
lacrosse with the assist.

00:01:39.680 --
Consider it if you don't know the looks.

00:01:43.570 --
If you don't know the luxurious.

00:01:46.810 --
And more.

00:01:49.340 --
So I don't know if you see this self.

00:01:52.570 --
You along with me along with

00:01:55.096 --
this commercial but you can see

00:01:57.888 --
Shaquille O'Neal sitting here.

00:01:59.940 --
They've obviously put the seat way back

00:02:02.495 --
so he could actually sit in the car.

00:02:05.390 --
You can see where his knees are

00:02:07.693 --
in relationship to the dashboard

00:02:09.563 --
and the steering wheel.

00:02:11.190 --
It's obvious that he doesn't

00:02:13.235 --
fit into this car very well.

00:02:15.770 --
He is a a big person.

00:02:18.660 --
And it's just almost ridiculous

00:02:20.525 --
that they have him trying to look

00:02:23.146 --
comfortable in this car because he

00:02:25.192 --
could not drive this car comfortably.

00:02:27.710 --
It be like me trying to fit in

00:02:30.998 --
my daughter's Honda Fit which is

00:02:33.748 --
about the same as Shaq sitting

00:02:36.590 --
in this Buick Lacrosse.

00:02:38.740 --
So again from anthropometric standpoint,

00:02:40.570 --
it's a mismatch.

00:02:41.830 --
He would be very uncomfortable

00:02:43.930 --
and probably sore at the end

00:02:46.020 --
of a very short drive.

00:02:51.800 --
So. We're going to talk about work related

00:02:57.095 --
musculoskeletal diseases of the spine.

00:03:01.300 --
And.

00:03:06.060 --
Paratroopers, helicopter pilots,

00:03:07.296 --
other people in the Military,

00:03:09.360 --
Navy Seals that have to ride in

00:03:12.314 --
the Zodiac boats quite a bit,

00:03:14.730 --
all experience a high degree of back

00:03:17.376 --
injuries associated with their professions.

00:03:19.690 --
Now these are militaries standpoint.

00:03:23.300 --
People of all professions.

00:03:25.460 --
Office workers,

00:03:26.540 --
people that are working on shop floors.

00:03:32.000 --
All experienced back problems

00:03:33.784 --
at various times depending on

00:03:36.014 --
the type of tests are doing.

00:03:38.230 --
There's some genetic components to it.

00:03:40.720 --
The fact that sometimes are not moving

00:03:43.583 --
around and so they can experience problems.

00:03:47.170 --
So what we're going to talk

00:03:49.606 --
about in this today's lecture,

00:03:51.980 --
our spine anatomy and then spinal work

00:03:55.452 --
related musculoskeletal diseases?

00:03:56.940 --
I do have several videos,

00:03:58.890 --
again talking about very aspects

00:04:01.200 --
of various aspects of.

00:04:03.050 --
Dumb.

00:04:04.900 --
No musculoskeletal diseases of

00:04:06.440 --
this particular one talks about

00:04:08.365 --
the anatomy of the spine.

00:04:10.040 --
This is when I found it's truly it.

00:04:12.970 --
More educational and in nature,

00:04:14.810 --
and then we'll go through it in

00:04:17.134 --
detail as we go through the lecture.

00:04:23.150 --
Hi there, I'm doctor Gary Simmons

00:04:25.412 --
of Curling Clinic neurosurgery

00:04:26.980 --
and we're going to talk a little

00:04:28.877 --
bit about the human spine today.

00:04:30.810 --
We talked in the past about

00:04:32.712 --
the anatomy of the spine,

00:04:34.470 --
but what I want to talk about

00:04:36.661 --
today is what goes into the spine,

00:04:39.130 --
because really,

00:04:39.902 --
that's the most important thing

00:04:41.832 --
about your spinal column and that

00:04:43.874 --
is what's on the inside of it.

00:04:45.790 --
Well, what's on the inside of it are nerves,

00:04:48.790 --
and they are the main wiring of your body.

00:04:51.790 --
When your brain tells you to move your hand.

00:04:55.140 --
That has to go through a network

00:04:57.317 --
of wires if you will.

00:04:58.960 --
That eventually goes from the part

00:05:00.904 --
of the brain giving the command out

00:05:03.178 --
to the muscles that move your hand,

00:05:05.320 --
and the same thing goes for if you

00:05:07.688 --
touch a hot stove that the message

00:05:10.054 --
of wow that's hot has to go through a

00:05:13.033 --
series of wires all the way back up

00:05:15.496 --
to your parts of your brain that say,

00:05:18.040 --
you're you're putting your hand

00:05:19.770 --
on a stove that's incredibly high

00:05:21.847 --
and that all goes through the main

00:05:23.828 --
wiring of your body, which is housed.

00:05:26.233 --
Within your spine. Now the the main wiring.

00:05:29.610 --
The principle wiring is in what

00:05:32.172 --
we call the spinal cord.

00:05:34.400 --
The spinal cord is a whole bunch of

00:05:37.360 --
wires bundled together basically,

00:05:39.620 --
and those wires run all the way from

00:05:42.996 --
the brain coming out of the head and

00:05:46.639 --
into the spinal column and run all

00:05:49.773 --
the way down through the canal of the

00:05:53.115 --
spine until it reaches somewhere in your.

00:05:56.230 --
Upper low back or your upper

00:05:58.834 --
lumbar region of your back there.

00:06:01.620 --
The bundling of the wires kind of

00:06:04.588 --
breaks up an each wires hanging down

00:06:07.724 --
from the end of the main wiring or

00:06:11.399 --
the spinal cord and almost looked

00:06:14.165 --
like a horses tail in the end part

00:06:17.784 --
of the spinal column.

00:06:19.580 --
In other words,

00:06:20.993 --
a whole bunch of wires just hanging

00:06:24.387 --
there off the end of your spinal cord.

00:06:27.900 --
Looking like a horses tail.

00:06:29.790 --
So in medicine we often use Latin

00:06:32.303 --
terms and that area of your spine

00:06:34.920 --
is called the cauda aquina and

00:06:37.196 --
that means horses tail in Latin,

00:06:39.590 --
and that's what that part of the

00:06:42.243 --
anatomy is now for all that main wiring

00:06:45.363 --
to connect out to your legs and arms

00:06:48.410 --
and lungs and all that sort of thing,

00:06:51.326 --
they have to get out of your spine somehow

00:06:55.255 --
and the way they do it is each time.

00:06:58.390 --
Two vertebrae,

00:06:59.404 --
2 bones of your spine come together.

00:07:02.960 --
There's a little hole on the side.

00:07:08.980 --
We give that yet another fancy term

00:07:11.528 --
we call that the nuro foramen,

00:07:13.990 --
but it's basically the nerve whole,

00:07:16.300 --
and that's all neural foramen means.

00:07:18.610 --
It's a nerve, whole.

00:07:20.158 --
It's a hole through which a nerve

00:07:22.963 --
jumps out of the spinal column and

00:07:25.728 --
goes off to where it needs to go

00:07:28.736 --
off to an everywhere two vertebrae

00:07:30.928 --
come together from your neck,

00:07:32.850 --
and your thoracic region or the

00:07:35.064 --
chest region to lumbar region,

00:07:37.090 --
which is your lower back region.

00:07:39.510 --
Nerves pop out of these little

00:07:41.928 --
holes now once they get out of

00:07:44.621 --
the holes they tend to go into the

00:07:47.558 --
little Los Angeles freeway exchange.

00:07:50.250 --
In other words,

00:07:51.456 --
several nerves will come out

00:07:53.466 --
of several holes,

00:07:54.790 --
and then they'll go and interchange

00:07:57.112 --
for awhile and then spring

00:07:59.186 --
out is totally different.

00:08:00.990 --
Nerves and those nerves are

00:08:03.050 --
are called peripheral nerves.

00:08:04.700 --
The nerves inside the holes.

00:08:07.920 --
Are called nerve roots,

00:08:09.440 --
so will often talk about nerve

00:08:11.792 --
roots in my business,

00:08:13.270 --
and that's what they're talking about.

00:08:15.560 --
It's the nerve after it comes off

00:08:18.045 --
the spinal cord and comes out the

00:08:20.635 --
little holes before they go into the

00:08:23.299 --
Los Angeles freeway exchanges and

00:08:25.364 --
become what we call peripheral nerves.

00:08:27.776 --
So if you talk about some people

00:08:30.422 --
might talk about the median

00:08:32.271 --
nerve which gets caught in your

00:08:34.448 --
wrist in carpal tunnel syndrome.

00:08:36.570 --
That's what's called a peripheral nerve.

00:08:38.860 --
It's well far away.

00:08:40.700 --
From the spinal nerves that are

00:08:43.558 --
coming out of your spinal column.

00:08:46.540 --
Now again, this is important stuff.

00:08:49.550 --
This spine is designed to give

00:08:52.772 --
you stability and mobility and

00:08:55.440 --
all that sort of thing,

00:08:57.560 --
but really it's designed to protect your

00:09:01.039 --
spinal nerves and your spinal cord,

00:09:04.080 --
and it's obviously made up of tough

00:09:07.545 --
bone and surrounds that, nor the.

00:09:10.262 --
Spinal cord,

00:09:10.934 --
as much as it can to give it protection.

00:09:14.550 --
You might even argue that some of

00:09:16.769 --
the stuff on the backside here

00:09:18.870 --
was to protect you and Saber.

00:09:21.030 --
Tooth tigers were trying to bite

00:09:22.920 --
you in the old days or something.

00:09:25.460 --
But All in all,

00:09:26.920 --
the spinal column is a protective

00:09:29.185 --
element for these very delicate

00:09:31.335 --
wiring of your body.

00:09:33.060 --
We'll talk more about this later

00:09:34.860 --
and further episodes.

00:09:35.760 --
Thank you very much for listening today.

00:09:37.860 --
Bye bye now.

00:09:48.370 --
I don't need a school to just promise me

00:09:51.016 --
the tools for change. I need to school.

00:09:58.340 --
That's the problem about using.

00:10:00.020 --
YouTube is then all the sudden.

00:10:02.030 --
All these advertisements pop up or

00:10:04.208 --
or other videos start to pop up.

00:10:06.380 --
You can't download the videos where

00:10:08.252 --
you can and keep them yourself,

00:10:10.400 --
but it's not the easiest thing to do as well.

00:10:15.470 --
So when we look at the general

00:10:18.228 --
population for every five people in

00:10:20.754 --
a classroom or an office building,

00:10:23.280 --
80% will experience significant back

00:10:25.925 --
pain at some point in their lives.

00:10:29.760 --
So four out of five people in a room

00:10:33.234 --
will experience some sort of back pain.

00:10:36.930 --
So when I was 20 years old,

00:10:39.290 --
I was working at a marine warehouse.

00:10:42.870 --
Truck driver pulled up.

00:10:44.686 --
Add 2/5 gallon buckets on the

00:10:47.498 --
back of the truck.

00:10:49.040 --
I assume that they were typical 5 gallon

00:10:52.176 --
buckets containing 5 gallons of paint,

00:10:54.290 --
so I grabbed both of them and pulled

00:10:57.794 --
him off the back of the truck.

00:11:00.970 --
And they turned out to be 100 pounds

00:11:03.666 --
of chain and each 5 gallon bucket.

00:11:06.300 --
And so I went straight down to the

00:11:08.836 --
ground and pulled my back muscles.

00:11:11.160 --
So do I tell anybody?

00:11:12.890 --
No, I was 20 years old.

00:11:14.980 --
This was a different era.

00:11:16.710 --
You didn't report every accident

00:11:18.445 --
that you had.

00:11:19.490 --
It was a small company.

00:11:21.220 --
I knew the owner well so you know,

00:11:24.000 --
I didn't report anything.

00:11:25.476 --
I didn't want anyone to

00:11:27.321 --
know that I had done this,

00:11:29.200 --
but that pain lasted for a couple

00:11:31.629 --
weeks and I still remember to

00:11:33.940 --
this day how painful it was.

00:11:36.310 --
And how long it took me to

00:11:38.907 --
overcome that pain?

00:11:40.020 --
At that time,

00:11:40.986 --
you really didn't even have things

00:11:42.918 --
like mottron readily available.

00:11:44.880 --
Ibuprofen there was Tylenol.

00:11:46.376 --
There was aspirin,

00:11:47.500 --
so I didn't really even have things to

00:11:50.588 --
help alleviate the pain at that point.

00:11:55.340 --
I'm lucky that I haven't had persistent

00:11:58.273 --
back pain since that point in time.

00:12:01.060 --
Other people have persistent

00:12:03.408 --
back pain their whole lives.

00:12:06.350 --
I've talked about my colleagues, husband.

00:12:08.581 --
You saw this.

00:12:09.694 --
The hardware that's in his back.

00:12:11.920 --
I have another colleague.

00:12:14.950 --
Who also her husband has significant

00:12:18.172 --
amount of hardware in his neck

00:12:21.375 --
and has constant back pain.

00:12:23.760 --
So back pain is second only to

00:12:26.350 --
the common cold for keeping

00:12:28.574 --
American workers from their jobs,

00:12:31.160 --
and this is from nine 2003 at.

00:12:34.200 --
The statistics still applies today.

00:12:36.380 --
Back pain is very significant amongst people.

00:12:40.040 --
As people get older generally

00:12:42.470 --
there they experience more back

00:12:44.980 --
pain for one reason or another.

00:12:47.450 --
Spinal stenosis is one of those things

00:12:49.823 --
that seems to crop up as people get older,

00:12:52.730 --
and that's where there's a narrowing in the

00:12:55.930 --
opening for the spinal cord to get through.

00:12:59.060 --
This final bones. So.

00:13:04.240 --
When we look at the spine.

00:13:07.240 --
Here's a couple.

00:13:09.490 --
Diagrams of it.

00:13:12.570 --
The diagram at the left.

00:13:14.710 --
Shows the various sections of the spine.

00:13:17.810 --
We have seven vertebrae

00:13:19.162 --
and the cervical spine.

00:13:20.520 --
The skull rests on top of the

00:13:22.550 --
top of the cervical spine.

00:13:24.590 --
They said, I think,

00:13:25.946 --
in the first day of lecture,

00:13:27.980 --
if you reach back and touch.

00:13:30.960 --
I'm going to stop sharing for a second.

00:13:35.720 --
If you reach back and fill that

00:13:37.869 --
lump on the back of your neck

00:13:40.246 --
right here, that's your C6.

00:13:41.915 --
Your cervical 6 vertebrae.

00:13:43.220 --
It's a really easy reference to find,

00:13:45.500 --
so you have one more cervical vertebrae.

00:13:47.780 --
Be a below that, and then it

00:13:49.971 --
starts the thoracic spine.

00:13:57.250 --
So the thoracic spine is the

00:13:59.950 --
least movable part of the spine.

00:14:02.740 --
There are 12 thoracic vertebrae

00:14:04.640 --
T1 to T12 as compared with seven

00:14:07.392 --
for this sort of cervical spine.

00:14:09.710 --
They provide some motion,

00:14:11.254 --
but they're more immobile.

00:14:12.800 --
The discs are not as thick in that region.

00:14:16.290 --
The cervical spine discs are fairly movable.

00:14:18.990 --
That's why we can move our

00:14:21.150 --
heads all the way around.

00:14:25.810 --
But the thoracic spine

00:14:27.710 --
is not as more moveable.

00:14:30.090 --
And then we have the lumbar spine.

00:14:33.090 --
Which is 5 vertebrae, L1 to L5,

00:14:35.860 --
and that's bears most of

00:14:37.835 --
the weight of our body,

00:14:39.810 --
and any load that we pick up.

00:14:43.340 --
So when we're talking about lifting tasks,

00:14:46.110 --
will talk about biomechanics

00:14:48.058 --
during the next couple lectures.

00:14:50.500 --
The server the lumbar spine is what

00:14:53.860 --
actually supports the load of our

00:14:56.602 --
bodies and anything we pick up.

00:14:59.020 --
And then the below the lumbar spine.

00:15:02.100 --
We have the sacrum,

00:15:03.632 --
and it consists of five fused

00:15:06.018 --
and modified vertebrae,

00:15:07.820 --
and with two ilium bones,

00:15:10.020 --
which completes the pelvic ring.

00:15:12.820 --
And then at the very end is the coccyx.

00:15:16.020 --
I know I've talked about a lot

00:15:18.533 --
of different injuries I've had.

00:15:20.300 --
I fell ice skating.

00:15:21.692 --
One time this we were skating on Hayden Lake,

00:15:24.920 --
outside Corda Lane which is in North

00:15:27.594 --
Idaho and all of a sudden we heard

00:15:30.387 --
a large crack of the ice through

00:15:32.750 --
the lake and we both took off.

00:15:35.250 --
A friend of mine and I both took

00:15:37.746 --
off on our skates skating as hard

00:15:40.410 --
as we could because of this crack.

00:15:43.330 --
And I fell and broke my coccyx

00:15:45.374 --
and that took several months to

00:15:47.435 --
to feel better again.

00:15:48.920 --
It's a really easy bone to break

00:15:51.839 --
if you fall on it. It doesn't it.

00:15:54.648 --
It heals by itself and less it gets

00:15:57.140 --
displaced and so it's it's just

00:15:59.234 --
something that a lot of people have

00:16:01.744 --
experienced in the course of their lives.

00:16:04.287 --
So in general we have this large

00:16:07.416 --
structure of bone and are back and in

00:16:10.671 --
between each of the vertebrae there's a disk,

00:16:14.430 --
except in the sacrum,

00:16:16.034 --
because again, they are fused bone.

00:16:22.630 --
So, interesting enough.

00:16:26.160 --
When we look at this final column.

00:16:29.270 --
And we just saw in that one video.

00:16:33.710 --
How the processes work?

00:16:38.600 --
On the back of the the spinal

00:16:41.456 --
column and again if he filled

00:16:43.983 --
at C6 vertebrae in the back,

00:16:46.410 --
those Bony processes project out.

00:16:49.860 --
And they protect ingeneral the spinal cord.

00:16:55.020 --
But the discs and the bulk of the bone.

00:16:58.710 --
Are medial to the body versus the

00:17:01.538 --
spinal cord, which is more distal?

00:17:03.966 --
So when you think about it,

00:17:06.390 --
the spinal cord is out away from the

00:17:09.894 --
body compared with where the discs and

00:17:13.229 --
the majority of the vertebral bone is.

00:17:16.390 --
So in this diagram on this slide,

00:17:19.360 --
you can see we have the intervertebral

00:17:22.720 --
disc where the spinal cord is.

00:17:25.620 --
That's right here.

00:17:28.550 --
The cursor is being able to be seen.

00:17:31.260 --
We have these processes that come

00:17:33.342 --
out and the processes have a lot

00:17:35.838 --
of different small muscle groups

00:17:37.573 --
attached to him and they provide us

00:17:39.880 --
the movement that we have back and

00:17:42.106 --
forth that control our body moves.

00:17:44.140 --
There's a lot of these little

00:17:46.780 --
muscles that help us move our

00:17:49.472 --
bodies in a whole variety of ways.

00:17:52.420 --
So vertebrae are similar to

00:17:54.005 --
STACK children's building blocks.

00:17:55.280 --
Best way to sit.

00:17:58.460 --
They physically are not connected

00:18:00.715 --
to each other.

00:18:02.070 --
By bone other than in the sacrum,

00:18:04.840 --
but they are test, of course,

00:18:07.210 --
via the discs in the back.

00:18:10.140 --
And then have a course.

00:18:11.300 --
The spinal cord that goes through.

00:18:14.430 --
If you look at the bottom diagram

00:18:16.775 --
you can see the the vertebrae.

00:18:19.200 --
You can see the disc in between,

00:18:21.770 --
which is that light blue color.

00:18:23.970 --
You can see how the nerves come

00:18:26.903 --
out in between the vertebral discs.

00:18:30.080 --
And they, as a video talked about.

00:18:32.580 --
They go out and they innervate

00:18:34.740 --
your whole body so that you can.

00:18:37.220 --
Your brain can talk to your arms or legs.

00:18:41.610 --
Body your skin,

00:18:43.176 --
your fingers,

00:18:44.220 --
everything within your body

00:18:46.760 --
has a connection to the brain.

00:18:50.570 --
So in an injury and will go back up.

00:19:00.620 --
Certain injury we've all heard about

00:19:02.804 --
people who broken their backs,

00:19:04.690 --
which is like crack in the vertebral

00:19:07.210 --
discs or severing the booty galore,

00:19:09.500 --
totally smashing a vertebral disc.

00:19:11.950 --
And then cutting the.

00:19:15.420 --
Spinal cord so dependent on where the

00:19:17.702 --
spinal cord is cut in an accident and

00:19:20.567 --
hopefully nobody ever watching this

00:19:22.451 --
video has not, but it does happen.

00:19:25.170 --
Determines where the body

00:19:27.010 --
is paralyzed or now.

00:19:28.570 --
You don't have that transmission of

00:19:30.820 --
the brain to the rest of the body,

00:19:33.630 --
or vice versa, because it's a two way St.

00:19:36.890 --
It's not just that the brain

00:19:39.260 --
sends signals out and also

00:19:41.425 --
collects signals coming back out.

00:19:43.930 --
So if the vertebrae or the spinal column.

00:19:47.960 --
Is broken twords the neck.

00:19:49.830 --
You may be a person will become

00:19:52.980 --
a quadriplegic versus if it's

00:19:55.272 --
lower down in the back and again

00:19:58.247 --
depending on where the break is.

00:20:00.630 --
Determines what level of paralysis

00:20:03.240 --
somebody might experience.

00:20:08.860 --
So again, we have the small bones

00:20:11.548 --
and project from each of the

00:20:13.998 --
corners of the vertebral disc,

00:20:16.020 --
and these processes, actors,

00:20:17.612 --
attachment points for muscles and ligaments.

00:20:23.960 --
So one of the interesting things is

00:20:26.508 --
this slide talks about in the morning.

00:20:29.150 --
You're about half an inch taller than you

00:20:31.862 --
are in the afternoon, and the reason is,

00:20:35.094 --
is why we're standing or sitting.

00:20:37.320 --
We compress those discs and

00:20:39.175 --
they tend to lose fluid.

00:20:41.030 --
If we're dehydrating,

00:20:42.488 --
we can lose fluid out of those discs.

00:20:46.550 --
People that are on the space station

00:20:49.399 --
astronauts actually become taller during

00:20:51.444 --
the period of time because their disks

00:20:54.069 --
along gate because there's no gravity

00:20:56.259 --
acting on the body and so they are.

00:21:01.570 --
They are a living thing.

00:21:02.960 --
I don't know how is this drive it.

00:21:05.170 --
Bone is a living thing also,

00:21:06.830 --
but disks actually change

00:21:08.250 --
during the course of a day.

00:21:10.380 --
So there are cushions of

00:21:13.445 --
tissue between most vertebrae.

00:21:15.900 --
Which absorbs shock and

00:21:17.744 --
protect the spine from impact.

00:21:20.050 --
So if you're going to be in a hard fall,

00:21:23.120 --
it's better to break a disc than

00:21:25.024 --
it is to break a vertebrae.

00:21:29.170 --
So they are an interesting

00:21:31.405 --
structure because they. The.

00:21:35.370 --
Connective tissue that they're

00:21:37.098 --
made up of are an annular rings,

00:21:40.230 --
and within each of these rings there's

00:21:43.457 --
a gelatinous substance we heard last.

00:21:45.980 --
Unless lecture people talked about something

00:21:48.746 --
similar to like crab meat consistency.

00:21:51.870 --
And that's basically what they're like.

00:21:54.400 --
They're not a solid thing.

00:21:56.500 --
They're not like a gummy bear,

00:21:59.030 --
though they probably are

00:22:00.938 --
closer to a gummy bear than.

00:22:03.800 --
Then a piece of steak.

00:22:06.030 --
But they are squishing,

00:22:07.726 --
but not like you could squish

00:22:10.350 --
him every different way.

00:22:12.270 --
They are hydrophilic,

00:22:13.728 --
meaning that water is attracted into

00:22:16.644 --
the disk versus going out of it,

00:22:19.410 --
and the whole idea is we want to

00:22:22.874 --
have water flowing into the disks

00:22:25.902 --
to keep the spine mobile and to

00:22:29.636 --
keep the the spinal cord protected.

00:22:32.920 --
And the endplates of the.

00:22:36.750 --
Discs are covered in cartilage, so it

00:22:39.854 --
makes it a very strong stuff structure.

00:22:46.440 --
Interesting enough.

00:22:49.440 --
When you look at those the way the stone

00:22:52.887 --
spine is built and the vertebral discs,

00:22:56.110 --
you can see that generally the

00:22:58.456 --
posterior side or the structured

00:23:00.563 --
towards your back distal from the

00:23:03.317 --
body is compared with medial is less

00:23:06.313 --
strong than the frontal part of it.

00:23:09.132 --
And for whatever reason,

00:23:11.180 --
I think it adds more mobility so

00:23:13.805 --
that you can bend forward better.

00:23:16.690 --
But if you're going to rupture disc,

00:23:18.730 --
more than likely you're going

00:23:20.635 --
to rupture it towards the back.

00:23:22.960 --
So herniated or ruptured

00:23:24.784 --
disc basically are similar.

00:23:26.610 --
The walls, the disk have broken

00:23:30.096 --
down and the fluid bulges out.

00:23:33.820 --
So in this diagram you can see on the

00:23:36.835 --
right side there's a ball in there.

00:23:39.520 --
Basically,

00:23:39.875 --
that's not really a ball,

00:23:41.650 --
it's just demonstrating the way

00:23:43.430 --
that the disk works,

00:23:44.860 --
that the posterior side is weaker

00:23:46.996 --
than the anterior side.

00:23:51.780 --
So the nerves emerge from the spinal

00:23:54.468 --
canal through openings in each

00:23:56.539 --
vertebrae and potential problems of

00:23:58.654 --
nerves become trapped or compressed.

00:24:00.910 --
So I want to show this diagram

00:24:03.066 --
for a couple of reasons.

00:24:04.850 --
We see the spinal nerves,

00:24:06.490 --
how they come out and you'll notice

00:24:08.765 --
how they kind of wrap around the body.

00:24:11.410 --
So on the on the anterior view or

00:24:13.826 --
the front of the body you can see

00:24:16.315 --
again how they kind of wrap around

00:24:18.690 --
the legs and the nerves innervate

00:24:20.880 --
the body and in various locations

00:24:22.890 --
as the physician talked about.

00:24:24.530 --
In that short video that we

00:24:26.498 --
just saw the spine,

00:24:27.810 --
the nerves come out from the vertebrae

00:24:30.309 --
and they branch into much smaller.

00:24:32.640 --
Nerves,

00:24:33.171 --
and then there's secondary nerves

00:24:35.826 --
that are the peripheral nerves that

00:24:39.104 --
interact with these spinal nerves.

00:24:41.790 --
So if a nerve becomes trapped

00:24:44.196 --
because of a compressed disk.

00:24:48.810 --
Then the person feels the pain.

00:24:51.920 --
Sometimes in the whole length of

00:24:54.002 --
the nerve for the nerve innervates.

00:24:56.640 --
So if we see that towards the the lumbar

00:24:59.313 --
part of the body lower part of the body

00:25:01.900 --
can see here this this is the spinal

00:25:04.593 --
column and these nerves that come out.

00:25:07.062 --
If this if the nerve is compressed in

00:25:10.107 --
this location, the person could feel that

00:25:12.670 --
compression all the way down to their toes,

00:25:15.330 --
for instance, or part of their foot.

00:25:19.590 --
If somebody is developing sciatica because

00:25:21.972 --
the sciatic nerve is compressed either from

00:25:24.737 --
the spinal column or from sitting in a chair,

00:25:27.910 --
that's not designed well.

00:25:30.490 --
People develop problems from sitting

00:25:31.905 --
at trucks for a long period of time.

00:25:34.120 --
Truck drivers.

00:25:35.186 --
Then that whole length of that nerve.

00:25:38.920 --
Can become irritated and people wish

00:25:41.416 --
filled out shooting pain all the way down.

00:25:44.310 --
I talked in the first class about my

00:25:47.150 --
problem with compressing nerves in my legs.

00:25:50.110 --
And this is a good diagram that shows if

00:25:53.386 --
I'm have my wallet in my front pocket.

00:25:56.660 --
And I can press that nerve that

00:26:00.132 --
nerve wraps around my leg.

00:26:02.420 --
I fill it in my heel.

00:26:04.420 --
And until you look at a diagram

00:26:06.835 --
like this and realize.

00:26:08.570 --
That depending on where

00:26:10.250 --
the nerve is compressed,

00:26:11.930 --
where you might actually feel the sensation

00:26:15.017 --
of that compression of that nerve.

00:26:17.390 --
Nerves are sensitive.

00:26:18.590 --
Some people's nerves are closer to the

00:26:21.466 --
surface than other peoples, obviously.

00:26:23.789 --
Mine I am sensitive to pressure on

00:26:27.422 --
my nerves in my arms go to sleep.

00:26:30.730 --
Without much pressure on him, for instance.

00:26:34.730 --
And so again,

00:26:35.963 --
you want to protect the spinal column.

00:26:38.840 --
Make sure people are sitting

00:26:40.895 --
in the proper chairs,

00:26:42.540 --
not doing activities that can injure

00:26:45.630 --
the spinal cord or the discs so that we

00:26:49.849 --
we don't have this pain in the future.

00:26:53.320 --
The majority of back pain comes

00:26:56.002 --
from just muscular issues and then

00:26:58.896 --
secondarily it's nerve issues.

00:27:06.030 --
So within the body.

00:27:08.386 --
We have these antagonistic muscle

00:27:11.331 --
pairs so one muscle will contract

00:27:14.521 --
while the other one is relaxed

00:27:17.651 --
and depending on how we move,

00:27:20.820 --
determines whether or not we have a

00:27:24.131 --
a muscle that's that's compressing

00:27:26.922 --
or contracting versus one that's at.

00:27:30.750 --
A relaxed state, so the diagrams

00:27:33.414 --
on this side shows some of this.

00:27:36.410 --
We see the in diagram.

00:27:38.580 --
A healthy muscle is balanced,

00:27:40.760 --
it's normal and either both of them are.

00:27:45.870 --
Not being flexed at that time.

00:27:48.620 --
Sometimes if there's an imbalance,

00:27:50.230 --
the stronger muscle pull to

00:27:52.540 --
one side or another.

00:27:54.390 --
In some cases where people's

00:27:56.550 --
muscles are flexed a lot,

00:27:58.710 --
they develop that pain in their back.

00:28:03.480 --
The 10s machine sometimes is

00:28:05.605 --
used to help relax the muscles.

00:28:08.490 --
They'll give a pulse of electric electrical

00:28:12.564 --
energy so that the back will relax.

00:28:16.420 --
In the abdominal muscles,

00:28:17.720 --
one idea is that to keep your core

00:28:20.475 --
muscles strong because of the spine

00:28:22.695 --
movement as well as back muscles,

00:28:24.870 --
thousands of muscles of rack

00:28:26.570 --
participate in every move you

00:28:28.331 --
make and keeping muscle strong.

00:28:30.150 --
The abdominal muscles and the back muscles.

00:28:33.650 --
An imbalance is a key to help prevent.

00:28:38.360 --
Pain and injury to the back.

00:28:40.450 --
With weak muscles,

00:28:41.428 --
there's little back support and

00:28:43.058 --
when muscles are imbalanced the

00:28:44.609 --
entire spine can be out of balance.

00:28:46.570 --
If we see somebody sitting

00:28:48.735 --
in an awkward posture.

00:28:50.470 --
This is sometimes how people can get to

00:28:53.262 --
where one muscles stronger than another.

00:28:56.170 --
Muscle or muscles are used adequately.

00:28:58.610 --
They'll atrophy,

00:28:59.422 --
meaning they get smaller,

00:29:01.050 --
and then there's more of a

00:29:03.546 --
potential for back injury as well.

00:29:12.080 --
So at the end of the lecture,

00:29:13.410 --
what we're going to do is we're

00:29:15.013 --
going to look at a couple of

00:29:16.709 --
videos we looked at before.

00:29:17.900 --
But when we see something like this,

00:29:20.510 --
you know what are the potential work

00:29:23.856 --
related musculoskeletal disorders?

00:29:25.290 --
So the diagram on the left

00:29:27.654 --
you see a person welding.

00:29:30.060 --
They're bending over at the waist.

00:29:32.900 --
Their head actually is at about a

00:29:35.406 --
90 degree angle with their torso,

00:29:37.800 --
but the torso is bent over

00:29:39.978 --
totally into 90 degree angle.

00:29:41.950 --
I mean the head is at a.

00:29:45.930 --
Correct angle to the torso,

00:29:47.490 --
but the back is bent at a 90 degree angle.

00:29:50.610 --
This is a very unhealthy posture and can put

00:29:53.418 --
a tremendous amount of pressure on the back.

00:29:56.660 --
On the right side we see that this

00:29:59.156 --
dental hygienist or dentist is

00:30:00.876 --
working on this person's teeth.

00:30:02.600 --
They're not only sitting cross.

00:30:05.960 --
Asymmetrically.

00:30:06.446 --
So there are twisted at the trunk.

00:30:09.850 --
His head is twisted and it's also bent.

00:30:13.330 --
When we talk about bio mechanics and

00:30:15.500 --
we get into these couple ergonomic

00:30:17.640 --
tools that are called Rula and Reba,

00:30:20.310 --
we'll talk about what the level of

00:30:23.145 --
stress that's actually putting on the body.

00:30:25.860 --
But in both diagrams,

00:30:27.668 --
the person could experience

00:30:29.476 --
Backcountry overtime on the right side.

00:30:31.610 --
The person could experience

00:30:33.254 --
neck injury on the left side,

00:30:35.720 --
not so much with neck injury because

00:30:38.597 --
the head is is in a relatively

00:30:41.840 --
good posture according to.

00:30:43.770 --
The persons torso.

00:30:48.760 --
Not sure. This little video

00:30:52.412 --
talks about back pain.

00:31:00.170 --
Sometimes I want to pinch myself

00:31:01.796 --
'cause I think I'm dreaming.

00:31:03.420 --
I've just been able to enjoy my life again.

00:31:06.070 --
It's a miracle I'm a miracle.

00:31:20.420 --
I had severe sciatica.

00:31:21.636 --
It was to the point where I couldn't

00:31:24.117 --
even get out of bed in the mornings.

00:31:26.500 --
I couldn't stand very long.

00:31:28.020 --
I couldn't sit very long.

00:31:30.760 --
Thing for a long period of time,

00:31:32.850 --
I mean more than five or 10 minutes

00:31:35.066 --
it had gotten to be that severe.

00:31:37.340 --
How's your pain today?

00:31:38.532 --
Zero pain.

00:31:39.130 --
That sounds very good.

00:31:52.290 --
She also had an unstable

00:31:53.815 --
condition or lumbar spine.

00:31:55.040 --
She had a condition called

00:31:56.830 --
spondylolisthesis where one

00:31:57.904 --
bone is slipped forward on top

00:31:59.829 --
of the other and that tends to

00:32:01.881 --
slowly get worse over the years

00:32:03.435 --
and it can cause a lot of pain.

00:32:05.750 --
It can even cause paralysis.

00:32:18.750 --
Of that operation, however,

00:32:20.042 --
is that in order to treat the problem,

00:32:22.780 --
we have to also cause a fair

00:32:25.076 --
amount of injury and damage

00:32:26.807 --
to the spine to the bones.

00:32:28.830 --
The muscles to the tendons,

00:32:30.510 --
which are all structures that are

00:32:32.484 --
very important in these patients

00:32:34.202 --
when it comes to recovery.

00:32:49.320 --
It's a 3 dimensional GPS system that

00:32:51.308 --
allows us to navigate very accurately

00:32:53.400 --
and very precisely within the spine.

00:32:55.760 --
Even though we're operating through

00:32:57.450 --
very small incisions, we equip the

00:32:59.487 --
tools that we use with little sensor.

00:33:01.860 --
You're operating on the patient,

00:33:03.560 --
but on the screen you see

00:33:05.636 --
exactly where you are.

00:33:07.020 --
Within the Spine 5 and then 14 millimeters

00:33:09.564 --
we're really at the forefront of

00:33:11.881 --
minimally invasive spinal surgery

00:33:13.501 --
patients benefit from this because

00:33:15.358 --
they recover now much faster from

00:33:17.332 --
these operations then they would have.

00:33:19.450 --
Maybe not a few years ago when I woke

00:33:22.186 --
up five hours after the surgery,

00:33:24.770 --
I had no more sciatica pain is scared.

00:33:28.290 --
'cause I haven't been paying

00:33:30.110 --
free for over a decade.

00:33:31.930 --
Yeah, life is real good.

00:33:33.750 --
It's extremely good.

00:33:34.842 --
You know.

00:33:35.570 --
I'm blessed.

00:33:45.120 --
So grateful for this new technology

00:33:46.962 --
that the Doctor performed on man,

00:33:48.600 --
you know I got my life back and there's not

00:33:51.941 --
enough time in hours in the day. For me,

00:33:54.912 --
'cause there's so much I want to do now.

00:34:20.230 --
So there's been quite a few advertisements.

00:34:22.620 --
It's usually around Christmas for teeters.

00:34:24.660 --
Hang up, teeter hang ups,

00:34:26.370 --
which basically you lock your feet in and

00:34:29.090 --
then you lean back and get to posture.

00:34:31.820 --
That feels comfortable for a person.

00:34:33.870 --
And that idea is the same thing.

00:34:36.260 --
It decompresses the spine,

00:34:37.624 --
takes the pressure off the nerves,

00:34:39.670 --
and people experience less back pain.

00:34:41.710 --
OK, so a couple of issues with

00:34:44.069 --
that before anybody ever uses

00:34:45.825 --
one of those types of devices,

00:34:47.850 --
they need to consult with their physician.

00:34:50.700 --
Because if you think about it,

00:34:53.570 --
you're upside down the pressure

00:34:56.610 --
and your pressure in your.

00:34:59.650 --
Brain increases because you're

00:35:00.958 --
in that inverted posture,

00:35:02.270 --
so you need to be checked out before

00:35:05.454 --
anybody uses it to make sure that

00:35:08.285 --
they're not a candidate for a stroke.

00:35:11.050 --
So no problems are commonly associated

00:35:13.024 --
with prolonged exposure to static postures,

00:35:15.210 --
typically as a consequence of

00:35:16.945 --
visual requirements of a task.

00:35:18.680 --
So we saw the dental hygienist,

00:35:20.770 --
and that one diagram a couple minutes ago,

00:35:23.540 --
and that person is at a higher.

00:35:26.980 --
Potential for.

00:35:29.494 --
Neck injuries and there is evidence

00:35:33.210 --
of flexion beyond 30 degrees.

00:35:36.780 --
Leads to more rapid onset of fatigue.

00:35:39.970 --
So if you're sitting in a posture again,

00:35:42.700 --
your natural posture for your neck is

00:35:44.702 --
about a three degree inclination forward.

00:35:47.130 --
If you're at a 30 degree inclination forward,

00:35:49.860 --
the idea is it puts pressure on the

00:35:52.612 --
nerves and blood vessels of the neck and

00:35:55.945 --
can increase your potential for fatigue.

00:35:58.630 --
People who use microscopes

00:36:00.498 --
for long periods of time,

00:36:02.840 --
like pathologists do experience potential

00:36:05.430 --
problems with fatigue and also the

00:36:08.496 --
potential for disc problems in the neck.

00:36:13.420 --
So disc generation.

00:36:15.121 --
Can happen and an older individuals

00:36:18.523 --
as well as younger individuals.

00:36:21.930 --
So we see here on this diagram

00:36:24.002 --
and this is pretty exaggerated.

00:36:26.300 --
On the left side we see a normal disc.

00:36:29.570 --
It's equal, it's not bulging out,

00:36:31.760 --
so it's not putting excess

00:36:33.580 --
pressure on the spinal cord.

00:36:37.520 --
The next diagram down is a herniated

00:36:40.586 --
disk and this is on the left side

00:36:43.786 --
and you can see where the walls.

00:36:46.550 --
Of the disc are starting to breakdown

00:36:49.154 --
and you see a bulging out and

00:36:51.988 --
putting pressure on the spinal cord.

00:36:54.450 --
So minor pressure is not a big

00:36:56.963 --
deal as it gets worse and worse.

00:36:59.970 --
It puts more pressure on and people

00:37:03.358 --
experience a higher degree of pain or

00:37:06.415 --
start to fill lack of use of a limb.

00:37:09.660 --
Or both legs, for instance,

00:37:11.530 --
both arms dependent on where

00:37:14.480 --
the disc is herniated.

00:37:16.840 --
A bulging disc is a little bit

00:37:19.073 --
different than a herniated disc.

00:37:21.120 --
It's the same idea.

00:37:22.488 --
Only in this case it's much worse,

00:37:25.050 --
and in this case the annulus outer layer

00:37:28.498 --
of the disc bulges into the spinal cord.

00:37:32.490 --
And then we have thinning discs and

00:37:35.535 --
this is on the right side as the disc

00:37:39.484 --
thins out that the spinal cord tends to.

00:37:43.270 --
Spinal column tends to compress more,

00:37:45.250 --
putting more pressure on those nerves that

00:37:47.966 --
are coming out of the various openings.

00:37:50.840 --
And then finally we have discussed

00:37:52.856 --
the generation and it's something

00:37:54.680 --
similar to osteoporosis where calcium

00:37:56.765 --
and phosphate or leaving the bone

00:37:59.079 --
making it much weaker and the bone

00:38:01.109 --
starts to get smaller and smaller.

00:38:03.160 --
So when you see somebody an older

00:38:05.575 --
person that maybe you haven't seen

00:38:07.715 --
for three or four years and before

00:38:10.200 --
they were your height and now you're

00:38:12.664 --
4 inches taller and taller than them.

00:38:15.128 --
But two things could have happened.

00:38:17.240 --
Either you grew or the disks in this

00:38:20.320 --
person's back. Hands for table.

00:38:24.660 --
Vertebrae have started to degrade

00:38:26.760 --
and the person is actually getting

00:38:29.513 --
shorter overtime.

00:38:33.670 --
So here's a diagram. An X ray of

00:38:36.158 --
a herniated disk on the left side.

00:38:38.410 --
You can see where it's actually bulging

00:38:40.629 --
out and pressing on the spinal column.

00:38:45.040 --
And you can see.

00:38:46.208 --
So this is on the right side.

00:38:48.400 --
Is the posterior view and the

00:38:50.056 --
left side is the anterior view.

00:38:52.060 --
You can also see at the

00:38:54.778 --
bottom of the Lombard.

00:38:56.590 --
Vertebrae these are the lumbar

00:38:58.415 --
vertebrae right here, and these.

00:39:00.560 --
This is the sacrum.

00:39:02.660 --
How that curve is and you

00:39:04.436 --
can see here at the bottom.

00:39:06.490 --
This disk also appears to

00:39:08.080 --
start to have problems,

00:39:09.360 --
and usually if you have problems

00:39:11.154 --
in one disc it can lead to

00:39:13.432 --
problems and other disks.

00:39:17.960 --
So on the right side.

00:39:20.260 --
You see a ruptured disc.

00:39:21.970 --
This is what the actual

00:39:23.670 --
disc material looks like.

00:39:25.030 --
As they said in the one deal

00:39:27.354 --
about looking like crab meat.

00:39:29.130 --
That's kind of what it looks like.

00:39:32.830 --
They see the tear through the.

00:39:35.330 --
The cartilage area.

00:39:39.440 --
And the concentric rings of

00:39:41.010 --
the disk material itself.

00:39:42.270 --
And if you look closely,

00:39:43.840 --
you can see a tear in this area

00:39:45.992 --
that tare allows the fluid to flow

00:39:48.210 --
through from one area to another area.

00:39:50.740 --
Generally again it's hydrophilic,

00:39:52.000 --
meaning it's water loving.

00:39:53.260 --
But still,

00:39:53.886 --
when you start to break those rings,

00:39:56.080 --
it starts to release fluid out and

00:39:58.250 --
this is where the disk and bulge.

00:40:00.480 --
I don't think in this particular

00:40:02.208 --
case this person is going to notice

00:40:04.433 --
because obviously it's a cadaver,

00:40:06.130 --
but that's beside the point.

00:40:11.050 --
So we're going to show this video.

00:40:13.140 --
I don't think I keyed it up. Oh, here it is.

00:40:22.130 --
Hi there, I'm doctor Gary Simmons

00:40:24.260 --
of Curling Clinic neurosurgery and

00:40:25.969 --
I'm going to talk to you a little

00:40:27.785 --
bit about lumbar disc surgery.

00:40:29.520 --
You may remember from previous

00:40:32.800 --
discussions that there are times

00:40:36.189 --
where a cushion or lumbar disc.

00:40:39.420 --
Has problems.

00:40:40.410 --
The disc is tough on the outside,

00:40:43.880 --
squishy on the inside.

00:40:45.308 --
The inside looks like crab meat

00:40:47.522 --
and sometimes a chunk of crabmeat

00:40:49.508 --
will rip out and push backwards and

00:40:51.953 --
to the side exactly where nerve is

00:40:54.410 --
trying to get out of your spine,

00:40:56.860 --
and when it pushes up against the

00:40:59.212 --
nerve the nerve gets irritable and

00:41:01.377 --
you may feel pain, numbness, tingling,

00:41:03.542 --
have some weakness all the way down your leg.

00:41:06.690 --
Usually it's just one leg,

00:41:08.450 --
but it can be miserable now.

00:41:10.550 --
Luckily most get better.

00:41:12.154 --
All by themselves,

00:41:13.360 --
but sometimes they don't,

00:41:15.092 --
and when they don't,

00:41:16.830 --
and that nerve is continuously

00:41:19.005 --
being pushed on,

00:41:20.310 --
it can be absolutely miserable and people

00:41:23.621 --
can be totally laid up by the pain.

00:41:26.820 --
And if the pain doesn't go away,

00:41:29.850 --
we sometimes will resort to surgery.

00:41:32.460 --
Now sometimes we can get by with

00:41:35.071 --
shots in the back where a numbing

00:41:38.274 --
medicine is used initially.

00:41:40.270 --
But really,

00:41:41.190 --
a steroid medicine is put on the nerve.

00:41:44.870 --
Now, this isn't an athlete steroid.

00:41:46.830 --
This is an anti inflammatory steroid

00:41:48.810 --
and the idea is to calm the nerves down.

00:41:51.720 --
But it doesn't do anything for the

00:41:53.925 --
crab meat that's sitting there on the nerve.

00:41:56.610 --
So if the nerve wants to stay

00:41:58.647 --
irritable it will stay irritable.

00:42:00.520 --
So sometimes we have to resort

00:42:02.398 --
to literally going in there and

00:42:04.396 --
removing the disk,

00:42:05.410 --
removing the crab meat that's

00:42:07.035 --
pushing on the nerve.

00:42:08.340 --
Now one of the misconceptions is

00:42:10.080 --
that we take the entire discount.

00:42:12.250 --
That's not the case at all really.

00:42:14.540 --
What we're going after.

00:42:16.040 --
Is that chunk of crab meat that

00:42:18.788 --
ripped out created out?

00:42:20.470 --
Herniated discs slip.

00:42:21.469 --
This ruptured disc.

00:42:22.470 --
They all mean the same thing.

00:42:24.470 --
In fact, we've got another name,

00:42:26.460 --
herniated nucleus pulposus

00:42:27.795 --
all mean the same thing.

00:42:30.020 --
We go in there surgically and

00:42:32.786 --
sometimes take the chunk off the nerve.

00:42:35.920 --
The way we do it is usually through

00:42:38.464 --
a small incision in the back.

00:42:40.740 --
This can be done through little

00:42:42.804 --
tubes with TV scopes,

00:42:44.180 --
or could be done with a microscope,

00:42:46.580 --
but usually it's a relatively small incision.

00:42:48.990 --
There are gaps between the vertebrae

00:42:51.096 --
here and we sneak in through the gap.

00:42:53.810 --
Sometimes we make the gap a little larger,

00:42:56.560 --
but we sneak in through the gap.

00:42:58.970 --
Find the nerve that's being pinched.

00:43:01.030 --
Find the crab meat that's pinching it,

00:43:03.440 --
grab the crab meat and we throw it away.

00:43:06.650 --
Literally throw it away.

00:43:08.498 --
We give it to the pathologists,

00:43:11.270 --
the.

00:43:12.810 --
All for all intents and purposes,

00:43:15.320 --
that surgery is now done.

00:43:18.910 --
Our goal is to get that nerve

00:43:21.024 --
swinging in the breeze.

00:43:22.470 --
Have nothing pushing on it.

00:43:24.090 --
I can't fix the nerve.

00:43:25.710 --
I can't make the nerve feel better

00:43:27.992 --
I can't make it less irritated

00:43:29.898 --
but I can get it out of

00:43:31.964 --
trouble. I can get the pressure off

00:43:34.518 --
of it and if I get the pressure off

00:43:37.452 --
of it 9 * 99 times out of 1095 times

00:43:40.296 --
at 100 it will feel much much better

00:43:42.927 --
off and it feels better instantly.

00:43:45.150 --
Patients can be wheeled out of the

00:43:47.285 --
operating room where they're going.

00:43:49.040 --
Oh my goodness, my leg is better already.

00:43:52.120 --
But it doesn't always happen that quick.

00:43:54.440 --
Sometimes it can take weeks for the nerve

00:43:57.032 --
to settle down while we're in there,

00:43:59.400 --
we usually will go into the disc itself

00:44:01.656 --
and try to grab any other loose pieces

00:44:04.152 --
so that another piece doesn't just

00:44:06.282 --
immediately follow the first piece,

00:44:08.340 --
but we don't take the whole disk out.

00:44:10.990 --
That's a misnomer,

00:44:11.980 --
is not what happens.

00:44:13.300 --
We don't take the whole disk app we leave,

00:44:16.280 --
we put everything back together and we leave

00:44:19.192 --
just trying to keep that nerve nice and calm.

00:44:22.140 --
But it often feels better

00:44:24.380 --
real quick afterwards.

00:44:25.730 --
Can you re herniated disc?

00:44:27.360 --
Can you have another chunk

00:44:28.985 --
of crabmeat come out?

00:44:30.290 --
Unfortunately yes,

00:44:30.942 --
10 to 15% of people who have had one

00:44:34.002 --
herniated disc will go on and do it again,

00:44:36.810 --
either at the same place or there

00:44:39.092 --
slightly more prone to having it occur

00:44:41.408 --
somewhere else in the lower back.

00:44:43.330 --
So it's not a cure all.

00:44:45.290 --
But boy,

00:44:45.890 --
if you're in that desperate shape where

00:44:47.990 --
it's been going on for weeks and weeks

00:44:50.214 --
and weeks and you're feeling absolutely

00:44:52.328 --
miserable and nothing is helping,

00:44:54.420 --
it really can feel like a miracle within.

00:44:57.250 --
Within often a matter of hours or

00:44:59.574 --
days if it's not getting better.

00:45:02.020 --
If that nerve decides not to settle down,

00:45:04.960 --
well, there's other tricks up our sleeves,

00:45:07.530 --
but the majority of the time getting

00:45:10.064 --
that hunk of crabmeat out of there and

00:45:13.042 --
off the nerve will make you feel much,

00:45:15.970 --
much better.

00:45:16.656 --
Why don't we do it the first day

00:45:19.477 --
that you have a herniated disc?

00:45:21.840 --
Because 80 plus percent of people

00:45:24.102 --
who have a herniated disc will

00:45:26.400 --
feel better within a few weeks.

00:45:28.550 --
So you can be saved from having to

00:45:31.262 --
have surgery if you just take it

00:45:33.676 --
easy and let things settle down,

00:45:35.770 --
but when it's not selling down,

00:45:37.840 --
it really is a wonderful operation in

00:45:40.171 --
that it helps a lot of people will

00:45:42.742 --
talk about other types of operations

00:45:44.718 --
in the spine in future sessions.

00:45:47.130 --
Bye bye now.

00:46:10.790 --
So if you want to watch the rest of

00:46:13.814 --
the series, it's pretty interesting

00:46:15.899 --
this guys are a good speaker and does

00:46:18.834 --
a good job about explaining these

00:46:21.180 --
various operations that they do.

00:46:22.930 --
Obviously we saw two videos today and you

00:46:26.386 --
could see how how well he explained things.

00:46:30.130 --
So there are other types of injuries,

00:46:33.160 --
and some of these you may have

00:46:36.044 --
experienced if you go into the workplace.

00:46:39.220 --
Many times you'll see these injuries

00:46:41.848 --
or these conditions of the spine.

00:46:44.420 --
Sometimes they're not injuries,

00:46:46.148 --
but they're just how people have

00:46:48.814 --
how their spines are basically,

00:46:50.910 --
so ideally we see that we have

00:46:54.529 --
our person on the left.

00:46:57.260 --
Who has his ears over shoulders,

00:46:59.260 --
shoulders over his hips,

00:47:00.588 --
hips over his knees,

00:47:01.920 --
knees over his ankles,

00:47:03.852 --
and the neutral posture?

00:47:05.790 --
The person that's diagram to the right of

00:47:09.334 --
him or her more likely him in this case.

00:47:13.360 --
You see that he's got extreme lordosis.

00:47:17.310 --
Meaning the upper part of the

00:47:19.842 --
spine is protruding out.

00:47:23.640 --
When we get into biomechanics two

00:47:25.578 --
and a couple of photos that I have,

00:47:28.200 --
this one person you can see has a

00:47:32.120 --
pronounced lordosis. Basically.

00:47:37.870 --
From working or kyphosis from working,

00:47:40.380 --
doing these laundry tasks

00:47:42.932 --
over a period of time.

00:47:46.130 --
So and somebody can experience a

00:47:48.446 --
couple of these conditions together,

00:47:50.650 --
kyphosis and lordosis and also

00:47:52.705 --
scoliosis at the same point.

00:47:57.620 --
If you've ever seen the movie Molly's game.

00:48:01.730 --
It talks about the star of the show,

00:48:04.170 --
so to speak, or what the story centers

00:48:07.018 --
around the person it centers around.

00:48:09.630 --
But she grew up and all the

00:48:11.933 --
sudden she developed scoliosis.

00:48:13.680 --
Severe case of scoliosis for spying

00:48:15.780 --
twisted and she had to undergo

00:48:18.007 --
surgery to straighten your spine out.

00:48:20.300 --
Scoliosis is is,

00:48:21.401 --
I don't wanna say real common,

00:48:23.610 --
but it is relatively common.

00:48:25.450 --
And when somebody experiences at a young age,

00:48:28.400 --
what they normally do is put

00:48:30.320 --
the person in a back brace to

00:48:32.928 --
help the spine straightened out.

00:48:35.020 --
In very severe cases,

00:48:36.652 --
they do have to do operations.

00:48:39.100 --
And they have to pin the spine so

00:48:42.228 --
that it is more straight in nature.

00:48:45.690 --
And you see,

00:48:46.761 --
water kyphosis is for this

00:48:48.546 --
bulges out at the top,

00:48:50.120 --
a lordosis where the lumbar area bulges in

00:48:53.168 --
and then scoliosis for the spine is crooked.

00:48:56.630 --
So with the ideal posture,

00:48:58.350 --
the forces are evenly distributed

00:49:00.080 --
through the body and all the joints are

00:49:02.818 --
in their neutral zone and this results

00:49:05.091 --
in minimal wear and good muscle and

00:49:07.590 --
stable stabilizer muscle recruitment.

00:49:09.150 --
When they talk about the fact that.

00:49:12.510 --
Oh you know, just.

00:49:15.852 --
When you're growing up and they

00:49:17.676 --
say you know have a good posture,

00:49:19.780 --
keep your head up.

00:49:20.888 --
Keep your shoulders back.

00:49:22.000 --
That helps put you in that neutral posture

00:49:24.296 --
and helps prevent some of these conditions.

00:49:26.760 --
Poor posture,

00:49:27.402 --
the joints are out of alignment,

00:49:29.330 --
their type,

00:49:30.320 --
the muscles are shortened or weak.

00:49:33.290 --
Jason muscles are weak and important.

00:49:36.010 --
Stabilizers are inefficient.

00:49:42.450 --
So we do have disk congenic and neurological

00:49:45.418 --
types for conditions where the disc

00:49:48.338 --
prolapses there's nerve irritation,

00:49:50.440 --
nerve entrapment.

00:49:52.360 --
We have muscular ligament and tendon

00:49:54.952 --
problems which are caused by trauma,

00:49:57.450 --
strain, sprain and tear.

00:49:59.186 --
And then we have muscle weaknesses

00:50:01.867 --
which cause imbalances.

00:50:03.560 --
And then we have structural

00:50:05.970 --
and genetic type problems.

00:50:07.900 --
Real common and thank God knock knock.

00:50:11.100 --
I don't experience this,

00:50:12.852 --
but my family has a history of stenosis,

00:50:16.580 --
meaning and narrowing of the.

00:50:20.470 --
Vertebral vertebrae,

00:50:21.326 --
where the spine goes through,

00:50:23.470 --
and this put can put pressure

00:50:26.416 --
on the spinal column.

00:50:28.380 --
There's cartilage damage,

00:50:30.063 --
bone where osteoarthritis and osteoporosis.

00:50:36.420 --
So why do people get back pain or

00:50:38.748 --
New Years starting up a new activity?

00:50:41.240 --
If you've never shoveled dirt before

00:50:43.262 --
and today you're out shoveling dirt or

00:50:45.518 --
like what we've had to do this winter,

00:50:47.980 --
is shovel a lot of snow,

00:50:49.900 --
and this is the first time you do it.

00:50:52.790 --
People can experience back pain.

00:50:55.070 --
There's misuse cumulative effect of bad

00:50:57.494 --
body use over a long period of time.

00:51:00.660 --
So poor postural alignment or

00:51:02.545 --
pushing their body too far too often?

00:51:05.170 --
There's overuse repetitive use of one

00:51:07.276 --
group of muscles causing an imbalance,

00:51:09.480 --
and then diseuse lack of exercise

00:51:11.484 --
may cause a back problem,

00:51:13.430 --
but one can result when we attempt an

00:51:16.158 --
activity requiring a certain degree

00:51:18.023 --
of strength or fact flexibility.

00:51:19.890 --
So if you don't do something for a

00:51:22.530 --
long period of time and then you try

00:51:25.245 --
doing it with without proper training,

00:51:27.790 --
so to speak, to get into the shape,

00:51:30.660 --
to do that activity, you can cause an injury.

00:51:36.150 --
So again, I've shown this picture before.

00:51:39.010 --
This is hardware and a colleague

00:51:41.428 --
of mine's husband's spine

00:51:43.113 --
that keeps his back together.

00:51:45.130 --
You can see in this X ray how

00:51:47.730 --
those two vertebrae aren't

00:51:49.466 --
really lined up as well either,

00:51:52.470 --
but without this he would have tremendous

00:51:55.333 --
pain with this hardware in his back.

00:51:58.180 --
What he does is he lacks flexibility.

00:52:02.740 --
But you can do stuff.

00:52:06.240 --
So from an economic perspective,

00:52:08.360 --
what can we do? We can rest.

00:52:11.330 --
We can change the risk factors.

00:52:13.870 --
We can get physical therapy.

00:52:15.990 --
We can do hold your holistic,

00:52:18.540 --
natural path type things.

00:52:22.020 --
If we have pain,

00:52:23.228 --
we can use over the counter

00:52:25.115 --
medication or prescribed medications.

00:52:27.660 --
One of the things that many

00:52:29.148 --
physicians talk about now and again.

00:52:30.660 --
I'm not a physician.

00:52:32.464 --
But again, using topical type pain relief

00:52:36.220 --
rather than consuming Mot ran or Tylenol,

00:52:40.220 --
but putting on like asper

00:52:43.075 --
cream or Salon pass patch.

00:52:45.930 --
One of those things that are

00:52:49.842 --
a topical type pain reliever.

00:52:53.810 --
Steroidal injections basically what

00:52:56.062 --
they do is they reduce inflammation.

00:52:59.440 --
Of course they have to be done by

00:53:02.496 --
a physician cauterizing nerves.

00:53:04.960 --
So when you cauterize the nerve,

00:53:06.330 --
what do you do?

00:53:08.480 --
You basically are killing the nerve.

00:53:10.980 --
But in some cases.

00:53:12.920 --
If there is an irritated

00:53:15.345 --
nerve that can't be called,

00:53:18.020 --
they will cauterize it to prevent it

00:53:22.521 --
from rapidly firing or firing at.

00:53:26.060 --
Overtime.

00:53:27.740 --
And then disc fusion or disc replacement.

00:53:29.930 --
And really it's not disc replacement.

00:53:31.810 --
They are getting to the point

00:53:33.688 --
of replacing disks.

00:53:34.630 --
You can look it up and you can

00:53:36.654 --
see the material they use diagrams

00:53:38.611 --
on the right here in this slide

00:53:41.083 --
shows some of those things that

00:53:43.039 --
are used as disc replacements.

00:53:44.908 --
Again,

00:53:45.352 --
this is really radical surgery

00:53:47.572 --
and rather risky,

00:53:48.930 --
but in cases where a person

00:53:51.150 --
is in constant pain,

00:53:52.630 --
it may be what is required

00:53:55.132 --
to help alleviate that pain.

00:53:57.320 --
And then from an ergonomic perspective,

00:53:59.350 --
that's why we're here.

00:54:00.710 --
Prevention is the best solution.

00:54:02.410 --
Not getting to the point of pain.

00:54:07.630 --
So this video and I'm not

00:54:09.322 --
going to show it here.

00:54:10.860 --
Because it's quite long and

00:54:12.440 --
also it's more like goes over

00:54:14.562 --
preventing various types of work

00:54:16.957 --
related musculoskeletal diseases,

00:54:18.400 --
music, orgonomic solutions,

00:54:19.591 --
but wanted to provide it.

00:54:21.580 --
Here is a link that you can

00:54:23.932 --
watch at your own convenience,

00:54:26.340 --
again on the GBU learn website.

00:54:28.730 --
All these video links will be

00:54:31.526 --
there along with the original

00:54:34.063 --
videos that I'll be showing.

00:54:36.940 --
So what I want to do?

00:54:40.710 --
Just go back to some of these videos

00:54:42.494 --
that we've watched in the past.

00:54:55.880 --
And have you think about what

00:54:58.118 --
types of injuries somebody could

00:55:00.120 --
develop from doing this activity?

00:55:02.290 --
Some of these you haven't seen before.

00:55:05.150 --
Show these first.

00:55:06.452 --
No, I had some students several

00:55:09.056 --
years ago and do a project at a

00:55:12.007 --
lamb Weston potato processing

00:55:13.736 --
facility in American Falls.

00:55:16.140 --
And some of these videos

00:55:17.785 --
we took when we were there,

00:55:19.950 --
and it's a potato processor in handling.

00:55:24.190 --
This first one.

00:55:35.240 --
Is a logging operation.

00:55:36.768 --
You can tell that it's loud also.

00:55:39.510 --
But when their one machine breaks down,

00:55:41.690 --
they have to stack boxes manually.

00:55:45.110 --
I'd like you to watch it and

00:55:46.601 --
just think about the types of

00:55:48.140 --
injuries this person could develop.

01:00:03.570 --
So I went back a couple of steps.

01:00:07.670 --
And this is a good place to

01:00:09.336 --
stop for a couple of minutes.

01:00:11.240 --
So you can see that he's picking

01:00:13.102 --
the boxes off a conveyor line.

01:00:14.890 --
You can see that how he's twisted.

01:00:17.720 --
His back is twisted.

01:00:18.884 --
He's got 1 foot planted.

01:00:20.340 --
He's got the other foot

01:00:22.390 --
slightly off the floor.

01:00:24.030 --
He's reaching for the box.

01:00:25.610 --
This is a posture he always uses to take the

01:00:29.372 --
boxes off the conveyor belt to stack him.

01:00:32.800 --
So of course, when he's on the 1st

01:00:34.936 --
tear down at the bottom of the pallet,

01:00:37.230 --
he asked to lower the box down.

01:00:39.790 --
When he's at the top of the pallet,

01:00:41.650 --
he has to raise the box all the way up.

01:00:44.730 --
So if you think about this posture and

01:00:46.794 --
the other postures that he develops

01:00:48.592 --
during the course of doing this task,

01:00:50.760 --
what types of entries could he

01:00:52.938 --
experience in the long run?

01:00:54.740 --
So you can see that at the end of

01:00:56.900 --
the time that he's left in his boxes,

01:00:59.360 --
so move forward just a little bit.

01:01:11.440 --
So watch here and see how fatigued he is

01:01:15.067 --
lifting this last box up to that top tier.

01:01:26.200 --
So just standing there you can see

01:01:29.007 --
that he's getting very fatigued.

01:01:31.370 --
That he's tired of moving these boxes

01:01:33.477 --
now I don't remember exactly weight,

01:01:35.930 --
but I think it's either 40 pounds,

01:01:38.390 --
35 pounds, forty pounds,

01:01:39.794 --
something like that.

01:01:40.850 --
It's not like a box of

01:01:43.292 --
potatoes that weighs £50.

01:01:44.920 --
But you can see the this posture that he has.

01:01:49.060 --
He's always twisting the same way.

01:01:51.500 --
You could develop the differential

01:01:53.885 --
muscle strength in his back.

01:01:56.270 --
With the muscles aren't pulling evenly

01:01:58.808 --
and he could develop a problem like

01:02:01.628 --
that doing this task all day long.

01:02:04.090 --
And again they this is.

01:02:06.050 --
This task is required when the stacking

01:02:09.291 --
machine breaks down the automatic stacker

01:02:12.112 --
so he has to stack things manually.

01:02:15.250 --
But it in this particular facility,

01:02:17.130 --
even though they had two of

01:02:19.386 --
these stacking machines.

01:02:20.520 --
They were breaking down quite frequently,

01:02:22.650 --
so one of the things we're looking

01:02:24.960 --
at is not only the ergonomics of it,

01:02:27.980 --
but also you know what was the

01:02:30.024 --
economical tradeoff of purchasing

01:02:31.459 --
another stacking machine,

01:02:32.950 --
or trying to find one that's more reliable.

01:02:37.280 --
OK.

01:02:47.310 --
This is not stocking

01:02:49.294 --
machine I'm talking about.

01:02:51.280 --
The two stocking machines.

01:02:53.920 --
So when they're working, they work great.

01:02:55.970 --
When they don't work,

01:02:57.782 --
they have to stack the boxes by hand.

01:03:01.320 --
So like I said, there's two of am.

01:03:03.110 --
You see the one on the left.

01:03:04.680 --
There's also one on the right

01:03:06.060 --
that's kind of out of you.

01:03:10.290 --
But they automatically palletized the boxes.

01:03:12.630 --
They stack a man.

01:03:14.242 --
Then they put shrink wrap or stretch

01:03:17.294 --
plastic around the outside of the pallet.

01:03:21.060 --
First four, then using a forklift

01:03:23.088 --
and then for putting in the back

01:03:25.428 --
of a truck so manually stacking.

01:03:27.270 --
They can't put the same number

01:03:29.094 --
of boxes on a pallet that they

01:03:31.415 --
can with a stack of machine.

01:04:30.810 --
And the third video is kind of interesting.

01:04:37.070 --
So these are £500 totes.

01:04:41.290 --
So when the one packaging

01:04:44.990 --
machine breaks down.

01:04:47.210 --
They would have to put the French fries

01:04:50.050 --
or tater tots in these 500 pound toes.

01:04:52.990 --
And so again, we were looking at.

01:04:56.730 --
What are the efficiencies or what's the

01:04:59.817 --
cost trade off on putting in another

01:05:03.287 --
packaging line versus storing these

01:05:05.862 --
spuds in in these 500 pound totes?

01:05:08.750 --
So what happens with these 500 pound toads

01:05:11.342 --
is they are stacked up on top of each other.

01:05:14.400 --
You know, they're fairly rigid boxes.

01:05:17.450 --
And they actually the stuff inside

01:05:20.534 --
the product inside helps provide

01:05:23.321 --
structural stability as well.

01:05:25.900 --
But they lose about 10% of the French

01:05:30.418 --
fries when they use these 500 pound totes.

01:05:35.870 --
So also when you see the person doing it,

01:05:38.530 --
the motions that they have to

01:05:40.324 --
have while they're putting the.

01:05:44.030 --
Product into those 500 pound toads.

01:05:53.390 --
Then once they get the toe down,

01:05:55.670 --
when they start to fill the packaging again,

01:05:58.270 --
there's some activities that they

01:06:00.685 --
have to do for that as well.

01:06:03.930 --
It's one of those things whether it's

01:06:06.359 --
a cost tradeoff to lose in a £500 to

01:06:08.999 --
losing 10% of the product which is.

01:06:11.700 --
£50 of French fries that

01:06:14.490 --
are ground to a pulp.

01:06:17.280 --
Or do they get another packaging

01:06:19.134 --
line which is several $100,000?

01:06:20.950 --
So that's another one of

01:06:22.620 --
those things we looked at.

01:06:24.290 --
And of course you see the worker here

01:06:27.410 --
wondering why in the world we're videotaping.

01:06:30.650 --
But we're we're doing that look

01:06:32.696 --
at efficiency of the operation.

01:06:38.900 --
So there is a lot of operations

01:06:41.112 --
associated with this.

01:06:42.060 --
It's not real simple. Again,

01:06:45.095 --
once the tow gets to certain level,

01:06:47.790 --
they've gotta move the product

01:06:50.130 --
around inside there manually.

01:06:52.010 --
So that the product is evenly spaced

01:06:55.167 --
and doesn't collapse the box when

01:06:57.738 --
it's stacked up on each other.

01:07:57.730 --
So we're going to go back and watch

01:08:00.074 --
the life raft one again and then

01:08:02.371 --
it'll be time to complete this.

01:08:04.410 --
But think about this operation.

01:08:06.270 --
Now that you know more about work

01:08:08.965 --
related musculoskeletal diseases and

01:08:10.506 --
think about the types of injuries

01:08:12.432 --
that these people could experience.

01:11:14.040 --
So if this were alive class we talked

01:11:17.088 --
about this as a goat, do this task.

01:11:19.813 --
But just think of this stress again.

01:11:22.340 --
What they're putting on their

01:11:23.920 --
bodies and the type of injuries

01:11:26.006 --
that they could experience.

01:11:27.760 --
'cause these aren't little

01:11:29.076 --
forces that they're using to to

01:11:31.108 --
put these clamshells together.

01:11:32.810 --
They're using a lot of force to

01:11:35.323 --
try to get that thing compressed.

01:11:38.370 --
And where it's not crimping the.

01:11:42.010 --
The raft inside.

01:13:52.170 --
So also think about what other tools they

01:13:54.874 --
might use to if this task weren't changed,

01:13:57.740 --
which we know that it was changed.

01:14:00.170 --
The pods are bigger now and

01:14:02.606 --
the equipment is different.

01:14:04.230 --
But think about the tools that

01:14:06.120 --
would help this. Then do this job.

01:14:09.570 --
Better than like a rubber mallet

01:14:12.120 --
and a handle that they push in.

01:14:15.020 --
5 minutes. Pushing for the raft.

01:16:01.150 --
So that's it today.

01:16:06.520 --
We'll talk a little bit about injuries,

01:16:08.760 --
the next lecture, and then

01:16:10.950 --
started in biomechanics. Thanks.