University of Idaho - I Banner
A student works at a computer

VandalStar

U of I's web-based retention and advising tool provides an efficient way to guide and support students on their road to graduation. Login to VandalStar.

Contact Us

Janssen Engineering Building Rooms 31 and 37

Mailing Address:

Engineering Outreach
University of Idaho
875 Perimeter Drive MS 1014
Moscow, ID 83844-1014

Phone: 208-885-6373

Fax: 208-885-6165

Email: eo-support@uidaho.edu

Web: eo.uidaho.edu

Demo a Course Session

The sessions below are from actual Engineering Outreach (EO) delivered courses, recorded in studio classrooms at the University of Idaho. If you register for a course, you will have access to all the course sessions online in the EO Portal. For future reference, learn more about the different viewing options.

CE 441: Reinforced Concrete Design

CS 420/520: Data Communication Systems

ECE 525: Power System Protection and Relaying

EM 510: Engineering Management Fundamentals

MATH 310: Ordinary Differential Equations

ME 412: Gas Dynamics

STAT 422: Sample Survey Methods

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:"00:47:49.8050000"



00:00:24.990 -- Hi welcome everybody to our 27th class. I guess I'm not even sure

00:00:28.916 -- if we're In Sync on the web.

00:00:33.100 -- So.

00:00:34.900 -- We second here less than we just about finished up the

00:00:41.467 -- wireless network section, except we didn't quite.

00:00:46.770 -- We didn't. We kind of hated for the last couple of slides and I

00:00:50.998 -- would like to just catch up there where we left off last

00:00:54.622 -- time hoops with the last slide. So in our in our hierarchy here.

00:00:59.970 -- Well.

00:01:02.180 -- Here.

00:01:03.740 -- So where we're sitting there at 802 eleven, which was a MIMO

00:01:09.656 -- MIMO scenario and.

00:01:12.140 -- In if you have now this, this capability can use different

00:01:17.520 -- type of strategies. You might use actually know aggregation

00:01:21.102 -- and remember aggregation means putting together or we can have

00:01:25.082 -- where we basically put a bunch of frames and we put a common

00:01:30.256 -- header in there.

00:01:32.030 -- And when you do that and it's called a MSUD. So it's basically

00:01:37.802 -- an aggregation where you put in these packets here, right

00:01:42.686 -- next to each other with one Mac header. So the advantage of such

00:01:48.458 -- a thing here is of course that.

00:01:53.560 -- You have less overhead, so the frame overhead compared to its

00:01:57.201 -- alternative, which would be like where you send it with their own

00:02:01.173 -- Mac overhead so we can look at this here and you will see that

00:02:05.807 -- the contribution of overhead of course here is much higher due

00:02:09.448 -- to that, but everything has a pro Ana con, so everything has

00:02:13.420 -- an advantage and a disadvantage from a overhead POV. This is

00:02:17.061 -- actually much better because you have only one header and then

00:02:20.702 -- this case works. Then we have

00:02:22.688 -- four protocol units. Data units, on the other hand, if we do have

00:02:28.270 -- a corruption, then we have an issue because that would mean

00:02:32.318 -- that every Mindy header actually has the ECS the see the error

00:02:36.734 -- correction code over the entire the CRC, and to say it has the

00:02:41.518 -- CRC over the entire. In this case 4 frame of four subframe

00:02:45.934 -- frame. Meaning if one goes bad it has to reset the whole thing.

00:02:51.450 -- And so that is not the case down here, where now, however, you

00:02:55.688 -- have to carry the burden of.

00:02:58.890 -- Of the different units with their own headers, so that's

00:03:03.290 -- essentially what we have, and then you can have, like

00:03:07.690 -- aggregation of multiple scenario would have like. In this case

00:03:12.090 -- two of those packed together with one physical header. So

00:03:16.490 -- these are the different options that we have on the plate. So

00:03:21.770 -- now this was for 802 eleven North, but it also transfers

00:03:26.610 -- into a 211.

00:03:29.020 -- At 802 eleven AC and in AC we looked at it. I mean, we had

00:03:35.065 -- several advantages in AC. First of all, we had a much bigger

00:03:39.901 -- bandwidth. We had 160 megahertz versus the small.

00:03:44.150 -- 40 megahertz that error to leaven in had we have more. My

00:03:49.514 -- more capability up to 8 doesn't have to be, but up to

00:03:54.878 -- 8 different antennas, and we had a modulation that went

00:03:59.348 -- from 64 quam for the North to 256 quam for the AC. So All in

00:04:06.053 -- all, that is where the big improvements occur.

00:04:13.990 -- So the advantage is now that if you have such a scenario, we can

00:04:19.380 -- have actually group, so we can have different constituents or

00:04:23.230 -- multiple users there. I can have a multi user MIMO where I'm

00:04:27.850 -- talking to you with one antenna. I'm talking to you with another

00:04:32.470 -- antenna and that is a very different scenario in a straight

00:04:36.705 -- out scenario where we have one antenna. Because I can first

00:04:40.940 -- talk to you and then I can talk

00:04:44.020 -- to you. But here I can actually split up the streams in

00:04:48.770 -- multiplayer games that are based now on antennas and that becomes

00:04:52.818 -- a variable. Very powerful means. So I might have. Now I'm sending

00:04:57.234 -- something to you and I will use my antennas to have different

00:05:01.650 -- data stream two antennas directed to one link to more

00:05:05.330 -- antennas, one each going to another device. So that is the

00:05:09.378 -- kind of advantage that you would have from, let's say, a router

00:05:13.794 -- point of view.

00:05:15.190 -- The router that is capable of AC can make these decisions, so if

00:05:20.572 -- you have like 4 different or eight different people in a

00:05:25.126 -- place, you can have 8 ongoing communications, otherwise they

00:05:28.852 -- would not be on this at the same time. So that's a huge advantage

00:05:34.648 -- of this multi user MIMO capability of AC.

00:05:40.310 -- So if everybody I know if everybody gets it here, but

00:05:44.281 -- essentially now if I'm sending it on the downlink. I

00:05:47.891 -- mean I'm sending it towards you here, I could use now

00:05:51.862 -- different antenna and do it all at the same time. So that

00:05:56.194 -- is quite some difference in mentality. There the other

00:05:59.443 -- tool of an NI don't think can do that. I'm not 100% sure

00:06:04.136 -- but I don't think with the four in Tennessee.

00:06:10.050 -- So the only disadvantage than this you have to send them as

00:06:13.878 -- individual frames. He cannot aggregated. You cannot aggregate

00:06:16.430 -- him in the fashion that we had here, so this won't work.

00:06:20.850 -- Which is the low overhead, so we have to go with this right

00:06:23.606 -- here with the higher overhead.

00:06:26.510 -- No, but that's essentially it. So NAD now, remember AD. The

00:06:30.437 -- biggest thing we should remember if anything at all like we were

00:06:34.721 -- in a complete different League here we're switching now from

00:06:38.291 -- the five Giga Hertz to the 60 Giga Hertz Band and that gives

00:06:42.932 -- you a huge advantage of.

00:06:46.070 -- Of bandwidth. The one thing is you will have very little

00:06:51.031 -- contention there at the moment and this is in devices will

00:06:55.200 -- trickle in that take over there. So that's one advantage. There

00:06:59.369 -- is little contention, whereas the 2.4 giga Hertz range is very

00:07:03.538 -- occupied. Everybody runs on 2.4 less people but more and more

00:07:07.707 -- run on five, and I don't have a single device that can run on

00:07:13.013 -- 60. At this point I think so that, but that's where things

00:07:17.561 -- are moving so.

00:07:19.160 -- Not everything is always great,

00:07:21.900 -- why? I mean, what are the disadvantages well?

00:07:26.820 -- You go to higher goal with your frequencies. The more lost you

00:07:32.436 -- have to endure, so that is one thing. So higher losses there

00:07:38.052 -- and multipath is also an issue. Multipath losses are a big

00:07:43.200 -- issue. Remember multipath is when a signal bounces off

00:07:47.412 -- somewhere. And obviously I get now are reflection. I get the

00:07:52.560 -- original one. I get the

00:07:54.900 -- reflection but. The reflection can interfere with my primary or

00:08:00.606 -- original signal. And that can cause big problems. So it's not

00:08:05.486 -- just that I get an echo, but the echo messes up my original 1 as

00:08:10.346 -- well. So that is a typical example of multi loss problems

00:08:13.910 -- here. The next thing that is a little bit of a pain is you go

00:08:18.770 -- that high with the frequencies and that will not be able to go

00:08:22.982 -- through objects anymore. So that is a big problem. For example of

00:08:26.870 -- fear and building. Or if you want to go through buildings.

00:08:32.840 -- We just ran some examples.

00:08:38.880 -- Just as a little side note here, we ran just week

00:08:45.930 -- ago, so we're an example where.

00:08:49.670 -- We're having a huge building

00:08:51.235 -- here. So this is a big building and we're trying out some

00:08:55.543 -- collision. Avoidance scenarios were.

00:09:00.100 -- In 811 Piso, there's another 802 eleven standard. This one

00:09:03.780 -- happens to be also in the five Giga Hertz range, but it's only

00:09:08.564 -- for vehicles, and we were trying to test the impact of.

00:09:13.390 -- These applications where this vehicle comes and if this one

00:09:17.100 -- doesn't stop, there should be a alert that tells her if you mean

00:09:21.923 -- watch out, you're on collision course with some other vehicle,

00:09:25.633 -- so that was the thing and we're testing. For example, in this

00:09:30.085 -- case, how much buildings would affect such measurements? And we

00:09:33.795 -- were in the five Giga Hertz Band, 5 GHz band and this year

00:09:38.618 -- is roughly what did we have? The 150 hundred 50 meter or

00:09:43.070 -- something like that? If I got the exact dimensions?

00:09:46.810 -- And it turned out that in the five Giga Hertz Band we had

00:09:50.177 -- fairly good communication, even though there's no line of sight.

00:09:52.767 -- You don't need that made with cell phones. You don't need line

00:09:55.875 -- of sight to the tower. I mean, we're in the building here. It

00:09:59.242 -- works just fine. I'm.

00:10:01.960 -- But if you were and we could run this very nicely. So we're

00:10:06.068 -- driving, measuring, logging, everything an yeah work just

00:10:08.596 -- fine. Incidentally, as we're doing it, one of people that

00:10:11.756 -- there was a car ahead of us and that car introduced exactly what

00:10:15.864 -- we're testing for, 'cause that car just about there was a girl

00:10:19.656 -- there on her phone, but she was paying attention. Run the stop

00:10:23.448 -- sign right in front of me. So unfortunately it didn't have a

00:10:27.240 -- webcam that would have been funnier than heck to show at a

00:10:31.032 -- conference. So like you were testing for this application,

00:10:33.876 -- and guess what happened?

00:10:35.200 -- The exact case that we tried to test for.

00:10:38.520 -- But if you were to experience, expect that experience.

00:10:41.445 -- Experiment now in the 60 Giga Hertz range the reliability

00:10:44.695 -- would definitely much different, 'cause the communications would

00:10:47.295 -- have been much more Hanford by the building here, which happens

00:10:50.870 -- to be in our case the Wallace complex. We use that as an

00:10:55.095 -- example. If we had been NYC with there being cooler 'cause we had

00:10:59.320 -- bigger buildings. But in Moscow we don't have big buildings.

00:11:04.780 -- So that can be a problem here. So these millimeter wavelengths

00:11:09.367 -- and remember higher frequency. The shorter the wavelength.

00:11:13.420 -- They have issues they don't like to go through objects anymore

00:11:17.061 -- and that becomes a real problem because that now has more of a

00:11:21.364 -- flavor of line of sight. That's the big problem that we run

00:11:25.336 -- into. So not everything is always perfect and this is

00:11:29.773 -- definitely one of them, where it's a compromise space.

00:11:35.160 -- So the biggest ones here turn out to be well here we have a

00:11:40.788 -- MIMO antenna conversion here. We have single one, but we

00:11:44.808 -- have a huge number of channels due to a big bandwidth at the

00:11:50.034 -- 60 giga Hertz Band.

00:11:52.900 -- Then they show you in the book a nice example here of

00:11:57.256 -- justice, different physical layers for us, I mean, for

00:12:00.523 -- the most users, the only thing that matters is the

00:12:04.153 -- bitrate. Here they care about how fast is it? So we see

00:12:08.509 -- here basically what the speeds are for.

00:12:12.890 -- 480 two 1180 depending on what the physical layer is, and so we

00:12:17.895 -- can just see what happens here. The modulation. Incidentally,

00:12:21.360 -- now you probably see what all is involved. We haven't really

00:12:25.595 -- talked about some of the flavors. You know, π / 2

00:12:29.830 -- lalalala so, but you probably get the feeling of what that

00:12:34.065 -- might be. Phase shift keying involved. There's a shift there.

00:12:37.915 -- When we looked at phase shift keying of 0 and 180, we.

00:12:42.970 -- Looked at when you do it differently, let's say like 90,

00:12:46.391 -- then 270 and so on. So it should give you an idea what's

00:12:50.434 -- happening here, so hopefully when you look at it gives an

00:12:53.855 -- idea you might have to kind of go back and say that guys not

00:12:58.209 -- forgotten what was the difference between this and

00:13:00.697 -- that. No.

00:13:03.660 -- So this obviously is a frequency division multiplexing and 16

00:13:07.610 -- qualm just means we have these different levels there to

00:13:11.560 -- differentiate with. That's the big one here, so anyway.

00:13:15.680 -- Just kind of cool to see the differences here.

00:13:22.680 -- So that's on the AD.

00:13:26.310 -- So then what we kind of just hand waved was the excess an

00:13:31.159 -- privacy information and anybody that had configured

00:13:33.770 -- wireless router would kind of have an idea what's involved

00:13:37.500 -- there. The first thing is to establish station. So if you

00:13:41.603 -- want to hook up to station you need to have access to it. So

00:13:46.825 -- if you're up to VandalWeb gold for the first time, well

00:13:51.301 -- it asks you for information and then it comes in there.

00:13:57.050 -- Once you're on there, well, then you expect and it turns out to

00:14:01.821 -- be the case here too that there will be some encryption in place

00:14:06.592 -- and that is now something that's not the access itself, but that

00:14:10.996 -- deals with the privacy and so.

00:14:14.330 -- The different type of author mean authorizations

00:14:17.473 -- authentication schemes that are offered, and the main thing for

00:14:21.963 -- us is just to see what we have and the typical ones are the

00:14:28.249 -- authentication itself. Do it to password. You can normally pick

00:14:32.739 -- the parameters for that.

00:14:35.140 -- You can use further.

00:14:38.450 -- Authorization by implementing things like lists of specific

00:14:41.066 -- devices that you allow and which ones you do not allow. That is

00:14:45.317 -- much more useful in an office environment, not at University

00:14:48.587 -- environment, 'cause that would be a maintenance nightmare or

00:14:51.530 -- maintaining a list where every day somebody comes and says like

00:14:55.127 -- I got rid of this machine. Now I have another machine and can you

00:14:59.705 -- lock the new Mac address? That would be really not a practical

00:15:03.629 -- thing, but in certain environments I would strongly

00:15:06.245 -- suggest doing exactly that,

00:15:07.553 -- meaning only. Those that have a particular MAC address can

00:15:11.436 -- actually join such a device, and the others don't. So just

00:15:15.528 -- because somebody would give you a password then to have access

00:15:19.620 -- to the note would not get you on there because you also would

00:15:24.456 -- have to be in the Mac list birth specifically. I mean there by

00:15:29.292 -- specifically allowing you to do that, it can become a bummer for

00:15:33.756 -- consumers if they have a guest network, because once

00:15:37.104 -- established, that's a list.

00:15:38.950 -- The guest network typically also likes to access such a list, and

00:15:42.514 -- that means now you have many kind of just give somebody the

00:15:46.078 -- password. So like hey, the guests are Hello World and then

00:15:49.345 -- it will tell you, well you know but I don't know you mattress. I

00:15:53.503 -- can't let you in here.

00:15:55.850 -- It's not like I'm VandalWeb guest. If you have your goal,

00:16:00.158 -- vandals password there when you can go on and there's no more

00:16:04.466 -- questions asked other than that, and that makes a lot of sense

00:16:08.774 -- from a privacy point of view. Of course we want to have

00:16:13.082 -- encryption involved, because otherwise if you sit there and

00:16:16.313 -- you run an unencrypted connection, all you need is a

00:16:19.903 -- packet sniffer and you can get the information. So we've tried

00:16:23.852 -- that before when we used to have a class here.

00:16:27.910 -- That already class called 421, which was the data

00:16:30.826 -- communications lab. So it was a one hour lap. We ran with the

00:16:35.038 -- Klausner. I got rid of it because it turned out to be too

00:16:39.250 -- much work for one credit hour class for me and the

00:16:42.814 -- infrastructure also was a little bit difficult. But let's take a

00:16:46.378 -- look at this here. So we had. Let's say we have a device here.

00:16:53.420 -- And we have now information that goes. He ran. It could

00:16:58.458 -- be, it could be.

00:17:01.680 -- On wireless this could be wireless. Here it could be

00:17:05.370 -- wired, you know it could be wired here, so we might have

00:17:09.798 -- wired notes here. Or maybe I have a router here like an 802

00:17:14.595 -- eleven type thing. So Whoops 802 eleven X or some whatever

00:17:18.654 -- you might have here. So now you're sitting there.

00:17:23.550 -- On a smart phone or what have you here?

00:17:28.670 -- So if you were to establish, let's say we pick the no.

00:17:34.800 -- Your other device on your laptop and your

00:17:37.848 -- establish a telnet connection. Telnet is

00:17:40.134 -- not, is not.

00:17:44.040 -- Tell that it's not encrypted.

00:17:46.970 -- And you do this in your favorite coffee shop that uses

00:17:50.567 -- no encryption or at the airport or in a hotel where

00:17:54.164 -- you just go on and there's no encryption, and you know when

00:17:58.088 -- that is because there's no encryption key there, you just

00:18:01.358 -- see the little symbols here for wireless, but you don't

00:18:04.628 -- see anything next to it, so you know this is an open

00:18:08.552 -- wireless an. Typically it tells you it's a non secure

00:18:11.822 -- line, so if you sit there and you run a packet sniffer.

00:18:20.910 -- And you can download those free from the Internet and it may be

00:18:24.784 -- there everywhere we use them always. When we run experiments.

00:18:28.660 -- You can just never packet an. You can get everything out, so

00:18:32.476 -- we used to do that in the networking lab, which we did

00:18:36.292 -- not. On Wi-Fi wireless, but we did it here on such a

00:18:40.108 -- scenario, and so I asked them to students. So like OK, you

00:18:43.924 -- type in your password you establish from here as a

00:18:47.104 -- server. So this is server and this is a client, so I'm

00:18:50.920 -- trying to establish telnet from here to there.

00:18:54.930 -- So now you start sitting there is typing telnet and then you

00:18:58.470 -- type your password and you would think like OK so I should get

00:19:02.305 -- now. The password in the packet. Well that happens to not be the

00:19:06.140 -- case because we are so slow in typing that it will already send

00:19:09.975 -- that packet with like 1 character at a time just because

00:19:13.220 -- we are so slow compared to the

00:19:15.285 -- data rate. So what you would have to do now on a sniffer.

00:19:20.060 -- You would, whether it's wireless or where it makes the

00:19:22.990 -- difference. Here you would target a machine. I target this

00:19:25.920 -- particular phony and I said I want to have only the packets

00:19:29.436 -- that are related to this phone that I'm trying to bring in, and

00:19:33.245 -- then I look at those packets a string him up here.

00:19:37.440 -- And then between those packets I will find the telnet. I mean

00:19:41.280 -- maybe T in here and El in here and letter at a time and then

00:19:46.080 -- we'll get the password. I will

00:19:48.000 -- get the password. And it will however only show up if I

00:19:52.353 -- capture all of the packets from this unit. Here, it's not as one

00:19:56.084 -- might think, like here is the packet that has the password.

00:19:59.241 -- No, it's just. Too slow, we're just too slow typing by the time

00:20:03.410 -- we're finally done, each packet gets sent out by itself.

00:20:08.000 -- And so, in an unencrypted environment is a real

00:20:12.360 -- problem. If however, you were sitting in this coffee shop and

00:20:17.156 -- now you use SSH instead of telnet, then actually this will

00:20:21.952 -- not be a problem because now your traffic itself with SSH is

00:20:27.184 -- encrypted and you can run a packet sniffer and all you get

00:20:32.416 -- is rip gibberish.

00:20:34.290 -- You cannot really use that, so that is the good part. The bad

00:20:38.684 -- part is that often when it comes, for example to web

00:20:42.402 -- context content. We don't really know is this not encrypted or

00:20:47.098 -- not. It's not always obvious whether it is encrypted or not,

00:20:51.300 -- like you're sitting in an Internet cafe at the McDonald's

00:20:55.120 -- in Paris or who knows were and you're trying to access your

00:20:59.704 -- account. Is this safe or not?

00:21:03.110 -- You know, and then the question really depends on the

00:21:06.320 -- application support for encryption, yes or no. If you

00:21:09.209 -- do have it, yes, if you don't have it, no. But how do you

00:21:13.703 -- know? And sometimes it's worth sniffing your own connections

00:21:16.592 -- to see how exposed you are.

00:21:19.680 -- I've done that not too long ago with the Mail

00:21:23.320 -- client on a machine where we tried it out and sure

00:21:27.324 -- enough, despite me thinking we had everything

00:21:29.872 -- set up right.

00:21:32.120 -- We did not have it right and there was a setting wrong. I

00:21:35.526 -- thought it was unencrypted, turned out not to be encrypted

00:21:38.146 -- so we could see the password

00:21:39.718 -- flying by. And I thought, like, woah, woah. Woah. How

00:21:44.310 -- would I have known that an so if you exercise this somewhere

00:21:48.210 -- where they have a sniffer running like at the airport, how

00:21:51.785 -- do I know not there's nobody there that actually just sits

00:21:55.360 -- there praying on just careless or ignorant users that don't

00:21:58.610 -- really understand it and run it. So that is a problem. So the

00:22:02.835 -- original able to 11 came with web that turned out to not be

00:22:07.060 -- that great of a thing. An incidentally if you own an old

00:22:10.960 -- machine like an old cell phone

00:22:12.910 -- and I. Old iPad or what might be what you might have. It might

00:22:18.382 -- just basically allow you only to use these old, not so secure.

00:22:23.840 -- Encryption methods and it might not let you in. For example, if

00:22:26.984 -- I use web here at the University, this I know can't do

00:22:30.128 -- that. So if I don't have the

00:22:34.034 -- WPA. Encryption I cannot get on at all, so they were not allowed

00:22:39.380 -- that. So one has to be aware of that. Different levels of

00:22:43.340 -- encryption. That's essentially all I wanted to discuss here. I

00:22:46.640 -- hope you have a feeling for things that didn't make us any

00:22:50.600 -- experts on wireless, but I hope you get to feeling for it.

00:22:55.530 -- There are other wireless definitions there.

00:23:00.570 -- Like I said, we work with 802 Eleven P at the moment, which is

00:23:05.694 -- something like 802, eleven, or 811 a, but it operates for it's

00:23:10.086 -- designed for vehicle and networks and some of the

00:23:13.380 -- parameters are a little bit different. Some of the

00:23:16.674 -- parameters like the it's the back of the medium access

00:23:20.334 -- parameters are different, so their minor changes, but enough

00:23:23.628 -- to make a difference there.

00:23:28.230 -- Any questions to any of the wireless stuff?

00:23:38.140 -- Alright.

00:23:40.390 -- When with it.

00:23:43.120 -- We're ready to go for the next one here, which turns out to be.

00:23:47.770 -- The Internet protocol, so we're going very. We're

00:23:51.250 -- almost there. I'm almost at the upper level now.

00:23:56.610 -- We have one more level to go through, and that's done the

00:24:01.338 -- transport transport layer, but here we're looking at the

00:24:04.884 -- Internet protocol. IP would be the Classic One that we have,

00:24:09.218 -- but Internet Protocol it doesn't have to be IP, we're just

00:24:13.552 -- talking about in general.

00:24:16.930 -- So before we go here, let's just look at a couple of notations

00:24:21.550 -- or not connotations like couple of terminologies that they use

00:24:24.850 -- here. I mean one over the communication network. While we

00:24:28.150 -- know what that is, a bunch of notes there, I mean for so to

00:24:32.770 -- provide data transfer among devices attached to the network.

00:24:35.740 -- Of course we have a network of notes. That's all we have. So

00:24:40.030 -- the network communication network that facilitates that

00:24:42.340 -- might be in the ether. Might it be using wire? What have you?

00:24:47.240 -- Then Internet here. That is a collection of.

00:24:52.680 -- In the networks interconnected with bridges and routers and

00:24:56.496 -- this and that. So it's a big mess. A big spaghetti of.

00:25:02.250 -- Smaller, bigger spaghetti of devices, links, etc networks.

00:25:10.660 -- And then we have intranet and this is actually when we scale

00:25:15.472 -- it down. Intranet Internet is bigger in between, intranet is

00:25:19.482 -- inside, so here it's like an Internet used by single

00:25:23.492 -- organization. So we're basically running this thing on our own

00:25:27.502 -- and typically it's like for World Wide Web so.

00:25:32.690 -- So it's like in self, perhaps even self contained Internet, so

00:25:37.794 -- it's like a part of it. A smaller contained portion of the

00:25:43.362 -- Internet, Internet. The big thing, intranet small single

00:25:47.074 -- organization. Child childish subset. That's what this would

00:25:51.919 -- be. Then we have separate

00:25:54.454 -- subnetworks. If you have a big network, sometimes she only

00:25:58.671 -- interested in a small portion of that and we would treat it as a

00:26:03.557 -- subnetwork. It means, like some constituent network of an

00:26:06.698 -- Internet, meaning a smaller segment in our organization.

00:26:09.490 -- Here for example, we have different subnetworks. CS has a

00:26:12.980 -- couple of so then if you're on these networks more than you're

00:26:17.168 -- in this CSS network.

00:26:19.170 -- And we see later on how one would treat the addressing of

00:26:23.646 -- the network itself, including the subnetworks. There's more

00:26:26.630 -- effect. You probably all have seen in your configurations that

00:26:30.360 -- sometimes you see there is a subnet mask and the subnet mask

00:26:34.836 -- typically is a mechanism to say, like all the bits that are one

00:26:39.685 -- later on, get XI mean ended with the real address to identify.

00:26:44.161 -- That's the network address and all the ones that have zero.

00:26:48.264 -- That turns out to be.

00:26:50.320 -- The host address, so we see that

00:26:52.917 -- later on. So then we have our end systems like my laptop, my

00:26:58.284 -- tablet, here that would be an end system at the moment. So

00:27:02.412 -- that is just something to be attached and we have

00:27:05.852 -- intermediate systems that would be some kind of a switch or

00:27:09.636 -- something that can hook up.

00:27:12.170 -- Two or more networks, and so device used to connect two

00:27:16.350 -- networks and permit communication between these

00:27:18.630 -- things and we might have them as bridges or routers where the

00:27:23.190 -- bridge is considered to be a lower level. It doesn't

00:27:26.990 -- translate, it doesn't do much thinking, it just forwards.

00:27:30.410 -- That's all they do and then the router is considered like a

00:27:34.970 -- bridge on steroids. I mean it would be a router that actually

00:27:39.530 -- looks at things can do certain

00:27:41.810 -- manipulation. Both of them will send traffic through in One

00:27:46.040 -- Direction if needed or not.

00:27:48.590 -- But this one here operates at Layer 3, where this one

00:27:52.231 -- operates at layer 2.

00:27:54.600 -- So layer two is a lower layer in the OS I hierarchy. Remember we

00:27:58.604 -- start out with the physical layer and work our way up.

00:28:02.490 -- So this is at a lower layer. The higher the layer, the more

00:28:06.767 -- knowledge you can apply, for example error checking

00:28:09.399 -- fragmentation, D. Later on we see that when taking something

00:28:12.689 -- apart of putting it back together all of that.

00:28:17.110 -- Should not be confused with.

00:28:20.310 -- Terms like I have a layer 2 switch or have a layer 3 switch

00:28:24.398 -- etc. That means simply.

00:28:26.320 -- From a device point of view, how far do you use hardware control?

00:28:31.820 -- And I can run a Linux box and we've done that as a router.

00:28:36.370 -- Press your Linux box as a

00:28:38.122 -- router. But I can also get a layer 3 switch that has this

00:28:43.466 -- hardware encoded and it will be so much faster than my Linux box

00:28:48.185 -- running as a router.

00:28:51.340 -- So the question is almost how much how much visibility you

00:28:54.442 -- have in terms of the smarts and how much of that is implemented

00:28:58.108 -- in hardware that determines the quality of the speed or the.

00:29:01.970 -- Typically the price tag also of these devices.

00:29:07.240 -- Alright, so these are the standard terms that the book

00:29:10.450 -- uses. And we would have no applications sitting like this,

00:29:15.599 -- so here would be the classic connection between two hosts A&B

00:29:20.670 -- and they have some applications that now interface with ports.

00:29:26.220 -- Like if it's a project would be port 80 if it was a Mail program

00:29:30.480 -- as a port 25.

00:29:32.260 -- So whatever port you might have, so these applications now want

00:29:35.934 -- to connect to some application on the other side. That's

00:29:39.274 -- typically what we have.

00:29:41.900 -- Sending something and let's say I do an FTP which is on port 20

00:29:46.226 -- and 21 if I recall right? So we would basically establish a

00:29:49.934 -- connection from one year to the other one. This is the server

00:29:53.642 -- and this is now a client, so I would say like I want to

00:29:57.968 -- download this file and

00:29:59.204 -- essentially these two. Logically, connect and request,

00:30:02.158 -- like I say one download so they would say OK here it comes. This

00:30:08.276 -- is simplified language here.

00:30:10.640 -- So. The application still themselves would now have these

00:30:15.252 -- access points which are ports, and then they would form a TCP

00:30:19.680 -- packet. Whether TCP packet. Now what could be UDP packet as

00:30:23.739 -- well. The main thing is that transfer transport layer

00:30:27.060 -- protocol we will put that and box it into the IP packet and

00:30:31.857 -- that's where our attention is right now. The IEP IP packet is

00:30:36.285 -- the one that has the IP address of the destination and we have

00:30:41.082 -- to find our way from here to that other host.

00:30:44.970 -- And we don't even know what's all in between in this

00:30:48.215 -- particular toy example here, there are two networks in

00:30:50.870 -- between, so we come from the host that lives in this

00:30:54.115 -- network. We go through router that will realize based on the

00:30:57.360 -- adressing, that I use in the information up here.

00:31:01.450 -- It will. It will figure out that it has to forward it to that

00:31:07.050 -- site here switching over.

00:31:09.400 -- The IP packet of course will be then brought down to the lower

00:31:13.248 -- link control to the Mac layer and then it will back. Here it

00:31:17.096 -- will look at it, receive it, bring it up, and will look

00:31:20.648 -- inside to peak. Where is it going to? So it has to look

00:31:24.496 -- into the header of the IP packet to make that decision.

00:31:29.140 -- So this is a router that has to know the IP address. Otherwise

00:31:33.066 -- we can do it and then there has to be a routing table here so

00:31:37.596 -- that it will find out OK. This particular traffic. Now I'm

00:31:40.918 -- sending out on that physical port here Becausw the

00:31:43.636 -- destination is attached to this port and there might be more

00:31:46.958 -- networks in between. This would

00:31:48.976 -- be a very simple. Where we have one, we have

00:31:53.814 -- a two hop scenario here.

00:31:57.230 -- Two edges in the graph.

00:32:00.950 -- So these are logical connections and these are

00:32:04.830 -- physical connections here and again from here to here we

00:32:09.680 -- have logical connections, so that's how that would work.

00:32:14.045 -- So the first question is, should IP be connection

00:32:18.410 -- oriented or connectionless?

00:32:21.050 -- And here's an example WHI perhaps we don't want to have

00:32:26.528 -- connection oriented traffic, because if we have now.

00:32:31.300 -- The application going from one machine 8 to be which is

00:32:35.040 -- far away. For example, an award to use connection

00:32:38.100 -- oriented and would first have to basically request a

00:32:41.160 -- connection, then the other side. Like Yup, I can. I can

00:32:44.900 -- do that, so there would be an accept. Now would

00:32:48.300 -- transfer my file.

00:32:51.160 -- You know one of the time here and then you have multiple

00:32:55.624 -- exchanges with acknowledgements and then I would terminate this

00:32:58.972 -- and finish this up and that would basically use up quite a

00:33:03.808 -- bit of time. Time goes in this direction and oops, the root

00:33:08.272 -- problem is here in the establishment of the connection,

00:33:11.620 -- the acceptance, determination etc in the middle. Here we don't

00:33:15.340 -- have a problem.

00:33:17.900 -- But this of course is now connection a.

00:33:22.650 -- An established connection, so we don't want to deal with the

00:33:26.632 -- overhead. Another part is the whole idea of the Internet in

00:33:30.614 -- its own right. Originally this came of course from a defense

00:33:34.596 -- point of view. DARPA, DARPA was the one that actually started

00:33:38.578 -- this whole thing. I mean, that was under defense thinking, and

00:33:42.560 -- it came in a time where people were afraid of the Cold War and

00:33:47.628 -- they would say like we don't want to have a network that

00:33:51.972 -- looks like this here.

00:33:55.490 -- Let's say I have here. Here is Seattle and here in New York.

00:34:03.010 -- If I had such a network here.

00:34:05.860 -- According to a military thinker, they would say, well, all you

00:34:09.941 -- need to do is bomb one of these links here and that's the that's

00:34:15.135 -- the end of the communication between those two. So the idea

00:34:19.216 -- was let's establish a network that is interconnected and

00:34:22.555 -- really has bunch of links there. We don't even know what all is

00:34:27.378 -- available here. So we have a lot of these things. Now it becomes

00:34:32.201 -- much more difficult to corrupt such a network by physically.

00:34:36.090 -- Damage in the system so you can drop a couple of bomb Siri can

00:34:40.024 -- blow this thing up. You can blow that edge up and you have a

00:34:43.958 -- fairly high resilience there.

00:34:45.720 -- It's not necessarily optimized.

00:34:48.680 -- To be cake connected.

00:34:51.540 -- Remember K connected means there are at least K disjoint

00:34:54.760 -- paths between any two. We don't have to have that, but

00:34:58.302 -- from an attacker POV, if I saw something, I would say like

00:35:02.166 -- what are the two weakest connected ones, the minimum?

00:35:06.250 -- Cut set.

00:35:08.580 -- Where the weights are equal, for example, and that would be my

00:35:12.144 -- most efficient attack point.

00:35:15.120 -- Find the one in this particular case here, while if

00:35:18.450 -- we're interested from here to here, where do I attack? Well,

00:35:22.113 -- it would be. Basically I take this no doubt in that no

00:35:26.109 -- doubt, and things are done.

00:35:32.680 -- Well, this is silly exactly because it's so, so we only are

00:35:36.880 -- two connected here. I can send it like this or can send it out

00:35:41.780 -- like this. These are vertex. These are vertex disjoint paths.

00:35:46.110 -- One here.

00:35:49.330 -- And one goes here.

00:35:53.030 -- So these are vertex disjoint

00:35:55.420 -- paths. Edge disjoint would be different, but edge disjoint is

00:35:59.829 -- a difficult thing to me. Can knockout an edge alright? Like a

00:36:03.921 -- backhoe is typically the cost for that. You have construction

00:36:07.331 -- project and somebody ***** into data cable. That's what would

00:36:10.741 -- happen here. But if a router goes out, all the links attached

00:36:14.833 -- to the router route. So this is this is a weaker thing. So at

00:36:19.607 -- the time the thinking was like let's come up with a highly

00:36:23.699 -- dynamic quickly changing very easily kind of figure big.

00:36:27.210 -- Mash big mash or should you smash 'cause that's normally

00:36:31.160 -- considered like a certain structure, but something

00:36:33.925 -- that's difficult to knockout? That was the overall

00:36:37.085 -- motivation, and that would mean such idea here may not be

00:36:41.430 -- it. It might be much better to set it up in a way that these

00:36:47.355 -- things right themselves.

00:36:49.590 -- Then we have flexibility, send it there and see how you make it

00:36:53.646 -- to the other side, regardless of

00:36:55.518 -- something failing perhaps. And that was it. So initially

00:37:00.451 -- developed by DARPA, the D for defense, of course.

00:37:05.320 -- So it was a defense project and the Internet protocol IP is

00:37:11.776 -- basically the outcome of this whole mess, so.

00:37:18.840 -- So now if and that uses connectionless.

00:37:22.910 -- Connection this communication. What does it mean? What we set

00:37:25.980 -- something out there packet and say go and make it to your

00:37:29.971 -- destination off you go.

00:37:32.110 -- So there are huge advantages to

00:37:34.174 -- that. For example.

00:37:38.050 -- Flexible something changes. This router goes out. This

00:37:40.810 -- router goes out due to maintenance or what? Who knows

00:37:44.260 -- what? Maybe they have a thunderstorm. They lost power.

00:37:48.550 -- So we can write differently.

00:37:52.210 -- Robust. Against. All sorts of things.

00:37:58.950 -- Typically I mean flexibility would be also like there's a

00:38:02.260 -- quicker link. There's a found link that is much less

00:38:05.570 -- utilized so I can go there rather than where there's a

00:38:09.211 -- lot of contention.

00:38:11.700 -- Robust means new links fail. The systems fail, we can do it and.

00:38:19.780 -- The other thing is, there's no overhead. There's no other.

00:38:23.590 -- There's no handshaking going on, their data crams IP is a

00:38:27.781 -- datagram thing. The datagram is the postcard. You drop it off

00:38:31.972 -- and you think it makes it there, but there's no guarantee

00:38:36.163 -- datagrams have no guarantee. It's the postcard of data

00:38:39.592 -- communication. You send it there and off it goes. We know also

00:38:44.164 -- that we have TCP and UDP.

00:38:48.560 -- And those are TCP is actually reliable and UDP is also

00:38:52.784 -- datagram. So we would have now day to cram in a datagram the IP

00:38:58.160 -- packet. The datagram in the datacom? Then you

00:39:01.019 -- send it off to China.

00:39:03.260 -- The reason we have of course TNTS UDP to have a port number

00:39:08.187 -- because our IP packet has no clue what application this is.

00:39:12.356 -- It doesn't know this is for.

00:39:15.570 -- The browser this is FTP. This is this or that you know. So the

00:39:19.000 -- port number has to be part of it, and that's at the higher

00:39:22.185 -- level. We stick that into the IP packet, but the upper layer

00:39:26.666 -- would have to deal, for example with reliability issues and the

00:39:30.252 -- only one we have there is TCP.

00:39:33.170 -- You DPS no reliability. It's also a data crime.

00:39:37.250 -- So that is the. This is advantage. It's not reliable.

00:39:41.848 -- There's no guaranteed delivery. There's no guaranteed order of

00:39:45.610 -- delivery, meaning I sent three things out. The last one might

00:39:50.208 -- arrive 1st, and so that becomes securing problem for the two

00:39:54.806 -- sides. If I send something from here to there, they can go do.

00:40:00.320 -- Different route so I don't know what they take. There's no

00:40:03.598 -- guarantee an I might be waiting here for awhile till that second

00:40:07.174 -- packet arrives because it's worse. The second packet,

00:40:09.558 -- whereas the second packet and it might not make it.

00:40:14.010 -- In which case then later on the layer above would have to say

00:40:18.014 -- like what the heck is going on? Where is my packet? So that

00:40:22.018 -- would be now where reliability would be based on TCP and TCP is

00:40:26.022 -- a protocol that actually does do reliability. There is a

00:40:29.102 -- handshake and if I send something in order to hear from

00:40:32.490 -- you, I assume you didn't get it and I would send it again.

00:40:37.840 -- Whether you never got it or whether your acknowledge was

00:40:40.420 -- lost, for me, there's no difference in that. All I can

00:40:43.258 -- say is I didn't hear back from

00:40:45.064 -- you. So that's the unreliable

00:40:47.912 -- part here. So now this would be the typical example of a

00:40:53.250 -- configuration and the packets that are being used here. For

00:40:57.010 -- example here I have some station that looks up to a router, then

00:41:01.898 -- it goes through some frame relay wide area network to another

00:41:06.034 -- router to another station, and in this case here.

00:41:11.260 -- We want to have a TCP package. Let's say we do an FTP transfer.

00:41:16.730 -- That would use TCP, whereas if you were to use, let's say,

00:41:20.738 -- WhatsApp or something like that audio video that is most likely

00:41:24.412 -- UDP, because So what a frame missed. No big deal. But if a

00:41:28.754 -- bit flips in a file executor that we transfer, that would be

00:41:32.762 -- a disaster. So from here it wants to talk to this site here

00:41:37.104 -- and it does so by now. Sending an IP packet to the lower link

00:41:41.780 -- control, which then brings it to the Mac layer, which using the

00:41:45.788 -- physical layer brings it out to the neighboring device which is.

00:41:49.590 -- In this case, this particular router in here you would go up

00:41:53.682 -- to ask the question, well, what's the IP address and I have

00:41:57.774 -- to unpack all the way to here. Remember the structure is.

00:42:02.180 -- The TCP packet.

00:42:05.410 -- Here with its header.

00:42:07.890 -- Get stuffed into, let's say the IP packet.

00:42:13.230 -- So now this is a header. This is now going in here.

00:42:17.970 -- Run and they should try the other direction here, so this

00:42:21.908 -- is now exactly this thing here and then. This one here gets

00:42:26.204 -- down until we're at the Mac layer. So until I'm down here

00:42:30.500 -- at the Mac layer.

00:42:33.620 -- Where is Santas across on the other side. In the router I have

00:42:37.494 -- to 1st get this the lower link control data units routes. So

00:42:41.070 -- this is my link control. Then I open up in a find the IP to get

00:42:45.838 -- the IP address here. So this is where. Whoops, I'm certainly in

00:42:49.414 -- the header here, so this is I'm interested in the address.

00:42:55.450 -- So we need to know the address where this is going,

00:42:58.981 -- the destination address and that would now be.

00:43:02.750 -- Then we would consult or their router would consult its routing

00:43:05.588 -- table to decide where does it go out and it would say OK out of

00:43:09.458 -- this link here. This might be rather than as many ports 32

00:43:12.554 -- ports or what have you, I don't

00:43:14.360 -- know. Then it would go to the next router. On this end here.

00:43:20.820 -- Same thing again. They would have to unpack it all the way to

00:43:24.395 -- here to find out what's the address and it would forward it

00:43:27.695 -- here. That's why if you think of the devices themselves, if you

00:43:30.995 -- do that a lot.

00:43:32.790 -- Like a gateway does or high in high throughput router, you

00:43:36.541 -- better get something that does most of the work in hardware

00:43:40.292 -- rather than software. If you configure your Linux system like

00:43:43.702 -- your laptop running Linux as a router for this you will not get

00:43:48.135 -- any glory for being a high speed

00:43:50.522 -- network. 'cause that would all be under software control. You

00:43:54.132 -- need hardware controller so the higher level you can buy, the

00:43:57.190 -- faster it would work. So there would be essentially happening

00:43:59.970 -- over and over and over until this system. Here a would talk

00:44:03.306 -- to the one in China which would be. So we're constantly go up to

00:44:07.198 -- the next one. Look at the table, go up next one, look at the

00:44:11.090 -- table. What we want to have of course, and then it will go to

00:44:14.982 -- some links that will either use satellite to go over the

00:44:18.040 -- continent or it will go through a cable in the ocean. There will

00:44:21.654 -- be a long link somewhere.

00:44:23.810 -- And the cable will be just about like 1 cable in reality. Of

00:44:27.892 -- course that cable segments that have to be powered because

00:44:31.032 -- there's no fiber optics that can send something over that length

00:44:34.486 -- without nothing coming out. So every so often you have to have

00:44:38.254 -- a repeat are station and you have companies that have big

00:44:41.708 -- boats that are traded at Mastec that would go and maintain those

00:44:45.476 -- huge cables and there would be there will be a link somewhere

00:44:49.244 -- where that cable will be part of the Lingard will be 1 edge in

00:44:53.640 -- that link. It will be a fast edge, so from a router POV

00:44:57.805 -- that will be attached to very fast device.

00:45:03.010 -- So connectionless is what we have here and connectionless has

00:45:09.100 -- this. Great thing flexibel

00:45:12.426 -- robust. And it does not do any additional overhead,

00:45:17.116 -- nor handshaking involves, so very little overhead.

00:45:21.620 -- So now the big problems when it comes to Internetworking would

00:45:25.228 -- be like how do I route the

00:45:27.524 -- packets? And how do I find my way through from here to China?

00:45:32.466 -- Great RFC? Or is it 1088? I think it's the one that gives

00:45:36.730 -- the tutorial on how this works.

00:45:39.960 -- Take a look at that one. That's the only one that I know that's

00:45:43.124 -- not a sleeping pill. That's actually kind of fun to read.

00:45:45.610 -- All the other RFC's are like Reading man pages for

00:45:47.870 -- entertainment. Then you have to have a mental problem to do

00:45:52.100 -- that, but not really, but you know what I mean. They're

00:45:56.096 -- not very entertaining and RFC's are not entertaining. I think

00:45:59.426 -- it's a 1088 that one actually because it's a tutorial of how

00:46:03.422 -- it would find its way. The first issue that we run into is like

00:46:08.084 -- the lifetime of a datagram. How long should it be defined and

00:46:12.080 -- the problem will be that there is a potential for example to

00:46:16.076 -- get a datagram into a loop

00:46:18.074 -- situation for example. It could, it might loop around in such a

00:46:22.095 -- loop, here where. We send it from here to there that goes

00:46:26.641 -- from here to there goes back here and then pretty soon we're

00:46:30.229 -- back here and we're whipping around the loop and there has to

00:46:33.817 -- be a way to kill it off so there will be a lifetime defined.

00:46:38.760 -- And if you exceed your lifetime, the router that sees a packet

00:46:42.636 -- with that light would simply just ignore it, destroy the

00:46:45.866 -- package. Therefore, I mean so you don't have it then.

00:46:49.650 -- Fragmentation reassembly because a lot of times we sent something

00:46:52.890 -- and we might not be able to keep the length of the packet we

00:46:57.426 -- might have to actually chop up the packet. It depends on what

00:47:01.314 -- we have in terms of the neighborhood network, what

00:47:04.230 -- technology we have, what capabilities etc. And so we

00:47:07.146 -- might have to shrink it down, cut it in half. For example we

00:47:11.358 -- call that fragmentation and at one point you have to reassemble

00:47:14.922 -- that as well and their issues that need to we need to look at

00:47:19.458 -- there. And would be error control and flow control,

00:47:22.202 -- and that's where we start next time. Have a nice day

00:47:24.996 -- and I see you on Wednesday.

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 -- consequense 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 becausw 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:"01:13:24.6740000"



00:00:28.270 -- Alright, welcome class. Today I'll we've got. It's one of my

00:00:33.242 -- favorite lectures is today, so I'm happy to share that joy with

00:00:38.666 -- all of you for class today. Alright, before we get going you

00:00:44.090 -- got your homeworks back just so that you know there are some

00:00:49.514 -- issues. A number of issues arose in this homework assignment, so

00:00:53.720 -- in problem 5 two finding the velocity downstream of the shock

00:00:57.724 -- appeared to be a problem. I think we talked a little bit

00:01:02.092 -- about that last time problem 5 seven finding the velocity

00:01:05.732 -- downstream of the shock appeared to be a problem as well, and

00:01:10.100 -- then finding the change in pressure in problem 20 was a

00:01:14.104 -- problem. Please the solutions are all on baby learn. Go look

00:01:18.108 -- at that and make sure that you can get those assignments done.

00:01:22.630 -- OK, I think for probably 5 two that a lot of you solve that as

00:01:26.590 -- a moving shock problem, and that's going to screw you up

00:01:29.494 -- from the get go. So it's just a stationary shock, that is, that

00:01:32.926 -- is a bread and butter. Normal

00:01:34.510 -- shock problem. OK, so make sure that again, compare

00:01:38.642 -- your solutions your homework with with the solutions that

00:01:42.476 -- are available online and make sure that you can solve

00:01:46.736 -- the problems correctly. OK, alright anybody go to the go

00:01:50.996 -- to career fair yesterday.

00:01:54.000 -- OK, engineers were in huge demand. I walked through, talk

00:01:58.920 -- to some of the employers navair. We have sent a number of

00:02:04.824 -- students to navair. They're looking for 250 engineers.

00:02:10.730 -- So if you're looking for work, it's a great place to

00:02:14.173 -- go, and you can apply gas dynamics to it. OK, you get

00:02:17.929 -- to work at airplanes to work on jets. I mean, how cool is

00:02:21.998 -- that? OK, so I've got just a little bit of information

00:02:25.441 -- here. If you are interested, come on by after class, OK?

00:02:31.020 -- Let's get on. Let's get on here. Alright we are going to be

00:02:35.622 -- reviewing oblique shockwaves, and then we're going to see some

00:02:39.162 -- applications of those shockwaves. We're going to see

00:02:41.994 -- why, why airplanes are designed the way they are now that we

00:02:46.242 -- know about oblique shockwaves here. OK, we're going to learn

00:02:49.782 -- about supersonic diffusers, and that's just a fancy name for an

00:02:53.676 -- inlet to a jet aircraft. That's all it is. OK, so we're going to

00:02:58.632 -- learn about jet inlets today.

00:03:00.550 -- We learn about reflected shockwaves and you have a

00:03:04.087 -- homework problem on reflected shock waves and then we'll talk

00:03:08.017 -- a little bit about the differences between subsonic and

00:03:11.554 -- supersonic aerodynamics. OK, so before we get going a couple of

00:03:15.877 -- principles I want you to keep in your noggins. What we talk about

00:03:20.986 -- some of our material today. OK,

00:03:23.344 -- First off. The change of entry is equal to that of the negative

00:03:29.051 -- natural log of the stagnation pressure ratio. OK, so if you

00:03:33.022 -- want to minimize the losses, if you want S 2 -- S one to be

00:03:38.437 -- close to 0 or as small as possible, you want this ratio

00:03:42.769 -- here on the right hand side to be as close to one as possible.

00:03:47.823 -- Can peanut to ever be greater than peanut one.

00:03:55.460 -- Because then what would happen to S 2 -- S one? What

00:03:58.820 -- happens and what that would violate what law?

00:04:02.550 -- Second law of Thermo dynamics.

00:04:05.170 -- If Pete shot 2 or greater than peanut one, that would be. That

00:04:10.084 -- would be negative.

00:04:12.000 -- Change there due decreasing the entropy. OK, not going to

00:04:15.740 -- happen. Alright, second thing to keep in mind we haven't. We

00:04:20.390 -- haven't developed this relationship, but we will

00:04:22.826 -- later on a semester. But I want you to keep this in mind

00:04:27.350 -- now and that is that the thrust generated an engine is

00:04:31.178 -- related to the stagnation pressure.

00:04:34.310 -- OK, the higher the stagnation pressure, the greater the thrust

00:04:38.460 -- that you can develop.

00:04:41.550 -- OK so again keep that in mind.

00:04:45.250 -- Stagnation, that the decrease in stagnation pressure is related

00:04:48.382 -- to the losses in the flow.

00:04:51.090 -- The thrust is related to the stagnation pressure. OK here we

00:04:55.248 -- go. Oblique shockwaves. This is just a review from what we did

00:04:59.784 -- last time, so.

00:05:01.790 -- We talked about. In fact, this is a hint for the first problem

00:05:05.755 -- we've talked about mock waves. That was the 2nd second lecture

00:05:09.110 -- I think second or third lecture in class and a mock wave occurs

00:05:13.075 -- when there is just a very small disturbance. We could measure

00:05:16.430 -- the angle and once we measure the angle we could calculate

00:05:19.785 -- with the model number was OK. That's a hint for one of your

00:05:23.750 -- homework problems. OK, now instead of just having a small

00:05:28.140 -- disturbance, just like a little Nick in the wall, now there's

00:05:32.375 -- going to be a large wedge or large angle right here. OK, when

00:05:37.380 -- that occurs, we have an oblique shockwave that forms, so flow

00:05:41.615 -- comes down. This way it has to be supersonic. Makes this turn

00:05:46.235 -- through this turning angle Delta. It creates a shock,

00:05:49.700 -- creates an oblique shock that has an angle of beta associated

00:05:53.935 -- with it right there.

00:05:56.110 -- OK, so again the turning angle Delta, the shock angle, beta,

00:06:01.962 -- animac angle, mu.

00:06:04.730 -- Make sure we've got those down there. OK, very good. An oblique

00:06:08.714 -- shock forms when a flow turns into itself, so you have a flow

00:06:13.030 -- that's coming down this way, and it's kind of like blocking it

00:06:17.014 -- off. OK, so flow comes in gets directed up into itself. An

00:06:20.998 -- oblique shockwave forms were going to talk next week about

00:06:24.318 -- what happens when you have a supersonic flow and the flow

00:06:27.970 -- turns away from itself.

00:06:30.170 -- OK, for now the flow is turning into itself. An

00:06:34.110 -- oblique shockwave forms, so here's something that's very

00:06:37.262 -- important to know. After that oblique shockwave, then

00:06:40.414 -- the flow follows the wall, so we have here flow that's

00:06:44.748 -- coming out in this duct. Supersonic flow makes it

00:06:48.294 -- turn Delta right here, creates an oblique shockwave

00:06:51.446 -- that has an angle beta here and the direction of the

00:06:55.780 -- flow is with the wall.

00:06:58.900 -- OK, yes.

00:07:05.750 -- The Mach angle is going to be somewhere likely in between

00:07:09.281 -- those right there. OK, so usually in oblique shock,

00:07:13.356 -- oblique shock problems, we don't use the mock angle very much.

00:07:19.170 -- OK so I just included it in this just so that you saw in fact,

00:07:23.325 -- the reason it's the dotted line is it's an imaginary angle. In

00:07:26.649 -- this problem, just so that you could distinguish the two other

00:07:29.696 -- angles from that. That's the only reason why it's there, so

00:07:32.743 -- we're primarily going to be concerned with the turning angle

00:07:35.513 -- and the shock angle.

00:07:37.330 -- OK, alright so here's a duct again. The flow follows the wall

00:07:41.398 -- in that direction. Here we have flow in. This wedge comes down

00:07:45.466 -- this way. Supersonic flow gets turned up at this angle Delta.

00:07:49.195 -- The flow follows the wall so we get the direction of the flow

00:07:53.602 -- there. This total angle right here is called the included

00:07:56.992 -- angle of the wedge.

00:07:59.190 -- Gate we're going to talk later on today about what happens when

00:08:03.186 -- you have a wedge like that at an angle of attack and see some of

00:08:08.181 -- the differences there. That's coming later on today. This just

00:08:11.511 -- review from last time. OK, we talked last time and showed how

00:08:15.507 -- the turning angle Delta, the shock angle, beta, and the

00:08:18.837 -- upstream Mach number M someone are related to each other

00:08:22.167 -- through this oblique shock equation. OK, so in any kind of

00:08:25.830 -- problem you're going to get two of those three values.

00:08:29.230 -- You'll get Delta. You'll get beta or M's of 1. Any two of

00:08:33.624 -- those, and if you know two, you can use the relation to

00:08:37.680 -- get three there OK. Appendix three. We talked about the

00:08:41.060 -- oblique shock chart. That's this right here. Here we have

00:08:44.440 -- the shock angle. Here is the turning angle right here, and

00:08:48.158 -- each one of those lines corresponds to a Mach number.

00:08:52.600 -- OK, so three variables here. That's all related through this

00:08:57.210 -- relationship again man use com problem. OK, it's going to make

00:09:02.281 -- your life much easier. Solvable shot problems. OK, alright or

00:09:06.891 -- your app? OK, good.

00:09:11.900 -- Right also recall that for every for every Mach number and

00:09:16.828 -- turning angle combination, so you have an upstream Mach number

00:09:21.308 -- Anna turning angle combination. There is a maximum turning angle

00:09:25.788 -- associated with that that maximum turning angle

00:09:28.924 -- corresponds to whether or not you have an attached oblique

00:09:33.404 -- shockwave right across here, or a detached shockwave. OK, if the

00:09:38.332 -- turning angle is greater than the maximum turning angle.

00:09:42.430 -- For that Mach number, then you have a detached shockwave. OK,

00:09:46.071 -- it's going to behave like a normal shock right up there if

00:09:50.043 -- the turning angles less than the maximum turning angle you have

00:09:53.684 -- an attached shockwave. How do you know what that maximum

00:09:56.994 -- turning angle is? Well, if you

00:09:58.980 -- go up here. Each one of these lines corresponds to a Mach

00:10:03.215 -- number. This let's if we look at 2.2 right here. Here's the line

00:10:07.700 -- from lot number of 2.2. This maximum point right there? The

00:10:11.495 -- tip of that little thumb that comes out there. If you go down.

00:10:16.950 -- You can read off what the maximum turning angle is going

00:10:21.064 -- to be. The turning angle is greater than that. Then what

00:10:25.178 -- is 2? That's about 25 or so degrees right there. The

00:10:29.292 -- turning angle is greater than 25 degrees from lot #22 you

00:10:33.406 -- have a detached shockwave.

00:10:36.350 -- OK.

00:10:39.160 -- That's a review from last time. Any questions?

00:10:43.410 -- Any questions at all? Yes.

00:10:48.860 -- Could you speak a little louder so I can hear very

00:10:50.598 -- well?

00:10:54.770 -- OK, so the very first slide right there. OK, the thrust is

00:11:00.158 -- proportional to the stagnation

00:11:01.954 -- pressure. So the higher the stagnation pressure, the higher

00:11:05.830 -- the thrust, the lower the stagnation pressure, the lower

00:11:08.665 -- the thrust. OK.

00:11:12.750 -- Good, any other questions?

00:11:16.350 -- OK, not not everything. Fly straight and level.

00:11:21.600 -- OK, so you could have say a wedge like we have here, so the

00:11:26.822 -- wedge is going to have some included angle right here, but

00:11:30.925 -- now this wedge, the wedge itself is bent down a little bit.

00:11:36.800 -- OK, so that means, so that means we're going to have different

00:11:41.528 -- conditions on the top and on the bottom of our wedge, right here.

00:11:47.250 -- OK, remember the flow follows the wall, so we have a flow

00:11:51.582 -- direction here and a flow direction here. Let's just let's

00:11:55.192 -- just draw this out here so we can see get an idea for what's

00:12:00.246 -- going on. OK, so let's say that we have a wedge here.

00:12:06.910 -- OK it has.

00:12:09.370 -- This angle Delta, so a total included angle of 2D right

00:12:14.122 -- across there we have flow that comes down this way some

00:12:18.874 -- supersonic flow. And the shockwave forms here. Anna

00:12:23.336 -- Shockwave forms here.

00:12:25.360 -- OK.

00:12:27.030 -- Nothing big there. Could you solve that problem if you knew

00:12:29.197 -- what the Mach number in the

00:12:30.379 -- turning angle was? Yeah, OK, look at com property. You get

00:12:33.832 -- the shock angle you could figure out what the pressure in each

00:12:36.880 -- one of those regions are.

00:12:39.610 -- And the directions of the flow. You could figure out what the

00:12:43.162 -- temperature is. All sorts of stuff. So now let's take this

00:12:46.418 -- wedge here and. Turn it up a little bit this way.

00:12:52.620 -- OK, so now we're going to have an angle of attack on this

00:12:57.924 -- wedge here. So now all exaggerate my turning angle.

00:13:01.596 -- So let's say that looks like this and like this, and the

00:13:06.492 -- flow comes this way. So the wedge still has a total

00:13:10.980 -- included angle of 2D. But now here is the centerline of the

00:13:15.876 -- wedge.

00:13:17.620 -- It makes an angle of attack.

00:13:20.610 -- Alpha

00:13:24.430 -- everybody see that.

00:13:27.700 -- OK, immediately, what could you see? What's going to be

00:13:30.570 -- different on the top part of the wedge compared to the bottom

00:13:34.014 -- part? What's different geometrically?

00:13:38.940 -- I heard somebody say someone.

00:13:44.040 -- Less flow.

00:13:46.830 -- OK, that might be the case. There's only going to be

00:13:50.680 -- differences. What's the turning angle for the flow on the top

00:13:54.530 -- compared to the floor on the

00:13:56.630 -- bottom? What's the turning angle?

00:14:00.610 -- So this half angle here is is

00:14:03.795 -- Delta. Right that half angle there is Delta, so knowing

00:14:07.531 -- that the half angles Delta and you have an angle of attack

00:14:10.879 -- Alpha, what's the turning angle there at the top?

00:14:16.590 -- It should be smaller.

00:14:18.900 -- Delta. Minus Alpha.

00:14:24.390 -- Right?

00:14:26.250 -- What's the turning angle going to be on the bottom?

00:14:31.610 -- Little bit here. How do we do it this way? So here is that

00:14:35.796 -- wedge it's coming in this way. So now the turning angle top

00:14:39.384 -- and bottom is Delta OK if it's just going in horizontally

00:14:42.673 -- here I take that angle down, has an angle of attack Alpha.

00:14:46.261 -- So what's the turning angle here at the bottom?

00:14:52.800 -- Here we go here. The turning

00:14:55.416 -- angles Delta. By now add.

00:14:59.570 -- An angle attack Alpha, what's the? What's the

00:15:01.770 -- turning angle on the bottom?

00:15:04.500 -- Delta plus Alpha.

00:15:06.820 -- So now I'm going to have a shockwave here and a shockwave

00:15:11.692 -- here, but this turning angle here at the bottom is going to

00:15:16.564 -- be Alpha plus Delta.

00:15:19.630 -- And here on the top, it's going to be.

00:15:23.780 -- Alpha minus depends on which one of those two is larger, but you

00:15:27.589 -- see, there's going to be different between those two

00:15:30.226 -- angles there. OK, so now let's think about this. You can you

00:15:33.742 -- see clearly, can you see clearly that there's going to be a

00:15:37.258 -- larger turning angle at the bottom and at the top you buy

00:15:40.774 -- that? I mean, if I kept this angle of attack this way,

00:15:45.395 -- eventually that's going to have no shockwave on top.

00:15:48.910 -- When Alpha is equal to Delta, when that turning angle is the

00:15:52.006 -- same as the wedge angle, there's no. There's no big shock that

00:15:55.102 -- forms, it's just a straight

00:15:56.392 -- line. OK, so now keep that in mind. So which

00:16:00.337 -- of those two shockwaves is going to be stronger?

00:16:08.500 -- Which is going to have the

00:16:10.666 -- highest change. Across there, what's going what, what? What do

00:16:14.858 -- you see with the flow going on there? Have a have a higher

00:16:19.421 -- turning there at the bottom.

00:16:22.230 -- Stronger shock. And the bottom everybody see that? OK, think of

00:16:26.998 -- it this way, you are turning that air in the higher

00:16:30.650 -- direction, you're deflecting it more on the bottom then you are

00:16:34.302 -- the top. OK, so there's going to be a stronger shock.

00:16:39.130 -- On the bottom.

00:16:41.670 -- And this is going to be a weaker shock here at the top.

00:16:46.670 -- OK, where is going? Where is the highest pressure going to be?

00:16:54.980 -- Top or on the bottom. The highest change in pressure on

00:16:58.687 -- the top is if we call this region one and this region 2 and

00:17:03.405 -- this region 3. Where's the higher pressure going to be in

00:17:07.112 -- region 2 or region three there?

00:17:09.920 -- Region 2.

00:17:12.000 -- That's why it's a stronger shock. There's a larger increase

00:17:15.510 -- in the pressure, so here P2.

00:17:18.380 -- Is going to be greater than P1 everybody by that.

00:17:23.310 -- K. Aerodynamicists what's that going to generate?

00:17:30.450 -- You have a wedge. Here you have an angle of attack right

00:17:33.906 -- here. The pressure on the bottom is higher on the is the

00:17:37.362 -- pressure on the bottom is higher than the pressure on

00:17:40.242 -- the top. What do you get lift?

00:17:43.660 -- That's supersonic aerodynamics, right there in a nutshell.

00:17:47.680 -- There's no nice curved airfoils.

00:17:51.800 -- OK, with this wedge right here, just just giving it an angle of

00:17:56.701 -- attack in a supersonic flow, you're going to generate a

00:18:00.471 -- higher pressure on the bottom then you will on the top and you

00:18:05.372 -- generate lift. Out of that?

00:18:09.570 -- OK. Next week, we'll talk more about supersonic airfoils

00:18:13.434 -- because there's one other. There's one other key ingredient

00:18:16.116 -- that we need to know more about that, but this is the crux right

00:18:20.288 -- here. OK, just because of that pressure difference because of

00:18:23.697 -- the way that you have a stronger shock on the bottom

00:18:26.370 -- then you have on the top, you're going to get higher

00:18:29.043 -- pressure on the bottom and lift.

00:18:33.590 -- That's supersonic aerodynamics right there, OK questions.

00:18:39.810 -- Alright.

00:18:41.650 -- Let's talk about diffusers. Now diffuser that is just a

00:18:45.160 -- fancy name for a jet inlet for the intake. That's where

00:18:49.021 -- the air comes into the airplane. Let's see now what

00:18:52.531 -- we can do in our now. Now that we know about oblique

00:18:56.743 -- shockwaves and normal shocks, let's apply those to see if

00:19:00.253 -- we can figure out why diffusers are designed the

00:19:03.412 -- way they are here. OK, again, here's the equation that we

00:19:07.273 -- started out class with.

00:19:10.200 -- That to minimize the change in entropy, we want to keep peanut

00:19:14.988 -- two as high as possible. OK, in supersonic aerospace design

00:19:18.978 -- that's called pressure recovery. We want to recover as much

00:19:22.968 -- pressure as possible here. OK, we want to keep peanut to as

00:19:27.756 -- high as possible here, OK?

00:19:30.640 -- So let's look at a couple of jet inlet designs and see how the

00:19:35.792 -- stagnation pressure is going to be here. OK, good, so we're

00:19:39.840 -- going to look at two inlets.

00:19:42.930 -- Air is coming into both of those inlets out of Mach

00:19:46.131 -- number of 2.5.

00:19:48.080 -- OK, in the first inlet design all we have is a normal shock.

00:19:54.510 -- OK, what is the stagnation pressure loss going to be in

00:19:58.019 -- that normal shock? OK.

00:20:00.340 -- Then we're going to have we're going to have air that

00:20:04.311 -- comes in again. Same lot number 2.5. Everything is the

00:20:07.921 -- same. It's going to go through a turn of 18 degrees.

00:20:12.930 -- So it's going to create an oblique shock. That's going to

00:20:16.263 -- slow it down, and then it goes through a normal shock.

00:20:20.720 -- OK, now you might ask, why does it have to be a normal shock at

00:20:25.550 -- the end there? So for jet turbine airplanes, the air inlet

00:20:29.092 -- always has to be subsonic.

00:20:31.720 -- OK, if you have jet turbines, OK, compressor blades that are

00:20:35.350 -- spinning that air has to go into that turban, sub sonically.

00:20:38.980 -- Otherwise you get shock waves that form along the blade, and

00:20:42.610 -- that's not a very good process. OK, so the idea in the jet

00:20:46.900 -- aircraft supersonic air comes in, you slow it down, recover as

00:20:50.530 -- much pressure as possible that sends it through the jet turbine

00:20:54.160 -- and then it goes out the

00:20:56.140 -- exhaust. OK, that's that's the process here. Alright, let's

00:21:00.488 -- look at this.

00:21:02.860 -- Get your books out.

00:21:07.380 -- And we have our very first inlet design right here, and let's see

00:21:13.893 -- what's going on here. OK, we have an inlet.

00:21:19.020 -- To this aircraft looks like

00:21:20.845 -- this. Looks like this here comes in at a Mach number of two

00:21:28.330 -- point 5K and as it enters this inlet here a normal shock.

00:21:35.800 -- Forms right at the inlet.

00:21:38.020 -- OK.

00:21:40.550 -- Good. We have that.

00:21:44.610 -- Will have that P1 is equal to 70 kilopascals and that T one is

00:21:49.902 -- equal to 200 degrees Kelvin.

00:21:52.880 -- OK, we want to know.

00:21:56.420 -- How much stagnation pressure is lossed in this process? Right

00:22:00.720 -- here? OK, so you can go to your normal shock tables. So go to

00:22:06.740 -- your normal shock tables and figure out for this inlet

00:22:11.040 -- design, what peanut too.

00:22:13.470 -- Over P, not one, is equal to.

00:22:21.160 -- What do you get?

00:22:26.200 -- 24 nine. 0.499 can we round that up to .5?

00:22:32.970 -- OK, that says that you have already lossed half the

00:22:39.180 -- available thrust.

00:22:42.040 -- In this design.

00:22:44.360 -- It's not very good.

00:22:46.970 -- That's terrible. OK, all the available thrust that you could

00:22:51.050 -- to generate to make your plane go faster. You've lost half of

00:22:55.250 -- it just because it sends through a normal shock.

00:22:59.940 -- OK, not good.

00:23:01.900 -- Not good, OK? Let's look at the second design now, here. So

00:23:06.460 -- let's go to the computer so we can see that again. So here now

00:23:11.780 -- we have a wedge right here. Flow comes in supersonically. There

00:23:15.960 -- is an oblique shock that's formed, and then a normal shock

00:23:20.140 -- that's formed here on the inside. OK, this normal shock,

00:23:23.940 -- right? There is called the terminal shock. It's the very

00:23:27.740 -- last shockwave in the system.

00:23:30.830 -- OK, remember as the air crosses it goes through the inlet an

00:23:34.634 -- approaches the engine. It has to

00:23:36.536 -- be subsonic. OK, so it goes. It's subsonic across a normal

00:23:41.039 -- shockwave. That's how it finally is going to slow down here. OK,

00:23:45.371 -- so let's calculate this problem right here, OK?

00:23:49.250 -- So we have a wedge. Looks like this and we have the top of

00:23:56.586 -- the inlet right there here.

00:24:00.630 -- OK, the flow comes in at a Mach number of 2.5 and there is an

00:24:07.605 -- oblique shock. That forms right across there and then a normal

00:24:13.078 -- shock right down here.

00:24:16.400 -- OK, we were given in this problem. This has a turning

00:24:21.834 -- angle. Delta is 18 degrees.

00:24:25.040 -- OK, let's we have three different flow regimes here, so

00:24:29.800 -- let's call this region 1.

00:24:32.980 -- Call this region 2 and Region 3 right there.

00:24:40.950 -- OK.

00:24:44.430 -- Are we good? Are we good with the visual here?

00:24:48.220 -- Pretty straightforward problem. We are now two separate

00:24:51.948 -- shockwaves. OK, so now you want to get your app out here for M1

00:24:58.472 -- equal to 2.5 and Delta of 18 degrees right there tell me what

00:25:04.530 -- you get. First off for M2 and then tell me what P not 2 /

00:25:11.520 -- P nought one is.

00:25:17.040 -- See if it comes with my numbers here.

00:25:20.840 -- Yep, 1.739 is the Mach number in region 2 peanut

00:25:26.720 -- two over peanut one.

00:25:30.750 -- 1.

00:25:32.240 -- 8870.88 seventh OK, I got 7 as well. I thought I heard you say

00:25:38.372 -- 6.8877 really that's one part out of 88,000. I'm not going to

00:25:43.628 -- worry about that too much. OK, we go there.

00:25:48.520 -- OK, you could go com prop gives you that you could go to the

00:25:52.300 -- charts and get the same thing. No big deal. Now what's the next

00:25:55.810 -- step in the problem?

00:25:57.580 -- What do we do?

00:26:00.860 -- It's a normal shock problem.

00:26:03.140 -- OK, so when we get to more complicated problems, we're

00:26:06.580 -- going to use the same process. You just go through a serially.

00:26:10.708 -- What's going on here? It's an oblique shock problem and then a

00:26:14.836 -- normal shock problem, but the Mach number in region 2 is

00:26:18.620 -- different than the model number in region 1, so you just have to

00:26:23.092 -- keep that into consideration there. OK, so for now we know

00:26:26.876 -- what the model number in Region 2 is. So from the normal shot

00:26:31.348 -- tables now. Read off

00:26:34.622 -- M3. And read off now Peanut three over peanut two.

00:26:40.574 -- What do you get?

00:26:48.350 -- What's M3 go into the normal shock tables for an M2 that you

00:26:52.198 -- could say that's one point 7 four just to read it off there?

00:26:56.990 -- What do you get?

00:27:01.730 -- 0.63 should it be subsonic?

00:27:06.860 -- Better be 'cause it's going across a normal shockwave right

00:27:09.980 -- there. What is peanut three over Peanut 2 for that normal shot?

00:27:18.500 -- Say that again.

00:27:20.480 -- .8 Four K 0.84.

00:27:26.690 -- OK, so we're going to look at some trends here before we

00:27:31.718 -- calculate our final number 'cause we want to know what

00:27:35.908 -- peanut three is compared to peanut one? That's our. That's

00:27:40.098 -- our stagnation. Pressure loss from this region to this region

00:27:44.288 -- right here. Look at look at these two numbers right here for

00:27:49.316 -- model number of 1.739. You lose

00:27:51.830 -- 16%. Of your stagnation

00:27:54.416 -- pressure. If you go up from 1.742 amount number 2.5, you

00:28:00.560 -- lose half. Of your stagnation pressure.

00:28:04.960 -- OK, let's look at those trends here.

00:28:09.680 -- OK, if you look at the normal shock tables right here.

00:28:15.730 -- Here is Peanut peanut, two over peanut one right there

00:28:20.070 -- for this mock number. Notice that to a mock number, let's

00:28:24.844 -- just say right here at amount number of 1.58 you lose 10%

00:28:30.052 -- of your stagnation pressure.

00:28:32.900 -- OK, for model number of 1.2 you only lose 1%.

00:28:39.190 -- Of your stagnation pressure. OK, if you go to a Mach number

00:28:45.430 -- of two right. Over here you lose

00:28:49.070 -- 28%. Of your stagnation

00:28:51.705 -- pressure. Everybody see what those values are coming from.

00:28:55.460 -- So. You're an aircraft designer. What should you do?

00:29:02.410 -- What should you do?

00:29:06.830 -- How about if you take this right here? Shouldn't you slow

00:29:10.350 -- that flow down as much as possible? It's going to have

00:29:13.870 -- to go through a normal shock.

00:29:17.110 -- But then you want that normal shock right there to

00:29:19.910 -- be as weak as possible.

00:29:22.460 -- Everybody see that. OK, so let's calculate now Peanut 20 excuse

00:29:28.168 -- me peanut three over peanut one that is the stagnation pressure

00:29:33.459 -- loss from this region to this region right here. OK so.

00:29:40.270 -- Peanut 3 / P nought one is equal to P not 3 / P

00:29:47.452 -- not two that's this.

00:29:50.370 -- Multiplied by peanut two over peanut one.

00:29:57.110 -- We know those two values .8.

00:30:00.330 -- 877 times .84.

00:30:07.840 -- I get a value of 0.745.

00:30:18.740 -- Compare values again. What have you done to your aircraft?

00:30:25.130 -- You have improved the pressure recovery by 25 points.

00:30:33.850 -- Instead of losing half of it, instead of losing half of your

00:30:37.786 -- stagnation pressure, now you lose just one quarter of it.

00:30:41.890 -- And what have you done?

00:30:44.210 -- All you did was put a little wedge at the inlet right there.

00:30:51.440 -- OK, This is why I wanted you to keep in your noggins. Delta S

00:30:56.410 -- changing entropy over R is equal to minus natural log of the

00:31:00.670 -- stagnation pressure loss.

00:31:02.590 -- Stagnation pressure is directly related to the thrust, so now

00:31:06.890 -- you have made your aircraft.

00:31:09.930 -- Actually 50% better you've improved in performance.

00:31:14.170 -- And all you did was put a wedge here before that terminal shock

00:31:19.110 -- is the only thing you did.

00:31:22.570 -- And you can get more thrust out

00:31:23.592 -- of your play. Is that cool or what?

00:31:26.920 -- OK, let's see. Here's an F-14 in low, by the way. Actually,

00:31:31.240 -- before we get to that before we get to that here.

00:31:36.750 -- Let's go to let's go to the overhead here. Could you see

00:31:41.526 -- that a natural extension to this problem might be if now you have

00:31:46.700 -- a wedge and you have a 9 degree

00:31:49.884 -- turn. And then, and another nine degree turn here and then.

00:31:57.270 -- It goes to the inlet right here. What have you got?

00:32:02.140 -- M1 is equal to 2.5. You'll have an oblique shock that

00:32:06.144 -- forms there.

00:32:08.700 -- The flow follows the wall. You have another oblique shock here.

00:32:15.650 -- Your total turning angle is 18 degrees, just like you did

00:32:19.236 -- before, but now you send it through two oblique shockwaves,

00:32:22.496 -- not just one. And then you have your terminal shock right there.

00:32:27.110 -- OK, as it goes into the inlet right here. So you have

00:32:30.446 -- region 1, Region 2, Region 3, Region 4. How would you solve

00:32:33.782 -- that problem?

00:32:37.080 -- Same way that we did the first problem. It's an oblique shock

00:32:40.488 -- across here with the turning angle of nine degrees and some

00:32:43.612 -- Mach number. Then over here you have a new model number M2

00:32:47.020 -- Anna Divina, same turning angle of 90 degrees there and

00:32:49.860 -- then you have a normal shock.

00:32:52.990 -- OK, in this design here Peanut 4 divided by peanut one is

00:33:00.550 -- equal to 0.79.

00:33:03.680 -- So you've improved the performance from 70 from losing

00:33:08.891 -- 25% to losing 21%.

00:33:12.880 -- OK.

00:33:14.970 -- Alright, now we can look at F-14

00:33:18.309 -- Tomcat here. Here is that inlet OK.

00:33:24.060 -- Uh, let's see what you can see here. OK, so actually, actually

00:33:27.852 -- here we'll look at it from here and then we'll see the picture.

00:33:31.960 -- So this is an F-14 Tomcat. We saw this in class last time

00:33:36.068 -- here. Here are the inlets here. Actually, if you look in the

00:33:39.860 -- overhead here, there's an inlet and there's an inlet there.

00:33:43.020 -- Notice it has a sharp leading

00:33:44.916 -- edge. OK, if you look at it on the side right there.

00:33:50.410 -- OK, there it has a very sharp leading edge. If you look

00:33:55.078 -- inside right here, zoom in. I'll just a little bit more.

00:33:59.357 -- You can see there's a hinge there and a hinge there.

00:34:06.080 -- So what this airplane is designed to do is that depending

00:34:10.469 -- on the speed, this inlet right here can change angles.

00:34:16.310 -- OK, and and what is going to be The upshot of changing the

00:34:20.561 -- angles? What is that? What is the trying to do?

00:34:25.230 -- Recover the pressure.

00:34:28.310 -- So now let's go look at the computer. You can get a better

00:34:32.301 -- idea of what it looks like here. There you can see a hinge Anna

00:34:36.599 -- plate right there. Here you can see another hinge and another

00:34:40.960 -- plate right there. So in this aircraft that's going to produce

00:34:44.645 -- three oblique shockwaves at the inlet, one at the very front. So

00:34:48.665 -- you can't see it. But that's right that first inlet. This is

00:34:52.685 -- where the second oblique shockwave forms. Here's where

00:34:55.365 -- the third oblique shockwave forms. And then inside here is

00:34:58.715 -- where the normal shock form. So very nice everybody see that we

00:35:02.735 -- can see it both at the inset right, right there in the upper

00:35:07.090 -- right corner. Thanks in the control room. That's very good,

00:35:10.878 -- OK? So good again, depending on the speed of the aircraft and

00:35:16.140 -- its conditions, it automatically adjusts the angles there.

00:35:20.410 -- To maximize the pressure recovery and generate the most

00:35:23.209 -- stress in the airplane.

00:35:25.910 -- Is that cool or what? That's awesome. That is awesome

00:35:29.210 -- engineering design right there. OK, so here. Here's a little

00:35:32.510 -- schematic of the inlets here. Here, the first one we see what

00:35:36.470 -- the flow pattern looks like for subsonic speeds, so obviously

00:35:39.770 -- there's going to be no shock waves that form there, so the

00:35:43.730 -- plane has to take off and ask to fly subsonic Lee at some point.

00:35:48.350 -- So it comes through here. It's got a little. It's got a little

00:35:52.640 -- bleed or there at the top. Air comes in this way and it goes

00:35:57.260 -- and notice here. It's always a

00:35:59.240 -- subsonic diffuser. Because you want the air going into the

00:36:02.668 -- engine and the jet turbine engine here to be subsonic. OK,

00:36:06.364 -- when it gets to transonic speeds, so that's from a model

00:36:10.060 -- number of .8 to about 1.2 ish in that range. OK, notice that you

00:36:14.764 -- have a normal shock that forms right there in the front, or

00:36:18.796 -- you're worried about the losses across that normal shock.

00:36:22.990 -- Because why Jesus? Why is that?

00:36:29.130 -- The upstream lot number here is really close to one and so the

00:36:33.745 -- stagnation pressure losses for Mott numbers close to one are

00:36:37.295 -- don't say negligible, but are pretty small, so not to worry

00:36:41.200 -- about that, OK?

00:36:43.700 -- In and out at supersonic speeds, look at this. There is an

00:36:48.068 -- oblique shockwave right there. There is an oblique shockwave

00:36:51.344 -- right there. There is an oblique shockwave right there and here

00:36:55.348 -- you can see the actuators. This is what moves those plates into

00:36:59.716 -- position to get the get the best pressure recovery and then

00:37:03.720 -- finally at this point is the terminal or the normal shockwave

00:37:07.724 -- right there behind that shock the flow subsonic and it goes

00:37:11.728 -- into the diffuser right here.

00:37:16.760 -- So now you could look at a jet aircraft and say I know why

00:37:19.406 -- it's designed that way.

00:37:21.270 -- To maximize stagnation pressure to maximize the pressure

00:37:25.382 -- recovery. OK, unfortunately, this plane does not fly anymore,

00:37:30.008 -- but just to let you know, there are aircraft companies are

00:37:35.662 -- looking to redesign or to remake this aircraft. In some sense,

00:37:41.316 -- this is a supersonic transport designed to fly from either

00:37:46.456 -- France or London, Paris or London across the Atlantic Ocean

00:37:51.596 -- supersonically. Has a cruising speed of Mach number

00:37:55.373 -- of two and land in New York OK. If you are ever in

00:38:01.340 -- Seattle, there's the Museum of Flight just South of

00:38:05.471 -- Seattle off of off of Hwy 5. I think there.

00:38:11.840 -- And there's a super Sonic.

00:38:14.670 -- There's there's this airplane there you can go check out OK,

00:38:19.730 -- look at the intakes here at the

00:38:22.950 -- bottom. OK, notice also even before we get there, notice the

00:38:28.090 -- Delta wing shape right there, because when this is flying

00:38:32.130 -- supersonically you want that conical you want the airplane to

00:38:36.170 -- sit inside that conical shockwave right there. Then as

00:38:39.806 -- it goes down inside here, notice the angle of those inlets right

00:38:44.654 -- there. Let's take a look and see what those inlets look like

00:38:49.502 -- right here. So you can see says danger. It's got hinges here.

00:38:54.620 -- And here as well.

00:38:57.370 -- So is this plane screws in over the Atlantic Ocean, creating

00:39:01.165 -- shockwaves? You remember the shockwave sounded like.

00:39:04.390 -- That's why it doesn't fly over the continental United States

00:39:07.750 -- flies over the ocean. OK, that those plates can go up and down

00:39:12.118 -- depending on its speed and the other conditions of the flight

00:39:15.814 -- there. To maximize the pressure recovery before it goes into the

00:39:19.510 -- engine there. OK fact, here's a schematic of that of that.

00:39:23.206 -- What's called the shock train? OK, so here's the first

00:39:26.566 -- shockwave that's an oblique shockwave. You know what? You

00:39:29.590 -- know, what oblique shockwaves are. So you can look at this

00:39:33.286 -- intelligently. Here's the 2nd.

00:39:34.700 -- Oblique shockwave right here. These are actually compression

00:39:37.756 -- waves and we'll talk about these next week, right here and

00:39:41.958 -- then another shockwave here. So 1/2 compression, 3 right there

00:39:45.778 -- and then finally the terminal shock there on the inside.

00:39:49.598 -- That's the normal shock. Downstream of that it's

00:39:52.654 -- subsonic flow and goes into the engine.

00:39:57.790 -- OK, and again you can adjust.

00:40:00.320 -- That ramp right there to maximize the pressure recovery.

00:40:05.120 -- Good, here is a MIG fighter aircraft, so this is a this is a

00:40:10.776 -- Russian Russian jet. It was used after World War Two during the

00:40:15.624 -- Korean War. OK, but notice it's design here. There's a spike

00:40:20.068 -- that sits there right in the center so the air comes in and

00:40:25.320 -- hits that spike. And what's going to form when it hits the

00:40:30.168 -- spike? An oblique shockwave. Actually, in this case of

00:40:33.804 -- conical shock, but.

00:40:35.090 -- Not a normal shot. OK can you see? Yeah you can see

00:40:39.074 -- on the screen there can you see this line right there?

00:40:44.140 -- What do you think that is?

00:40:47.670 -- An angle change.

00:40:50.040 -- So it comes in and the initial change in the flow is half

00:40:54.408 -- whatever that conical angle is right there. Then it hits this

00:40:58.104 -- an another oblique shockwave forms follows the wall, and it

00:41:01.464 -- eventually goes into its inlet right here and down inside

00:41:04.824 -- there's going to be normal shock.

00:41:08.700 -- OK. Here's another one right here. This is from a. I think

00:41:14.908 -- this is an F-104 Starfighter, so again, an older supersonic jet

00:41:19.506 -- fighter here. You can see the inlet right here, Annacone.

00:41:24.480 -- OK, so the flow goes over this and forms a conical shockwave.

00:41:28.032 -- Here it's probably a little hard to see on your on your on

00:41:31.880 -- the TV screens there, but you see these two little Nicks

00:41:35.136 -- right up there. OK, this cone. In fact you could see it right

00:41:38.984 -- there from this line that cone can move in and out.

00:41:45.180 -- So again, depending on the speed of the aircraft that cone is

00:41:49.476 -- going to go out or kind of go in to generate whatever sort of

00:41:54.488 -- oblique shockwave you need to maximize the pressure recovery.

00:41:57.710 -- OK, this is an older fighter aircraft in the 1960s and so

00:42:02.006 -- that moving the moving inlet technology isn't quite as mature

00:42:05.586 -- as it was for the SST, and some of the other aircraft. OK, but

00:42:10.598 -- the same principle holds. It adjusts this cone, moves in and

00:42:14.536 -- out so that.

00:42:15.760 -- So that the flow field generates the maximum amount of pressure

00:42:20.380 -- recovery in the airplane, Sir.

00:42:24.030 -- Square.

00:42:28.080 -- It depends. OK, so that's that's a great question. It

00:42:31.390 -- depends on where you put the inlets. Usually on the side

00:42:35.031 -- of the aircraft, right? Here, 'cause the flows coming right

00:42:38.341 -- down the this part of the fuselage. It tends to hug the

00:42:42.313 -- wall a little bit better. Then you haven't inlet here.

00:42:47.170 -- That that really isn't going to work for the F-14 Tomcat because

00:42:50.698 -- of the armaments and other stuff that you had on the side there.

00:42:54.520 -- So depends on the design. Depends on the design there and

00:42:57.754 -- how you want your fuselages to

00:42:59.518 -- work there. OK, any questions?

00:43:04.170 -- OK, this is a

00:43:08.162 -- subsonic turbofan. Jet inlet.

00:43:13.490 -- Can you tell the difference between that inlet and the other

00:43:16.548 -- inlets that we saw before?

00:43:18.940 -- OK, are shockwaves going to form here?

00:43:23.530 -- Negative. OK, So what you see here are nice curved surface

00:43:27.710 -- is you don't see any sharp surfaces on a subsonic

00:43:31.510 -- aircraft. OK, nice curved surface. Is there? These

00:43:34.550 -- compressor blades spin this way and compress the air as it

00:43:38.730 -- goes inside and comes out the engine. There's already coming

00:43:42.530 -- in subsonic Lee.

00:43:44.800 -- OK, so that's the difference between a subsonic inlet and

00:43:50.530 -- a supersonic inlet.

00:43:53.990 -- OK, let's just hypothesize here. Let's say that we use

00:43:57.790 -- this plane in a fly supersonically. What's going

00:44:00.830 -- to form on the outside right there?

00:44:05.640 -- Shock waves normal shocks, oblique shocks. What do

00:44:07.976 -- you think?

00:44:10.770 -- OK, since that surrounded surface right there, it's not

00:44:13.443 -- a sharp surface. You're likely going to get a

00:44:16.116 -- detached bow shock that's there. And what kind of

00:44:18.789 -- losses are associated with that?

00:44:21.710 -- Huge.

00:44:23.390 -- OK, we've just shown here that in oblique shockwave the losses

00:44:26.195 -- are less than for a normal shot.

00:44:28.930 -- OK. Good alright?

00:44:34.390 -- Questions on this?

00:44:37.270 -- We'll talk more. We'll talk more about it. OK, alright, you're

00:44:41.615 -- going to have a homework problem or some homework problems

00:44:45.565 -- related to reflected shockwaves. OK, so let's look at this. Let's

00:44:49.910 -- look at this particular diagram

00:44:51.885 -- right here. So we have flow that's in a duct.

00:44:56.706 -- Duct is coming down here has a Mach number of one.

00:45:01.403 -- It's coming down Supersonically and now

00:45:03.965 -- here we have an angle change of 12 degrees.

00:45:08.840 -- OK, so what's going to happen? Well, add this for this Mach

00:45:12.368 -- number and this turning angle of 12 degrees you're going to get a

00:45:16.190 -- shock angle. And the flow turns Y.

00:45:21.340 -- The flow follows the wall.

00:45:25.050 -- OK, so it's going to come down this way and it sees this little

00:45:28.858 -- change right there and it changes direction, so it's going

00:45:31.578 -- down horizontally and then it turns up 12 degrees.

00:45:35.290 -- OK. Then the flow comes this way right here, and then it sees

00:45:41.310 -- this wall on the top side right

00:45:43.830 -- there. So now the flow is going to change directions again.

00:45:50.270 -- So it's coming down.

00:45:52.620 -- It goes up 12 degrees. It's going to hit the wall on the top

00:45:56.134 -- that's parallel to the bottom wall on the other side. Here,

00:45:58.895 -- it's going to hit that wall and

00:46:00.652 -- change directions again. So now this direction of M3 is the same

00:46:05.413 -- as M1. The directions the same.

00:46:08.890 -- How would you solve that problem?

00:46:15.480 -- Could you solve the problem from Region 1 to region 2?

00:46:20.110 -- You know in one you know the turning angle. You could get the

00:46:23.711 -- shock angle and you could get the Mach number right there.

00:46:27.490 -- In order to see that.

00:46:29.570 -- OK, how would you solve it from Region 2 to region 3?

00:46:35.010 -- Same thing.

00:46:37.270 -- However, however, are the turning angles the same?

00:46:43.260 -- Turning angles are the same, what's different?

00:46:48.640 -- Get shock angles gonna be different? How does

00:46:51.016 -- M2 compared to M1?

00:46:53.850 -- Smaller.

00:46:56.800 -- OK, so you solve it from Region 1 to region 2.

00:47:00.672 -- From this Mach number M1 and that turning angle.

00:47:05.060 -- Then you're going to calculate or determine what your M2 is.

00:47:09.100 -- And then solve this turning angle problem right here with

00:47:12.900 -- M2, not M1.

00:47:14.930 -- M2 with the turning angle of 12 degrees and it comes

00:47:18.590 -- out this way right here.

00:47:22.260 -- Everybody see that.

00:47:26.100 -- That's all reflected shock is all. Reflected shock is, it's

00:47:29.490 -- just, it's just another in a series of oblique shockwaves as

00:47:33.219 -- it comes down the duck there.

00:47:36.080 -- Nothing more than that. OK, and all because of the changes here

00:47:40.892 -- in the angles.

00:47:43.790 -- OK.

00:47:45.780 -- I believe that you have a homework problem, will just

00:47:49.960 -- outline it here. OK, you have a homework problem.

00:47:55.230 -- Let's see here.

00:47:57.330 -- Have a duct comes down here and

00:48:00.032 -- there's some. Change here Mitch was at 5 degrees.

00:48:06.100 -- We talked about this in class. I think this is 5 degree change

00:48:10.247 -- here. OK then you have another

00:48:12.161 -- wall. Here, and this is bent down at 2 degrees.

00:48:22.770 -- 2 degrees right there.

00:48:24.960 -- OK, so you have a flow.

00:48:28.100 -- Coming down this way, M1, what's going to form first?

00:48:34.060 -- What do you get? 'cause of this turn right up there?

00:48:39.150 -- An oblique shot.

00:48:41.360 -- So I'm going to be shocked that comes here.

00:48:44.960 -- OK, and this region 1 this is Region 2 right here. Given

00:48:49.124 -- that turn and that model number, can you find the

00:48:52.594 -- pressure and all the good stuff in region two there?

00:48:58.020 -- It's just an oblique shock problem. OK, now remember the

00:49:02.180 -- flow follows the wall.

00:49:04.750 -- So now it's coming down here at 5 degrees.

00:49:08.290 -- OK, coming in this direction.

00:49:10.440 -- However. This turn, this wall at the bottom is not.

00:49:16.700 -- 5 degrees.

00:49:19.680 -- OK.

00:49:22.000 -- Let's do a hypothetical. If this wall did come down at 5 degrees.

00:49:29.360 -- What would form from region 2 to this region down here?

00:49:33.910 -- Actually nothing.

00:49:37.550 -- 'cause it's going to go down this duck and turn this way.

00:49:41.650 -- You could have a normal shock sometime later on there, but you

00:49:44.134 -- all you do is turn in the flow.

00:49:46.860 -- OK, if this were five degrees. However, now this angle is 2

00:49:52.872 -- degrees from the horizontal.

00:49:55.800 -- So guess what's going to form.

00:49:59.270 -- No big shockwave.

00:50:00.590 -- Right here.

00:50:04.110 -- OK.

00:50:06.530 -- I will leave it up to your geometrical Wiles

00:50:09.959 -- to figure out what this turning angle has to be.

00:50:15.750 -- Actually kind of hinted on how you could solve it. OK, the

00:50:19.698 -- turning angle is what you're going to figure out. OK, this

00:50:23.317 -- turn here is 2 degrees. What is the turning angle of that flow?

00:50:30.880 -- Think about it, yes.

00:50:36.130 -- What is the form here? Because this is where it's being turned.

00:50:43.390 -- OK, so it's coming OK. So the reason the reason it's attached

00:50:46.762 -- here 'cause the flow comes down and that's where it turns.

00:50:50.780 -- OK, so in this problem it's just kind of hypothetical that had

00:50:54.416 -- this turn right. Here we have all the conditions such that

00:50:57.749 -- this oblique shockwave comes down right to that point.

00:51:02.210 -- OK, now it's being turned again.

00:51:06.130 -- From here. Again, if this wall were turned down 5 degrees, it

00:51:10.540 -- would be parallel with the one at the top. It's only turned

00:51:14.308 -- down 2 degrees.

00:51:16.480 -- So that means there's an angle change there. An since

00:51:19.360 -- there is an angle change right there, and oblique

00:51:21.952 -- shockwaves going to form.

00:51:25.180 -- That makes sense. You still look.

00:51:28.740 -- How about how about since since we're talking about fine

00:51:33.030 -- degrees, let's blow up the picture a little bit. OK, let's

00:51:37.749 -- say this makes a turn of of, let's say, 20 degrees.

00:51:43.660 -- K and this makes a turn of five degrees. Let's just say so this

00:51:50.310 -- is 20 degrees.

00:51:53.010 -- So we have an oblique shockwave that's here OK. Can

00:51:55.750 -- you see now? The flow follows the wall. It's going to come

00:51:59.038 -- down this direction right here, but what does it see

00:52:01.778 -- when it hits that wall?

00:52:05.170 -- Can you see how it's getting

00:52:06.370 -- bent up a little bit? OK, so this was 20 degrees. We said

00:52:10.610 -- that this is 5 degrees right here, so it's running into

00:52:14.185 -- this wall so it has to change directions.

00:52:18.030 -- That's why I emphasized the flow

00:52:19.572 -- follows the wall. Comes down here now it's going to get bent.

00:52:24.990 -- Here, if this were 20 degrees

00:52:27.810 -- down here. If this bottom were bent at 20 degrees in, that flow

00:52:31.563 -- would just follow the wall all

00:52:32.721 -- the way through. But now it's only turned 5 degrees though,

00:52:36.032 -- so there's an angle change and you create an oblique

00:52:38.722 -- shockwave and the flow is going to follow this wall.

00:52:42.520 -- So I've exaggerated the angles here.

00:52:46.330 -- But it's the same principle about what's going on in that

00:52:48.574 -- part of the problem.

00:52:50.620 -- Good good.

00:52:53.310 -- Anybody else?

00:52:55.490 -- OK, don't let reflected shocks get to you. It's nothing but a

00:53:00.074 -- series of single oblique shockwaves, so if you can

00:53:03.512 -- solve one oblique shockwave, you just add on whatever the

00:53:07.332 -- turns are and keep going from there. It's all it is OK.

00:53:11.916 -- Don't let it intimidate you.

00:53:15.230 -- OK, let's see. We got here. Let's look at now the inlets

00:53:22.334 -- to the SR-71.

00:53:25.560 -- OK, here we go right here and notice that these inlets are

00:53:32.196 -- spiked. OK, so you see this spike right here. This is where

00:53:38.151 -- the air enters OK, and guess what those spikes move in and

00:53:42.963 -- out depending on the speed of

00:53:45.369 -- the aircraft. To recover as much stagnation pressure as possible.

00:53:51.030 -- OK, let's see what the shock train looks like for this. In

00:53:55.650 -- fact, we'll do that little inset trick again in the room. There.

00:54:00.270 -- Let's go to the computer. OK, and here is what that here's

00:54:04.890 -- what the inlet to the SR-71 looks like. Check this out. Here

00:54:09.510 -- is the first oblique shockwave that's formed because of the

00:54:13.360 -- nose cone. OK, so it comes down this way. It follows the wall

00:54:20.088 -- comes in here now this is the first. This is the cowl lip

00:54:26.172 -- right there, so there's a second oblique shockwave and then this

00:54:31.320 -- inlet is designed to go through now a number of reflected

00:54:36.468 -- shocks, 123456 oblique

00:54:37.872 -- shockwaves. Before it reaches its terminal shock, right

00:54:40.942 -- there and then, the flow subsonic all the way through

00:54:43.802 -- there. Why is that?

00:54:47.590 -- What's that going really fast? OK, this this

00:54:52.510 -- particular design? This aircraft recovers. I think

00:54:56.815 -- it's 97% of the stagnation pressure.

00:55:03.140 -- It cruises that amount number of

00:55:04.886 -- three. Remember the problem that we had earlier in class? We had

00:55:09.650 -- a model number 2.5. It just went through a normal shock. It lost

00:55:14.070 -- half of its stagnation pressure through this design right here.

00:55:17.470 -- Sending it through all these small oblique shockwaves. OK,

00:55:20.530 -- this small weak shockwave oblique shockwave. Then it

00:55:23.250 -- recovers more that pressure, it just sends it through a bunch of

00:55:27.330 -- 'em before it goes through that final normal shock, which is a

00:55:31.410 -- very weak and or shockwave.

00:55:34.230 -- So this particular inlet design then slows the fluid down the

00:55:38.927 -- air down very efficiently.

00:55:41.330 -- It loses 3% of the stagnation pressure.

00:55:45.970 -- That's awesome. That is awesome. OK, and again as this is taking

00:55:50.960 -- off and landing and cruising up to speed that cone goes in and

00:55:55.601 -- out there again to maximize the pressure recovery as it goes

00:55:59.528 -- through those. Parts right there.

00:56:03.290 -- I love that, OK?

00:56:07.030 -- Will talk about ramjet engines now before we talk about ramjet

00:56:11.584 -- engines. Let's talk, let's just talk general engine like

00:56:15.310 -- internal combustion engines first, so we have some. We have

00:56:19.450 -- some members of the snowmobile team here is that right? OK,

00:56:24.004 -- what is what is the pressure ratio in your combustion engine?

00:56:28.558 -- So pressure ratio. So that means the air goes into the piston

00:56:33.526 -- cylinder head. There piston

00:56:35.182 -- compresses it. So the pressure gets high. What does that

00:56:38.986 -- increase in pressure? What is it about? About 10K so air comes in

00:56:43.367 -- an atmospheric pressure. You compress it to get high pressure

00:56:46.737 -- so you have fuel that's in there air at high pressure you ignite

00:56:51.118 -- it so you have high temperature, high pressure air that expands

00:56:54.825 -- the piston goes down right? So that's that's the compression

00:56:58.195 -- ratio in an aircraft engine will be there. OK, so now let's think

00:57:02.576 -- about that problem. Let's think about that problem an for. Right

00:57:06.283 -- now we're going to hypothetical. Let's pretend no shocks.

00:57:09.410 -- Let's just pretend no shocks. OK, no shocks here. So I have

00:57:14.138 -- air that's coming this way and it goes into an engine right

00:57:18.866 -- here. And let's just say.

00:57:22.230 -- Let's just say that I want to have that same pressure

00:57:26.850 -- recovery here P.

00:57:29.660 -- If I write it down, I kind of give it away here. I'll just

00:57:34.280 -- call it P2 over P1, no shocks. Remember the hypothetically no

00:57:37.910 -- shockwave here, so the air comes in and that pressure goes up by

00:57:42.200 -- 10. So we want that increasing pressure to be 10. OK, let's

00:57:46.160 -- just say that no shocks, so remember what happens to the

00:57:49.790 -- speed of the flow of the pressure goes up? What happens

00:57:53.420 -- to the speed the flow goes down? OK, so let's look at now. This

00:57:58.040 -- air that comes in.

00:57:59.440 -- It has some static atmospheric pressure. It's going to slow

00:58:02.870 -- down before it gets into the

00:58:04.928 -- compressor blades. Right here. OK, well actually no no.

00:58:08.617 -- Compressor blades here. It's just going to come down and it's

00:58:12.148 -- going to slow down and let's just say that the Mach number is

00:58:16.321 -- about 0. Let's just say so. We slow it down a bunch there. What

00:58:20.258 -- kind of pressure are we talking about there for the model number

00:58:22.586 -- 0? Stagnation, so look up in your tables. Look

00:58:27.046 -- up in your tables for P, not over P equal to 10.

00:58:33.800 -- What do you get?

00:58:37.010 -- Peanut over P is equal to 10, so you go to the isentropic tables.

00:58:48.610 -- 2.16 is perfect.

00:58:52.210 -- So now think about this engine design. Think about this. So M1

00:58:57.166 -- is 2, what do we say? 2.16 that we said 2.16. OK so think about

00:59:03.361 -- this. You could have an engine design where you take high speed

00:59:08.317 -- air that goes into it and all you have to do is slow it down.

00:59:15.790 -- And what happens to the pressure?

00:59:18.830 -- Goes up yeah supersonic flow that enters this and there's

00:59:22.310 -- this right here you don't have to have any compressor blades.

00:59:26.138 -- You don't have to have a piston to compress the air. All you're

00:59:30.662 -- doing is slowing the air down.

00:59:34.510 -- By slowing it down.

00:59:36.550 -- From what number of two .16 to about zero could be a model

00:59:40.190 -- number .1 whatever it's going to be slightly you get a

00:59:43.270 -- pressure increase of 10.

00:59:45.740 -- OK, that is essentially how now we can go to our

00:59:51.306 -- computer here. That is how a ramjet engine works.

00:59:57.240 -- It has no moving parts.

01:00:01.640 -- There are no compressor blades, there are no Pistons.

01:00:05.250 -- All it does is take air that comes in right here. Obviously

01:00:11.154 -- high speed air slows it down that's slowing down. Is the

01:00:16.566 -- compression process.

01:00:19.020 -- You inject fuel into it, combust it, and comes out

01:00:21.800 -- the nozzle right there.

01:00:25.930 -- That's what are antigens?

01:00:28.290 -- No moving parts. What's the downside to it?

01:00:32.870 -- How does it have to work?

01:00:35.270 -- You already have to be traveling at a Mach number of two.

01:00:39.440 -- OK, ramjet engine doesn't work when you're on the runway an you

01:00:42.980 -- accelerate down and go up.

01:00:45.080 -- That's all subsonic flow. You have to get that pressure

01:00:49.000 -- increase by the speed of the air going into that to get it up

01:00:54.488 -- there. OK, ramjet engines typically function at a Mach

01:00:58.016 -- number of about 3:00, so if you're looking here in our

01:01:02.328 -- tables here for a model number of three, look at what that

01:01:07.032 -- pressure increase would be about 36 times. That's assuming no

01:01:10.952 -- shocks, so assuming no shocks was obviously in this problem,

01:01:14.872 -- they're going to be shocked

01:01:16.832 -- there. OK, so for a ramjet engine to work, you already

01:01:22.730 -- have to be flying at supersonic speeds.

01:01:27.800 -- Happens is that they'll have a little rocket boost, or, uh,

01:01:31.727 -- it's usually a rocket boost. Or actually, in the case of

01:01:35.654 -- this aircraft that this does have, this does have ramjet

01:01:39.224 -- engines in it, so there's a jet turbine engine here, and

01:01:43.151 -- it actually ducks the flow around that engine and turns

01:01:46.721 -- it into a ramjet engine, flying fast enough.

01:01:50.900 -- OK, so this is a combination jet turbine and ramjet engine.

01:01:56.125 -- There OK, obviously we want to recover as much pressure as

01:02:01.350 -- possible so here.

01:02:04.250 -- Then yeah, right there. OK, so let's look at here's another

01:02:09.904 -- diagram of it. Here's the cone here on the inside. Notice that

01:02:16.072 -- you see oblique shockwaves. There an look at the shock train

01:02:21.726 -- 1234556 oblique shockwaves, so it's slowing it down through a

01:02:26.866 -- series of oblique shockwaves. Before the terminal shock right

01:02:31.492 -- there. So now it's subsonic

01:02:34.062 -- flow. Then in that subsonic flow, you inject the fuel. You

01:02:37.730 -- combust it. Here the flame holders and then it comes out

01:02:40.766 -- the backside right there.

01:02:43.760 -- So it uses the fact that you transforms high speed flow

01:02:47.511 -- with low pressure, high speed, low pressure to low

01:02:50.580 -- speed, high pressure flow, just by slowing it down.

01:02:55.170 -- OK, good, that's how ramjet engine works. A scramjet engine

01:02:59.110 -- is a supersonic combustion ramjet engine that's the SC in

01:03:03.050 -- the scramjet, so now it slows it down, but there is no terminal

01:03:08.172 -- shock. OK, you have supersonic combustion that occurs in this

01:03:12.112 -- region and goes out the back.

01:03:15.430 -- For scramjet engine, you typically flying around 7:00 AM

01:03:19.111 -- on #7 or 8.

01:03:23.120 -- OK, we'll talk about that in

01:03:25.346 -- class. Alright.

01:03:29.020 -- Let's let's now talk a little bit about the difference between

01:03:33.145 -- subsonic and supersonic aerodynamics. OK, so here is

01:03:36.145 -- this is this is a subsonic airfoil right here at the top

01:03:40.645 -- and and we have a supersonic airfoil here on the bottom, can

01:03:45.145 -- you see the difference between those two? This is kind of fat

01:03:49.645 -- in the front, got a rounded edge? Kind of hard to see the

01:03:54.520 -- rounded edge, but here's the supersonic airfoil down there.

01:03:57.895 -- Thin with a sharp leading edge.

01:04:00.830 -- OK, this is at subsonic speeds here at transonic speeds. Now

01:04:05.274 -- shockwaves begin to form here at the top because you've got this

01:04:10.122 -- rounded front here and this thin supersonic airfoil, oblique

01:04:13.758 -- shockwaves start to form OK, it's in the transonic regime,

01:04:17.798 -- but now look here in the supersonic regime. Notice that

01:04:21.838 -- there is a bow shock that forms in front of the airfoil.

01:04:27.260 -- And now for supersonic airflow. You see these oblique shockwaves

01:04:30.660 -- that form. OK.

01:04:33.930 -- Let's talk about this. So here we have you have a subsonic.

01:04:42.130 -- Airfoil looks something like that, and here we have a

01:04:46.630 -- supersonic airfoil thin and sharp right there. OK, subsonic.

01:04:53.020 -- Super Sonic

01:04:56.470 -- K alright.

01:04:59.660 -- This is this is a great airfoil in subsonic flow.

01:05:04.690 -- Pilots, what kind of airfoil is that in subsonic

01:05:07.543 -- flow right there?

01:05:09.800 -- Andrew.

01:05:11.690 -- It's not. It's awful, right?

01:05:15.500 -- OK, so subsonic flow this kind of what you learned in is what

01:05:19.933 -- you learned in your influence classes. You know you get a nice

01:05:24.025 -- smooth flow that's over there. It flows faster on the top then

01:05:28.117 -- on the bottom, so you have a lower pressure region on the top

01:05:32.550 -- so it generates lift. Here this airfoil is awful subsonic Lee.

01:05:38.290 -- OK, so now let's go. Let's go. This is a subsonic airfoil and

01:05:42.788 -- supersonic airfoil, and here both Mach numbers are less than

01:05:46.248 -- one lot number less than one right here. And this is just

01:05:50.400 -- kind of flow over this way. Now let's let's beef up things here.

01:05:56.050 -- Mott numbers greater than one lot. Numbers greater

01:05:58.810 -- than one. We have a nice, beautiful rounded airfoil

01:06:01.915 -- right there in a supersonic flow. What's going to form?

01:06:06.780 -- What's going to form right up there?

01:06:09.310 -- A detached bow shock or it's going to be pretty

01:06:13.250 -- much normal shock.

01:06:16.630 -- Right across here and right across there, what forms and

01:06:21.430 -- supersonic flow in our supersonic airfoil right here?

01:06:26.780 -- What forms? Oblique shocks

01:06:31.050 -- here. In here.

01:06:34.520 -- OK.

01:06:36.070 -- Can you see the conundrum?

01:06:38.930 -- Between subsonic and supersonic.

01:06:43.060 -- Airfoil or aerodynamic design? What is good subsonic Lee?

01:06:49.830 -- Is awful supersonically

01:06:53.520 -- OK, this is one reason why airplanes in the 1940s.

01:06:57.390 -- Propeller driven aircraft couldn't break the sound

01:07:00.099 -- barrier.

01:07:01.910 -- OK, that they would use subsonic airfoils. That's what they knew.

01:07:07.150 -- They started getting up into the transonic regime and all of a

01:07:11.734 -- sudden these bow shocks form the drag went Sky high. That's what

01:07:16.318 -- that's what the sound barrier is is extreme increase in the drag

01:07:20.902 -- propeller driven aircraft couldn't overcome that. So now

01:07:23.958 -- we have a supersonic airfoil design like we see here, which

01:07:28.160 -- behaves awfully. Terribly in

01:07:31.124 -- subsonic design. Or in subsonic flows I should say, but

01:07:36.008 -- beautifully in supersonic flows.

01:07:39.650 -- So now. Aircraft designers have to balance those two out when

01:07:44.556 -- you're making aircraft. If you fly supersonically if you if you

01:07:48.450 -- fly supersonic fighter jet, do you ever fly subsonic Lee in it?

01:07:52.698 -- You gotta take off, you have to land and I presume you want to

01:07:57.654 -- land safely, right?

01:07:59.610 -- Yeah, you know. Depends on the pilot I guess. OK, so that

01:08:04.206 -- means. So that means the aircraft designer has to take a

01:08:08.419 -- supersonic airfoil and make it

01:08:10.334 -- function. For the time that that plane is in flight, subsonic

01:08:14.100 -- Lee. We see that.

01:08:18.050 -- And there are tricks and will show some tricks that that

01:08:22.340 -- designers use. In fact, one of

01:08:24.680 -- 'em is. You can kind of see

01:08:27.635 -- here. That in the root of this airplane, right here, it

01:08:32.190 -- has a very thick airfoil right there in there, but

01:08:35.590 -- when it expands out, if you look at the wings, the wings

01:08:39.670 -- are actually pretty thin.

01:08:42.910 -- OK, so this plane actually uses a lot of the fuselage and put it

01:08:47.446 -- this way. Uses a lot of this fuselage. That flat area right

01:08:51.334 -- there to generate lift when it's taking off and landing. You see

01:08:55.222 -- how that see how that works there and then. As it goes

01:08:59.110 -- supersonic, it comes back here. It uses these airfoils that are

01:09:02.674 -- actually pretty thin, not as soon as other aircraft OK, but

01:09:06.238 -- you see then the conundrum that designers have to work with when

01:09:10.126 -- they develop airplanes like

01:09:11.422 -- that. Let's look at the SR-71 and check out this

01:09:15.407 -- wing right here.

01:09:17.720 -- OK, put in the background. Look at that. That is really thin.

01:09:21.344 -- That's a very sharp edge by the way. The Museum of Flight has an

01:09:25.572 -- SR-71, so when you're in Seattle you can look at all these

01:09:29.196 -- airplanes OK, this has very thin wing. It's kind of hard to

01:09:32.820 -- notice, but do you see that there's a little kind of a

01:09:36.444 -- divot? A little curve right

01:09:37.954 -- there? You see that.

01:09:41.120 -- Right there.

01:09:43.380 -- And there this is the aerodynamicists answer to the

01:09:46.719 -- subsonic supersonic flow conundrum. Here it's got a

01:09:49.687 -- little curve, so it has a little curvature in that airflow right

01:09:54.139 -- there so that it can take off and land somewhat safely. You

01:09:58.591 -- get better control on that.

01:10:00.820 -- It's not a straight flat airfoil as it goes across there.

01:10:04.620 -- OK, same thing on the other side you can see you can kind of see

01:10:09.375 -- that curve right there.

01:10:12.360 -- OK.

01:10:14.330 -- Good, I just want you to

01:10:16.430 -- appreciate. The difference here of the designs of what a

01:10:20.262 -- supersonic aircraft does and what a subsonic aircraft does.

01:10:23.034 -- Let's look at two of 'em here.

01:10:25.890 -- OK, the plane on the left is a P51 Mustang, a workhorse in

01:10:32.338 -- World War Two great great airplane fun fact. This went

01:10:37.298 -- from this. Went from initial design when pencil first went to

01:10:42.754 -- paper to prototype in 90 days.

01:10:48.400 -- Now, remember the United States was on war footing at the time,

01:10:52.684 -- so it had to get things out quickly, but this plane was

01:10:56.968 -- designed in that length of time there. Look at underneath here.

01:11:00.895 -- These are external fuel tanks.

01:11:03.960 -- See that right there? See one there there in there?

01:11:07.650 -- What's that shape?

01:11:10.050 -- It's like a teardrop design.

01:11:11.980 -- Right? Here is, I think this is an F15 right here. Same kind of

01:11:17.335 -- design. Look at the inlet right there. You know now why those

01:11:21.115 -- inlets are designed the way they are. Look at those external

01:11:24.580 -- tanks. What does that look like?

01:11:28.640 -- Kind of a bull. It's got a very sharp point there

01:11:31.896 -- and there. Why is that?

01:11:36.080 -- Minimize what? Drag, let's look at those. So the P51 Mustang has

01:11:42.820 -- a teardrop shape.

01:11:45.740 -- External fuel tanks.

01:11:48.260 -- Which turns out to be wonderful for subsonic flows.

01:11:52.980 -- OK, this minimizes both the pressure and the friction drag.

01:11:57.990 -- OK, if I had that fuel tank flying supersonically, what

01:12:01.190 -- would you see?

01:12:03.850 -- Normal shock bow shock right there in the front. Great sub.

01:12:09.295 -- Sonically awful supersonically.

01:12:11.550 -- OK, the F15 right there has a tank that looks like this.

01:12:19.070 -- Right there sharpoint. So now you get oblique shockwaves that

01:12:24.200 -- form minimizing the drag.

01:12:28.290 -- Appreciate now the difference between subsonic flows and

01:12:31.818 -- supersonic flows in aircraft design. Good any questions?

01:12:37.110 -- OK. Dismiss, good luck.

01:12:41.790 -- And let me know if you have any questions on the

01:12:44.375 -- homeworks at all.

01:12:46.510 -- What a beautiful day for gas dynamics. I can't believe

01:12:49.330 -- they pay me money to teach this class.

01:12:53.230 -- I should have to pay to teach it.

01:12:56.740 -- Have a great day.

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.

Contact Us

Janssen Engineering Building Rooms 31 and 37

Mailing Address:

Engineering Outreach
University of Idaho
875 Perimeter Drive MS 1014
Moscow, ID 83844-1014

Phone: 208-885-6373

Fax: 208-885-6165

Email: eo-support@uidaho.edu

Web: eo.uidaho.edu