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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


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.


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.


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 --


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.


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.


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.


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.


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.

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