1 00:00:16,295 --> 00:00:17,420 TINA SRIVASTAVA: All right. 2 00:00:17,420 --> 00:00:21,160 So as we discussed, we're going to start off 3 00:00:21,160 --> 00:00:24,970 with the most basic question-- how do airplanes fly? 4 00:00:24,970 --> 00:00:26,560 It's a very critical question. 5 00:00:26,560 --> 00:00:29,980 I think everybody should know the answer to this. 6 00:00:29,980 --> 00:00:32,229 Going back to the comic that Minachi 7 00:00:32,229 --> 00:00:36,400 had with Calvin and Hobbes, and not knowing how airplanes fly, 8 00:00:36,400 --> 00:00:38,290 and thinking that it's magic is not the way 9 00:00:38,290 --> 00:00:40,550 that any MIT student should be. 10 00:00:40,550 --> 00:00:43,210 So we're going to cover how airplanes fly. 11 00:00:43,210 --> 00:00:45,220 And we're actually going to go beyond what 12 00:00:45,220 --> 00:00:46,720 the FAA requires you to know. 13 00:00:46,720 --> 00:00:51,710 Because frankly, you should know how airplanes fly. 14 00:00:51,710 --> 00:00:54,497 So just so that we have a common vocabulary with which 15 00:00:54,497 --> 00:00:56,330 to discuss, we're going to talk a little bit 16 00:00:56,330 --> 00:00:58,130 about airplane parts. 17 00:00:58,130 --> 00:01:03,360 So here in my little airplane, it's kind of a model 18 00:01:03,360 --> 00:01:08,370 there so you can see that at the front you have your propeller. 19 00:01:08,370 --> 00:01:11,220 And so the engine and the propeller in this little plane 20 00:01:11,220 --> 00:01:13,200 is up here at the front. 21 00:01:13,200 --> 00:01:16,360 Who knows what a fuselage is? 22 00:01:16,360 --> 00:01:18,430 Just shout it out. 23 00:01:18,430 --> 00:01:19,750 AUDIENCE: The middle part. 24 00:01:19,750 --> 00:01:21,520 TINA SRIVASTAVA: The middle part. 25 00:01:21,520 --> 00:01:22,410 The body. 26 00:01:22,410 --> 00:01:24,580 It's where the passengers sit. 27 00:01:24,580 --> 00:01:27,160 Yeah, so that whole middle part where people sit. 28 00:01:27,160 --> 00:01:29,993 So if you're thinking about a big jet engine, 29 00:01:29,993 --> 00:01:32,410 it's where all the rows of seats are where everybody sits. 30 00:01:32,410 --> 00:01:34,690 That tube in the middle is called the fuselage. 31 00:01:34,690 --> 00:01:36,490 And the wings stick out the sides. 32 00:01:36,490 --> 00:01:39,130 So the middle part is the fuselage. 33 00:01:39,130 --> 00:01:41,590 And then one thing that's interesting 34 00:01:41,590 --> 00:01:44,740 is the tail actually has a lot more components. 35 00:01:44,740 --> 00:01:47,350 People kind of casually refer to it as the tail. 36 00:01:47,350 --> 00:01:50,260 But there's a vertical part that comes up 37 00:01:50,260 --> 00:01:52,660 in the back of the vertical part of the tail 38 00:01:52,660 --> 00:01:54,790 can actually tilt side to side. 39 00:01:54,790 --> 00:01:57,880 And then you have a flat horizontal part. 40 00:01:57,880 --> 00:02:01,330 And that actually has a back part that can go down and up. 41 00:02:01,330 --> 00:02:04,720 And so we're going to talk about what all of these are. 42 00:02:04,720 --> 00:02:07,720 So the back vertical part when it goes side to side 43 00:02:07,720 --> 00:02:09,350 is your rudder. 44 00:02:09,350 --> 00:02:12,880 The flat part is your elevator that you can move up and down, 45 00:02:12,880 --> 00:02:15,360 allows you to control the airplane. 46 00:02:15,360 --> 00:02:18,280 We also have, of course, the wings. 47 00:02:18,280 --> 00:02:21,220 Sometimes, there are struts that support the wings. 48 00:02:21,220 --> 00:02:23,980 So they go from the wing down to that fuselage. 49 00:02:23,980 --> 00:02:25,780 And then you have landing gear. 50 00:02:25,780 --> 00:02:29,890 In this case, you have these wheels down at the bottom. 51 00:02:29,890 --> 00:02:32,660 We're also going to talk to you during this course about sea 52 00:02:32,660 --> 00:02:33,400 planes. 53 00:02:33,400 --> 00:02:35,860 So they have slightly different landing gear. 54 00:02:35,860 --> 00:02:37,570 But this is a good place to start. 55 00:02:39,900 --> 00:02:41,650 The other thing that we need to talk about 56 00:02:41,650 --> 00:02:45,730 are just the main four forces that are on an airplane. 57 00:02:45,730 --> 00:02:47,890 So they're pretty straightforward. 58 00:02:47,890 --> 00:02:52,510 So the force going up is lift. 59 00:02:52,510 --> 00:02:57,940 And that force is opposed by the downward force of weight. 60 00:02:57,940 --> 00:03:01,930 And then when you're moving the airplane forward, 61 00:03:01,930 --> 00:03:03,610 that's thrust. 62 00:03:03,610 --> 00:03:06,990 And it is opposed by drag. 63 00:03:06,990 --> 00:03:08,370 So what we're going to talk about 64 00:03:08,370 --> 00:03:11,220 is that in order for an airplane to go up, 65 00:03:11,220 --> 00:03:14,113 the lift has to exceed the drag. 66 00:03:14,113 --> 00:03:15,780 In order for the airplane to go forward, 67 00:03:15,780 --> 00:03:18,310 the thrust has to exceed the-- 68 00:03:18,310 --> 00:03:18,810 excuse me. 69 00:03:18,810 --> 00:03:20,227 The lift has to exceed the weight. 70 00:03:20,227 --> 00:03:22,930 And the thrust has to exceed the drag. 71 00:03:22,930 --> 00:03:24,990 So those are the main four forces 72 00:03:24,990 --> 00:03:27,513 we're going to be working with today. 73 00:03:27,513 --> 00:03:29,430 So now I'm going to spend a little bit of time 74 00:03:29,430 --> 00:03:33,005 over here on the blackboard. 75 00:03:33,005 --> 00:03:35,750 AUDIENCE: Hey video folks, is it easier to use that blackboard? 76 00:03:35,750 --> 00:03:37,100 TINA SRIVASTAVA: They said this blackboard. 77 00:03:37,100 --> 00:03:37,620 AUDIENCE: This one's better? 78 00:03:37,620 --> 00:03:38,537 TINA SRIVASTAVA: Yeah. 79 00:03:41,859 --> 00:03:45,220 AUDIENCE: These are all chalks of color. 80 00:03:45,220 --> 00:03:47,060 TINA SRIVASTAVA: Yeah, fancy-colored chalk. 81 00:03:47,060 --> 00:03:47,560 All right. 82 00:03:47,560 --> 00:03:48,680 AUDIENCE: Chalks of color. 83 00:03:48,680 --> 00:03:49,790 TINA SRIVASTAVA: Chalks of color. 84 00:03:49,790 --> 00:03:50,290 All right. 85 00:03:55,840 --> 00:04:01,930 So I will preface the discussion about lift with the fact 86 00:04:01,930 --> 00:04:04,730 that there are a lot of theories of lift out there, 87 00:04:04,730 --> 00:04:06,370 some of which are wrong. 88 00:04:06,370 --> 00:04:09,370 So if you spent some time googling lift 89 00:04:09,370 --> 00:04:11,980 before coming here, you might have actually found 90 00:04:11,980 --> 00:04:15,190 a couple scenarios that are completely false. 91 00:04:15,190 --> 00:04:17,649 So we're going to focus on what's true, 92 00:04:17,649 --> 00:04:20,440 but I will cover least one of those false theories 93 00:04:20,440 --> 00:04:24,130 to make sure you guys don't get hung up on that. 94 00:04:24,130 --> 00:04:27,450 So in order to talk about it, we're 95 00:04:27,450 --> 00:04:30,510 going to think about an airplane. 96 00:04:30,510 --> 00:04:33,450 And we're going to do a cross-section of the airplane. 97 00:04:33,450 --> 00:04:37,440 So if you took a saw, and you cut off the wing, 98 00:04:37,440 --> 00:04:38,790 what are you left with? 99 00:04:38,790 --> 00:04:40,850 And I'll do it this way. 100 00:04:40,850 --> 00:04:43,080 So if you cut off the wing, at the front of the wing 101 00:04:43,080 --> 00:04:44,210 is the leading edge. 102 00:04:44,210 --> 00:04:45,960 The back of the wing is the trailing edge. 103 00:04:45,960 --> 00:04:49,010 If you did it-- if you cut that off, what does it look like? 104 00:04:56,910 --> 00:04:58,320 So it looks like this. 105 00:04:58,320 --> 00:05:00,960 And this shape is called an airfoil. 106 00:05:00,960 --> 00:05:03,720 And we'll get into the specifics later. 107 00:05:03,720 --> 00:05:05,460 But first we'll just-- 108 00:05:05,460 --> 00:05:10,080 we'll talk about a simple way to understand how lift works. 109 00:05:10,080 --> 00:05:16,890 So if this is the wing, and you have air coming in, 110 00:05:16,890 --> 00:05:21,780 the air is pushed down by the shape of this wing. 111 00:05:26,370 --> 00:05:31,260 So that means is as air flows by, it gets pushed down. 112 00:05:31,260 --> 00:05:33,390 Now what is air? 113 00:05:33,390 --> 00:05:34,710 Air is not nothing. 114 00:05:34,710 --> 00:05:35,880 Air has molecules. 115 00:05:35,880 --> 00:05:37,320 It has mass. 116 00:05:37,320 --> 00:05:40,043 So if you think about conservation of momentum, 117 00:05:40,043 --> 00:05:42,210 this is I think the easiest way to think about lift. 118 00:05:42,210 --> 00:05:46,890 So conservation of momentum, you have a bunch of air molecules. 119 00:05:46,890 --> 00:05:48,870 And those air molecules are pushed down. 120 00:05:48,870 --> 00:05:51,300 So you have mass being pushed down. 121 00:05:51,300 --> 00:05:54,630 So if mass is being pushed down for conservation of momentum, 122 00:05:54,630 --> 00:05:56,250 something must be pushed up. 123 00:05:56,250 --> 00:05:57,638 And that's the wing. 124 00:05:57,638 --> 00:05:59,430 So that's the easiest way to think about it 125 00:05:59,430 --> 00:06:02,430 that if you're deflecting the air downward in order to have 126 00:06:02,430 --> 00:06:06,000 conservation of momentum, the mass of the wing 127 00:06:06,000 --> 00:06:08,068 is lifted upwards. 128 00:06:08,068 --> 00:06:09,860 We're going to break that down, but I think 129 00:06:09,860 --> 00:06:11,140 that's a good place to start. 130 00:06:13,870 --> 00:06:15,780 I'm just going to take one moment to talk 131 00:06:15,780 --> 00:06:19,590 about an incorrect theory of lift. 132 00:06:19,590 --> 00:06:22,800 So let me emphasize it's wrong. 133 00:06:22,800 --> 00:06:25,860 One of them is called equal transit theory. 134 00:06:25,860 --> 00:06:27,420 Has anyone heard about this? 135 00:06:27,420 --> 00:06:29,680 Getting a lot of head nods. 136 00:06:29,680 --> 00:06:30,180 It's wrong. 137 00:06:37,660 --> 00:06:40,870 Equal transit theory, which is incorrect, 138 00:06:40,870 --> 00:06:46,120 says that basically a molecule of air that's coming over 139 00:06:46,120 --> 00:06:48,130 that starts over here at the front 140 00:06:48,130 --> 00:06:53,050 has to go around the bottom and meet the tail at the same time 141 00:06:53,050 --> 00:06:55,510 that a molecule that goes over the top 142 00:06:55,510 --> 00:06:57,800 has to meet it at the back. 143 00:06:57,800 --> 00:07:00,440 There is no physical principle that says that. 144 00:07:00,440 --> 00:07:01,700 It is false. 145 00:07:01,700 --> 00:07:05,180 And in fact, we have measured that they don't. 146 00:07:05,180 --> 00:07:06,860 The molecules that go under the bottom 147 00:07:06,860 --> 00:07:08,870 of the wing versus the top of the wing 148 00:07:08,870 --> 00:07:11,880 don't actually reach the end at the same time. 149 00:07:11,880 --> 00:07:14,750 But in this false theory, equal transit theory, 150 00:07:14,750 --> 00:07:18,860 they say that you have to reach the bottom at the same time. 151 00:07:18,860 --> 00:07:23,180 They also say that there is more distance basically 152 00:07:23,180 --> 00:07:26,420 to cover because of the shape of the airfoil. 153 00:07:26,420 --> 00:07:28,490 So in order for the molecules going over 154 00:07:28,490 --> 00:07:30,590 the top to reach at the same time 155 00:07:30,590 --> 00:07:34,070 as the molecules over the bottom, they have to go faster. 156 00:07:34,070 --> 00:07:35,960 And so since the air is moving faster 157 00:07:35,960 --> 00:07:38,840 over the top and the bottom, that's what creates lift. 158 00:07:38,840 --> 00:07:39,950 So that's false. 159 00:07:39,950 --> 00:07:43,070 And there are many reasons why it's false, 160 00:07:43,070 --> 00:07:46,940 the biggest one being that there is no physical principle that 161 00:07:46,940 --> 00:07:50,510 says that two molecules starting at the same time, one going 162 00:07:50,510 --> 00:07:52,520 over the top and one going over the bottom, 163 00:07:52,520 --> 00:07:54,020 reaches the end at the same time. 164 00:07:54,020 --> 00:07:55,460 That's just not true. 165 00:07:55,460 --> 00:07:58,580 And we'll show you some more diagrams that show in fact 166 00:07:58,580 --> 00:08:00,890 it doesn't happen, that molecules don't 167 00:08:00,890 --> 00:08:02,690 reach at the same time anyway. 168 00:08:02,690 --> 00:08:06,830 So please despite that being very widely propagated, 169 00:08:06,830 --> 00:08:08,610 that is not true. 170 00:08:08,610 --> 00:08:12,880 And please don't spend time on that theory. 171 00:08:12,880 --> 00:08:18,070 So let's focus on what is true, how does it really work. 172 00:08:18,070 --> 00:08:21,340 Actually, let me give you one more reason why that's false. 173 00:08:21,340 --> 00:08:23,950 The real reason that equal transit theory 174 00:08:23,950 --> 00:08:26,500 is trying to tell you that that generates lift 175 00:08:26,500 --> 00:08:30,490 is that because of the shape of the airfoil, the shape 176 00:08:30,490 --> 00:08:33,730 of the wing, that's why the distance that it has to travel 177 00:08:33,730 --> 00:08:37,360 is different over the top versus the bottom. 178 00:08:37,360 --> 00:08:39,909 But one reason that's wrong-- can you pass me 179 00:08:39,909 --> 00:08:41,919 that paper airplane please? 180 00:08:41,919 --> 00:08:44,590 Who has built a paper airplane before? 181 00:08:47,440 --> 00:08:49,720 I see at least two people who didn't raise their hand. 182 00:08:49,720 --> 00:08:52,000 Do we need to do a class exercise? 183 00:08:52,000 --> 00:08:53,800 If you have not built a paper airplane, 184 00:08:53,800 --> 00:08:58,540 it's really important that you do just as a general childhood 185 00:08:58,540 --> 00:09:01,330 experience. 186 00:09:01,330 --> 00:09:02,330 Here's a paper airplane. 187 00:09:02,330 --> 00:09:05,560 Thank you, Minachi, for building it for me. 188 00:09:05,560 --> 00:09:11,230 If we took this paper airplane instead of this fancy airplane, 189 00:09:11,230 --> 00:09:14,830 and we did a cross-section of this wing, 190 00:09:14,830 --> 00:09:17,780 what would it look like? 191 00:09:17,780 --> 00:09:18,410 Yes. 192 00:09:18,410 --> 00:09:20,627 You demonstrated with your hands, but shout it out. 193 00:09:20,627 --> 00:09:23,210 AUDIENCE: It's going to be the same at the top and the bottom. 194 00:09:23,210 --> 00:09:24,335 It's just a piece of paper. 195 00:09:24,335 --> 00:09:25,710 TINA SRIVASTAVA: Yeah, it's going 196 00:09:25,710 --> 00:09:27,450 to be the same at the top and the bottom. 197 00:09:27,450 --> 00:09:28,990 It's just a piece of paper. 198 00:09:28,990 --> 00:09:29,490 Exactly. 199 00:09:29,490 --> 00:09:32,950 It's just like a little flat rectangle. 200 00:09:32,950 --> 00:09:35,850 So instead of this fancy shape that you have here-- 201 00:09:39,693 --> 00:09:41,110 we're going to use red for wrong-- 202 00:09:45,040 --> 00:09:47,740 it's like a little rectangle. 203 00:09:47,740 --> 00:09:50,590 That's what a paper airplane's cross-section of its wing 204 00:09:50,590 --> 00:09:51,100 looks like. 205 00:09:51,100 --> 00:09:52,480 Well, surprise. 206 00:09:52,480 --> 00:09:53,200 Surprise. 207 00:09:53,200 --> 00:09:55,840 As you said, it's the same at the top and the bottom. 208 00:09:55,840 --> 00:09:57,740 So the distance that a air molecule 209 00:09:57,740 --> 00:09:59,740 would have to travel over the top and the bottom 210 00:09:59,740 --> 00:10:01,040 is identical. 211 00:10:01,040 --> 00:10:05,260 So really, the equal transit theory completely falls apart. 212 00:10:05,260 --> 00:10:07,750 Yet, a paper airplane still flies. 213 00:10:07,750 --> 00:10:09,220 So why is that the case? 214 00:10:09,220 --> 00:10:11,560 Again, remember the actual reason 215 00:10:11,560 --> 00:10:15,250 is that if this paper airplane is inclined, 216 00:10:15,250 --> 00:10:17,510 it is pushing air down. 217 00:10:17,510 --> 00:10:19,660 So air that's coming up is bumping into it 218 00:10:19,660 --> 00:10:21,110 and being pushed down. 219 00:10:21,110 --> 00:10:24,340 And therefore, as you deflect air molecules down, 220 00:10:24,340 --> 00:10:26,980 conservation of momentum-- the wing is lifted up. 221 00:10:34,170 --> 00:10:36,720 So now we're going to break this down in a little bit more 222 00:10:36,720 --> 00:10:37,220 detail. 223 00:10:44,750 --> 00:10:48,910 And I'm going to go back over here to the slides. 224 00:10:48,910 --> 00:10:52,700 So one thing that's important, as I said, 225 00:10:52,700 --> 00:10:56,080 a really detailed mathematical description 226 00:10:56,080 --> 00:10:59,350 is not really necessary to fly a plane or become a pilot. 227 00:10:59,350 --> 00:11:01,750 The FAA doesn't require some of this detail. 228 00:11:01,750 --> 00:11:03,820 But it is important to know it to the extent 229 00:11:03,820 --> 00:11:07,240 that it helps you control the airplane and fly it. 230 00:11:07,240 --> 00:11:10,190 So here's a good reference in terms of that. 231 00:11:10,190 --> 00:11:14,740 But one of the biggest things is just that for lift, you 232 00:11:14,740 --> 00:11:19,360 have to increase that downward momentum of the air. 233 00:11:19,360 --> 00:11:22,750 And airfoils are-- the shape which 234 00:11:22,750 --> 00:11:26,200 is called an airfoil is a type of shape that 235 00:11:26,200 --> 00:11:31,340 is very efficient at increasing that downward momentum. 236 00:11:31,340 --> 00:11:35,510 Now, who knows what Bernoulli's principle is? 237 00:11:35,510 --> 00:11:38,080 Who's heard of Bernoulli? 238 00:11:38,080 --> 00:11:38,580 Good. 239 00:11:38,580 --> 00:11:40,410 Everyone's heard of Bernoulli. 240 00:11:40,410 --> 00:11:43,170 Can anyone articulate Bernoulli's principle? 241 00:11:46,116 --> 00:11:47,098 Yes. 242 00:11:47,098 --> 00:11:51,675 AUDIENCE: I think it's like p plus one half of mv squared 243 00:11:51,675 --> 00:11:53,300 equals constant the difference squared. 244 00:11:53,300 --> 00:11:55,008 So when the pressure goes down somewhere, 245 00:11:55,008 --> 00:11:58,805 the speed of the particle has to go up. 246 00:11:58,805 --> 00:11:59,680 TINA SRIVASTAVA: Yes. 247 00:11:59,680 --> 00:12:00,540 Absolutely. 248 00:12:00,540 --> 00:12:01,380 Absolutely. 249 00:12:01,380 --> 00:12:05,770 So what Bernoulli observed was the case 250 00:12:05,770 --> 00:12:08,380 that when there is a decrease in pressure, 251 00:12:08,380 --> 00:12:11,410 there's an increase in velocity. 252 00:12:11,410 --> 00:12:15,710 That's the core concept that you have to understand. 253 00:12:15,710 --> 00:12:20,410 And so when we think about an airfoil, when we see that-- 254 00:12:20,410 --> 00:12:23,530 and I'll draw another airfoil for us to talk about. 255 00:12:29,010 --> 00:12:31,590 When we have air that's moving very 256 00:12:31,590 --> 00:12:34,230 fast over the top of the wing, that 257 00:12:34,230 --> 00:12:36,360 means an increase in velocity means 258 00:12:36,360 --> 00:12:38,440 there's a decrease in pressure. 259 00:12:38,440 --> 00:12:40,440 So this is the extent to which you really need 260 00:12:40,440 --> 00:12:42,750 to know it for the FAA exam. 261 00:12:42,750 --> 00:12:45,870 So which statement relates to Bernoulli's principle? 262 00:12:45,870 --> 00:12:47,580 I'll let you read those answers. 263 00:13:03,550 --> 00:13:05,260 So is it A, B, or C? 264 00:13:05,260 --> 00:13:05,950 Shout it out. 265 00:13:05,950 --> 00:13:06,990 AUDIENCE: C. 266 00:13:06,990 --> 00:13:08,620 TINA SRIVASTAVA: C. Good job. 267 00:13:08,620 --> 00:13:10,480 Well done. 268 00:13:10,480 --> 00:13:13,020 We're going to discuss a little bit more details though. 269 00:13:19,640 --> 00:13:23,330 In order for any wing to generate lift, 270 00:13:23,330 --> 00:13:25,670 it has to be in a fluid. 271 00:13:25,670 --> 00:13:30,050 If this airplane was in space or in a vacuum, 272 00:13:30,050 --> 00:13:32,630 and there wasn't any fluid passing by it, 273 00:13:32,630 --> 00:13:36,020 then there wouldn't be any molecules to deflect downward. 274 00:13:36,020 --> 00:13:39,530 And therefore, you couldn't push the wing up. 275 00:13:39,530 --> 00:13:41,570 But the fluid doesn't always have to be air. 276 00:13:41,570 --> 00:13:44,900 You might see similar designs underwater 277 00:13:44,900 --> 00:13:46,970 for underwater drones. 278 00:13:46,970 --> 00:13:50,405 It just has to be a fluid that's passing by the object. 279 00:14:02,180 --> 00:14:08,660 So when you have this airfoil in a fluid, when the fluid is not 280 00:14:08,660 --> 00:14:12,530 moving, when it's stationary, then all of the fluid 281 00:14:12,530 --> 00:14:15,860 is exerting pressure on the airfoil. 282 00:14:15,860 --> 00:14:19,190 So you get all these little normal forces 283 00:14:19,190 --> 00:14:20,000 exerting pressure. 284 00:14:25,940 --> 00:14:28,630 When the fluid is not moving, and the airfoil 285 00:14:28,630 --> 00:14:32,360 is stationary in the fluid, then all of those pressure 286 00:14:32,360 --> 00:14:36,380 forces, all those normal forces or forces perpendicular, 287 00:14:36,380 --> 00:14:39,170 sum to zero because there's no net force. 288 00:14:39,170 --> 00:14:40,970 It's just sitting in the fluid. 289 00:14:40,970 --> 00:14:44,375 But when that fluid is moving, it generates a force. 290 00:15:01,390 --> 00:15:04,280 So that's the force it generates generally when 291 00:15:04,280 --> 00:15:06,280 the fluid is moving forward. 292 00:15:06,280 --> 00:15:08,220 And a force is a vector. 293 00:15:08,220 --> 00:15:11,540 So it has direction as well as magnitude. 294 00:15:11,540 --> 00:15:15,740 So there is a vertical component and a horizontal component 295 00:15:15,740 --> 00:15:17,030 to that. 296 00:15:17,030 --> 00:15:21,970 So we call the vertical component the lift. 297 00:15:21,970 --> 00:15:25,020 Does anyone know what we call the horizontal component? 298 00:15:25,020 --> 00:15:25,720 AUDIENCE: Drag. 299 00:15:25,720 --> 00:15:26,860 TINA SRIVASTAVA: Drag. 300 00:15:26,860 --> 00:15:27,370 Good job. 301 00:15:33,090 --> 00:15:39,670 Now, here's a dumb question. 302 00:15:39,670 --> 00:15:43,005 What part of the aircraft generates lift? 303 00:15:47,460 --> 00:15:47,960 Yes. 304 00:15:47,960 --> 00:15:48,980 AUDIENCE: The whole aircraft. 305 00:15:48,980 --> 00:15:50,480 TINA SRIVASTAVA: The whole aircraft. 306 00:15:50,480 --> 00:15:51,170 Good job. 307 00:15:51,170 --> 00:15:55,070 So a lot of people might be under the misimpression 308 00:15:55,070 --> 00:15:58,460 that it's only the wings that are generating the lift. 309 00:15:58,460 --> 00:16:01,970 Well, actually, the whole aircraft is generating lift. 310 00:16:01,970 --> 00:16:03,620 And it's not just aircraft. 311 00:16:03,620 --> 00:16:06,740 Any objects that are moving through fluid 312 00:16:06,740 --> 00:16:09,740 have this phenomenon. 313 00:16:09,740 --> 00:16:11,760 And sometimes, it's not a good thing. 314 00:16:11,760 --> 00:16:13,820 So what is this a picture of? 315 00:16:17,180 --> 00:16:17,930 A race car. 316 00:16:17,930 --> 00:16:20,070 Come on, guys. 317 00:16:20,070 --> 00:16:24,050 I know we're in an airplane class but-- 318 00:16:24,050 --> 00:16:26,480 who can tell me what is that thing sticking up 319 00:16:26,480 --> 00:16:28,210 at the back of the race car? 320 00:16:28,210 --> 00:16:29,105 AUDIENCE: A spoiler. 321 00:16:29,105 --> 00:16:30,230 TINA SRIVASTAVA: A spoiler. 322 00:16:30,230 --> 00:16:32,937 What's a spoiler? 323 00:16:32,937 --> 00:16:34,270 AUDIENCE: It spoils the airflow. 324 00:16:34,270 --> 00:16:36,280 TINA SRIVASTAVA: It spoils the airflow. 325 00:16:36,280 --> 00:16:39,640 So when a race car is driving on a race track, 326 00:16:39,640 --> 00:16:43,570 and it's going through the air-- the fluid is air-- 327 00:16:43,570 --> 00:16:48,820 actually just the race car itself is generating lift. 328 00:16:48,820 --> 00:16:52,930 And that lift can cause the race car to kind of lift 329 00:16:52,930 --> 00:16:58,188 upward and not be as much in traction with the ground. 330 00:16:58,188 --> 00:17:00,730 And when you're a race car, and you want to go really, really 331 00:17:00,730 --> 00:17:02,770 fast, you want to have very good traction 332 00:17:02,770 --> 00:17:04,410 with your wheels against the ground 333 00:17:04,410 --> 00:17:06,079 so you can go as fast as you can. 334 00:17:06,079 --> 00:17:08,380 So the reason that you have a spoiler at the back 335 00:17:08,380 --> 00:17:12,130 is actually to counteract the lift that's being generated 336 00:17:12,130 --> 00:17:13,450 by the race car. 337 00:17:13,450 --> 00:17:17,050 So it's not just airplanes and wings that generate lift, 338 00:17:17,050 --> 00:17:19,390 but really anything moving through a fluid 339 00:17:19,390 --> 00:17:20,790 can generate lift. 340 00:17:26,783 --> 00:17:28,950 So we're going to talk a little bit about equations. 341 00:17:28,950 --> 00:17:30,840 Don't get scared here. 342 00:17:30,840 --> 00:17:34,860 We'll just dive into it step by step. 343 00:17:34,860 --> 00:17:38,400 So we have f equals ma. 344 00:17:38,400 --> 00:17:40,970 Hopefully, this is not the first time 345 00:17:40,970 --> 00:17:43,900 you're hearing about that equation. 346 00:17:43,900 --> 00:17:48,807 So can somebody just shout out what is acceleration? 347 00:17:48,807 --> 00:17:50,890 AUDIENCE: Change in velocity with respect to time. 348 00:17:50,890 --> 00:17:52,807 TINA SRIVASTAVA: Change in velocity over time. 349 00:17:52,807 --> 00:17:53,440 Very good. 350 00:17:53,440 --> 00:17:57,000 So velocity again is also a vector. 351 00:17:57,000 --> 00:18:02,090 So velocity being a vector has both a magnitude and direction. 352 00:18:02,090 --> 00:18:04,120 So you can change the velocity either 353 00:18:04,120 --> 00:18:07,600 by changing the magnitude or the direction. 354 00:18:07,600 --> 00:18:10,210 In the case of an airfoil, we're changing 355 00:18:10,210 --> 00:18:13,090 the direction of the air. 356 00:18:13,090 --> 00:18:14,205 So the air has velocity. 357 00:18:14,205 --> 00:18:14,830 It's coming in. 358 00:18:14,830 --> 00:18:17,110 We're changing the direction of that air. 359 00:18:17,110 --> 00:18:19,240 And that's generating the lift. 360 00:18:19,240 --> 00:18:23,230 So because we changed the direction of the velocity, 361 00:18:23,230 --> 00:18:24,340 that creates a force. 362 00:18:24,340 --> 00:18:25,780 That's our force f. 363 00:18:25,780 --> 00:18:27,460 So f is actually here representing 364 00:18:27,460 --> 00:18:30,610 the rate of change of momentum of pushing those air 365 00:18:30,610 --> 00:18:33,310 molecules down and generating a force, 366 00:18:33,310 --> 00:18:36,650 creating the airfoil to be lifted up. 367 00:18:36,650 --> 00:18:40,610 So that's why we discussed again that equal transit 368 00:18:40,610 --> 00:18:41,450 theory is false. 369 00:18:41,450 --> 00:18:46,790 Because even an paper airplane with a completely flat 370 00:18:46,790 --> 00:18:48,830 cross-section of its wing, as long 371 00:18:48,830 --> 00:18:51,440 as it's inclined upward such that the air is 372 00:18:51,440 --> 00:18:55,360 being pushed down will fly. 373 00:18:55,360 --> 00:18:57,430 So here's another question. 374 00:18:57,430 --> 00:19:02,740 Which moves faster-- the wing through the air 375 00:19:02,740 --> 00:19:04,390 or the air past the wing? 376 00:19:14,040 --> 00:19:15,800 Wow, you're very quiet. 377 00:19:15,800 --> 00:19:16,800 Which moves faster? 378 00:19:16,800 --> 00:19:17,300 Yes. 379 00:19:17,300 --> 00:19:18,440 AUDIENCE: The air over the wing. 380 00:19:18,440 --> 00:19:20,065 TINA SRIVASTAVA: The air over the wing. 381 00:19:20,065 --> 00:19:22,910 We have one for the air over the wing is moving faster 382 00:19:22,910 --> 00:19:24,470 than the wing through the air. 383 00:19:24,470 --> 00:19:25,760 Anyone else? 384 00:19:25,760 --> 00:19:26,672 Yes. 385 00:19:26,672 --> 00:19:28,150 AUDIENCE: Depends on where on the wing you're talking about. 386 00:19:28,150 --> 00:19:30,025 TINA SRIVASTAVA: Depends on where on the wing 387 00:19:30,025 --> 00:19:31,240 you're talking about. 388 00:19:31,240 --> 00:19:32,000 Yes. 389 00:19:32,000 --> 00:19:33,458 AUDIENCE: Because if you define air 390 00:19:33,458 --> 00:19:35,590 to be the air that's immediately next to the-- 391 00:19:35,590 --> 00:19:39,340 that is in contact with the wing or the general air 392 00:19:39,340 --> 00:19:41,470 as in the air space. 393 00:19:41,470 --> 00:19:42,542 TINA SRIVASTAVA: Yes. 394 00:19:42,542 --> 00:19:45,290 AUDIENCE: If it's the air that's in contact with the wing, 395 00:19:45,290 --> 00:19:46,623 they're going at the same speed. 396 00:19:46,623 --> 00:19:48,415 TINA SRIVASTAVA: So it depends on which air 397 00:19:48,415 --> 00:19:49,570 you're talking about. 398 00:19:49,570 --> 00:19:51,100 True. 399 00:19:51,100 --> 00:19:55,430 Actually, what we're discussing is about frame of reference. 400 00:19:55,430 --> 00:19:58,630 So depending on your frame of reference, 401 00:19:58,630 --> 00:20:01,480 if your frame of reference is the airfoil, 402 00:20:01,480 --> 00:20:04,690 you can take it to be that the airfoil is stationary. 403 00:20:04,690 --> 00:20:08,710 And you see the wing to be stationary and the air 404 00:20:08,710 --> 00:20:10,180 to be moving past you. 405 00:20:10,180 --> 00:20:12,490 If your frame of reference is out here, 406 00:20:12,490 --> 00:20:17,500 you might see the air to be stationary and the airplane 407 00:20:17,500 --> 00:20:19,340 to be moving through it. 408 00:20:19,340 --> 00:20:21,370 So depending on what your frame of reference is, 409 00:20:21,370 --> 00:20:25,210 you can actually have the identical result. 410 00:20:25,210 --> 00:20:27,580 So the answer is actually that it's the same. 411 00:20:27,580 --> 00:20:29,750 So depending on your frame of reference, 412 00:20:29,750 --> 00:20:32,350 it's exactly the same the speed of the air moving 413 00:20:32,350 --> 00:20:37,100 past the airfoil versus the airfoil moving through the air. 414 00:20:37,100 --> 00:20:41,500 And the reason-- so does anyone want to dive more into that? 415 00:20:41,500 --> 00:20:44,720 Are you guys familiar with this concept of frame of reference? 416 00:20:44,720 --> 00:20:45,220 Yes. 417 00:20:45,220 --> 00:20:47,420 A lot of head nodding. 418 00:20:47,420 --> 00:20:48,010 Great. 419 00:20:48,010 --> 00:20:52,270 So the reason that's significant is that as we learn about lift 420 00:20:52,270 --> 00:20:56,050 and as we study this, we actually 421 00:20:56,050 --> 00:20:59,410 could create a whole bunch of different airfoils, 422 00:20:59,410 --> 00:21:02,800 and then build airplanes, and then fly them through the air, 423 00:21:02,800 --> 00:21:03,880 and measure them. 424 00:21:03,880 --> 00:21:06,560 But that's very expensive. 425 00:21:06,560 --> 00:21:14,740 So instead, what we do is we basically take the airfoil. 426 00:21:14,740 --> 00:21:17,380 And we put it on a stick, and then we 427 00:21:17,380 --> 00:21:20,880 put it inside a wind tunnel. 428 00:21:20,880 --> 00:21:23,620 Has anyone been in a wind tunnel? 429 00:21:23,620 --> 00:21:26,130 Got a couple people. 430 00:21:26,130 --> 00:21:29,600 Hey, we saw that like over 60 of you guys were aero-astro. 431 00:21:29,600 --> 00:21:31,980 You need to go to your Wright brothers wind tunnel. 432 00:21:31,980 --> 00:21:34,980 It's being upgraded actually right now 433 00:21:34,980 --> 00:21:37,260 over in your building 33. 434 00:21:37,260 --> 00:21:40,060 So because it's exactly identical, 435 00:21:40,060 --> 00:21:43,290 the air moving past the airfoil or the airfoil 436 00:21:43,290 --> 00:21:46,140 moving through the air, it's a lot cheaper 437 00:21:46,140 --> 00:21:49,260 to put the airfoil on a stick in a wind tunnel, 438 00:21:49,260 --> 00:21:53,040 and then shoot air past it, and then do your measurements 439 00:21:53,040 --> 00:21:56,520 rather than continuing to take off airplanes and fly them 440 00:21:56,520 --> 00:21:57,870 through the air. 441 00:21:57,870 --> 00:22:00,920 So we're going to be talking about that a little bit. 442 00:22:04,940 --> 00:22:10,870 So the question is, what factors affect lift? 443 00:22:10,870 --> 00:22:13,570 So there are a lot of things that affect lift. 444 00:22:13,570 --> 00:22:15,860 So one has to do with the object itself. 445 00:22:15,860 --> 00:22:19,570 So I was talking about the shape of the airfoil. 446 00:22:19,570 --> 00:22:21,340 So we talked about a different shape, 447 00:22:21,340 --> 00:22:23,770 which is just a flat piece of paper 448 00:22:23,770 --> 00:22:25,660 or a rectangle as a shape. 449 00:22:25,660 --> 00:22:27,760 You can have a more slender shape. 450 00:22:27,760 --> 00:22:29,800 And the way that you modify the shape 451 00:22:29,800 --> 00:22:32,650 can significantly impact your lift. 452 00:22:32,650 --> 00:22:35,770 So for example, one of the modifications 453 00:22:35,770 --> 00:22:38,470 can be back here at the end. 454 00:22:38,470 --> 00:22:42,870 If you made your airfoil longer like this 455 00:22:42,870 --> 00:22:45,340 and point even farther down, then it 456 00:22:45,340 --> 00:22:48,410 would push the air in a slightly different way. 457 00:22:48,410 --> 00:22:51,340 So that would affect the lift that that airfoil 458 00:22:51,340 --> 00:22:52,000 could generate. 459 00:22:52,000 --> 00:22:57,350 It would also affect the drag that it induces. 460 00:22:57,350 --> 00:23:01,117 Another aspect is just the size of the wing 461 00:23:01,117 --> 00:23:02,200 and the shape of the wing. 462 00:23:02,200 --> 00:23:03,850 So we see a lot of different kinds. 463 00:23:03,850 --> 00:23:09,150 So this is a big rectangular wing. 464 00:23:09,150 --> 00:23:12,440 In a jet, you might see a swept wing. 465 00:23:12,440 --> 00:23:14,250 There are different types of shapes. 466 00:23:14,250 --> 00:23:16,050 And then there's also just the area. 467 00:23:16,050 --> 00:23:17,850 So regardless of whether-- 468 00:23:17,850 --> 00:23:19,230 if this is your-- 469 00:23:19,230 --> 00:23:22,170 if you're looking down at an airplane-- 470 00:23:22,170 --> 00:23:25,830 so this is kind of the broad, flat wings, 471 00:23:25,830 --> 00:23:28,650 or you could have very thin, skinny wings 472 00:23:28,650 --> 00:23:30,870 that you might see on a glider. 473 00:23:30,870 --> 00:23:35,760 Regardless, there is a surface area of the wing. 474 00:23:35,760 --> 00:23:40,230 That area also impacts the lift quite a bit. 475 00:23:40,230 --> 00:23:45,460 And the aspect ratio as we just discussed in the shape 476 00:23:45,460 --> 00:23:47,050 can affect lift. 477 00:23:47,050 --> 00:23:49,480 The other thing other than the object itself, 478 00:23:49,480 --> 00:23:52,210 other than the wing itself, motion 479 00:23:52,210 --> 00:23:56,140 can affect lift, so the velocity of the air. 480 00:23:56,140 --> 00:23:58,960 And the very importantly is what's 481 00:23:58,960 --> 00:24:01,150 called the angle of attack. 482 00:24:01,150 --> 00:24:05,960 So it's the angle with which this airfoil has to the air. 483 00:24:05,960 --> 00:24:11,670 So if you had one airfoil that was pointed up 484 00:24:11,670 --> 00:24:17,840 like this versus one, the same one but it was not tilted up, 485 00:24:17,840 --> 00:24:22,460 this airfoil would be having a higher angle of attack or angle 486 00:24:22,460 --> 00:24:24,950 to the wind than this one. 487 00:24:24,950 --> 00:24:27,800 Now, this might seem like a very fancy description, 488 00:24:27,800 --> 00:24:31,340 but who has been in a car driving down the highway, 489 00:24:31,340 --> 00:24:34,220 and you stuck your hand out outside? 490 00:24:34,220 --> 00:24:35,970 And if you tilt your hand up a little bit, 491 00:24:35,970 --> 00:24:38,720 you'll see that the wind kind of pushes your hand up. 492 00:24:38,720 --> 00:24:42,110 And if you tilt it down, your hand pushes up. 493 00:24:42,110 --> 00:24:44,510 And you kind of glide your hand out the window. 494 00:24:44,510 --> 00:24:47,310 So I'm getting a lot of head nods. 495 00:24:47,310 --> 00:24:49,460 So that's really all that angle of attack 496 00:24:49,460 --> 00:24:52,910 is talking about that if you angle your hand up, 497 00:24:52,910 --> 00:24:55,040 it gets pushed up a lot more. 498 00:24:55,040 --> 00:24:57,110 If you angle it down, it gets pushed down. 499 00:24:57,110 --> 00:24:59,820 That's the angle of attack. 500 00:24:59,820 --> 00:25:02,040 And we're going to define it more specifically when 501 00:25:02,040 --> 00:25:04,530 we talk about the terms associated 502 00:25:04,530 --> 00:25:06,300 with an airfoil in the shape, but it's 503 00:25:06,300 --> 00:25:11,070 good to get the general concept first. 504 00:25:11,070 --> 00:25:13,710 And then another factor affecting lift 505 00:25:13,710 --> 00:25:17,190 is the air, the fluid that it's in, so 506 00:25:17,190 --> 00:25:20,970 the actual mass of the airflow coming around you. 507 00:25:20,970 --> 00:25:22,980 So there are a lot of aspects to that. 508 00:25:22,980 --> 00:25:24,670 We talked about whether you're in water, 509 00:25:24,670 --> 00:25:28,690 whether you're in air, or the density of the air. 510 00:25:28,690 --> 00:25:32,100 Another component of that air is the viscosity. 511 00:25:32,100 --> 00:25:34,100 Does anyone know what viscosity is? 512 00:25:38,490 --> 00:25:39,345 Yes. 513 00:25:39,345 --> 00:25:40,560 AUDIENCE: Resistance to flow. 514 00:25:40,560 --> 00:25:42,870 TINA SRIVASTAVA: Resistance to flow. 515 00:25:42,870 --> 00:25:44,550 The way I like to think about it is 516 00:25:44,550 --> 00:25:49,695 if you've ever baked brownies, and you have your mixing bowl 517 00:25:49,695 --> 00:25:51,960 and your spatula in there, and if you just 518 00:25:51,960 --> 00:25:54,900 have the water and the oil and eggs, 519 00:25:54,900 --> 00:25:58,170 and you're mixing it around, you can mix pretty quickly. 520 00:25:58,170 --> 00:26:01,270 And it doesn't stick to the spatula that much. 521 00:26:01,270 --> 00:26:03,780 But if you were mixing molasses or once you 522 00:26:03,780 --> 00:26:08,310 get all that brownie batter in there, it's harder to do it. 523 00:26:08,310 --> 00:26:10,140 And it sticks to the spatula. 524 00:26:10,140 --> 00:26:12,000 So that's what we're talking about when 525 00:26:12,000 --> 00:26:13,350 we're talking about viscosity. 526 00:26:13,350 --> 00:26:15,420 So it's the tendency for these molecules 527 00:26:15,420 --> 00:26:19,440 to stick to each other and to stick to the object that's 528 00:26:19,440 --> 00:26:20,970 moving through them. 529 00:26:20,970 --> 00:26:23,910 So with the case of the airfoil, we're talking about-- 530 00:26:23,910 --> 00:26:28,140 and we were discussing this just a moment ago about which 531 00:26:28,140 --> 00:26:29,490 air were we talking about. 532 00:26:29,490 --> 00:26:31,680 So some air that might be very close 533 00:26:31,680 --> 00:26:34,890 might kind of stick to that airfoil 534 00:26:34,890 --> 00:26:38,340 or stick to the wing versus just moving smoothly past it. 535 00:26:38,340 --> 00:26:40,680 So viscosity has a big impact. 536 00:26:40,680 --> 00:26:43,920 And then compressibility also affects lift. 537 00:26:43,920 --> 00:26:46,340 So the compressibility of the air-- 538 00:26:46,340 --> 00:26:47,530 did I turn off my mic? 539 00:26:51,750 --> 00:26:54,900 So certain types of fluids are compressible. 540 00:26:54,900 --> 00:26:57,540 So you could take a balloon of air. 541 00:26:57,540 --> 00:26:59,970 And you can move it into a cold environment 542 00:26:59,970 --> 00:27:02,520 and have it shrink or in a hot environment 543 00:27:02,520 --> 00:27:05,550 and have it expand while having the same amount of mass 544 00:27:05,550 --> 00:27:06,390 inside the balloon. 545 00:27:06,390 --> 00:27:07,900 So I'm getting a lot of head nods. 546 00:27:07,900 --> 00:27:10,950 So that just shows the compressibility of the air, 547 00:27:10,950 --> 00:27:13,320 whereas some types of fluids are not compressible. 548 00:27:13,320 --> 00:27:14,640 They're incompressible. 549 00:27:14,640 --> 00:27:18,080 And they affect lift in a different way. 550 00:27:18,080 --> 00:27:19,880 So although I've told you all these things 551 00:27:19,880 --> 00:27:23,240 that affects lift, one thing I will admit to you is 552 00:27:23,240 --> 00:27:27,980 that calculating lift is difficult. It's very difficult. 553 00:27:27,980 --> 00:27:31,700 In fact, we don't really know how to do it properly. 554 00:27:31,700 --> 00:27:34,820 This is a snapshot from Wikipedia 555 00:27:34,820 --> 00:27:37,340 of all the different theories of lift. 556 00:27:37,340 --> 00:27:39,020 So there are a lot of different ways 557 00:27:39,020 --> 00:27:42,770 that people go about trying to calculate lift. 558 00:27:42,770 --> 00:27:46,440 And it turns out that it's very hard to do. 559 00:27:46,440 --> 00:27:53,130 So one that you see up there is Navier-Stokes. 560 00:27:53,130 --> 00:27:55,950 So Navier-Stokes is a set of equations 561 00:27:55,950 --> 00:28:00,720 that does a really good job of predicting lift. 562 00:28:00,720 --> 00:28:05,180 And it really takes into account a lot of things. 563 00:28:05,180 --> 00:28:07,880 It takes into account conservation of energy, 564 00:28:07,880 --> 00:28:10,760 conservation of mass, conservation of momentum, 565 00:28:10,760 --> 00:28:15,320 viscosity, even a lot of things like thermal conductivity 566 00:28:15,320 --> 00:28:17,390 and a whole bunch of considerations. 567 00:28:17,390 --> 00:28:23,660 But the problem is that solving those equations is very hard. 568 00:28:23,660 --> 00:28:27,560 We try to use supercomputers to estimate every little aspect. 569 00:28:27,560 --> 00:28:29,310 And it's very difficult to do. 570 00:28:29,310 --> 00:28:30,950 And we're not really able to solve 571 00:28:30,950 --> 00:28:34,010 those equations to determine precisely what the lift is 572 00:28:34,010 --> 00:28:36,820 going to be. 573 00:28:36,820 --> 00:28:38,930 Let me talk about some of the limitations 574 00:28:38,930 --> 00:28:42,510 that we have in solving these equations. 575 00:28:42,510 --> 00:28:46,190 So first of all, it has to do with how 576 00:28:46,190 --> 00:28:48,950 the air flows over the wing. 577 00:28:48,950 --> 00:28:54,230 If the air is moving very smoothly past the airfoil, 578 00:28:54,230 --> 00:28:56,240 then it's very easy to come up-- 579 00:28:56,240 --> 00:28:58,850 not easy, but it's easier to approximate. 580 00:28:58,850 --> 00:29:03,260 We can predict what a particular air molecule is going to do. 581 00:29:03,260 --> 00:29:05,720 But as you see there, when it starts spinning around 582 00:29:05,720 --> 00:29:07,570 and becoming turbulent-- 583 00:29:07,570 --> 00:29:11,900 so if you start seeing a particular air molecule that's 584 00:29:11,900 --> 00:29:15,320 moving around, and becoming turbulent, so not doing 585 00:29:15,320 --> 00:29:18,590 laminar flow but turbulent, and moving around, and bumping 586 00:29:18,590 --> 00:29:21,050 into other air molecules, then predicting 587 00:29:21,050 --> 00:29:23,600 what that molecule does and what all the molecules do around 588 00:29:23,600 --> 00:29:25,710 it become very, very difficult. In fact, 589 00:29:25,710 --> 00:29:28,260 we have a very hard time doing that. 590 00:29:28,260 --> 00:29:32,718 And so instead, we basically assume 591 00:29:32,718 --> 00:29:33,760 that that doesn't happen. 592 00:29:36,340 --> 00:29:40,870 And we impose some limitations or conditions 593 00:29:40,870 --> 00:29:43,480 on the airflow which are not actually true 594 00:29:43,480 --> 00:29:46,180 but help us with approximating lift. 595 00:29:46,180 --> 00:29:48,400 So one of those is the Kutta condition 596 00:29:48,400 --> 00:29:52,390 that you see at the bottom left, which is this smooth flow off. 597 00:29:52,390 --> 00:29:55,510 So basically, you say that none of this turbulence 598 00:29:55,510 --> 00:29:57,440 is happening. 599 00:29:57,440 --> 00:30:01,220 And the air moves very cleanly off. 600 00:30:01,220 --> 00:30:04,370 And you also have a couple other specific requirements 601 00:30:04,370 --> 00:30:07,220 such as that no air molecule from the top 602 00:30:07,220 --> 00:30:10,640 comes over to the bottom, and no air molecule from the bottom 603 00:30:10,640 --> 00:30:12,250 goes around to the top. 604 00:30:12,250 --> 00:30:16,430 And you just assume that they move smoothly off. 605 00:30:16,430 --> 00:30:18,200 And so that Kutta condition is actually 606 00:30:18,200 --> 00:30:23,210 very helpful in approximating lift. 607 00:30:23,210 --> 00:30:26,810 We also make other assumptions that there's no viscosity 608 00:30:26,810 --> 00:30:29,390 or that the fluid is not compressible. 609 00:30:29,390 --> 00:30:32,660 Sometimes, these assumptions are appropriate. 610 00:30:32,660 --> 00:30:35,560 And sometimes, they're not. 611 00:30:35,560 --> 00:30:39,520 Another thing that's really critical about our ability 612 00:30:39,520 --> 00:30:42,610 to estimate lift is that as I've been talking to you here 613 00:30:42,610 --> 00:30:46,150 on the blackboard, I have talked about a cross-section, 614 00:30:46,150 --> 00:30:46,910 that you just-- 615 00:30:46,910 --> 00:30:47,920 you cut off the wing. 616 00:30:47,920 --> 00:30:50,215 And you're only looking at one cross-section. 617 00:30:50,215 --> 00:30:52,090 So since we're talking about a cross-section, 618 00:30:52,090 --> 00:30:55,640 we're talking in two-dimensional space. 619 00:30:55,640 --> 00:30:57,460 Well, we can actually do a pretty good job 620 00:30:57,460 --> 00:31:01,120 of estimating lift in a two-dimensional environment. 621 00:31:01,120 --> 00:31:04,900 But the fact of the matter is wings are not two dimensional. 622 00:31:04,900 --> 00:31:06,790 And the wing comes out into the classroom 623 00:31:06,790 --> 00:31:09,170 and back into the blackboard. 624 00:31:09,170 --> 00:31:12,100 And to estimate actually how all these air flows 625 00:31:12,100 --> 00:31:15,370 work at the edge of the wing is very difficult. 626 00:31:15,370 --> 00:31:19,150 Has anyone heard about tip vortices? 627 00:31:19,150 --> 00:31:21,520 Couple head nods. 628 00:31:21,520 --> 00:31:24,490 So we have a picture there that shows a jet 629 00:31:24,490 --> 00:31:26,860 to just show a little bit about what 630 00:31:26,860 --> 00:31:32,980 the air does when it comes off the edge, the end of the wing. 631 00:31:32,980 --> 00:31:36,640 We're going to talk about tip vortices a little bit. 632 00:31:36,640 --> 00:31:40,210 But the problem is that it no longer is adhering 633 00:31:40,210 --> 00:31:42,100 to all of our conditions. 634 00:31:42,100 --> 00:31:44,110 Now, we don't have smooth flow. 635 00:31:44,110 --> 00:31:45,640 We definitely have turbulent flow. 636 00:31:45,640 --> 00:31:46,760 We have spinning flow. 637 00:31:46,760 --> 00:31:49,060 And we have air molecules hitting other air molecules. 638 00:31:49,060 --> 00:31:51,640 And it becomes extremely difficult for us 639 00:31:51,640 --> 00:31:54,520 to model all of those air molecules. 640 00:31:54,520 --> 00:31:55,520 We really can't do it. 641 00:31:55,520 --> 00:31:58,510 So going from two dimensions to three dimensions 642 00:31:58,510 --> 00:32:00,760 is really a limitation of a lot of the equations 643 00:32:00,760 --> 00:32:04,300 that we have to approximate lift. 644 00:32:04,300 --> 00:32:06,640 So what do we do? 645 00:32:06,640 --> 00:32:10,720 Well, first of all, we go back to our two-dimensional surface. 646 00:32:10,720 --> 00:32:14,530 And we talked about all of these normal forces, 647 00:32:14,530 --> 00:32:16,900 so when you have all the fluid going past, 648 00:32:16,900 --> 00:32:19,240 and it has pressure, and it's supplying 649 00:32:19,240 --> 00:32:23,570 all these forces perpendicular to the airfoil all around. 650 00:32:23,570 --> 00:32:25,178 So how do you approximate lift? 651 00:32:25,178 --> 00:32:26,470 Well, you say, oh, that's fine. 652 00:32:26,470 --> 00:32:30,430 You just sum all those forces around. 653 00:32:30,430 --> 00:32:33,850 Well, that's great if you know what all of those forces are, 654 00:32:33,850 --> 00:32:37,370 but it's not great if you don't know what all of them are. 655 00:32:37,370 --> 00:32:40,862 So what is the solution that we-- 656 00:32:40,862 --> 00:32:42,250 what we do? 657 00:32:42,250 --> 00:32:44,450 Basically, we calculate what we can, 658 00:32:44,450 --> 00:32:47,600 and then we measure the rest experimentally. 659 00:32:47,600 --> 00:32:50,740 So in this equation of lift, for example, so we have 660 00:32:50,740 --> 00:32:52,480 L is for lift. 661 00:32:52,480 --> 00:32:56,830 Some of the other terms that you have there-- 662 00:32:56,830 --> 00:32:59,240 rho is the one that looks like a p. 663 00:32:59,240 --> 00:33:02,590 So rho is talking about the air density. 664 00:33:02,590 --> 00:33:04,060 You have velocity. 665 00:33:04,060 --> 00:33:08,060 And A is the wing area we talked about. 666 00:33:08,060 --> 00:33:12,910 And then we have this fancy little symbol there C sub 667 00:33:12,910 --> 00:33:15,670 L or the coefficient of lift. 668 00:33:15,670 --> 00:33:18,400 And basically, we say that I don't 669 00:33:18,400 --> 00:33:21,490 know how to come up with characterizing 670 00:33:21,490 --> 00:33:25,270 all those complications about viscosity 671 00:33:25,270 --> 00:33:30,610 and some of the effects like that have to do with turbulence 672 00:33:30,610 --> 00:33:34,000 and shock waves, Mach number, Reynolds number, all 673 00:33:34,000 --> 00:33:35,180 these types of things. 674 00:33:35,180 --> 00:33:37,840 And so we say we'll measure what we can, 675 00:33:37,840 --> 00:33:40,460 and then we'll-- or we'll calculate what we can, 676 00:33:40,460 --> 00:33:43,420 and then we'll actually, in a wind tunnel where we put this 677 00:33:43,420 --> 00:33:46,990 guy on a stick, we'll actually measure the coefficient 678 00:33:46,990 --> 00:33:47,800 of lift. 679 00:33:47,800 --> 00:33:50,170 And that's how we really calculate lift 680 00:33:50,170 --> 00:33:52,900 these days is using a lot of measurement 681 00:33:52,900 --> 00:33:55,570 to inform what's actually happening because it's just 682 00:33:55,570 --> 00:33:57,960 very complicated. 683 00:33:57,960 --> 00:34:01,140 AUDIENCE: Tina, that velocity is squared, right? 684 00:34:01,140 --> 00:34:04,800 So if you go twice as fast, you get four times as much lift. 685 00:34:04,800 --> 00:34:06,550 TINA SRIVASTAVA: That is the relationship. 686 00:34:06,550 --> 00:34:08,469 Absolutely. 687 00:34:08,469 --> 00:34:11,199 And the other thing that's really important 688 00:34:11,199 --> 00:34:13,750 is that that coefficient of lift is measured 689 00:34:13,750 --> 00:34:15,969 for a given angle of attack. 690 00:34:15,969 --> 00:34:18,100 So we talked a little bit about angle of attack 691 00:34:18,100 --> 00:34:20,150 with your hand outside the window. 692 00:34:20,150 --> 00:34:24,170 So let's get into defining it a little bit more in detail. 693 00:34:24,170 --> 00:34:26,800 So in order to describe it, I have to come up with a few 694 00:34:26,800 --> 00:34:29,920 more terms that have to do with the airfoil. 695 00:34:29,920 --> 00:34:32,050 So we talked about the very front 696 00:34:32,050 --> 00:34:35,679 of the airfoil or the front of the wing 697 00:34:35,679 --> 00:34:40,300 is called the leading edge, and then the back 698 00:34:40,300 --> 00:34:41,469 is the trailing edge. 699 00:34:45,409 --> 00:34:47,840 And we talked about the trailing edge a little bit 700 00:34:47,840 --> 00:34:50,090 when we were talking about the Kutta condition 701 00:34:50,090 --> 00:34:53,719 that no air molecule-- we're assuming no air molecule 702 00:34:53,719 --> 00:34:58,310 can cross the trailing edge to the other side. 703 00:34:58,310 --> 00:35:00,510 So then the camber is in there. 704 00:35:00,510 --> 00:35:03,260 So that's just talking about really representing 705 00:35:03,260 --> 00:35:08,450 the curvature of that airfoil and then a chord line 706 00:35:08,450 --> 00:35:12,410 that goes in between so you can measure how that is. 707 00:35:12,410 --> 00:35:20,727 So try and do your little zoom in fanciness 708 00:35:20,727 --> 00:35:21,560 that you were doing. 709 00:35:21,560 --> 00:35:23,852 AUDIENCE: I think I set-- yeah, maybe it went to sleep. 710 00:35:29,958 --> 00:35:31,440 Giving up? 711 00:35:31,440 --> 00:35:33,330 TINA SRIVASTAVA: I'll just point at it. 712 00:35:33,330 --> 00:35:35,370 So this is the chord line of the wing. 713 00:35:35,370 --> 00:35:37,620 So you can see that this is a full airplane. 714 00:35:37,620 --> 00:35:39,580 The airfoil is right here. 715 00:35:39,580 --> 00:35:41,730 And you see this chord line going from the back 716 00:35:41,730 --> 00:35:42,300 to the front. 717 00:35:48,631 --> 00:35:51,330 Is somebody trying to come in the door there? 718 00:35:54,510 --> 00:35:55,040 Great. 719 00:35:55,040 --> 00:35:57,940 And then we'll talk about some of these terms. 720 00:35:57,940 --> 00:36:00,140 Basically, the most important thing to think about 721 00:36:00,140 --> 00:36:02,280 is the angle of attack. 722 00:36:02,280 --> 00:36:06,080 Thank you for checking on the door. 723 00:36:06,080 --> 00:36:08,870 So talking about how we can control the lift, 724 00:36:08,870 --> 00:36:10,370 so some of the things we can do have 725 00:36:10,370 --> 00:36:11,720 to do with the aircraft design. 726 00:36:11,720 --> 00:36:13,940 So we can build an airfoil. 727 00:36:13,940 --> 00:36:18,860 And we can talk about how curved that airfoil is, the curvature 728 00:36:18,860 --> 00:36:20,600 on the top, how curved it is. 729 00:36:20,600 --> 00:36:23,090 We can design the wing area. 730 00:36:23,090 --> 00:36:26,330 When we're flying, we can control the airspeed. 731 00:36:26,330 --> 00:36:28,460 And then the angle of attack is something 732 00:36:28,460 --> 00:36:30,950 that you can control when you're in the airplane 733 00:36:30,950 --> 00:36:33,320 by pitching down or pitching up. 734 00:36:33,320 --> 00:36:36,290 And we'll describe pitching and how you control 735 00:36:36,290 --> 00:36:38,790 an airplane in more detail. 736 00:36:38,790 --> 00:36:41,030 Another thing that's relevant is flaps. 737 00:36:41,030 --> 00:36:43,850 So I talked about in this drawing right 738 00:36:43,850 --> 00:36:48,260 here where I added this white part of the trailing edge that 739 00:36:48,260 --> 00:36:51,680 moves down, that really is kind of similar to flaps. 740 00:36:51,680 --> 00:36:54,920 So when your flaps are up, they're sort of in line 741 00:36:54,920 --> 00:36:56,090 with the rest of the wing. 742 00:36:56,090 --> 00:36:57,950 But when your flaps are down, it's 743 00:36:57,950 --> 00:37:00,530 the effective thing like pushing-- 744 00:37:00,530 --> 00:37:04,250 pulling a piece of your trailing edge downward, 745 00:37:04,250 --> 00:37:08,510 which causes again more of that air to be deflected downward. 746 00:37:08,510 --> 00:37:11,600 So it increases your drag, but it also 747 00:37:11,600 --> 00:37:14,060 increases your lift because you're deflecting more air 748 00:37:14,060 --> 00:37:15,770 molecules down. 749 00:37:15,770 --> 00:37:18,530 And then we also talked about spoilers, for example, 750 00:37:18,530 --> 00:37:20,960 as something that can, like on a car, 751 00:37:20,960 --> 00:37:26,190 that can actually disrupt the lift by disrupting the airflow. 752 00:37:26,190 --> 00:37:29,790 And when we talked about the four forces of flight, 753 00:37:29,790 --> 00:37:31,890 if you're doing steady flight, you're not climbing 754 00:37:31,890 --> 00:37:34,350 or you're descending, but you're just flying straight, 755 00:37:34,350 --> 00:37:37,350 that means that your lift and your weight 756 00:37:37,350 --> 00:37:41,710 basically cancel each other out. 757 00:37:41,710 --> 00:37:43,870 If your lift is greater than your weight, 758 00:37:43,870 --> 00:37:45,220 then you can climb. 759 00:37:45,220 --> 00:37:47,110 And if your weight is greater than your lift, 760 00:37:47,110 --> 00:37:48,112 then you descend. 761 00:37:48,112 --> 00:37:49,570 But if you're just flying straight, 762 00:37:49,570 --> 00:37:54,680 you're in an equilibrium where those two forces cancel out. 763 00:37:54,680 --> 00:37:55,180 So good. 764 00:37:55,180 --> 00:37:58,440 I have a more detailed diagram of angle of attack. 765 00:37:58,440 --> 00:38:01,360 So you can see here the chord line. 766 00:38:01,360 --> 00:38:05,080 You can also see the relative wind and same things 767 00:38:05,080 --> 00:38:06,130 that I drew here-- 768 00:38:06,130 --> 00:38:10,120 the lift and the drag and then that resultant force vector. 769 00:38:16,420 --> 00:38:20,070 So you can actually control the angle of attack 770 00:38:20,070 --> 00:38:22,190 in a number of ways. 771 00:38:22,190 --> 00:38:27,250 One of the ways that we talked about is pitching down. 772 00:38:27,250 --> 00:38:31,460 So pushing your yoke forward causes the airplane 773 00:38:31,460 --> 00:38:33,100 to pitch down. 774 00:38:33,100 --> 00:38:36,340 And it does that by changing the elevator 775 00:38:36,340 --> 00:38:37,540 at the back of the airplane. 776 00:38:37,540 --> 00:38:39,430 We'll describe that in more detail. 777 00:38:39,430 --> 00:38:42,440 But the other things that can affect the angle of attack, 778 00:38:42,440 --> 00:38:45,050 you can actually affect before you even take off. 779 00:38:45,050 --> 00:38:47,410 So it has to do with your aircraft weight, 780 00:38:47,410 --> 00:38:50,350 for example, and the center of gravity, 781 00:38:50,350 --> 00:38:53,210 as well as your airspeed when you're flying. 782 00:38:53,210 --> 00:38:57,320 So here are a couple of diagrams that show you 783 00:38:57,320 --> 00:39:02,210 how the lift changes with the effective angle of attack, 784 00:39:02,210 --> 00:39:04,500 and then there is a critical angle of attack. 785 00:39:04,500 --> 00:39:07,860 So that's when you can keep climbing for a while. 786 00:39:07,860 --> 00:39:11,240 But if you get too steep, what happens? 787 00:39:11,240 --> 00:39:13,197 Who knows what happens when you go to steep? 788 00:39:13,197 --> 00:39:14,030 AUDIENCE: You stall. 789 00:39:14,030 --> 00:39:15,155 TINA SRIVASTAVA: You stall. 790 00:39:15,155 --> 00:39:15,900 That's right. 791 00:39:15,900 --> 00:39:19,620 So the air can't really effectively go over the wing. 792 00:39:19,620 --> 00:39:21,420 And it starts separating. 793 00:39:21,420 --> 00:39:23,220 And so you're no longer effectively 794 00:39:23,220 --> 00:39:25,020 pushing the air down. 795 00:39:25,020 --> 00:39:28,520 And you lose the lift that you were generating. 796 00:39:28,520 --> 00:39:30,920 And one thing I also want to point out here 797 00:39:30,920 --> 00:39:37,130 in these diagrams is you see with these little colored lines 798 00:39:37,130 --> 00:39:39,440 the air that's coming in. 799 00:39:39,440 --> 00:39:40,370 And it's going out. 800 00:39:40,370 --> 00:39:43,280 And you can see that in this case, 801 00:39:43,280 --> 00:39:46,190 the blue lines are showing that the air that 802 00:39:46,190 --> 00:39:50,810 went over the top of the airfoil went faster and actually got 803 00:39:50,810 --> 00:39:54,630 to the back faster than the air that went from the bottom. 804 00:39:54,630 --> 00:39:59,870 So again, please don't fall for the equal transit theory. 805 00:39:59,870 --> 00:40:01,010 So practice question. 806 00:40:19,410 --> 00:40:20,950 A, B, or C? 807 00:40:20,950 --> 00:40:21,870 AUDIENCE: A. 808 00:40:21,870 --> 00:40:24,420 TINA SRIVASTAVA: A. Good. 809 00:40:24,420 --> 00:40:27,417 So the angle of attack is defined there. 810 00:40:27,417 --> 00:40:29,250 And one thing that I would like to point out 811 00:40:29,250 --> 00:40:31,800 is that this is also the case for a propeller. 812 00:40:31,800 --> 00:40:35,880 So your propeller also looks a lot like an airfoil 813 00:40:35,880 --> 00:40:39,720 or like a wing that's sideways and spinning around. 814 00:40:39,720 --> 00:40:42,840 And so also the angle of attack for a propeller 815 00:40:42,840 --> 00:40:44,670 is defined basically the same way 816 00:40:44,670 --> 00:40:46,770 is the angle between the propeller's chord 817 00:40:46,770 --> 00:40:50,280 line and the relative wind. 818 00:40:50,280 --> 00:40:52,770 So let's define the center of pressure. 819 00:40:52,770 --> 00:40:56,880 So it's basically the point on the wing 820 00:40:56,880 --> 00:40:59,850 where the lift is centered. 821 00:40:59,850 --> 00:41:04,650 And so that can actually move as you can see in this figure. 822 00:41:04,650 --> 00:41:08,280 Based on the angle of attack, the center of pressure 823 00:41:08,280 --> 00:41:11,560 can act in a different location. 824 00:41:11,560 --> 00:41:14,380 And that's really important to understand also 825 00:41:14,380 --> 00:41:17,110 that it's not that the lift is always coming right 826 00:41:17,110 --> 00:41:17,655 at the front. 827 00:41:17,655 --> 00:41:19,780 Depending on where you are, it might be pulling you 828 00:41:19,780 --> 00:41:21,230 in different directions. 829 00:41:21,230 --> 00:41:23,110 And that can affect the maneuverability 830 00:41:23,110 --> 00:41:23,860 of your aircraft. 831 00:41:23,860 --> 00:41:26,837 And we'll get into that in more detail. 832 00:41:26,837 --> 00:41:28,420 So we talked a little bit about flaps, 833 00:41:28,420 --> 00:41:31,570 that flaps actually can increase the lift 834 00:41:31,570 --> 00:41:33,130 that you're able to produce. 835 00:41:33,130 --> 00:41:37,160 But it's a trade-off because it also increases the drag. 836 00:41:37,160 --> 00:41:43,000 So when in the course of the flight, takeoff, cruise, 837 00:41:43,000 --> 00:41:46,950 or landing, when do you use flaps? 838 00:41:46,950 --> 00:41:48,650 Does anyone know? 839 00:41:48,650 --> 00:41:50,178 AUDIENCE: Takeoff and landing. 840 00:41:50,178 --> 00:41:51,720 TINA SRIVASTAVA: Takeoff and landing. 841 00:41:51,720 --> 00:41:52,920 Landing. 842 00:41:52,920 --> 00:41:57,240 Yeah, the reason that you, especially on landing-- 843 00:41:57,240 --> 00:41:59,370 many times people use flaps on takeoff as well. 844 00:41:59,370 --> 00:42:01,185 But the reason is just that you like 845 00:42:01,185 --> 00:42:03,060 to have your aircraft configured that in case 846 00:42:03,060 --> 00:42:05,370 you didn't take off, you can land without making 847 00:42:05,370 --> 00:42:08,310 a lot of dramatic changes. 848 00:42:08,310 --> 00:42:10,530 The reason that you do that is basically 849 00:42:10,530 --> 00:42:16,930 that by increasing your lift but also increasing the drag, 850 00:42:16,930 --> 00:42:20,460 drag affects how fast you're moving forward. 851 00:42:20,460 --> 00:42:24,550 And so you can actually have the airspeed 852 00:42:24,550 --> 00:42:28,830 be higher with the ground speed being lower. 853 00:42:28,830 --> 00:42:33,380 What it does is it allows you to go very slow without stalling. 854 00:42:33,380 --> 00:42:36,180 And so that really helps you land an airplane. 855 00:42:36,180 --> 00:42:38,490 So basically, it allows you to come 856 00:42:38,490 --> 00:42:41,730 in at a kind of steeper angle to land, 857 00:42:41,730 --> 00:42:45,660 maintaining the airspeed that you need in order to do that. 858 00:42:45,660 --> 00:42:49,230 And you'll notice that there are different flap settings. 859 00:42:49,230 --> 00:42:53,340 So you can either have flaps at 10 degrees, 20 degrees, 30 860 00:42:53,340 --> 00:42:53,980 degrees. 861 00:42:53,980 --> 00:42:55,440 We'll discuss that in more detail. 862 00:42:55,440 --> 00:42:57,065 And Phillip will talk about it in terms 863 00:42:57,065 --> 00:43:00,240 of performance I think as well. 864 00:43:00,240 --> 00:43:03,930 Thrust-- so we talked about that forward force thrust. 865 00:43:03,930 --> 00:43:06,990 In this type of an aircraft, a single engine propeller 866 00:43:06,990 --> 00:43:09,270 aircraft, it's the propeller that's 867 00:43:09,270 --> 00:43:13,390 rotating that is really producing the thrust. 868 00:43:13,390 --> 00:43:16,350 And it's really, as I said, the propeller blades 869 00:43:16,350 --> 00:43:17,970 are kind of like an airplane wing-- 870 00:43:17,970 --> 00:43:19,428 it's a good way to think about it-- 871 00:43:19,428 --> 00:43:23,310 that are just spinning round and round and generating lift. 872 00:43:23,310 --> 00:43:26,460 But in this case, it's moving air molecules front to 873 00:43:26,460 --> 00:43:28,380 behind your airplane. 874 00:43:28,380 --> 00:43:32,160 And then although this is also just a force, instead 875 00:43:32,160 --> 00:43:33,900 of talking about it in pounds, we usually 876 00:43:33,900 --> 00:43:36,090 talk about the horsepower required 877 00:43:36,090 --> 00:43:39,470 to drive the propeller. 878 00:43:39,470 --> 00:43:41,150 So let me also talk about drag. 879 00:43:41,150 --> 00:43:43,700 So there are a couple different types of drag. 880 00:43:43,700 --> 00:43:47,870 So one drag is just what's called parasitic drag 881 00:43:47,870 --> 00:43:48,900 or parasite drag. 882 00:43:48,900 --> 00:43:52,280 It's basically when the aircraft is moving through the air 883 00:43:52,280 --> 00:43:55,760 that you get some kind of resistance to that. 884 00:43:55,760 --> 00:44:00,840 That's parasitic drag, whereas this drag is induced drag, 885 00:44:00,840 --> 00:44:04,840 which is the drag that's created by the lift, so this backwards 886 00:44:04,840 --> 00:44:07,760 D. And so you can see in this figure 887 00:44:07,760 --> 00:44:11,270 that the total drag is a sum of that induced drag 888 00:44:11,270 --> 00:44:12,890 and the parasite drag. 889 00:44:16,740 --> 00:44:19,870 AUDIENCE: Do we also call the induced drag just lift 890 00:44:19,870 --> 00:44:21,540 in an unwanted direction? 891 00:44:21,540 --> 00:44:24,130 TINA SRIVASTAVA: Lift in an unwanted direction. 892 00:44:24,130 --> 00:44:28,390 Sure, whatever can have you associate induced drag 893 00:44:28,390 --> 00:44:29,140 with lift. 894 00:44:29,140 --> 00:44:31,210 That's the drag created by lift. 895 00:44:34,460 --> 00:44:37,460 Ground effect-- does anyone know a ground effect is? 896 00:44:40,010 --> 00:44:42,620 Only a couple of you. 897 00:44:42,620 --> 00:44:45,450 So let's talk about it a little bit. 898 00:44:45,450 --> 00:44:48,590 So basically, when you're very close to the ground within one 899 00:44:48,590 --> 00:44:51,260 wing span of the ground, you actually 900 00:44:51,260 --> 00:44:55,310 have some of the airflow going on with your airplane is 901 00:44:55,310 --> 00:44:56,990 blocked by the ground. 902 00:44:56,990 --> 00:45:00,580 And so your induced drag decreases. 903 00:45:00,580 --> 00:45:02,210 Now, with the induced drag decreases, 904 00:45:02,210 --> 00:45:04,700 it's actually the case that your airplane 905 00:45:04,700 --> 00:45:10,010 can become airborne at a lower speed than it's supposed to. 906 00:45:10,010 --> 00:45:12,740 So what you might notice is that when 907 00:45:12,740 --> 00:45:14,780 you're on the runway taking off-- 908 00:45:14,780 --> 00:45:17,300 this is probably the first part of your flights. 909 00:45:17,300 --> 00:45:19,730 After you did your pre-flight, your engine runup, 910 00:45:19,730 --> 00:45:21,500 you pulled out onto the runway. 911 00:45:21,500 --> 00:45:24,050 And you'll have determined in advance 912 00:45:24,050 --> 00:45:28,190 what is the air speed at which you should rotate. 913 00:45:28,190 --> 00:45:29,540 Now, that's really important. 914 00:45:29,540 --> 00:45:35,720 With a Cessna 172, for example, it's around 55 knots. 915 00:45:35,720 --> 00:45:38,390 And you want to look at your airspeed indicator. 916 00:45:38,390 --> 00:45:40,550 Because if you just feel yourself, 917 00:45:40,550 --> 00:45:44,600 you might notice that much lower, like 40 knots, 918 00:45:44,600 --> 00:45:46,760 that the plane has already taken off. 919 00:45:46,760 --> 00:45:48,050 You're already floating. 920 00:45:48,050 --> 00:45:49,030 You're flying. 921 00:45:49,030 --> 00:45:50,990 And you might be very excited about that. 922 00:45:50,990 --> 00:45:55,910 And you might want to just pull back on your yoke to take off. 923 00:45:55,910 --> 00:45:59,450 Well, you won't be able to sustain flight. 924 00:45:59,450 --> 00:46:02,810 And so this is what why ground effect is really important 925 00:46:02,810 --> 00:46:05,150 is that you can kind of float over the ground 926 00:46:05,150 --> 00:46:06,800 because you're so close to the ground 927 00:46:06,800 --> 00:46:10,913 that the ground is blocking some of the effects of the air. 928 00:46:10,913 --> 00:46:12,830 And so what you want to do is really make sure 929 00:46:12,830 --> 00:46:15,968 that you continue your ground roll, continue. 930 00:46:15,968 --> 00:46:17,510 Even if you're a little bit airborne, 931 00:46:17,510 --> 00:46:20,360 stay close to the ground until your airspeed comes up 932 00:46:20,360 --> 00:46:23,930 to that rotate speed, so in this case, 55 knots, 933 00:46:23,930 --> 00:46:29,060 and then you pull back on your yoke to take off. 934 00:46:29,060 --> 00:46:32,045 So again, so when does ground effect happen? 935 00:46:32,045 --> 00:46:33,420 When you're close to the ground-- 936 00:46:33,420 --> 00:46:37,940 when you're within one wing span of the ground 937 00:46:37,940 --> 00:46:40,850 So let's talk a little bit about stability. 938 00:46:40,850 --> 00:46:44,420 And we'll start by just talking about the three axes of flight. 939 00:46:44,420 --> 00:46:49,790 So there is a longitudinal axis, which 940 00:46:49,790 --> 00:46:54,130 is basically from the nose to the tail of your airplane. 941 00:46:54,130 --> 00:46:56,180 And there's a lateral axis, which 942 00:46:56,180 --> 00:47:00,560 is from wingtip to wingtip and then vertical going straight 943 00:47:00,560 --> 00:47:01,880 through the plane. 944 00:47:01,880 --> 00:47:04,310 So you have the ability to control all three 945 00:47:04,310 --> 00:47:06,470 of those axes. 946 00:47:06,470 --> 00:47:10,100 So the elevator, which I keep talking about is like your yoke 947 00:47:10,100 --> 00:47:12,530 where you push it forward or you pull it back, 948 00:47:12,530 --> 00:47:14,960 that allows you to pitch the airplane. 949 00:47:14,960 --> 00:47:17,930 So pitch nose up, pitch nose down-- 950 00:47:17,930 --> 00:47:21,680 that's you controlling the back part of this tail, 951 00:47:21,680 --> 00:47:25,730 the elevator, which allows you to have 952 00:47:25,730 --> 00:47:29,240 motion in this direction, so pitch nose down. 953 00:47:29,240 --> 00:47:30,620 So you might hear that a lot. 954 00:47:30,620 --> 00:47:32,358 In case you're getting close to stalling 955 00:47:32,358 --> 00:47:34,400 because your angle of attack is getting too high, 956 00:47:34,400 --> 00:47:39,010 they might say, nose down or pitch nose down. 957 00:47:39,010 --> 00:47:41,650 You also have ailerons, which are out 958 00:47:41,650 --> 00:47:44,410 on the side of your wings. 959 00:47:44,410 --> 00:47:47,290 And those ailerons control the roll. 960 00:47:47,290 --> 00:47:50,230 So that's rolling along the longitudinal axis. 961 00:47:53,520 --> 00:47:57,170 And then your rudder, which is at the back of the tail, 962 00:47:57,170 --> 00:47:59,180 the vertical part of the tail-- 963 00:47:59,180 --> 00:48:00,650 that controls yaw. 964 00:48:00,650 --> 00:48:03,980 So this is called yaw, this type of motion. 965 00:48:03,980 --> 00:48:07,220 So when you're turning, you actually kind of do a roll 966 00:48:07,220 --> 00:48:10,520 and yaw usually to enact a turn. 967 00:48:13,880 --> 00:48:16,340 There are some cases where you actually 968 00:48:16,340 --> 00:48:21,680 want to have adverse yaw or you actually-- 969 00:48:21,680 --> 00:48:23,960 adverse yaw means basically you're 970 00:48:23,960 --> 00:48:27,170 using the yaw direction in maybe the opposite direction at which 971 00:48:27,170 --> 00:48:31,040 you're trying to turn with the roll or other angles 972 00:48:31,040 --> 00:48:32,120 of your plane. 973 00:48:32,120 --> 00:48:37,630 And so this just talks about an adverse yaw 974 00:48:37,630 --> 00:48:42,040 is when you're not turning the rudder in the same direction 975 00:48:42,040 --> 00:48:44,620 that you're using your aileron. 976 00:48:44,620 --> 00:48:47,650 And so this is where you talk about coordinated flight 977 00:48:47,650 --> 00:48:49,210 or uncoordinated flight. 978 00:48:49,210 --> 00:48:53,530 When you're actually in an airplane, the rudder or the yaw 979 00:48:53,530 --> 00:48:54,800 is controlled by your feet. 980 00:48:54,800 --> 00:48:58,930 So you have feet pedals that control the rudder. 981 00:48:58,930 --> 00:49:01,810 And the yoke that you're holding onto 982 00:49:01,810 --> 00:49:04,690 or a joystick that you're holding onto front and back 983 00:49:04,690 --> 00:49:07,210 controls the pitch. 984 00:49:07,210 --> 00:49:10,540 And then turning it like in the steering wheel of a car 985 00:49:10,540 --> 00:49:12,700 is only controlling the roll. 986 00:49:12,700 --> 00:49:14,680 So you actually also use your feet 987 00:49:14,680 --> 00:49:17,350 for that third direction of the yaw. 988 00:49:19,900 --> 00:49:24,250 So just talking about stability in general, 989 00:49:24,250 --> 00:49:26,770 this isn't going to dive into a whole diffy q 990 00:49:26,770 --> 00:49:28,090 discussion or anything. 991 00:49:28,090 --> 00:49:31,390 But just in general, something that's stable-- 992 00:49:31,390 --> 00:49:33,490 so it's just talking about like a little bowl 993 00:49:33,490 --> 00:49:36,790 if you have a ball in a bowl, even if the ball gets jostled 994 00:49:36,790 --> 00:49:39,880 around, it'll return to the center point. 995 00:49:39,880 --> 00:49:41,590 Unstable would be the opposite. 996 00:49:41,590 --> 00:49:44,500 So if you have a convex surface, then if the ball moves 997 00:49:44,500 --> 00:49:46,210 even just a little bit, it'll really 998 00:49:46,210 --> 00:49:48,410 get moved out of control. 999 00:49:48,410 --> 00:49:51,670 So the reason that we talk about this 1000 00:49:51,670 --> 00:49:54,990 is basically when you're flying in an airplane, 1001 00:49:54,990 --> 00:49:56,840 and you're talking about stable aircraft, 1002 00:49:56,840 --> 00:50:02,050 for example, the reason I really love flying a Cessna 172, even 1003 00:50:02,050 --> 00:50:04,210 though it's kind of the training airplane, 1004 00:50:04,210 --> 00:50:07,280 is that the-- as people call it, it flies itself. 1005 00:50:07,280 --> 00:50:10,000 So if you notice the plane's doing something weird 1006 00:50:10,000 --> 00:50:12,130 and turning, almost the best thing you can do 1007 00:50:12,130 --> 00:50:13,810 is just let go. 1008 00:50:13,810 --> 00:50:16,540 And the controls will normalize, and then the plane 1009 00:50:16,540 --> 00:50:19,870 will fly straight and level, which is really great. 1010 00:50:19,870 --> 00:50:21,640 There are other types of aircraft 1011 00:50:21,640 --> 00:50:23,780 that are inherently unstable. 1012 00:50:23,780 --> 00:50:26,320 So we have Minachi and Oxsana over here 1013 00:50:26,320 --> 00:50:29,140 who do aerobatic flights. 1014 00:50:29,140 --> 00:50:31,425 And Mark will be talking about that tomorrow. 1015 00:50:31,425 --> 00:50:32,800 So that's where you actually want 1016 00:50:32,800 --> 00:50:35,470 an airplane that's not so stable so that you 1017 00:50:35,470 --> 00:50:39,220 can cause it to do all kinds of crazy maneuvers and turns 1018 00:50:39,220 --> 00:50:41,320 and twists very easily. 1019 00:50:41,320 --> 00:50:43,900 You pretty much can't get a Cessna to do that. 1020 00:50:43,900 --> 00:50:46,000 It really wants to fly straight and level. 1021 00:50:51,440 --> 00:50:53,660 So then there are also other aspects 1022 00:50:53,660 --> 00:50:56,810 that can affect stability, such as your center of gravity, 1023 00:50:56,810 --> 00:50:58,790 so how you load the airplane. 1024 00:50:58,790 --> 00:51:01,010 We'll have a specific lecture that just 1025 00:51:01,010 --> 00:51:03,110 talks about weight and balance. 1026 00:51:03,110 --> 00:51:06,560 But one thing to keep in mind is that as people 1027 00:51:06,560 --> 00:51:08,660 sit in your airplane or as you put bags 1028 00:51:08,660 --> 00:51:11,820 in the baggage compartment, you're loading the airplane. 1029 00:51:11,820 --> 00:51:15,590 And so if you have too much weight aft of the CG 1030 00:51:15,590 --> 00:51:17,840 or behind the center of gravity, you 1031 00:51:17,840 --> 00:51:19,310 can cause the plane to basically go 1032 00:51:19,310 --> 00:51:22,730 like this, which isn't very helpful when you're flying. 1033 00:51:22,730 --> 00:51:25,070 If you have things a little too forward, 1034 00:51:25,070 --> 00:51:26,960 it actually pushes the nose down. 1035 00:51:26,960 --> 00:51:29,300 In general, the nose down is a little bit 1036 00:51:29,300 --> 00:51:33,080 more stable from the perspective of lift 1037 00:51:33,080 --> 00:51:34,412 and getting air to fly over. 1038 00:51:34,412 --> 00:51:35,870 You don't want something that keeps 1039 00:51:35,870 --> 00:51:39,910 trying to stall whenever you let go of it. 1040 00:51:39,910 --> 00:51:43,690 And then similarly, you can talk about the stability 1041 00:51:43,690 --> 00:51:47,900 in the lateral direction in the roll direction. 1042 00:51:47,900 --> 00:51:50,980 And some of these things like swept-back wings 1043 00:51:50,980 --> 00:51:54,580 like you see on a jet can affect that type of stability. 1044 00:51:57,920 --> 00:51:59,750 And then finally, there's stability 1045 00:51:59,750 --> 00:52:02,840 about the vertical axes. 1046 00:52:02,840 --> 00:52:05,990 Generally, this is going to be kind of fixed for the given 1047 00:52:05,990 --> 00:52:07,680 aircraft that you're in. 1048 00:52:07,680 --> 00:52:10,990 But you can affect it as you design an aircraft. 1049 00:52:10,990 --> 00:52:13,890 So we started talking about stall already. 1050 00:52:13,890 --> 00:52:17,760 So when you have your angle of attack 1051 00:52:17,760 --> 00:52:21,420 past its so-called critical angle of attack, 1052 00:52:21,420 --> 00:52:25,020 it can cause the air to basically no longer be 1053 00:52:25,020 --> 00:52:28,620 able to flow over the top and no longer be able to effectively 1054 00:52:28,620 --> 00:52:30,480 deflect air down. 1055 00:52:30,480 --> 00:52:33,000 And so the air kind of separates. 1056 00:52:33,000 --> 00:52:34,710 And you can stall. 1057 00:52:34,710 --> 00:52:36,960 So it's really important to know that you can actually 1058 00:52:36,960 --> 00:52:40,020 stall at any airspeed. 1059 00:52:40,020 --> 00:52:42,720 Even with full power, you can stall. 1060 00:52:42,720 --> 00:52:44,220 In fact, one of the maneuvers you'll 1061 00:52:44,220 --> 00:52:46,680 have to do in order to get your pilot's license 1062 00:52:46,680 --> 00:52:49,560 is a power on stall. 1063 00:52:49,560 --> 00:52:52,500 So you can stall both where your engine is idle, 1064 00:52:52,500 --> 00:52:55,650 like you're coming in for a landing, and you get too steep, 1065 00:52:55,650 --> 00:52:58,080 but you can also stall with full power. 1066 00:52:58,080 --> 00:53:02,280 And you just made your angle go too steep. 1067 00:53:02,280 --> 00:53:06,570 So it's really affecting that critical angle of attack. 1068 00:53:06,570 --> 00:53:09,390 And again, once you have that angle of attack too steep, 1069 00:53:09,390 --> 00:53:12,958 then there's a very significant loss of lift, which is not good 1070 00:53:12,958 --> 00:53:14,250 when you're flying an airplane. 1071 00:53:17,870 --> 00:53:20,870 So when can you stall? 1072 00:53:20,870 --> 00:53:25,460 At any airspeed and any power setting, 1073 00:53:25,460 --> 00:53:29,840 and it's really based on the angle of attack. 1074 00:53:29,840 --> 00:53:31,952 So if you-- yes, go ahead. 1075 00:53:31,952 --> 00:53:34,160 AUDIENCE: So what happens after the end of the graph? 1076 00:53:34,160 --> 00:53:35,670 Does it just plunge zero? 1077 00:53:35,670 --> 00:53:37,840 Is it not like any solution? 1078 00:53:37,840 --> 00:53:39,237 Like why does it stall? 1079 00:53:39,237 --> 00:53:40,820 TINA SRIVASTAVA: Yeah, basically, it's 1080 00:53:40,820 --> 00:53:42,510 not generating any lift. 1081 00:53:42,510 --> 00:53:43,010 Right. 1082 00:53:43,010 --> 00:53:46,280 You can see this like with a paper airplane. 1083 00:53:46,280 --> 00:53:49,760 Sometimes, if you-- it kind of stops and kind of crashes. 1084 00:53:49,760 --> 00:53:52,790 We'll see how Minachi's paper airplane does here. 1085 00:53:55,740 --> 00:53:56,740 Well, that one-- 1086 00:53:56,740 --> 00:54:00,190 I definitely had a low angle of attack, so it flew very well. 1087 00:54:00,190 --> 00:54:01,780 Let's see if I can get it to stall 1088 00:54:01,780 --> 00:54:03,970 or if it's too stable of an airplane. 1089 00:54:07,270 --> 00:54:09,420 That one-- basically, after it stalled, 1090 00:54:09,420 --> 00:54:12,180 it basically went nose down, which is good. 1091 00:54:12,180 --> 00:54:14,530 It has a little extra paper folding at the front 1092 00:54:14,530 --> 00:54:16,520 so that the nose will go down. 1093 00:54:16,520 --> 00:54:18,700 But it's really bad basically. 1094 00:54:18,700 --> 00:54:22,880 If you stall, it can go that way. 1095 00:54:22,880 --> 00:54:25,700 The other thing that can happen after you stall a lot 1096 00:54:25,700 --> 00:54:28,600 usually is you can enter a spin, which 1097 00:54:28,600 --> 00:54:30,190 is actually the next case. 1098 00:54:30,190 --> 00:54:35,170 So this is when you're uncoordinated in your stall. 1099 00:54:35,170 --> 00:54:36,880 So what I mean by uncoordinated? 1100 00:54:36,880 --> 00:54:39,500 So that's what I was just talking about before, 1101 00:54:39,500 --> 00:54:42,280 where your roll and your yaw are not 1102 00:54:42,280 --> 00:54:44,450 going in the same direction. 1103 00:54:44,450 --> 00:54:46,990 And here you can have a situation where 1104 00:54:46,990 --> 00:54:48,820 both of the wings have stalled. 1105 00:54:48,820 --> 00:54:51,880 So the airflow has separated over both of the wings. 1106 00:54:51,880 --> 00:54:54,940 But one may be more stalled than the other. 1107 00:54:54,940 --> 00:54:59,770 And it causes the airplane to have a very, very hazardous 1108 00:54:59,770 --> 00:55:02,740 condition or an intentional condition 1109 00:55:02,740 --> 00:55:04,540 if you're Oxsana over there, and you're 1110 00:55:04,540 --> 00:55:08,130 trying to spin your airplane to do a fancy trick. 1111 00:55:08,130 --> 00:55:11,330 This is very dangerous close to the ground. 1112 00:55:11,330 --> 00:55:13,670 As you'll hear, you only intentionally 1113 00:55:13,670 --> 00:55:15,230 do this in certain types of aircraft 1114 00:55:15,230 --> 00:55:17,510 when you're wearing parachutes in certain airspace 1115 00:55:17,510 --> 00:55:19,520 when you're very high above the ground. 1116 00:55:19,520 --> 00:55:21,480 You don't want to do this. 1117 00:55:21,480 --> 00:55:23,960 And in fact, if you're just getting your private pilot's 1118 00:55:23,960 --> 00:55:27,890 license or your PPL, you're not going 1119 00:55:27,890 --> 00:55:30,830 to practice a spin because it's pretty dangerous thing 1120 00:55:30,830 --> 00:55:32,420 to do in many aircraft. 1121 00:55:32,420 --> 00:55:34,280 But you do have to learn about it 1122 00:55:34,280 --> 00:55:36,590 and make sure you don't get into a spin. 1123 00:55:39,430 --> 00:55:43,165 So let's talk a little bit about maneuvering flight. 1124 00:55:43,165 --> 00:55:44,540 So basically, that means when you 1125 00:55:44,540 --> 00:55:46,360 were flying straight and level, that's 1126 00:55:46,360 --> 00:55:48,580 kind of when you're at an equilibrium where 1127 00:55:48,580 --> 00:55:50,710 your lift and your weight kind of cancel out. 1128 00:55:50,710 --> 00:55:53,080 And the plane's just going straight and level 1129 00:55:53,080 --> 00:55:54,520 at the same altitude. 1130 00:55:54,520 --> 00:55:58,720 But climbing is when your lift temporarily exceeds the weight 1131 00:55:58,720 --> 00:56:00,670 so you can actually climb. 1132 00:56:00,670 --> 00:56:03,320 So once you are in a steady climb, 1133 00:56:03,320 --> 00:56:06,350 then you can actually still have your forces be in equilibrium. 1134 00:56:06,350 --> 00:56:08,680 So remember f equals ma. 1135 00:56:08,680 --> 00:56:12,130 So a is acceleration, which is a change in velocity. 1136 00:56:12,130 --> 00:56:13,840 So if you're not changing your velocity, 1137 00:56:13,840 --> 00:56:16,070 and you're just in a steady climb, 1138 00:56:16,070 --> 00:56:18,341 then you're also not accelerating. 1139 00:56:21,500 --> 00:56:24,400 Now, this is a little bit complicated, 1140 00:56:24,400 --> 00:56:26,840 so I will say this is a little bit tricky. 1141 00:56:26,840 --> 00:56:33,770 There is a tendency for these airplanes to turn left. 1142 00:56:33,770 --> 00:56:35,620 And there are actually multiple things 1143 00:56:35,620 --> 00:56:39,460 that contribute to this left-turning tendency. 1144 00:56:39,460 --> 00:56:41,620 And when you're in an airplane flying, 1145 00:56:41,620 --> 00:56:45,350 you might hear your instructor say right rudder. 1146 00:56:45,350 --> 00:56:47,410 And it is really to counteract some 1147 00:56:47,410 --> 00:56:49,510 of these left-turning tendencies. 1148 00:56:49,510 --> 00:56:53,110 So we're going to break them down and talk about them. 1149 00:56:53,110 --> 00:56:55,180 But this can be a very in-depth subject, 1150 00:56:55,180 --> 00:56:58,360 so I will definitely refer to the PHAK, which 1151 00:56:58,360 --> 00:57:01,240 is the Pilot Handbook of Aeronautical Knowledge. 1152 00:57:01,240 --> 00:57:04,640 Chapter 5 goes into all of these. 1153 00:57:04,640 --> 00:57:07,070 So the first one is torque. 1154 00:57:07,070 --> 00:57:10,160 So basically, the thing is when you're-- if you're sitting 1155 00:57:10,160 --> 00:57:12,470 in the airplane, and you're looking forward 1156 00:57:12,470 --> 00:57:17,180 at your propeller, most US engines actually have 1157 00:57:17,180 --> 00:57:19,910 the propeller rotating clockwise. 1158 00:57:19,910 --> 00:57:22,910 So and you can see that arrow that says action. 1159 00:57:22,910 --> 00:57:25,430 That's the propeller rotating clockwise. 1160 00:57:25,430 --> 00:57:30,060 And so because of Newton, we know for every action, 1161 00:57:30,060 --> 00:57:31,910 there's an equal and opposite reaction. 1162 00:57:31,910 --> 00:57:34,190 So because the propeller is turning to the right, 1163 00:57:34,190 --> 00:57:37,070 the whole airplane is trying to roll to the left. 1164 00:57:37,070 --> 00:57:41,290 So that is the first left-turning tendency. 1165 00:57:41,290 --> 00:57:43,660 Before we move to the next one, are there any questions 1166 00:57:43,660 --> 00:57:45,405 on this left-turning tendency? 1167 00:57:50,170 --> 00:57:51,960 Great. 1168 00:57:51,960 --> 00:57:54,840 So the next one is p-factor, which 1169 00:57:54,840 --> 00:57:57,280 is an asymmetrical thrust. 1170 00:57:57,280 --> 00:58:00,810 This happens when the airplane has a high angle of attack, 1171 00:58:00,810 --> 00:58:04,800 so either when it's climbing or in this condition called 1172 00:58:04,800 --> 00:58:08,340 slow flight, which is where it's kind of an uncomfortable thing. 1173 00:58:08,340 --> 00:58:10,590 You have to do this in your flight training. 1174 00:58:10,590 --> 00:58:13,620 So basically, you have your power setting pretty high, 1175 00:58:13,620 --> 00:58:16,470 but you've kind of pitched the airplane up. 1176 00:58:16,470 --> 00:58:21,000 And so you're not getting as much airflow over your control 1177 00:58:21,000 --> 00:58:23,280 surfaces like your ailerons and your elevator. 1178 00:58:23,280 --> 00:58:25,798 So they call your controls mushy. 1179 00:58:25,798 --> 00:58:27,840 So it's hard to kind of coordinate your airplane. 1180 00:58:27,840 --> 00:58:30,210 But you kind of sit in that environment 1181 00:58:30,210 --> 00:58:32,460 to basically understand how it's difficult to control 1182 00:58:32,460 --> 00:58:33,940 the airplane in that environment. 1183 00:58:33,940 --> 00:58:36,960 So if you're pitched up, and you have a-- so you have a high 1184 00:58:36,960 --> 00:58:39,210 angle of attack, and you're either climbing or in slow 1185 00:58:39,210 --> 00:58:43,650 flight, you have this tendency where the-- 1186 00:58:43,650 --> 00:58:46,140 because you're angled to the wind, 1187 00:58:46,140 --> 00:58:49,170 the right propeller blade, which is descending, 1188 00:58:49,170 --> 00:58:52,450 is kind of cutting into the air as it's coming in. 1189 00:58:52,450 --> 00:58:54,660 So it's actually generating more thrust, 1190 00:58:54,660 --> 00:58:58,460 whereas the ascending left propeller blade, 1191 00:58:58,460 --> 00:59:01,410 so the propeller blade that's going up on the left side 1192 00:59:01,410 --> 00:59:04,230 is kind of coming away from the wind that's coming at it. 1193 00:59:04,230 --> 00:59:07,020 And so it's not generating as much thrust 1194 00:59:07,020 --> 00:59:08,820 as the right propeller blade. 1195 00:59:08,820 --> 00:59:11,400 So that causes the center of thrust 1196 00:59:11,400 --> 00:59:13,650 to move towards the right. 1197 00:59:13,650 --> 00:59:19,695 And that creates a little bit of a yaw tendency of the airplane. 1198 00:59:19,695 --> 00:59:20,570 Does that make sense? 1199 00:59:24,240 --> 00:59:24,740 Great. 1200 00:59:24,740 --> 00:59:25,630 Lot of head nods. 1201 00:59:25,630 --> 00:59:28,300 P-factor was one that both Phillip and I 1202 00:59:28,300 --> 00:59:30,760 spent quite a bit of time getting our heads around. 1203 00:59:30,760 --> 00:59:32,760 And Professor Hansman helped us out there. 1204 00:59:35,550 --> 00:59:38,890 So another one is called the corkscrew effect. 1205 00:59:38,890 --> 00:59:41,550 Sometimes, it's called slipstream 1206 00:59:41,550 --> 00:59:43,830 or spiraling slipstream. 1207 00:59:43,830 --> 00:59:45,990 It basically has to do with the fact 1208 00:59:45,990 --> 00:59:50,070 that that propeller remember is just kind of like a wing that's 1209 00:59:50,070 --> 00:59:51,300 spinning around. 1210 00:59:51,300 --> 00:59:57,630 And so it's basically pushing the air back. 1211 00:59:57,630 --> 01:00:00,060 And since the propeller is spinning around, 1212 01:00:00,060 --> 01:00:02,850 that air that's coming back from the propeller 1213 01:00:02,850 --> 01:00:05,760 is spinning around the airplane. 1214 01:00:05,760 --> 01:00:09,330 And as it spins around, when it comes up to the back, 1215 01:00:09,330 --> 01:00:12,750 it pushes on the vertical stabilizer, that tail piece, 1216 01:00:12,750 --> 01:00:18,590 and causes the plane also to do a left yaw. 1217 01:00:18,590 --> 01:00:21,730 Does that make sense? 1218 01:00:21,730 --> 01:00:24,120 Some good head nods. 1219 01:00:24,120 --> 01:00:24,620 Yes. 1220 01:00:24,620 --> 01:00:28,390 AUDIENCE: Why doesn't it also cause it to roll? 1221 01:00:28,390 --> 01:00:30,730 TINA SRIVASTAVA: Why doesn't it also cause it to roll 1222 01:00:30,730 --> 01:00:32,550 was the question. 1223 01:00:32,550 --> 01:00:36,040 And it could, especially if it's hitting the wing. 1224 01:00:36,040 --> 01:00:37,480 But in general, what we've seen is 1225 01:00:37,480 --> 01:00:39,400 that it can depend on whether you're 1226 01:00:39,400 --> 01:00:40,720 in a high wing or low wing. 1227 01:00:40,720 --> 01:00:44,610 But the biggest thing that it sort of hits is here. 1228 01:00:44,610 --> 01:00:46,570 Now, in general, when you get to a left yaw, 1229 01:00:46,570 --> 01:00:48,850 you sort of kind of roll. 1230 01:00:48,850 --> 01:00:52,310 These are connected angles. 1231 01:00:52,310 --> 01:00:54,890 But I think just what we've observed 1232 01:00:54,890 --> 01:00:57,110 is primarily that the air, when it hits 1233 01:00:57,110 --> 01:01:00,050 the vertical stabilizer, is the biggest surface that's 1234 01:01:00,050 --> 01:01:02,660 kind of pushing it and the angle that it's at. 1235 01:01:02,660 --> 01:01:04,520 So if you sum it all together, yes. 1236 01:01:04,520 --> 01:01:06,990 I'm actually quite confident you'll get some roll, 1237 01:01:06,990 --> 01:01:09,620 but the biggest thing that you notice is the yaw. 1238 01:01:13,580 --> 01:01:16,310 So let's see if we understood p-factor 1239 01:01:16,310 --> 01:01:17,480 as well as we think we did. 1240 01:01:36,450 --> 01:01:38,266 A, B, or C? 1241 01:01:38,266 --> 01:01:38,766 AUDIENCE: A. 1242 01:01:38,766 --> 01:01:40,450 TINA SRIVASTAVA: A. Good job. 1243 01:01:40,450 --> 01:01:43,540 I actually have my little hint there that the B is actually 1244 01:01:43,540 --> 01:01:47,560 talking about torque, which is a different left-turning 1245 01:01:47,560 --> 01:01:48,507 tendency. 1246 01:01:48,507 --> 01:01:50,590 And then finally, we're going to talk a little bit 1247 01:01:50,590 --> 01:01:54,180 about gyroscopic precession. 1248 01:01:54,180 --> 01:01:56,110 It's a little bit complicated if you're not 1249 01:01:56,110 --> 01:01:57,760 familiar with the gyroscope. 1250 01:01:57,760 --> 01:01:59,980 But when Phillip talks to you about all 1251 01:01:59,980 --> 01:02:01,690 the different controls in your airplane, 1252 01:02:01,690 --> 01:02:03,760 you'll have to learn about gyroscopes all over 1253 01:02:03,760 --> 01:02:04,840 again in a little bit. 1254 01:02:04,840 --> 01:02:08,890 But in general, what do you need to know about a gyroscope? 1255 01:02:08,890 --> 01:02:10,030 What is a gyroscope? 1256 01:02:10,030 --> 01:02:12,460 A gyroscope is something you can hold. 1257 01:02:12,460 --> 01:02:13,090 It's spinning. 1258 01:02:13,090 --> 01:02:14,920 You can play with them. 1259 01:02:14,920 --> 01:02:17,800 What they allow you to do is have rigidity in space. 1260 01:02:17,800 --> 01:02:20,860 And they also have this concept of precession. 1261 01:02:20,860 --> 01:02:25,240 And precession is basically that the resultant action 1262 01:02:25,240 --> 01:02:28,870 of a spinning rotor when a deflecting force is applied 1263 01:02:28,870 --> 01:02:32,990 happens 90 degrees ahead of that rotation. 1264 01:02:32,990 --> 01:02:38,210 And so because of that, you can consider that the-- 1265 01:02:38,210 --> 01:02:41,510 you have the propeller spinning, and that causes 1266 01:02:41,510 --> 01:02:43,550 this gyroscopic precession. 1267 01:02:43,550 --> 01:02:46,040 And that basically causes 90 degrees out 1268 01:02:46,040 --> 01:02:49,330 of that sink is this force which causes 1269 01:02:49,330 --> 01:02:53,765 a yawing movement, a pitching and a yawing in this case. 1270 01:02:58,810 --> 01:03:03,110 Once we talk more about gyroscopes and how they work, 1271 01:03:03,110 --> 01:03:05,260 you'll also learn different flight controls 1272 01:03:05,260 --> 01:03:09,160 that you look at in the plane, leverage these gyroscopes. 1273 01:03:09,160 --> 01:03:10,990 And we'll come back and circle back 1274 01:03:10,990 --> 01:03:14,440 to making sure we understand the key fundamentals of gyroscopes. 1275 01:03:14,440 --> 01:03:14,940 Yes. 1276 01:03:14,940 --> 01:03:17,107 AUDIENCE: So why is p-factor a left-turning tendency 1277 01:03:17,107 --> 01:03:18,653 and not a pitch up tendency? 1278 01:03:18,653 --> 01:03:19,570 TINA SRIVASTAVA: Sure. 1279 01:03:19,570 --> 01:03:20,778 So let's go back to p-factor. 1280 01:03:27,480 --> 01:03:30,020 So what we're talking about is the difference 1281 01:03:30,020 --> 01:03:31,850 in the center of thrust. 1282 01:03:31,850 --> 01:03:35,300 So the thrust, when you're straight and level, 1283 01:03:35,300 --> 01:03:37,370 the thrust is just forward. 1284 01:03:37,370 --> 01:03:41,900 But what we're seeing is that when the right blade, 1285 01:03:41,900 --> 01:03:44,310 because when you're in a high angle of attack, 1286 01:03:44,310 --> 01:03:46,730 the right blade is generating more thrust 1287 01:03:46,730 --> 01:03:47,630 than the left blade. 1288 01:03:47,630 --> 01:03:51,540 So the center of thrust is slightly to the right. 1289 01:03:51,540 --> 01:03:54,920 So that is why because it's to the right and not up or down. 1290 01:03:54,920 --> 01:03:57,050 Up or down would cause a pitch up or down. 1291 01:03:57,050 --> 01:03:59,000 But since it's to the right, that's 1292 01:03:59,000 --> 01:04:01,322 why it's causing the yaw action. 1293 01:04:01,322 --> 01:04:04,094 AUDIENCE: So it is not 90 degrees ahead because 1294 01:04:04,094 --> 01:04:05,020 of precession. 1295 01:04:05,020 --> 01:04:07,910 TINA SRIVASTAVA: So precession is separate. 1296 01:04:07,910 --> 01:04:11,660 It is generating its own factors and dynamics. 1297 01:04:11,660 --> 01:04:14,300 So both of these things are acting at the same time. 1298 01:04:14,300 --> 01:04:17,360 So precession does in fact affect pitch 1299 01:04:17,360 --> 01:04:19,280 just like you correctly recognized. 1300 01:04:19,280 --> 01:04:22,010 But this is an additional factor that's 1301 01:04:22,010 --> 01:04:24,020 happening is that since the center of thrust 1302 01:04:24,020 --> 01:04:28,310 is actually moved to the right, it's causing the yawing. 1303 01:04:28,310 --> 01:04:29,820 Did that answer your question? 1304 01:04:29,820 --> 01:04:31,200 AUDIENCE: No, but that's OK. 1305 01:04:31,200 --> 01:04:33,210 TINA SRIVASTAVA: You want to chime in, Phillip? 1306 01:04:33,210 --> 01:04:35,740 AUDIENCE: It's an external force, as opposed to generating 1307 01:04:35,740 --> 01:04:37,758 by the propeller. 1308 01:04:37,758 --> 01:04:39,550 PHILLIP GREENSPUN: It's a little bit tough. 1309 01:04:39,550 --> 01:04:43,360 I think, yeah, we should table it and refer you 1310 01:04:43,360 --> 01:04:46,300 to that physics book See How It Flies, which has some of it. 1311 01:04:46,300 --> 01:04:48,970 But the one thing I would add on p-factor 1312 01:04:48,970 --> 01:04:52,540 is another thing to keep in mind is 1313 01:04:52,540 --> 01:04:56,560 whether the propeller is advancing or retreating 1314 01:04:56,560 --> 01:04:57,820 into the wind. 1315 01:04:57,820 --> 01:05:00,610 So if you think about it, when the airplane is level, 1316 01:05:00,610 --> 01:05:08,230 the propeller is not moving relative to the oncoming wind. 1317 01:05:08,230 --> 01:05:12,640 But if you tilt the airplane up, as the propeller goes down, 1318 01:05:12,640 --> 01:05:15,010 it's actually advancing into the wind 1319 01:05:15,010 --> 01:05:18,010 and getting a little bit of an efficiency boost that way. 1320 01:05:18,010 --> 01:05:19,642 Whereas when it's coming up, it's 1321 01:05:19,642 --> 01:05:21,850 going from the front of the airplane towards the back 1322 01:05:21,850 --> 01:05:22,550 of the airplane. 1323 01:05:22,550 --> 01:05:24,365 So it's retreating 1324 01:05:24,365 --> 01:05:26,490 TINA SRIVASTAVA: Yeah, so what Phillip's describing 1325 01:05:26,490 --> 01:05:29,913 is why the right propeller blade is generating more thrust 1326 01:05:29,913 --> 01:05:31,830 than the left propeller blade, which is what's 1327 01:05:31,830 --> 01:05:33,690 moving the center of thrust. 1328 01:05:33,690 --> 01:05:36,570 So I think the real thing to answer your question 1329 01:05:36,570 --> 01:05:39,060 is that there's more than one effect happening 1330 01:05:39,060 --> 01:05:40,560 simultaneously. 1331 01:05:40,560 --> 01:05:41,180 Yeah, so the-- 1332 01:05:41,180 --> 01:05:42,847 PHILLIP GREENSPUN: I'm not sure that you 1333 01:05:42,847 --> 01:05:46,110 get gyroscopic precession from that action 1334 01:05:46,110 --> 01:05:50,760 here because it's generating lift by pushing air. 1335 01:05:50,760 --> 01:05:52,710 I'm not sure that all the thrust really 1336 01:05:52,710 --> 01:05:57,290 has to go through, for p-factor at least, 1337 01:05:57,290 --> 01:06:01,760 through the center of the spinning propeller. 1338 01:06:01,760 --> 01:06:06,770 Also, I know in helicopters, the physics 101 answer 1339 01:06:06,770 --> 01:06:07,730 is 90 degrees. 1340 01:06:07,730 --> 01:06:11,975 But the real answer for engineering it is 72 degrees. 1341 01:06:11,975 --> 01:06:13,100 So it does get complicated. 1342 01:06:13,100 --> 01:06:16,760 Fortunately, it's beyond the scope of what the FAA tests you 1343 01:06:16,760 --> 01:06:19,100 on because they themselves, I'm sure, 1344 01:06:19,100 --> 01:06:20,405 don't understand it fully. 1345 01:06:20,405 --> 01:06:21,322 TINA SRIVASTAVA: Yeah. 1346 01:06:21,322 --> 01:06:23,930 How about we come back after we've talked about gyroscopes 1347 01:06:23,930 --> 01:06:27,380 in excruciating detail and then we have a set of terminology 1348 01:06:27,380 --> 01:06:31,130 to talk about, let's come back to discussing that more. 1349 01:06:31,130 --> 01:06:32,035 Thanks. 1350 01:06:32,035 --> 01:06:34,160 AUDIENCE: I have a simple question for you maybe. 1351 01:06:34,160 --> 01:06:35,410 TINA SRIVASTAVA: Yes. 1352 01:06:35,410 --> 01:06:36,130 AUDIENCE: Just to help me remember, 1353 01:06:36,130 --> 01:06:37,312 why is it called p-factor? 1354 01:06:37,312 --> 01:06:38,810 What is the p for? 1355 01:06:38,810 --> 01:06:40,850 TINA SRIVASTAVA: Power or propeller. 1356 01:06:40,850 --> 01:06:46,852 So the p is referring to that propeller, 1357 01:06:46,852 --> 01:06:48,310 right propeller more than the left. 1358 01:06:48,310 --> 01:06:52,310 It also usually happens when you're at a higher power. 1359 01:06:52,310 --> 01:06:54,560 So some flight instructors like you 1360 01:06:54,560 --> 01:06:58,260 to think about when you have higher power in the airplane, 1361 01:06:58,260 --> 01:06:59,990 you need to put on more right rudder 1362 01:06:59,990 --> 01:07:02,904 to counteract that left-turning tendency. 1363 01:07:02,904 --> 01:07:04,779 PHILLIP GREENSPUN: We're a little bit behind. 1364 01:07:04,779 --> 01:07:07,140 Should we take our bathroom break now and then-- 1365 01:07:07,140 --> 01:07:08,890 TINA SRIVASTAVA: I'm actually almost done, 1366 01:07:08,890 --> 01:07:11,480 so I think we can finish there. 1367 01:07:11,480 --> 01:07:15,320 So one thing is to talk-- so we talked about with climbing 1368 01:07:15,320 --> 01:07:17,840 flight, f equals ma. 1369 01:07:17,840 --> 01:07:20,480 So once you're done changing the velocity, 1370 01:07:20,480 --> 01:07:22,490 and you don't have a change in velocity, 1371 01:07:22,490 --> 01:07:23,990 your forces are in equilibrium. 1372 01:07:23,990 --> 01:07:27,710 So the same is the case with a descending flight. 1373 01:07:27,710 --> 01:07:30,878 When you're actually turning, your forces 1374 01:07:30,878 --> 01:07:32,420 are not in equilibrium because you're 1375 01:07:32,420 --> 01:07:35,340 having this change in velocity. 1376 01:07:35,340 --> 01:07:40,880 And so you actually have a number of changes happening. 1377 01:07:40,880 --> 01:07:44,150 And it's basically considered accelerated flight, 1378 01:07:44,150 --> 01:07:46,940 which is same as when you're driving if you're turning. 1379 01:07:46,940 --> 01:07:49,040 So when you're flying, when you're doing a turn, 1380 01:07:49,040 --> 01:07:51,440 you're accelerating because you're constantly changing 1381 01:07:51,440 --> 01:07:54,230 the direction of your velocity. 1382 01:07:54,230 --> 01:07:56,750 You also have load factor, which we'll 1383 01:07:56,750 --> 01:07:59,840 get into in more detail when we talk about performance 1384 01:07:59,840 --> 01:08:02,960 of an aircraft and how the load affects your performance. 1385 01:08:02,960 --> 01:08:05,180 But another thing to think about back 1386 01:08:05,180 --> 01:08:08,330 when we were talking about that zero gravity flight and a plane 1387 01:08:08,330 --> 01:08:11,218 flying in a parabolic trajectory or a roller 1388 01:08:11,218 --> 01:08:12,510 coaster when you're at the top. 1389 01:08:12,510 --> 01:08:14,677 But when you're at the bottom of the roller coaster, 1390 01:08:14,677 --> 01:08:17,660 you really feel like you're being pressed down 1391 01:08:17,660 --> 01:08:19,520 into your seat. 1392 01:08:19,520 --> 01:08:22,819 In fact, when we run that zero gravity flight, 1393 01:08:22,819 --> 01:08:25,529 although at the top, we had 30 seconds of weightlessness 1394 01:08:25,529 --> 01:08:27,080 so we could do our experiments, when 1395 01:08:27,080 --> 01:08:29,040 you go to the bottom of the parabola, 1396 01:08:29,040 --> 01:08:32,660 you basically get 2G or twice what you normally feel. 1397 01:08:32,660 --> 01:08:35,630 And so you have to kind of lay down and let that happen 1398 01:08:35,630 --> 01:08:37,020 before you come up again. 1399 01:08:37,020 --> 01:08:38,960 And so when you think about load factor, 1400 01:08:38,960 --> 01:08:40,819 just think about you being at the bottom 1401 01:08:40,819 --> 01:08:43,010 of your roller coaster and really feeling 1402 01:08:43,010 --> 01:08:46,640 a kind of twice that force on you. 1403 01:08:46,640 --> 01:08:48,710 And then just to kind of end, we want 1404 01:08:48,710 --> 01:08:52,100 to talk about most of the time we're talking about the planes 1405 01:08:52,100 --> 01:08:54,710 that you'd be flying, but another type of aircraft 1406 01:08:54,710 --> 01:08:58,729 altogether is a blended wing body aircraft. 1407 01:08:58,729 --> 01:09:01,680 So just like this is one example of that. 1408 01:09:01,680 --> 01:09:04,130 So what it means is that that fuselage 1409 01:09:04,130 --> 01:09:06,770 or that kind of tube in the middle that you sit in 1410 01:09:06,770 --> 01:09:11,210 is blended into the wings so that the whole body is 1411 01:09:11,210 --> 01:09:14,000 generating more lift because the whole surface is 1412 01:09:14,000 --> 01:09:15,500 kind of designed that way. 1413 01:09:15,500 --> 01:09:17,060 It's really kind of cool. 1414 01:09:17,060 --> 01:09:19,310 And from an aerodynamic perspective, 1415 01:09:19,310 --> 01:09:22,430 it's got a much better lift to drag ratio 1416 01:09:22,430 --> 01:09:24,590 because the whole thing is really 1417 01:09:24,590 --> 01:09:27,800 deflecting the air molecules downward and generating 1418 01:09:27,800 --> 01:09:29,180 that lift. 1419 01:09:29,180 --> 01:09:31,460 So I just asked kind of a thought question. 1420 01:09:31,460 --> 01:09:35,330 If this is so much better, it's more efficient of an aircraft 1421 01:09:35,330 --> 01:09:39,529 and aerodynamically has much better properties, why do you-- 1422 01:09:39,529 --> 01:09:41,569 it actually-- we've also found that it's 1423 01:09:41,569 --> 01:09:43,279 better in terms of fuel efficiency 1424 01:09:43,279 --> 01:09:45,560 because it has less drag and more lift. 1425 01:09:45,560 --> 01:09:49,819 Why do you think that JetBlue and American Airlines 1426 01:09:49,819 --> 01:09:53,136 don't fly aircraft that look like this? 1427 01:09:53,136 --> 01:09:55,800 AUDIENCE: They don't have routes with a thousand passengers. 1428 01:09:55,800 --> 01:09:56,480 TINA SRIVASTAVA: They don't have routes 1429 01:09:56,480 --> 01:09:57,605 with a thousand passengers? 1430 01:09:57,605 --> 01:10:02,250 Well, you could make a smaller blended wing body aircraft. 1431 01:10:02,250 --> 01:10:02,910 Yes. 1432 01:10:02,910 --> 01:10:04,590 AUDIENCE: Passengers like windows. 1433 01:10:04,590 --> 01:10:06,298 TINA SRIVASTAVA: Passengers like windows. 1434 01:10:06,298 --> 01:10:07,270 That's actually a big-- 1435 01:10:07,270 --> 01:10:09,990 it's a big reason truthfully. 1436 01:10:09,990 --> 01:10:10,770 Yes. 1437 01:10:10,770 --> 01:10:13,145 AUDIENCE: It's very different from what's currently made, 1438 01:10:13,145 --> 01:10:15,250 so the development would be expensive and risky. 1439 01:10:15,250 --> 01:10:16,500 TINA SRIVASTAVA: So it's very different from what's 1440 01:10:16,500 --> 01:10:17,160 currently made. 1441 01:10:17,160 --> 01:10:18,660 And then you said so the development 1442 01:10:18,660 --> 01:10:19,830 would be very risky. 1443 01:10:19,830 --> 01:10:22,110 Actually, I think it's more than just the development. 1444 01:10:22,110 --> 01:10:24,690 Because it's different from what's currently made, 1445 01:10:24,690 --> 01:10:28,860 the entire infrastructure supports the current format 1446 01:10:28,860 --> 01:10:30,990 of an airplane with a tube and wings. 1447 01:10:30,990 --> 01:10:34,140 So we're talking about airports, jet bridges, 1448 01:10:34,140 --> 01:10:38,185 the way that people load food carts onto a plane, 1449 01:10:38,185 --> 01:10:39,810 the way that passengers get on and off, 1450 01:10:39,810 --> 01:10:41,430 the fact the passengers don't have 1451 01:10:41,430 --> 01:10:43,950 as many windows on this type of aircraft. 1452 01:10:43,950 --> 01:10:45,900 It's unfortunately that whole infrastructure 1453 01:10:45,900 --> 01:10:49,860 that surrounds it that is a big contributing factor to why, 1454 01:10:49,860 --> 01:10:52,470 even though there's a better design, why 1455 01:10:52,470 --> 01:10:53,770 we don't move towards that. 1456 01:10:53,770 --> 01:10:55,950 So this was a big, big thing for me 1457 01:10:55,950 --> 01:10:59,730 when I was an undergrad at MIT aero-astro. 1458 01:10:59,730 --> 01:11:02,970 I'm thinking I'm going to design the next best amazing airplane. 1459 01:11:02,970 --> 01:11:06,240 But even if you do design the next best amazing airplane, 1460 01:11:06,240 --> 01:11:08,370 it may not be widely deployed because 1461 01:11:08,370 --> 01:11:11,370 of these other infrastructure aspects, which really got me 1462 01:11:11,370 --> 01:11:13,090 into systems engineering. 1463 01:11:13,090 --> 01:11:15,450 But enough with that thought exercise. 1464 01:11:15,450 --> 01:11:18,690 For time, we'll just summarize what did we learn today. 1465 01:11:18,690 --> 01:11:21,270 So we talked about how does an airplane generate lift? 1466 01:11:21,270 --> 01:11:23,940 And we talked about different factors that affect lift. 1467 01:11:23,940 --> 01:11:26,890 We also discussed that lift is very hard to calculate. 1468 01:11:26,890 --> 01:11:30,600 And so we experimentally measure a lot of aspects of it. 1469 01:11:30,600 --> 01:11:34,260 And we discussed the different forces on an airplane-- 1470 01:11:34,260 --> 01:11:37,470 stability, and kind of this left-turning tendencies, 1471 01:11:37,470 --> 01:11:40,860 and some of the different aircraft configurations. 1472 01:11:40,860 --> 01:11:42,443 So are there any questions about that? 1473 01:11:42,443 --> 01:11:43,902 PHILLIP GREENSPUN: Yeah, Tina, what 1474 01:11:43,902 --> 01:11:45,750 do you think about let's do questions, 1475 01:11:45,750 --> 01:11:47,510 let's take a bathroom break, and then-- 1476 01:11:47,510 --> 01:11:48,880 TINA SRIVASTAVA: Yeah, so you can think about it. 1477 01:11:48,880 --> 01:11:49,530 PHILLIP GREENSPUN: People with questions talk. 1478 01:11:49,530 --> 01:11:50,947 I'm going to call the pizza people 1479 01:11:50,947 --> 01:11:53,150 and give them my credit card.