1 00:00:00,030 --> 00:00:02,470 The following content is provided under a Creative 2 00:00:02,470 --> 00:00:04,000 Commons license. 3 00:00:04,000 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,690 continue to offer high-quality educational resources for free. 5 00:00:10,690 --> 00:00:13,300 To make a donation or view additional materials 6 00:00:13,300 --> 00:00:17,025 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,025 --> 00:00:17,650 at ocw.mit.edu. 8 00:00:26,595 --> 00:00:28,970 PROFESSOR: All right, then, I guess we may as well start. 9 00:00:28,970 --> 00:00:30,820 So what I wanted to talk about today 10 00:00:30,820 --> 00:00:35,660 was natural sandwich panels and sandwich beams. 11 00:00:35,660 --> 00:00:38,850 So there's lots of examples of sandwich structures in nature, 12 00:00:38,850 --> 00:00:41,050 and we've been looking at the engineering sandwich 13 00:00:41,050 --> 00:00:41,929 structures. 14 00:00:41,929 --> 00:00:44,220 And we've seen that you can get a lightweight structure 15 00:00:44,220 --> 00:00:47,136 by having this sandwich construction. 16 00:00:47,136 --> 00:00:48,510 And so there are several examples 17 00:00:48,510 --> 00:00:50,290 I was going to talk about today. 18 00:00:50,290 --> 00:00:53,310 And I think because this isn't really on the test, 19 00:00:53,310 --> 00:00:55,060 I'm not going to write a lot on the board. 20 00:00:55,060 --> 00:00:56,050 So there's some notes. 21 00:00:56,050 --> 00:00:56,930 I'll just put them on the website, 22 00:00:56,930 --> 00:00:58,471 and you can look at that if you want. 23 00:00:58,471 --> 00:01:02,920 Because we have kind of a shorter time today. 24 00:01:02,920 --> 00:01:05,461 I'll just try and talk and explain what's what. 25 00:01:05,461 --> 00:01:05,960 Hey, Bruno. 26 00:01:05,960 --> 00:01:08,310 How are you? 27 00:01:08,310 --> 00:01:09,880 So this is the first example. 28 00:01:09,880 --> 00:01:13,090 So many leaves of Monocotyledon plants 29 00:01:13,090 --> 00:01:14,550 have a sandwich structure. 30 00:01:14,550 --> 00:01:17,840 And this is an iris plant and iris leaves. 31 00:01:17,840 --> 00:01:20,020 And for those of you in 3032, I think 32 00:01:20,020 --> 00:01:22,180 you know that these are glass flowers. 33 00:01:22,180 --> 00:01:24,510 So the Harvard Museum of Natural History 34 00:01:24,510 --> 00:01:27,907 has a glass flower collection that was made in the 1800s. 35 00:01:27,907 --> 00:01:29,490 And there was a botany professor there 36 00:01:29,490 --> 00:01:35,041 who made these as sort of a lecture demonstration vehicle. 37 00:01:35,041 --> 00:01:36,540 And so he would bring then to class, 38 00:01:36,540 --> 00:01:37,750 and he would show different things 39 00:01:37,750 --> 00:01:39,520 about the plants with the glass flowers. 40 00:01:39,520 --> 00:01:41,140 But now they're just in the museum, 41 00:01:41,140 --> 00:01:42,490 and they're very realistic. 42 00:01:42,490 --> 00:01:45,880 So I just wanted to show you those. 43 00:01:45,880 --> 00:01:47,860 So let's see, it's not working. 44 00:01:47,860 --> 00:01:48,840 Turn it on. 45 00:01:48,840 --> 00:01:49,770 There we go. 46 00:01:49,770 --> 00:01:52,220 So if we look at a cross-section of an iris leaf, 47 00:01:52,220 --> 00:01:55,439 it looks like the diagram on the left. 48 00:01:55,439 --> 00:01:56,230 So here's the iris. 49 00:01:56,230 --> 00:01:59,470 And you can see there's these kind of solid fibers, 50 00:01:59,470 --> 00:02:02,220 and those solid fibers are called schlerchyma. 51 00:02:02,220 --> 00:02:05,290 And they only exist at the top and the bottom of the leaf. 52 00:02:05,290 --> 00:02:06,680 So I went out this morning. 53 00:02:06,680 --> 00:02:09,050 And if you look outside of the Stata building, 54 00:02:09,050 --> 00:02:10,940 there's that little kind of river-y thing, 55 00:02:10,940 --> 00:02:13,160 and there's some iris leaves growing there. 56 00:02:13,160 --> 00:02:14,995 So I went and got some iris leaves. 57 00:02:14,995 --> 00:02:17,370 And you can tell we had a horrible winter because usually 58 00:02:17,370 --> 00:02:18,995 when I give this lecture in the spring, 59 00:02:18,995 --> 00:02:21,530 the leaves are like twice as big. 60 00:02:21,530 --> 00:02:23,970 But this year, they're just little, short, wimpy ones. 61 00:02:23,970 --> 00:02:25,330 But I'm going to pass it around. 62 00:02:25,330 --> 00:02:27,700 And if you just like move your thumb over the top, 63 00:02:27,700 --> 00:02:30,180 you can feel little ridges, little bumps. 64 00:02:30,180 --> 00:02:32,800 And those little ridges that you can feel 65 00:02:32,800 --> 00:02:34,940 are these little schlerchyma fibers. 66 00:02:34,940 --> 00:02:37,120 So you kind of see they kind of stick up a little. 67 00:02:37,120 --> 00:02:40,650 And so when you move your thumb over it, you can feel that. 68 00:02:40,650 --> 00:02:43,010 And then you can see that the middle of the iris leaf 69 00:02:43,010 --> 00:02:46,160 has this kind of foamy-type structure here, 70 00:02:46,160 --> 00:02:48,180 and that's called parenchyma cells. 71 00:02:48,180 --> 00:02:50,910 So you can think of the leaf as very much like one 72 00:02:50,910 --> 00:02:51,670 of the sandwiches. 73 00:02:51,670 --> 00:02:54,580 This is like a fiber-reinforced composite at the top 74 00:02:54,580 --> 00:02:55,630 and at the bottom. 75 00:02:55,630 --> 00:02:58,320 And then this is kind of like a foam core in between, 76 00:02:58,320 --> 00:03:01,070 separating the fiber-reinforced faces. 77 00:03:01,070 --> 00:03:03,970 And so the iris leaf behaves mechanically 78 00:03:03,970 --> 00:03:04,845 like a sandwich beam. 79 00:03:04,845 --> 00:03:07,303 So I'm going to talk a little bit about how we can actually 80 00:03:07,303 --> 00:03:09,860 demonstrate that using the equations that we developed 81 00:03:09,860 --> 00:03:11,040 in class. 82 00:03:11,040 --> 00:03:12,150 This is another example. 83 00:03:12,150 --> 00:03:14,660 This is, I guess, what Americans call the cat tail, 84 00:03:14,660 --> 00:03:17,687 but Canadians and English people call it a bull rush. 85 00:03:17,687 --> 00:03:19,520 And you can see this is a slightly different 86 00:03:19,520 --> 00:03:22,060 construction, but there's the same sort of idea. 87 00:03:22,060 --> 00:03:25,190 So instead of having a foamy core as in the iris leaf, 88 00:03:25,190 --> 00:03:27,100 you've got these kind of webs here 89 00:03:27,100 --> 00:03:29,120 that go in between the top and the bottom, 90 00:03:29,120 --> 00:03:31,664 and that forms like a series of I-beams almost. 91 00:03:31,664 --> 00:03:33,580 And you can think of that also like a sandwich 92 00:03:33,580 --> 00:03:35,100 panel or a sandwich beam. 93 00:03:35,100 --> 00:03:37,834 So you've got two stiff top and bottom pieces, 94 00:03:37,834 --> 00:03:40,250 and then you've got these kind of webs that separate them, 95 00:03:40,250 --> 00:03:42,340 kind of like a honeycomb core would be. 96 00:03:42,340 --> 00:03:45,100 So that's another example of a leaf that has 97 00:03:45,100 --> 00:03:46,580 the sandwich-type structure. 98 00:03:46,580 --> 00:03:48,970 And this is very common in these Monocotyledon leaves. 99 00:03:48,970 --> 00:03:51,480 So if you think of a cat tail or you think of an iris, 100 00:03:51,480 --> 00:03:53,440 they tend to be kind of narrow at the base, 101 00:03:53,440 --> 00:03:55,023 maybe an inch or two wide at the base, 102 00:03:55,023 --> 00:03:56,330 and they can be quite tall. 103 00:03:56,330 --> 00:03:58,570 The iris leaves can get two or three feet tall. 104 00:03:58,570 --> 00:04:01,560 The cat tails can get five or six feet tall. 105 00:04:01,560 --> 00:04:03,789 And they stand up more or less straight. 106 00:04:03,789 --> 00:04:06,080 They bend over a little, but they stand up more or less 107 00:04:06,080 --> 00:04:06,910 straight. 108 00:04:06,910 --> 00:04:08,509 And this sandwich structure is one 109 00:04:08,509 --> 00:04:10,425 of the things that lets them stand up straight 110 00:04:10,425 --> 00:04:12,730 at a fairly low weight. 111 00:04:12,730 --> 00:04:15,930 And from the plant's point of view, 112 00:04:15,930 --> 00:04:17,950 there's a sort of metabolic cost associated 113 00:04:17,950 --> 00:04:19,190 with making more material. 114 00:04:19,190 --> 00:04:21,399 So it we can minimize the amount of material, 115 00:04:21,399 --> 00:04:24,080 it's a better thing for the plant. 116 00:04:24,080 --> 00:04:28,650 These are some other examples of grasses that are 117 00:04:28,650 --> 00:04:29,940 sandwich-type constructions. 118 00:04:29,940 --> 00:04:32,320 This is from some papers by Julian Vincent. 119 00:04:32,320 --> 00:04:35,700 And the black little circles here are the schlerchyma, 120 00:04:35,700 --> 00:04:37,570 are those sort of dense fibers. 121 00:04:37,570 --> 00:04:39,690 Then you can see in both of these cases, 122 00:04:39,690 --> 00:04:41,470 the dense fibers are on the outside, 123 00:04:41,470 --> 00:04:43,410 and the parenchyma cells, which is the white, 124 00:04:43,410 --> 00:04:45,290 are on the inside. 125 00:04:45,290 --> 00:04:50,411 And so this is sort of another set of micrographs of the iris. 126 00:04:50,411 --> 00:04:51,910 So this is just showing the outside, 127 00:04:51,910 --> 00:04:54,590 and these are the ribs viewed from the outside. 128 00:04:54,590 --> 00:04:56,680 And this is the core, just sort of viewed 129 00:04:56,680 --> 00:04:58,460 along the length of it. 130 00:04:58,460 --> 00:05:00,660 And so you can idealize the structure 131 00:05:00,660 --> 00:05:03,760 as being like a sandwich that's got sort of fibers on the top 132 00:05:03,760 --> 00:05:04,580 and on the bottom. 133 00:05:04,580 --> 00:05:06,788 So the top and the bottom are like a fiber composite. 134 00:05:06,788 --> 00:05:08,990 And the middle part, with the parenchyma cells, 135 00:05:08,990 --> 00:05:10,430 is kind of like a foam. 136 00:05:10,430 --> 00:05:14,585 And so we did a little project on iris leaves, 137 00:05:14,585 --> 00:05:15,960 and we wanted to see if you could 138 00:05:15,960 --> 00:05:17,560 show that they behave mechanically, 139 00:05:17,560 --> 00:05:19,210 like a sandwich beam. 140 00:05:19,210 --> 00:05:22,030 So you remember that we had that equation for the deflection 141 00:05:22,030 --> 00:05:23,570 of the sandwich beam. 142 00:05:23,570 --> 00:05:24,990 There were two terms. 143 00:05:24,990 --> 00:05:32,800 There was a bending term, and then there was a shearing term. 144 00:05:37,810 --> 00:05:40,530 And so we took some little sandwich beams. 145 00:05:40,530 --> 00:05:43,222 We cut little kind of rectangular beams. 146 00:05:43,222 --> 00:05:44,180 We hung little weights. 147 00:05:44,180 --> 00:05:45,707 We measured how much they deflected, 148 00:05:45,707 --> 00:05:47,790 and we wanted to see if we could use this equation 149 00:05:47,790 --> 00:05:50,445 to predict their stiffness and how much they deflected. 150 00:05:50,445 --> 00:05:52,570 So to do that, we needed to know a bunch of things. 151 00:05:52,570 --> 00:05:55,160 We needed to know some of the geometrical parameters. 152 00:05:55,160 --> 00:05:58,820 So we needed to know what volume fraction of the face 153 00:05:58,820 --> 00:06:02,630 is those solid ribs, how thick's the core, how thick's the face? 154 00:06:02,630 --> 00:06:05,780 And so we measured a bunch of these geometrical parameters. 155 00:06:05,780 --> 00:06:10,030 We tested it like a cantilever so we knew what B1 and B2 were 156 00:06:10,030 --> 00:06:11,800 for the cantilever. 157 00:06:11,800 --> 00:06:15,220 We knew how long the beam was, so we know what l is. 158 00:06:15,220 --> 00:06:17,920 We knew what loads we applied, so we knew what P was. 159 00:06:17,920 --> 00:06:19,610 But we needed to make some estimate 160 00:06:19,610 --> 00:06:22,350 of what the face modulus was and what the core shear 161 00:06:22,350 --> 00:06:23,850 modulus was, too. 162 00:06:23,850 --> 00:06:26,950 And so we made some estimates of that. 163 00:06:26,950 --> 00:06:29,710 So this table here just shows some 164 00:06:29,710 --> 00:06:31,570 of the dimensions of the leaf. 165 00:06:31,570 --> 00:06:34,270 The leaf tapers, and this is at the thin end, 166 00:06:34,270 --> 00:06:36,760 so here's the face thickness. 167 00:06:36,760 --> 00:06:38,845 Here's the sort of length of this. 168 00:06:38,845 --> 00:06:40,610 Some square cells in the face. 169 00:06:40,610 --> 00:06:42,912 This is the core thickness here. 170 00:06:42,912 --> 00:06:44,620 This is the dimensions of the core cells. 171 00:06:44,620 --> 00:06:47,120 This is the diameter of the ribs, the spacing of the ribs, 172 00:06:47,120 --> 00:06:49,041 the volume fraction of solids in the ribs. 173 00:06:49,041 --> 00:06:50,540 And we did that at different lengths 174 00:06:50,540 --> 00:06:53,700 along the different positions along the length of the rib, 175 00:06:53,700 --> 00:06:55,710 or length of the leaf. 176 00:06:55,710 --> 00:06:57,260 So we had the geometrical parameters, 177 00:06:57,260 --> 00:07:02,010 but we needed to get this E of the face and G of the core. 178 00:07:02,010 --> 00:07:04,590 And to do that, we looked at the literature. 179 00:07:04,590 --> 00:07:07,775 And people had done tests on the fiber parts of leaves. 180 00:07:07,775 --> 00:07:09,150 They'd done little tensile tests, 181 00:07:09,150 --> 00:07:11,500 and they'd measured modulii between about two 182 00:07:11,500 --> 00:07:13,330 and 20 gigapascals. 183 00:07:13,330 --> 00:07:15,960 And then we did some tension tests on the iris leaf. 184 00:07:15,960 --> 00:07:17,460 And in tension, those ribs are going 185 00:07:17,460 --> 00:07:19,340 to take most of the stress. 186 00:07:19,340 --> 00:07:21,340 And if you know the volume fraction of the ribs, 187 00:07:21,340 --> 00:07:24,520 you can back out what the stiffness of the ribs 188 00:07:24,520 --> 00:07:25,187 must have been. 189 00:07:25,187 --> 00:07:26,770 If you know the stiffness of the ribs, 190 00:07:26,770 --> 00:07:28,644 you can figure out the stiffness of the face. 191 00:07:28,644 --> 00:07:31,940 So we calculated that, and then we looked at the literature. 192 00:07:31,940 --> 00:07:34,510 And people have done tests on parenchyma cells 193 00:07:34,510 --> 00:07:37,320 and different types of tissue on things like apples and potatoes 194 00:07:37,320 --> 00:07:38,420 and carrots. 195 00:07:38,420 --> 00:07:41,010 And these are the values for the Young's modulus they get. 196 00:07:41,010 --> 00:07:47,850 They're between about 1, and the highest one was 14 megapascals. 197 00:07:47,850 --> 00:07:49,970 But most of these values for the Young's modulus 198 00:07:49,970 --> 00:07:51,570 are around about four. 199 00:07:51,570 --> 00:07:53,540 And the shear modulus is roughly about half 200 00:07:53,540 --> 00:07:54,710 of the Young's modulus. 201 00:07:54,710 --> 00:07:56,820 So we said the shear modulus was around two. 202 00:07:56,820 --> 00:08:00,500 So we have these values we could plug it in and then calculate 203 00:08:00,500 --> 00:08:04,300 what the stiffness would be for the iris leaf. 204 00:08:04,300 --> 00:08:06,030 And so this was a little analysis we did. 205 00:08:06,030 --> 00:08:08,030 So this was the measured beam stiffness up here. 206 00:08:08,030 --> 00:08:11,130 We had four beams, and they were different stiffnesses. 207 00:08:11,130 --> 00:08:12,630 They all had the same length. 208 00:08:12,630 --> 00:08:14,910 They all the same face thickness. 209 00:08:14,910 --> 00:08:16,484 The core thickness varied. 210 00:08:16,484 --> 00:08:17,650 They all had the same width. 211 00:08:17,650 --> 00:08:20,090 We cut them to have the same width so we could 212 00:08:20,090 --> 00:08:21,700 calculate a flexural rigidity. 213 00:08:21,700 --> 00:08:24,130 That's the EI equivalent. 214 00:08:24,130 --> 00:08:27,050 We could calculate the bending deflection term, the shear 215 00:08:27,050 --> 00:08:28,290 deflection term. 216 00:08:28,290 --> 00:08:30,690 And this is the calculated beam stiffness. 217 00:08:30,690 --> 00:08:32,539 And then this is the ratio of the calculated 218 00:08:32,539 --> 00:08:33,590 over the measured. 219 00:08:33,590 --> 00:08:35,450 So it's not exactly right. 220 00:08:35,450 --> 00:08:38,120 Obviously, there's some difference here. 221 00:08:38,120 --> 00:08:39,929 But it's in the same order of magnitude. 222 00:08:39,929 --> 00:08:41,357 It's in the same ballpark. 223 00:08:41,357 --> 00:08:43,440 And one of the complications that we didn't really 224 00:08:43,440 --> 00:08:46,240 try to take into account was that the leaf isn't 225 00:08:46,240 --> 00:08:47,630 a nice rectangular structure. 226 00:08:47,630 --> 00:08:50,630 The leaf has this kind of curved cross-section to it. 227 00:08:50,630 --> 00:08:52,920 And we made a bit of an approximation to that, 228 00:08:52,920 --> 00:08:54,389 but it wasn't that close, really. 229 00:08:54,389 --> 00:08:56,180 We could have probably done better on that. 230 00:09:00,400 --> 00:09:04,790 But I think the idea that the iris behaves like a sandwich is 231 00:09:04,790 --> 00:09:06,330 a reasonable one. 232 00:09:06,330 --> 00:09:08,570 So that was the iris leaf. 233 00:09:08,570 --> 00:09:11,220 And then I wanted to show you some other structures in nature 234 00:09:11,220 --> 00:09:12,760 that are sandwiches. 235 00:09:12,760 --> 00:09:15,800 So this is a seakelp, help like a seaweed thing, 236 00:09:15,800 --> 00:09:17,760 in New Zealand. 237 00:09:17,760 --> 00:09:20,150 This is the largest intertidal seaweed. 238 00:09:20,150 --> 00:09:23,930 The fronds, the sort of long pieces of it, 239 00:09:23,930 --> 00:09:25,330 are up to 12 meters long. 240 00:09:25,330 --> 00:09:26,960 So that's almost 40 feet. 241 00:09:26,960 --> 00:09:29,340 So 40 feet is probably like from one side of this room 242 00:09:29,340 --> 00:09:30,590 to the other side of the room. 243 00:09:30,590 --> 00:09:31,720 It's quite long. 244 00:09:31,720 --> 00:09:34,700 And you can see, if you look at this section here, 245 00:09:34,700 --> 00:09:37,910 this is all like a honeycomb-type section here. 246 00:09:37,910 --> 00:09:42,430 And the honeycomb is like a honeycomb in a sandwich, 247 00:09:42,430 --> 00:09:44,190 and the top and the bottom faces are 248 00:09:44,190 --> 00:09:45,471 like the face of the sandwich. 249 00:09:45,471 --> 00:09:46,970 So this would be like the face here. 250 00:09:46,970 --> 00:09:48,345 That would be the honeycomb core. 251 00:09:48,345 --> 00:09:51,570 And that would be the other face on the other side over there. 252 00:09:51,570 --> 00:09:53,880 And those honeycomb-like cores, apparently, 253 00:09:53,880 --> 00:09:57,390 have some gas-filled pockets that then provide buoyancy 254 00:09:57,390 --> 00:09:58,790 to keep the whole thing floating. 255 00:09:58,790 --> 00:10:00,630 So it photosynthesizes. 256 00:10:00,630 --> 00:10:02,270 So one of the things about these leaves 257 00:10:02,270 --> 00:10:04,392 is that they have multiple functions. 258 00:10:04,392 --> 00:10:06,725 It's not just that they have to have a certain stiffness 259 00:10:06,725 --> 00:10:08,930 so they don't fall over. 260 00:10:08,930 --> 00:10:10,630 The plant wants to photosynthesize, 261 00:10:10,630 --> 00:10:12,760 so you want to maximize the surface area as well, 262 00:10:12,760 --> 00:10:14,790 and you want to have exposure to the sunlight. 263 00:10:14,790 --> 00:10:16,998 So there's a number of things that the plant's trying 264 00:10:16,998 --> 00:10:19,770 to do in having this structure. 265 00:10:19,770 --> 00:10:22,820 So that seakelp is one example. 266 00:10:22,820 --> 00:10:25,410 These are skulls from birds. 267 00:10:25,410 --> 00:10:27,160 And so this is a pigeon here. 268 00:10:27,160 --> 00:10:28,680 This is a magpie. 269 00:10:28,680 --> 00:10:30,950 If you come from the West you see magpies out West. 270 00:10:30,950 --> 00:10:32,490 You see them in Europe as well. 271 00:10:32,490 --> 00:10:34,190 And this is a long-eared owl. 272 00:10:34,190 --> 00:10:37,420 This long-eared owl's around here. 273 00:10:37,420 --> 00:10:40,540 And I brought in a couple of bird skulls as well. 274 00:10:40,540 --> 00:10:42,880 And you can see that all of those birds skulls 275 00:10:42,880 --> 00:10:44,450 are sandwich structures. 276 00:10:44,450 --> 00:10:48,690 The one for the pigeon has sort of a foam-like core here. 277 00:10:48,690 --> 00:10:50,960 And you can see that the two faces 278 00:10:50,960 --> 00:10:53,470 aren't sort of concentric for the pigeon skull. 279 00:10:53,470 --> 00:10:56,820 They sort of not following each other. 280 00:10:56,820 --> 00:11:00,440 But here, this would be, say, on the top shell 281 00:11:00,440 --> 00:11:04,680 of the magpie, where the two, the inner and outer face, 282 00:11:04,680 --> 00:11:06,080 are sort of concentric. 283 00:11:06,080 --> 00:11:08,800 Then you get these kind of little ribs of trabecular bone 284 00:11:08,800 --> 00:11:11,410 in between them, and then the same with a long-eared owl. 285 00:11:11,410 --> 00:11:13,390 You get these little ribs in between them. 286 00:11:13,390 --> 00:11:15,887 And so you can see that there's a sandwich structure there. 287 00:11:15,887 --> 00:11:17,470 And obviously, birds want to be light. 288 00:11:17,470 --> 00:11:20,290 They have to be light to fly, to take off, 289 00:11:20,290 --> 00:11:22,300 and so they want to be light. 290 00:11:22,300 --> 00:11:24,857 So I've got two skulls here. 291 00:11:24,857 --> 00:11:25,940 And I'll pass them around. 292 00:11:25,940 --> 00:11:28,064 Please be careful because they're kind of delicate. 293 00:11:28,064 --> 00:11:31,170 This one is from a screech owl, and you see screech owls 294 00:11:31,170 --> 00:11:31,710 around here. 295 00:11:31,710 --> 00:11:36,350 This was a screech owl that had an intersection with a car. 296 00:11:36,350 --> 00:11:38,780 Yeah, so the skull fractured, but you can see the sandwich 297 00:11:38,780 --> 00:11:39,280 right there. 298 00:11:39,280 --> 00:11:41,030 You see the two little bits? 299 00:11:41,030 --> 00:11:43,610 So you can see the inner plate and the outer plate 300 00:11:43,610 --> 00:11:46,206 and the foam, the trabecular bone. 301 00:11:46,206 --> 00:11:49,580 So that's the screech owl. 302 00:11:49,580 --> 00:11:52,110 And this is a red tail hawk. 303 00:11:52,110 --> 00:11:54,385 So you can't really see the shell and the sandwich 304 00:11:54,385 --> 00:11:55,010 structure here. 305 00:11:55,010 --> 00:11:56,077 But I want to pass it around just 306 00:11:56,077 --> 00:11:57,368 so you can see how light it is. 307 00:11:57,368 --> 00:11:58,580 So it's amazingly light. 308 00:11:58,580 --> 00:12:01,470 So a red tail hawk is probably about this big, 309 00:12:01,470 --> 00:12:02,700 something like that. 310 00:12:02,700 --> 00:12:09,490 And this is one of the things that makes them very light. 311 00:12:09,490 --> 00:12:10,929 So those are the bird skulls. 312 00:12:10,929 --> 00:12:12,970 Oh, yes, so now I have to tell you about the owl. 313 00:12:12,970 --> 00:12:15,178 So I think the people in 3032 have heard this before. 314 00:12:15,178 --> 00:12:16,960 But the other people haven't. 315 00:12:16,960 --> 00:12:19,064 So one of the things about the owl 316 00:12:19,064 --> 00:12:20,480 is if you look at the whole skull, 317 00:12:20,480 --> 00:12:22,970 if you look at this picture here, one of the things 318 00:12:22,970 --> 00:12:26,210 is that this bone here is not symmetrical with that bone 319 00:12:26,210 --> 00:12:26,810 there. 320 00:12:26,810 --> 00:12:29,290 Normally, when you think of a body, 321 00:12:29,290 --> 00:12:31,250 you think of the bones being symmetrical. 322 00:12:31,250 --> 00:12:32,770 But those bones are not symmetrical, 323 00:12:32,770 --> 00:12:35,660 and those bones are near where the ear is. 324 00:12:35,660 --> 00:12:38,140 And it turns out on owls, at least on some owls, 325 00:12:38,140 --> 00:12:41,490 the ears are at different heights on their heads. 326 00:12:41,490 --> 00:12:44,060 And people think that one of the things that 327 00:12:44,060 --> 00:12:47,660 allows the owls to do is it allows their hearing 328 00:12:47,660 --> 00:12:50,090 to sort of pinpoint where something is. 329 00:12:50,090 --> 00:12:53,440 And owls can catch little creatures at night, 330 00:12:53,440 --> 00:12:56,100 but they can also catch little creatures underneath the snow. 331 00:12:56,100 --> 00:12:58,420 So they can catch things that they can't even see. 332 00:12:58,420 --> 00:13:01,400 And they have a number of adaptations 333 00:13:01,400 --> 00:13:03,660 to improve their hearing, but this is one of them. 334 00:13:03,660 --> 00:13:08,100 So here's a little owl Allison Curtis is a Canadian friend who 335 00:13:08,100 --> 00:13:10,460 lives in northern Ontario, and this is looking out 336 00:13:10,460 --> 00:13:11,900 of her living room window. 337 00:13:11,900 --> 00:13:12,994 And that's a barred owl. 338 00:13:12,994 --> 00:13:14,410 And you can see the barred owl has 339 00:13:14,410 --> 00:13:16,156 caught this little vole here. 340 00:13:16,156 --> 00:13:17,530 And you can see in the background 341 00:13:17,530 --> 00:13:18,910 it's winter in Canada. 342 00:13:18,910 --> 00:13:20,860 and there's snow all over the place. 343 00:13:20,860 --> 00:13:22,980 So this owl has probably caught that little vole 344 00:13:22,980 --> 00:13:24,520 underneath the snow. 345 00:13:24,520 --> 00:13:26,840 And then it's come to eat it. 346 00:13:26,840 --> 00:13:28,490 And this is another picture of-- you 347 00:13:28,490 --> 00:13:31,960 can see this is where an owl landed in the snow. 348 00:13:31,960 --> 00:13:36,290 It's wings hit the snow, trying to catch something underneath. 349 00:13:36,290 --> 00:13:39,280 And this is another kind of beautiful print 350 00:13:39,280 --> 00:13:44,150 of the owl's wings hitting the snow in the winter time. 351 00:13:44,150 --> 00:13:46,427 So did I show you the fox video? 352 00:13:46,427 --> 00:13:47,760 Should I show you the fox video? 353 00:13:50,850 --> 00:13:51,600 You saw it, right? 354 00:13:51,600 --> 00:13:53,472 I think I showed it last time in 3032. 355 00:13:53,472 --> 00:13:54,680 But you guys haven't seen it. 356 00:13:54,680 --> 00:13:56,697 Let me show you the fox video because foxes 357 00:13:56,697 --> 00:13:57,780 do the same kind of thing. 358 00:13:57,780 --> 00:13:59,420 Their ears are the same as ours. 359 00:13:59,420 --> 00:14:01,190 They're in the same position. 360 00:14:04,537 --> 00:14:05,870 But they have this-- let me see. 361 00:14:05,870 --> 00:14:06,870 Where's the sound thing? 362 00:14:06,870 --> 00:14:08,590 We don't really need the sound for this, 363 00:14:08,590 --> 00:14:11,210 but there's BBC sound. 364 00:14:11,210 --> 00:14:14,445 So we get this music, even though the fox 365 00:14:14,445 --> 00:14:16,680 can't hear the music. 366 00:14:16,680 --> 00:14:18,610 Here we go, fox no drive. 367 00:14:18,610 --> 00:14:21,340 Check this out. 368 00:14:21,340 --> 00:14:22,436 Is it going to come up? 369 00:14:26,635 --> 00:14:27,810 Is that going to play? 370 00:14:27,810 --> 00:14:28,310 OK 371 00:14:28,310 --> 00:14:29,684 [VIDEO PLAYBACK] 372 00:14:29,684 --> 00:14:32,890 -It listens for the tiny sounds of its prey moving about below. 373 00:14:32,890 --> 00:14:34,723 PROFESSOR: So you see how it cocks its head, 374 00:14:34,723 --> 00:14:36,496 and it does this with its head? 375 00:14:36,496 --> 00:14:38,245 It's putting its ears at different heights 376 00:14:38,245 --> 00:14:39,200 when it does that. 377 00:14:58,120 --> 00:14:59,140 So check this out. 378 00:14:59,140 --> 00:15:01,380 And look carefully, you can see the little animal 379 00:15:01,380 --> 00:15:03,557 it's got in its mouth when it comes out. 380 00:15:03,557 --> 00:15:04,473 There's a little tail. 381 00:15:07,290 --> 00:15:10,690 So part of the reason dogs and foxes and coyotes 382 00:15:10,690 --> 00:15:12,510 do that thing, I think, is because they 383 00:15:12,510 --> 00:15:14,010 put their ears at different heights, 384 00:15:14,010 --> 00:15:17,230 and it helps them pinpoint where something is. 385 00:15:17,230 --> 00:15:17,989 [END PLAYBACK] 386 00:15:17,989 --> 00:15:19,780 You know I love these Nature videos, right? 387 00:15:19,780 --> 00:15:20,779 So that's the fox video. 388 00:15:20,779 --> 00:15:23,115 Let me see if I can stop that. 389 00:15:26,256 --> 00:15:28,380 So that's one of the interesting things about owls. 390 00:15:33,860 --> 00:15:35,965 Let me go back to my little PowerPoints. 391 00:15:39,010 --> 00:15:42,570 So here's another example of a creature that 392 00:15:42,570 --> 00:15:44,430 has a sandwich-type structures. 393 00:15:44,430 --> 00:15:45,810 So here's the sandwich here. 394 00:15:45,810 --> 00:15:49,100 Here is the ever so charming looking cuttlefish. 395 00:15:49,100 --> 00:15:52,040 And the cuttlefish is not actually a fish. 396 00:15:52,040 --> 00:15:53,570 It's a mollusk. 397 00:15:53,570 --> 00:15:56,090 So it's related to things like octopus, things like that, 398 00:15:56,090 --> 00:15:57,480 and squids. 399 00:15:57,480 --> 00:16:00,870 It's a cephalopod. 400 00:16:00,870 --> 00:16:03,040 And you can't see it so well in this picture, 401 00:16:03,040 --> 00:16:04,400 but I'm going to show you something else and you see it. 402 00:16:04,400 --> 00:16:05,691 It's got like little tentacles. 403 00:16:05,691 --> 00:16:08,140 These things here are actually separate little tentacles. 404 00:16:08,140 --> 00:16:11,220 And because it's not a fish, it doesn't have like fins 405 00:16:11,220 --> 00:16:12,780 that can kind of swim with. 406 00:16:12,780 --> 00:16:15,370 And it's got this thing called the cuttlefish bone. 407 00:16:15,370 --> 00:16:17,670 And this is a cuttlefish bone here. 408 00:16:17,670 --> 00:16:20,262 And that bone has the sandwich structure here. 409 00:16:20,262 --> 00:16:21,470 And it's not actually a bone. 410 00:16:21,470 --> 00:16:22,790 It's really a shell. 411 00:16:22,790 --> 00:16:27,160 It's a calcium carbonate thing, not a calcium phosphate thing. 412 00:16:27,160 --> 00:16:29,600 But the cuttlefish can control how much air 413 00:16:29,600 --> 00:16:31,010 goes into those little pockets. 414 00:16:31,010 --> 00:16:34,120 And it can control its buoyancy by controlling how much air 415 00:16:34,120 --> 00:16:35,650 goes into those little pockets. 416 00:16:35,650 --> 00:16:39,680 And I brought with me a cuttlefish bone. 417 00:16:39,680 --> 00:16:41,970 Have you ever owned like, I don't know, 418 00:16:41,970 --> 00:16:44,880 like a parrot or a pet bird? 419 00:16:44,880 --> 00:16:47,150 Apparently, pet birds love to sharpen their beaks 420 00:16:47,150 --> 00:16:48,700 on this cuttlefish bone. 421 00:16:48,700 --> 00:16:51,700 So if you go to a pet store, you can buy this stuff. 422 00:16:51,700 --> 00:16:54,370 So you won't be able to see the little sandwich 423 00:16:54,370 --> 00:16:56,695 structure because it's a very small length scale. 424 00:16:56,695 --> 00:16:59,490 But you can kind of see there's a sort 425 00:16:59,490 --> 00:17:01,390 of different material on the inside 426 00:17:01,390 --> 00:17:04,410 than there is on the outside of that. 427 00:17:04,410 --> 00:17:07,530 So do people know the other thing 428 00:17:07,530 --> 00:17:09,950 that cuttlefish are famous for, besides the bone? 429 00:17:09,950 --> 00:17:10,923 Change colors. 430 00:17:10,923 --> 00:17:13,089 Can I show you a video of cuttlefish changing color? 431 00:17:13,089 --> 00:17:14,837 Yeah, of course. 432 00:17:14,837 --> 00:17:16,170 So let me get rid of this again. 433 00:17:16,170 --> 00:17:18,869 Go back to this. 434 00:17:18,869 --> 00:17:21,589 Let's see, somewhere-- where's the cuttlefish? 435 00:17:21,589 --> 00:17:22,099 Here we go. 436 00:17:27,210 --> 00:17:27,719 Did I do it? 437 00:17:27,719 --> 00:17:29,760 Is it thinking? 438 00:17:29,760 --> 00:17:30,260 Here we go. 439 00:17:30,260 --> 00:17:31,190 Where's the cuttlefish? 440 00:17:31,190 --> 00:17:33,106 So this is another one of these Science Friday 441 00:17:33,106 --> 00:17:37,944 videos from National Public Radio with Flora Lichtman. 442 00:17:37,944 --> 00:17:38,610 [VIDEO PLAYBACK] 443 00:17:38,610 --> 00:17:39,650 -OK, let's play a game. 444 00:17:39,650 --> 00:17:42,608 [GAME SHOW MUSIC PLAYING] 445 00:17:42,608 --> 00:17:44,670 [APPLAUSE] 446 00:17:44,670 --> 00:17:45,420 PROFESSOR: See it? 447 00:17:48,720 --> 00:17:51,290 -Biologist Sarah Zielinski took these shots. 448 00:17:51,290 --> 00:17:54,860 And if you needed a helping hand to find the cuttlefish, 449 00:17:54,860 --> 00:17:55,559 don't feel bad. 450 00:17:55,559 --> 00:17:57,850 -I've certainly taken photos in the past then come back 451 00:17:57,850 --> 00:18:00,420 to look at them and gone, I'm sure there was a cuttlefish 452 00:18:00,420 --> 00:18:02,762 in there somewhere! 453 00:18:02,762 --> 00:18:06,160 -These cephalopods are master camouflagers. 454 00:18:06,160 --> 00:18:07,690 But while they're hiding their body, 455 00:18:07,690 --> 00:18:10,590 they're revealing something about their mind, 456 00:18:10,590 --> 00:18:12,236 or at least their visual system. 457 00:18:12,236 --> 00:18:13,860 -In very simple terms, they can tell us 458 00:18:13,860 --> 00:18:15,944 what they can see by the body patterns they 459 00:18:15,944 --> 00:18:16,860 produce on their skin. 460 00:18:16,860 --> 00:18:18,330 -They produce these body patterns 461 00:18:18,330 --> 00:18:21,010 by expanding or contracting chromatophores, 462 00:18:21,010 --> 00:18:22,820 these little ink sacks on their skin. 463 00:18:22,820 --> 00:18:25,070 And they use different displays for different reasons, 464 00:18:25,070 --> 00:18:27,130 like for male-to-male combat. 465 00:18:27,130 --> 00:18:28,920 -Two males will turn into each other 466 00:18:28,920 --> 00:18:31,950 and pass these kind of waves of dark chromatophores 467 00:18:31,950 --> 00:18:35,840 over a really bright sort of iridescent stripey body pattern 468 00:18:35,840 --> 00:18:39,140 and somehow solve these combats. 469 00:18:39,140 --> 00:18:43,110 Eventually, one male gives up and goes away. 470 00:18:43,110 --> 00:18:44,971 -And then there's this unsolved mystery. 471 00:18:48,780 --> 00:18:51,170 It changes color when it grabs a snack. 472 00:18:51,170 --> 00:18:53,240 -That doesn't make perfect sense because it seems 473 00:18:53,240 --> 00:18:54,440 to make it very conspicuous. 474 00:18:54,440 --> 00:18:58,240 So one theory is that it's just a happy signal 475 00:18:58,240 --> 00:18:59,920 of how excited it is to have caught 476 00:18:59,920 --> 00:19:02,980 something, some response that it doesn't have any control over. 477 00:19:02,980 --> 00:19:04,810 -But most of the time they seem to be 478 00:19:04,810 --> 00:19:07,320 using their chromatophores more intentionally, 479 00:19:07,320 --> 00:19:08,796 primarily to blend in. 480 00:19:08,796 --> 00:19:10,920 -Because otherwise they're more likely to be eaten, 481 00:19:10,920 --> 00:19:13,050 so it's very important they don't make mistakes 482 00:19:13,050 --> 00:19:15,240 about ambiguous visual information. 483 00:19:15,240 --> 00:19:16,970 -And ambiguous visual information 484 00:19:16,970 --> 00:19:20,360 is specifically what Zielinski's interested in. 485 00:19:20,360 --> 00:19:21,980 So here's the experimental setup. 486 00:19:21,980 --> 00:19:24,910 Print out laminated patterns, like this checkerboard, 487 00:19:24,910 --> 00:19:26,310 and stick them in a tank. 488 00:19:26,310 --> 00:19:29,000 -And we place the animals in the tank. 489 00:19:29,000 --> 00:19:31,140 And we record the body patterns that they produce. 490 00:19:31,140 --> 00:19:33,690 -You're seeing them on squares, but they do the same thing 491 00:19:33,690 --> 00:19:35,330 on top of circles. 492 00:19:35,330 --> 00:19:36,030 They produce-- 493 00:19:36,030 --> 00:19:38,610 - --the disruptive pattern, where you get these blocky 494 00:19:38,610 --> 00:19:40,700 components of high-contrast components. 495 00:19:40,700 --> 00:19:43,765 -But when you put a cuttlefish over squiggles, it produces-- 496 00:19:43,765 --> 00:19:46,140 - --a sort of mottley pattern, where you get these little 497 00:19:46,140 --> 00:19:48,870 groups of dark spots showing across the body. 498 00:19:48,870 --> 00:19:51,690 -So what happens when you put a cuttlefish on something 499 00:19:51,690 --> 00:19:57,240 in between, when you put them on incomplete circles? 500 00:19:57,240 --> 00:19:59,930 When we see something like this, our visual system 501 00:19:59,930 --> 00:20:03,660 likes to fill in the blanks, something we do constantly, 502 00:20:03,660 --> 00:20:04,570 Zielinski says. 503 00:20:04,570 --> 00:20:07,350 -The reason why cartoons and sketches work 504 00:20:07,350 --> 00:20:09,270 is because we can recognize objects 505 00:20:09,270 --> 00:20:10,630 based on their edges alone. 506 00:20:10,630 --> 00:20:13,310 -And we can identify objects even if they're broken up or-- 507 00:20:13,310 --> 00:20:15,679 - --have an object that is occluded by another object. 508 00:20:15,679 --> 00:20:16,720 That's no problem for us. 509 00:20:16,720 --> 00:20:19,430 We can still work out what the object is most of the time. 510 00:20:19,430 --> 00:20:21,460 And I was interested to know whether cuttlefish 511 00:20:21,460 --> 00:20:23,690 can solve similar problems. 512 00:20:23,690 --> 00:20:26,380 -And Zielinski and colleagues report this week that 513 00:20:26,380 --> 00:20:28,230 cuttlefish do seem to-- 514 00:20:28,230 --> 00:20:31,920 - --fill in those gaps and interpret those little segments 515 00:20:31,920 --> 00:20:33,440 as a whole circle. 516 00:20:33,440 --> 00:20:36,500 -Or anyway, the broken circles prompted the same camo pattern 517 00:20:36,500 --> 00:20:37,690 as full circles. 518 00:20:37,690 --> 00:20:41,140 So if you're wondering, uh, I see these as circles, too. 519 00:20:41,140 --> 00:20:43,020 What's the big deal? 520 00:20:43,020 --> 00:20:47,360 The weird thing here is that there's no reason why 521 00:20:47,360 --> 00:20:48,763 cuttlefish, which are-- 522 00:20:48,763 --> 00:20:51,820 - --invertebrates, and they're in the same group as slugs 523 00:20:51,820 --> 00:20:52,450 and snails. 524 00:20:52,450 --> 00:20:55,080 - --should see the world the way we do. 525 00:20:55,080 --> 00:20:57,162 -Yes, it's like they're alien, but we also 526 00:20:57,162 --> 00:20:58,870 seem to have so much in common with them. 527 00:20:58,870 --> 00:21:00,120 -So the next step? 528 00:21:00,120 --> 00:21:02,410 -Because we can't share the perceptive experience 529 00:21:02,410 --> 00:21:05,190 of a cuttlefish, it's hard to know 530 00:21:05,190 --> 00:21:09,660 exactly what it is that they're doing to fill in that missing 531 00:21:09,660 --> 00:21:10,340 information. 532 00:21:10,340 --> 00:21:12,298 And I want to try to get a better grasp on that 533 00:21:12,298 --> 00:21:14,070 and also see whether they actually respond 534 00:21:14,070 --> 00:21:15,760 to true illusory contours. 535 00:21:15,760 --> 00:21:19,630 -So you're going to show optical illusions to cuttlefish? 536 00:21:19,630 --> 00:21:22,676 -(LAUGHING) That's what I'm hoping to do, yes. 537 00:21:22,676 --> 00:21:27,010 [END PLAYBACK] 538 00:21:29,760 --> 00:21:32,400 PROFESSOR: So let's go back to sandwiches. 539 00:21:32,400 --> 00:21:36,160 I think I have-- do I have one more? 540 00:21:36,160 --> 00:21:37,870 There we go. 541 00:21:37,870 --> 00:21:39,930 So horseshoe crab shells, so different sorts 542 00:21:39,930 --> 00:21:42,390 of arthropods, the shells are sandwiched too. 543 00:21:42,390 --> 00:21:44,649 This is from Mark Myers' work. 544 00:21:44,649 --> 00:21:46,190 So we're looking at the cross-section 545 00:21:46,190 --> 00:21:47,692 of a horseshoe crab shell. 546 00:21:47,692 --> 00:21:49,650 So again, it's the same idea-- the animal wants 547 00:21:49,650 --> 00:21:51,066 to minimize the amount of material 548 00:21:51,066 --> 00:21:54,160 or minimize the weight, and this is a way of doing that. 549 00:21:54,160 --> 00:21:57,540 And I went to the Galapagos about a year ago. 550 00:21:57,540 --> 00:22:01,530 And there was a place where they had these giant Galapagos 551 00:22:01,530 --> 00:22:02,632 tortoise shells. 552 00:22:02,632 --> 00:22:04,090 And one of them was broken, and you 553 00:22:04,090 --> 00:22:06,465 could see there was a sandwich structure in the Galapagos 554 00:22:06,465 --> 00:22:07,260 tortoise shells. 555 00:22:07,260 --> 00:22:10,377 These Galapagos tortoises, their shell is like this big. 556 00:22:10,377 --> 00:22:11,085 They're gigantic. 557 00:22:11,085 --> 00:22:12,560 They're huge. 558 00:22:12,560 --> 00:22:16,920 So those are my examples of sandwich panels and beams 559 00:22:16,920 --> 00:22:18,710 and shells and whatnot in nature. 560 00:22:18,710 --> 00:22:20,800 So the idea is that nature too wants 561 00:22:20,800 --> 00:22:24,140 to minimize weight and minimize the amount of material, 562 00:22:24,140 --> 00:22:27,181 and the sandwich structure is a way of doing that. 563 00:22:27,181 --> 00:22:29,430 So I have one more thing I wanted to talk about today. 564 00:22:29,430 --> 00:22:31,490 So this isn't quite sandwich structures, 565 00:22:31,490 --> 00:22:34,780 but it's looking at another kind of natural structure 566 00:22:34,780 --> 00:22:38,340 that is designed to reduce the weight of plant stems, 567 00:22:38,340 --> 00:22:40,160 in this case, palm stems. 568 00:22:40,160 --> 00:22:42,590 And there's a couple of interesting things about this. 569 00:22:42,590 --> 00:22:44,910 So when you look at palms, like let's pretend 570 00:22:44,910 --> 00:22:45,840 we're not in Boston. 571 00:22:45,840 --> 00:22:48,120 We're in California, where they have palms. 572 00:22:48,120 --> 00:22:50,370 And we're in LA, and they don't have winter. 573 00:22:50,370 --> 00:22:53,860 And if you look at the palms growing, when the palm's short, 574 00:22:53,860 --> 00:22:55,590 it's about this big in diameter. 575 00:22:55,590 --> 00:22:56,966 And as it gets taller and taller, 576 00:22:56,966 --> 00:22:58,423 the diameter doesn't really change. 577 00:22:58,423 --> 00:23:00,020 It gets taller and taller and taller, 578 00:23:00,020 --> 00:23:02,970 but the diameter doesn't change, at least in some species. 579 00:23:02,970 --> 00:23:04,554 Whereas if you think of a tree, a tree 580 00:23:04,554 --> 00:23:06,261 starts out with a little skinny diameter. 581 00:23:06,261 --> 00:23:08,560 And as the tree gets taller, the diameter gets bigger. 582 00:23:08,560 --> 00:23:10,630 And it sort of tapers and does that whole thing. 583 00:23:10,630 --> 00:23:11,700 So palms don't do that. 584 00:23:11,700 --> 00:23:13,040 And palms are not trees. 585 00:23:13,040 --> 00:23:16,510 They're a botanically different thing from trees. 586 00:23:16,510 --> 00:23:18,450 So here's a coconut palm. 587 00:23:18,450 --> 00:23:22,090 And so the question is, as the stem gets taller and taller, 588 00:23:22,090 --> 00:23:23,934 how does it resist the bending loads that 589 00:23:23,934 --> 00:23:24,850 get bigger and bigger? 590 00:23:24,850 --> 00:23:27,790 So probably, the main load on these sorts of things 591 00:23:27,790 --> 00:23:29,330 is from the wind. 592 00:23:29,330 --> 00:23:31,735 And often these plants are in areas 593 00:23:31,735 --> 00:23:32,860 where they have hurricanes. 594 00:23:32,860 --> 00:23:34,318 And you see them in hurricanes, you 595 00:23:34,318 --> 00:23:37,930 see the pictures of the palm stem blowing way over. 596 00:23:37,930 --> 00:23:41,110 And so how do they resist the larger internal stresses 597 00:23:41,110 --> 00:23:43,740 as they get taller and taller, if the diameter doesn't 598 00:23:43,740 --> 00:23:44,990 get bigger and bigger? 599 00:23:44,990 --> 00:23:48,760 And the way they do that is that they deposit additional layers 600 00:23:48,760 --> 00:23:51,650 of cell wall as the plant ages. 601 00:23:51,650 --> 00:23:54,040 So if you think of a tree, when a tree grows, 602 00:23:54,040 --> 00:23:55,884 it just deposits more and more cells. 603 00:23:55,884 --> 00:23:57,800 And the cells have roughly the same thickness. 604 00:23:57,800 --> 00:23:59,880 So there's ones that are deposited in the spring have 605 00:23:59,880 --> 00:24:00,410 thinner walls. 606 00:24:00,410 --> 00:24:02,409 Then the summer and the fall have thicker walls. 607 00:24:02,409 --> 00:24:04,620 But more or less, it's similar. 608 00:24:04,620 --> 00:24:06,710 Whereas the palm, it deposit cells, 609 00:24:06,710 --> 00:24:08,780 and then as the trunk of the palm 610 00:24:08,780 --> 00:24:10,540 gets taller, as the stem gets taller, 611 00:24:10,540 --> 00:24:13,550 it deposits more layers on the cell wall. 612 00:24:13,550 --> 00:24:15,300 So this is an example in an SCM. 613 00:24:15,300 --> 00:24:18,340 You can see here this is a young cell, 614 00:24:18,340 --> 00:24:21,760 and it's got-- this one that's not marked is a primary cell 615 00:24:21,760 --> 00:24:24,420 wall, and then this is the first layer of the secondary cell 616 00:24:24,420 --> 00:24:25,450 wall. 617 00:24:25,450 --> 00:24:27,360 And then this is an older palm. 618 00:24:27,360 --> 00:24:29,250 And you can see here it's got more layers, 619 00:24:29,250 --> 00:24:31,800 and so the cell wall itself has gotten thicker. 620 00:24:31,800 --> 00:24:33,800 So that means that the density of the tissue 621 00:24:33,800 --> 00:24:36,310 changes as the palm ages. 622 00:24:36,310 --> 00:24:39,120 And it does so in a very kind of clever way. 623 00:24:39,120 --> 00:24:41,550 If you think of the palm as being like a cantilever that's 624 00:24:41,550 --> 00:24:45,510 vertical and it's bending in the wind, when we have a cantilever 625 00:24:45,510 --> 00:24:47,094 beam or any kind of beam, the stresses 626 00:24:47,094 --> 00:24:49,093 are going to be biggest on the periphery, right? 627 00:24:49,093 --> 00:24:51,040 They're going to be biggest on the outside. 628 00:24:51,040 --> 00:24:52,920 And if you think of the palm as having 629 00:24:52,920 --> 00:24:56,299 a circular cross-section, that outer periphery 630 00:24:56,299 --> 00:24:57,840 is going to see the biggest stresses. 631 00:24:57,840 --> 00:25:00,570 So it would make the most sense if that was the densest tissue. 632 00:25:00,570 --> 00:25:02,659 And that's exactly what the palm does. 633 00:25:02,659 --> 00:25:04,700 So there was a nice study done by Paul Rich quite 634 00:25:04,700 --> 00:25:06,010 a number of years ago. 635 00:25:06,010 --> 00:25:07,920 And he studied palms in Central America 636 00:25:07,920 --> 00:25:09,787 and looked at the density and measured 637 00:25:09,787 --> 00:25:10,870 the mechanical properties. 638 00:25:10,870 --> 00:25:13,190 And I'm going to talk about his stuff today. 639 00:25:13,190 --> 00:25:14,830 So the white is the low density. 640 00:25:14,830 --> 00:25:17,060 The gray's the medium, and the black's the high. 641 00:25:17,060 --> 00:25:18,976 So you can see the low density's on the middle 642 00:25:18,976 --> 00:25:21,320 of the young stem, and just at the very base 643 00:25:21,320 --> 00:25:23,870 and then the periphery is the dense tissue. 644 00:25:23,870 --> 00:25:26,450 But as the stem gets taller and gets older, 645 00:25:26,450 --> 00:25:30,110 then stuff that was low density is now high density. 646 00:25:30,110 --> 00:25:33,584 And only the very middle here is the low density. 647 00:25:33,584 --> 00:25:35,250 And that some stuff that was low density 648 00:25:35,250 --> 00:25:36,459 has turned to middle density. 649 00:25:36,459 --> 00:25:37,916 And some stuff that was low density 650 00:25:37,916 --> 00:25:39,140 has turned to high density. 651 00:25:39,140 --> 00:25:41,670 So it's done this by adding more and more layers to the cell 652 00:25:41,670 --> 00:25:43,400 wall, making the cell wall thicker 653 00:25:43,400 --> 00:25:46,410 and making the cells themselves denser. 654 00:25:46,410 --> 00:25:49,060 So this is looking just at a single palm. 655 00:25:49,060 --> 00:25:52,370 So each one of these lines is a single palm. 656 00:25:52,370 --> 00:25:54,810 And this is looking at how the density changes 657 00:25:54,810 --> 00:25:57,540 from the periphery to the center of the palm. 658 00:25:57,540 --> 00:26:00,140 So if you cut the palm down and, say, 659 00:26:00,140 --> 00:26:04,480 we take a little sample radially from the middle to the outside 660 00:26:04,480 --> 00:26:06,910 or from the outside to the middle, 661 00:26:06,910 --> 00:26:08,570 he then measured the density. 662 00:26:08,570 --> 00:26:11,911 And it's probably easiest to think about the dry ones 663 00:26:11,911 --> 00:26:14,160 because that's kind of what you would compare wood to. 664 00:26:14,160 --> 00:26:17,240 So the dry densities varied from about one gram per CC, 665 00:26:17,240 --> 00:26:20,080 that's about 1,000 kilograms per cubic meter, 666 00:26:20,080 --> 00:26:23,020 down to almost zero in this particular species 667 00:26:23,020 --> 00:26:25,222 here, probably like 50 or something like that. 668 00:26:25,222 --> 00:26:26,680 And if you compare this with woods, 669 00:26:26,680 --> 00:26:30,520 this little arrow here is the density of most common woods. 670 00:26:30,520 --> 00:26:33,840 So if you looked at pine and spruce an oak and maple 671 00:26:33,840 --> 00:26:36,930 and ash and hickory, they would all be in that little range 672 00:26:36,930 --> 00:26:37,580 there. 673 00:26:37,580 --> 00:26:40,680 So a single palm stem can have a bigger range 674 00:26:40,680 --> 00:26:44,400 of densities than many different species of wood. 675 00:26:44,400 --> 00:26:47,825 So it has this kind of profile of the density. 676 00:26:47,825 --> 00:26:49,200 And the thing I was interested in 677 00:26:49,200 --> 00:26:51,030 is seeing how mechanically efficient 678 00:26:51,030 --> 00:26:54,010 that was to put the denser material at the outside. 679 00:26:54,010 --> 00:26:56,310 So I looked at the stiffness of the palm, 680 00:26:56,310 --> 00:26:59,120 and I also looked at the strength. 681 00:26:59,120 --> 00:27:03,880 So I just replotted that data on this slightly different axes 682 00:27:03,880 --> 00:27:04,560 here. 683 00:27:04,560 --> 00:27:08,020 So this is the radial position relative to the outer radius, 684 00:27:08,020 --> 00:27:09,290 and this is the density. 685 00:27:09,290 --> 00:27:12,700 And I subtracted off the minimum and then took the range. 686 00:27:12,700 --> 00:27:14,830 And for this species here, the minimum density 687 00:27:14,830 --> 00:27:15,600 was almost zero. 688 00:27:15,600 --> 00:27:18,420 So this expression simplifies to something like that. 689 00:27:18,420 --> 00:27:20,332 And just because it's mathematically simpler, 690 00:27:20,332 --> 00:27:21,790 that's what we're going to look at. 691 00:27:21,790 --> 00:27:26,720 So the density goes roughly as the radius squared. 692 00:27:26,720 --> 00:27:30,030 And Paul Rich also did a lot of mechanical tests on the palm, 693 00:27:30,030 --> 00:27:32,530 and he took out little beams of different densities. 694 00:27:32,530 --> 00:27:35,420 And he measured the stiffness and the strength of the beams. 695 00:27:35,420 --> 00:27:39,100 So he measured the modulus of elasticity here versus density. 696 00:27:39,100 --> 00:27:41,550 And he measured the modulus of rupture here. 697 00:27:41,550 --> 00:27:43,410 And these are all along the grain. 698 00:27:43,410 --> 00:27:47,450 And he found that the Young's modulus varied with the density 699 00:27:47,450 --> 00:27:50,390 to the 2.5 power, and the strength 700 00:27:50,390 --> 00:27:53,020 varied as the density squared. 701 00:27:53,020 --> 00:27:53,810 And if the-- 702 00:27:53,810 --> 00:27:54,560 [BUZZING SOUND] 703 00:27:54,560 --> 00:27:55,110 Oh, hello. 704 00:27:55,110 --> 00:27:57,194 [LAUGHTER] 705 00:27:57,194 --> 00:27:59,110 So these were just sorts of empirical findings 706 00:27:59,110 --> 00:28:00,540 that he made. 707 00:28:00,540 --> 00:28:03,180 If you have prismatic cells and you deform them axially, 708 00:28:03,180 --> 00:28:07,110 and the cell wall was the same in the different specimens, 709 00:28:07,110 --> 00:28:09,260 then the solid modulus would be a constant. 710 00:28:09,260 --> 00:28:11,530 And you would expect that the modulus of the beam 711 00:28:11,530 --> 00:28:14,720 would go just linearly with the density, sort 712 00:28:14,720 --> 00:28:16,600 of like a honeycomb loaded [? at a ?] plane. 713 00:28:16,600 --> 00:28:20,000 But what he measured was that the modulus and the strength 714 00:28:20,000 --> 00:28:22,024 varied with some power of the density. 715 00:28:22,024 --> 00:28:23,440 And the reason for that really was 716 00:28:23,440 --> 00:28:27,760 that the cell walls of the denser material 717 00:28:27,760 --> 00:28:29,090 had more layers. 718 00:28:29,090 --> 00:28:32,214 And in the additional layers, the cellulose microfibular 719 00:28:32,214 --> 00:28:34,630 angle was probably different, so that the different layers 720 00:28:34,630 --> 00:28:36,230 had different stiffnesses. 721 00:28:36,230 --> 00:28:38,370 And if you have layers of differences, 722 00:28:38,370 --> 00:28:42,090 then you're going to get this power relationship. 723 00:28:42,090 --> 00:28:44,990 So what I then did was I took his data, 724 00:28:44,990 --> 00:28:48,190 and I tried to see how efficient that would be in bending. 725 00:28:48,190 --> 00:28:51,600 So he had found that the density varied with the radius raised 726 00:28:51,600 --> 00:28:52,300 to some power. 727 00:28:52,300 --> 00:28:54,550 This power n was 2, but I wanted to do it just 728 00:28:54,550 --> 00:28:56,760 for a general case, so I said I was just n. 729 00:28:56,760 --> 00:28:59,000 And he said that he found that the modulus varied 730 00:28:59,000 --> 00:29:02,392 with the density raised to some other power m. 731 00:29:02,392 --> 00:29:05,131 And for him, m was 2 and 1/2. 732 00:29:05,131 --> 00:29:06,880 And so I could write just another equation 733 00:29:06,880 --> 00:29:10,800 saying that the modulus goes as the radius to the mn power. 734 00:29:10,800 --> 00:29:12,550 And then you could do a little calculation 735 00:29:12,550 --> 00:29:14,884 where you work out with the equivalent flexural rigidity 736 00:29:14,884 --> 00:29:15,383 is. 737 00:29:15,383 --> 00:29:16,620 So you have to integrate up. 738 00:29:16,620 --> 00:29:18,370 You kind of say you have a little band 739 00:29:18,370 --> 00:29:19,400 at a certain radius. 740 00:29:19,400 --> 00:29:22,480 That radius has a certain modulus. 741 00:29:22,480 --> 00:29:24,360 And you can figure out the moment of inertia 742 00:29:24,360 --> 00:29:25,943 that goes with that particular radius. 743 00:29:25,943 --> 00:29:28,230 And then if you integrate it up over the whole thing, 744 00:29:28,230 --> 00:29:29,950 you can say that the flexural rigidity 745 00:29:29,950 --> 00:29:33,370 for the gradient density is some constant times 746 00:29:33,370 --> 00:29:36,640 pi times the outer radius to the fourth power divided 747 00:29:36,640 --> 00:29:39,370 by those two powers mn plus 4. 748 00:29:39,370 --> 00:29:41,310 So m was the power here for the modulus. 749 00:29:41,310 --> 00:29:43,826 And n was the power there for the density. 750 00:29:43,826 --> 00:29:46,200 And then you could compare that with having the same mass 751 00:29:46,200 --> 00:29:49,560 just uniformly distributed over the whole cross-section. 752 00:29:49,560 --> 00:29:53,060 And then if you take the ratio of the flexural rigidity 753 00:29:53,060 --> 00:29:56,630 for the density gradient versus the flexural rigidity 754 00:29:56,630 --> 00:29:59,390 for the uniform density, you can show 755 00:29:59,390 --> 00:30:01,240 that it's this equation here. 756 00:30:01,240 --> 00:30:03,510 And then if you plug in these measured values 757 00:30:03,510 --> 00:30:05,720 for those exponents for n and m, you 758 00:30:05,720 --> 00:30:09,270 find that the flexural rigidity with the gradient density 759 00:30:09,270 --> 00:30:12,400 relative to the uniform density is a factor of 2 and 1/2. 760 00:30:12,400 --> 00:30:14,560 So the stem is 2 and 1/2 times stiffer 761 00:30:14,560 --> 00:30:16,450 by having that density profile. 762 00:30:16,450 --> 00:30:18,670 So there's a huge sort of mechanical advantage 763 00:30:18,670 --> 00:30:19,580 to doing that. 764 00:30:19,580 --> 00:30:21,100 And just sort of physically, if you 765 00:30:21,100 --> 00:30:24,330 know the stresses our biggest on the outside, 766 00:30:24,330 --> 00:30:27,211 it would make sense to put the denser material on the outside. 767 00:30:27,211 --> 00:30:28,710 And then the other thing I looked at 768 00:30:28,710 --> 00:30:32,250 was the strength of the palm. 769 00:30:32,250 --> 00:30:34,640 So imagine this is our very schematic palm here, 770 00:30:34,640 --> 00:30:36,800 and then there's a circular cross section. 771 00:30:36,800 --> 00:30:39,270 So I wanted to compare the bending stress distribution 772 00:30:39,270 --> 00:30:41,650 with the bending strength distribution. 773 00:30:41,650 --> 00:30:45,625 So the stress goes as the modulus times the strain, 774 00:30:45,625 --> 00:30:47,100 just Hooke's law. 775 00:30:47,100 --> 00:30:50,650 And here we're assuming that plane sections remain plane, 776 00:30:50,650 --> 00:30:53,450 like that's the standard assumption of bending. 777 00:30:53,450 --> 00:30:55,730 So if you assume plane sections remain plane, 778 00:30:55,730 --> 00:30:59,140 then the strain goes with the curvature times the distance y 779 00:30:59,140 --> 00:31:01,460 from the neutral axis, the distance from the middle. 780 00:31:01,460 --> 00:31:03,585 So this distance here would be the dis-- [? same ?] 781 00:31:03,585 --> 00:31:05,390 at loaded with a loaded p here. 782 00:31:05,390 --> 00:31:07,404 That distance would be y there. 783 00:31:07,404 --> 00:31:09,070 And then I can plug in some things here. 784 00:31:09,070 --> 00:31:11,340 So instead of E, I'm going to plug-in my relationship 785 00:31:11,340 --> 00:31:14,060 with the radius to that mn power. 786 00:31:14,060 --> 00:31:15,920 And here's my curvature, and instead of y, 787 00:31:15,920 --> 00:31:17,420 if I say that some radius, I'm going 788 00:31:17,420 --> 00:31:19,840 to say y is our r cos theta. 789 00:31:19,840 --> 00:31:21,930 And so I'm going to say that the stress goes-- 790 00:31:21,930 --> 00:31:22,430 [SNEEZE] 791 00:31:22,430 --> 00:31:23,450 Bless you. 792 00:31:23,450 --> 00:31:27,430 Goes as radius raised to some power mn plus 1. 793 00:31:27,430 --> 00:31:30,380 And again, for the species I know what n and m are, 794 00:31:30,380 --> 00:31:34,280 so the stress goes as the radius to the sixth power. 795 00:31:34,280 --> 00:31:37,090 And then I can also compare with what Paul Rich had 796 00:31:37,090 --> 00:31:38,270 found for the strength. 797 00:31:38,270 --> 00:31:41,380 He found that the strength-- so sigma star is the strength-- 798 00:31:41,380 --> 00:31:44,320 was proportional to the density raised to some power q, 799 00:31:44,320 --> 00:31:48,600 and that power was 2 in the measurements that he made. 800 00:31:48,600 --> 00:31:50,550 And so I can say that the strength 801 00:31:50,550 --> 00:31:55,150 goes as the radius to this power nq, so to the fourth power. 802 00:31:55,150 --> 00:31:59,170 And then if I plot the stress distribution and the strength 803 00:31:59,170 --> 00:32:02,230 distribution-- so imagine, this is through the cross-section 804 00:32:02,230 --> 00:32:02,730 here. 805 00:32:02,730 --> 00:32:06,950 So this is the diameter of the stem. 806 00:32:06,950 --> 00:32:09,400 And this is the neutral axis here in the middle. 807 00:32:09,400 --> 00:32:15,280 The strength goes as that solid line there. 808 00:32:15,280 --> 00:32:17,380 It goes as the fourth power. 809 00:32:17,380 --> 00:32:19,490 And the stress goes as that dashed line there, 810 00:32:19,490 --> 00:32:21,160 as the sixth power. 811 00:32:21,160 --> 00:32:23,190 So they're not exactly on top of each other, 812 00:32:23,190 --> 00:32:25,430 but they're very close to being on top of each other. 813 00:32:25,430 --> 00:32:27,260 So basically what the palm has done 814 00:32:27,260 --> 00:32:29,850 is it's arranged the material in such a way 815 00:32:29,850 --> 00:32:32,040 that the strength matches the stresses that 816 00:32:32,040 --> 00:32:33,140 are applied to it. 817 00:32:33,140 --> 00:32:37,090 So if I just had a constant density, 818 00:32:37,090 --> 00:32:39,880 my stress profile would look like that. 819 00:32:39,880 --> 00:32:42,290 And if I had a constant density, the strength profile 820 00:32:42,290 --> 00:32:43,460 would kind of like that. 821 00:32:43,460 --> 00:32:46,220 So the strength here would be a constant, 822 00:32:46,220 --> 00:32:48,554 and this would be the stress here. 823 00:32:48,554 --> 00:32:50,470 So the stuff in the middle, it's much stronger 824 00:32:50,470 --> 00:32:51,460 than it needs to be. 825 00:32:51,460 --> 00:32:53,930 Whereas the palm has arranged things so that it's got 826 00:32:53,930 --> 00:32:57,890 just the right amount of strength for the stress, 827 00:32:57,890 --> 00:32:59,490 as a function of the radial position. 828 00:32:59,490 --> 00:33:01,130 So it's kind of a clever thing. 829 00:33:01,130 --> 00:33:03,180 So that's kind of a beautiful thing. 830 00:33:03,180 --> 00:33:04,850 And I think that is it. 831 00:33:04,850 --> 00:33:07,380 I think that's-- yeah, that's the end of it. 832 00:33:07,380 --> 00:33:11,260 So all these images came from this other book that we wrote. 833 00:33:11,260 --> 00:33:12,930 And if you wanted to get the sources, 834 00:33:12,930 --> 00:33:14,330 you could get them from there. 835 00:33:14,330 --> 00:33:16,470 So that all I wanted to talk about today 836 00:33:16,470 --> 00:33:20,130 was some examples of sort of efficient mechanical design 837 00:33:20,130 --> 00:33:22,940 in nature and the sandwich panel structures as one, 838 00:33:22,940 --> 00:33:26,230 and these radial density gradients is another. 839 00:33:26,230 --> 00:33:28,620 We have a project on bamboo right now, 840 00:33:28,620 --> 00:33:31,120 and the bamboo also has a radial density gradient, 841 00:33:31,120 --> 00:33:32,120 and it's the same thing. 842 00:33:32,120 --> 00:33:33,703 The densest material's on the outside, 843 00:33:33,703 --> 00:33:36,280 and the least dense is on the inside. 844 00:33:36,280 --> 00:33:39,750 So I think I'm going to stop there for today. 845 00:33:39,750 --> 00:33:41,790 So what I was going to do on Monday 846 00:33:41,790 --> 00:33:45,690 is talk a little bit about bio-mimicking. 847 00:33:45,690 --> 00:33:47,960 And that won't take the whole class at all. 848 00:33:47,960 --> 00:33:50,043 And I thought we could spend the rest of the class 849 00:33:50,043 --> 00:33:51,380 on Monday just doing a review. 850 00:33:51,380 --> 00:33:53,410 So the test's on Wednesday. 851 00:33:53,410 --> 00:33:55,050 So if you want to bring questions, 852 00:33:55,050 --> 00:33:58,020 that would be a beautiful thing. 853 00:33:58,020 --> 00:34:00,510 I can't really can I review the whole last six weeks 854 00:34:00,510 --> 00:34:03,390 or something in an hour and a half or something. 855 00:34:03,390 --> 00:34:05,430 So if you want to bring questions, I'll be here 856 00:34:05,430 --> 00:34:07,280 and we can just go over questions. 857 00:34:07,280 --> 00:34:09,310 Does that sound good?