WEBVTT 00:00:00.030 --> 00:00:02.470 The following content is provided under a Creative 00:00:02.470 --> 00:00:04.000 Commons license. 00:00:04.000 --> 00:00:06.330 Your support will help MIT OpenCourseWare 00:00:06.330 --> 00:00:10.690 continue to offer high-quality educational resources for free. 00:00:10.690 --> 00:00:13.300 To make a donation or view additional materials 00:00:13.300 --> 00:00:17.025 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.025 --> 00:00:17.650 at ocw.mit.edu. 00:00:26.595 --> 00:00:28.970 PROFESSOR: All right, then, I guess we may as well start. 00:00:28.970 --> 00:00:30.820 So what I wanted to talk about today 00:00:30.820 --> 00:00:35.660 was natural sandwich panels and sandwich beams. 00:00:35.660 --> 00:00:38.850 So there's lots of examples of sandwich structures in nature, 00:00:38.850 --> 00:00:41.050 and we've been looking at the engineering sandwich 00:00:41.050 --> 00:00:41.929 structures. 00:00:41.929 --> 00:00:44.220 And we've seen that you can get a lightweight structure 00:00:44.220 --> 00:00:47.136 by having this sandwich construction. 00:00:47.136 --> 00:00:48.510 And so there are several examples 00:00:48.510 --> 00:00:50.290 I was going to talk about today. 00:00:50.290 --> 00:00:53.310 And I think because this isn't really on the test, 00:00:53.310 --> 00:00:55.060 I'm not going to write a lot on the board. 00:00:55.060 --> 00:00:56.050 So there's some notes. 00:00:56.050 --> 00:00:56.930 I'll just put them on the website, 00:00:56.930 --> 00:00:58.471 and you can look at that if you want. 00:00:58.471 --> 00:01:02.920 Because we have kind of a shorter time today. 00:01:02.920 --> 00:01:05.461 I'll just try and talk and explain what's what. 00:01:05.461 --> 00:01:05.960 Hey, Bruno. 00:01:05.960 --> 00:01:08.310 How are you? 00:01:08.310 --> 00:01:09.880 So this is the first example. 00:01:09.880 --> 00:01:13.090 So many leaves of Monocotyledon plants 00:01:13.090 --> 00:01:14.550 have a sandwich structure. 00:01:14.550 --> 00:01:17.840 And this is an iris plant and iris leaves. 00:01:17.840 --> 00:01:20.020 And for those of you in 3032, I think 00:01:20.020 --> 00:01:22.180 you know that these are glass flowers. 00:01:22.180 --> 00:01:24.510 So the Harvard Museum of Natural History 00:01:24.510 --> 00:01:27.907 has a glass flower collection that was made in the 1800s. 00:01:27.907 --> 00:01:29.490 And there was a botany professor there 00:01:29.490 --> 00:01:35.041 who made these as sort of a lecture demonstration vehicle. 00:01:35.041 --> 00:01:36.540 And so he would bring then to class, 00:01:36.540 --> 00:01:37.750 and he would show different things 00:01:37.750 --> 00:01:39.520 about the plants with the glass flowers. 00:01:39.520 --> 00:01:41.140 But now they're just in the museum, 00:01:41.140 --> 00:01:42.490 and they're very realistic. 00:01:42.490 --> 00:01:45.880 So I just wanted to show you those. 00:01:45.880 --> 00:01:47.860 So let's see, it's not working. 00:01:47.860 --> 00:01:48.840 Turn it on. 00:01:48.840 --> 00:01:49.770 There we go. 00:01:49.770 --> 00:01:52.220 So if we look at a cross-section of an iris leaf, 00:01:52.220 --> 00:01:55.439 it looks like the diagram on the left. 00:01:55.439 --> 00:01:56.230 So here's the iris. 00:01:56.230 --> 00:01:59.470 And you can see there's these kind of solid fibers, 00:01:59.470 --> 00:02:02.220 and those solid fibers are called schlerchyma. 00:02:02.220 --> 00:02:05.290 And they only exist at the top and the bottom of the leaf. 00:02:05.290 --> 00:02:06.680 So I went out this morning. 00:02:06.680 --> 00:02:09.050 And if you look outside of the Stata building, 00:02:09.050 --> 00:02:10.940 there's that little kind of river-y thing, 00:02:10.940 --> 00:02:13.160 and there's some iris leaves growing there. 00:02:13.160 --> 00:02:14.995 So I went and got some iris leaves. 00:02:14.995 --> 00:02:17.370 And you can tell we had a horrible winter because usually 00:02:17.370 --> 00:02:18.995 when I give this lecture in the spring, 00:02:18.995 --> 00:02:21.530 the leaves are like twice as big. 00:02:21.530 --> 00:02:23.970 But this year, they're just little, short, wimpy ones. 00:02:23.970 --> 00:02:25.330 But I'm going to pass it around. 00:02:25.330 --> 00:02:27.700 And if you just like move your thumb over the top, 00:02:27.700 --> 00:02:30.180 you can feel little ridges, little bumps. 00:02:30.180 --> 00:02:32.800 And those little ridges that you can feel 00:02:32.800 --> 00:02:34.940 are these little schlerchyma fibers. 00:02:34.940 --> 00:02:37.120 So you kind of see they kind of stick up a little. 00:02:37.120 --> 00:02:40.650 And so when you move your thumb over it, you can feel that. 00:02:40.650 --> 00:02:43.010 And then you can see that the middle of the iris leaf 00:02:43.010 --> 00:02:46.160 has this kind of foamy-type structure here, 00:02:46.160 --> 00:02:48.180 and that's called parenchyma cells. 00:02:48.180 --> 00:02:50.910 So you can think of the leaf as very much like one 00:02:50.910 --> 00:02:51.670 of the sandwiches. 00:02:51.670 --> 00:02:54.580 This is like a fiber-reinforced composite at the top 00:02:54.580 --> 00:02:55.630 and at the bottom. 00:02:55.630 --> 00:02:58.320 And then this is kind of like a foam core in between, 00:02:58.320 --> 00:03:01.070 separating the fiber-reinforced faces. 00:03:01.070 --> 00:03:03.970 And so the iris leaf behaves mechanically 00:03:03.970 --> 00:03:04.845 like a sandwich beam. 00:03:04.845 --> 00:03:07.303 So I'm going to talk a little bit about how we can actually 00:03:07.303 --> 00:03:09.860 demonstrate that using the equations that we developed 00:03:09.860 --> 00:03:11.040 in class. 00:03:11.040 --> 00:03:12.150 This is another example. 00:03:12.150 --> 00:03:14.660 This is, I guess, what Americans call the cat tail, 00:03:14.660 --> 00:03:17.687 but Canadians and English people call it a bull rush. 00:03:17.687 --> 00:03:19.520 And you can see this is a slightly different 00:03:19.520 --> 00:03:22.060 construction, but there's the same sort of idea. 00:03:22.060 --> 00:03:25.190 So instead of having a foamy core as in the iris leaf, 00:03:25.190 --> 00:03:27.100 you've got these kind of webs here 00:03:27.100 --> 00:03:29.120 that go in between the top and the bottom, 00:03:29.120 --> 00:03:31.664 and that forms like a series of I-beams almost. 00:03:31.664 --> 00:03:33.580 And you can think of that also like a sandwich 00:03:33.580 --> 00:03:35.100 panel or a sandwich beam. 00:03:35.100 --> 00:03:37.834 So you've got two stiff top and bottom pieces, 00:03:37.834 --> 00:03:40.250 and then you've got these kind of webs that separate them, 00:03:40.250 --> 00:03:42.340 kind of like a honeycomb core would be. 00:03:42.340 --> 00:03:45.100 So that's another example of a leaf that has 00:03:45.100 --> 00:03:46.580 the sandwich-type structure. 00:03:46.580 --> 00:03:48.970 And this is very common in these Monocotyledon leaves. 00:03:48.970 --> 00:03:51.480 So if you think of a cat tail or you think of an iris, 00:03:51.480 --> 00:03:53.440 they tend to be kind of narrow at the base, 00:03:53.440 --> 00:03:55.023 maybe an inch or two wide at the base, 00:03:55.023 --> 00:03:56.330 and they can be quite tall. 00:03:56.330 --> 00:03:58.570 The iris leaves can get two or three feet tall. 00:03:58.570 --> 00:04:01.560 The cat tails can get five or six feet tall. 00:04:01.560 --> 00:04:03.789 And they stand up more or less straight. 00:04:03.789 --> 00:04:06.080 They bend over a little, but they stand up more or less 00:04:06.080 --> 00:04:06.910 straight. 00:04:06.910 --> 00:04:08.509 And this sandwich structure is one 00:04:08.509 --> 00:04:10.425 of the things that lets them stand up straight 00:04:10.425 --> 00:04:12.730 at a fairly low weight. 00:04:12.730 --> 00:04:15.930 And from the plant's point of view, 00:04:15.930 --> 00:04:17.950 there's a sort of metabolic cost associated 00:04:17.950 --> 00:04:19.190 with making more material. 00:04:19.190 --> 00:04:21.399 So it we can minimize the amount of material, 00:04:21.399 --> 00:04:24.080 it's a better thing for the plant. 00:04:24.080 --> 00:04:28.650 These are some other examples of grasses that are 00:04:28.650 --> 00:04:29.940 sandwich-type constructions. 00:04:29.940 --> 00:04:32.320 This is from some papers by Julian Vincent. 00:04:32.320 --> 00:04:35.700 And the black little circles here are the schlerchyma, 00:04:35.700 --> 00:04:37.570 are those sort of dense fibers. 00:04:37.570 --> 00:04:39.690 Then you can see in both of these cases, 00:04:39.690 --> 00:04:41.470 the dense fibers are on the outside, 00:04:41.470 --> 00:04:43.410 and the parenchyma cells, which is the white, 00:04:43.410 --> 00:04:45.290 are on the inside. 00:04:45.290 --> 00:04:50.411 And so this is sort of another set of micrographs of the iris. 00:04:50.411 --> 00:04:51.910 So this is just showing the outside, 00:04:51.910 --> 00:04:54.590 and these are the ribs viewed from the outside. 00:04:54.590 --> 00:04:56.680 And this is the core, just sort of viewed 00:04:56.680 --> 00:04:58.460 along the length of it. 00:04:58.460 --> 00:05:00.660 And so you can idealize the structure 00:05:00.660 --> 00:05:03.760 as being like a sandwich that's got sort of fibers on the top 00:05:03.760 --> 00:05:04.580 and on the bottom. 00:05:04.580 --> 00:05:06.788 So the top and the bottom are like a fiber composite. 00:05:06.788 --> 00:05:08.990 And the middle part, with the parenchyma cells, 00:05:08.990 --> 00:05:10.430 is kind of like a foam. 00:05:10.430 --> 00:05:14.585 And so we did a little project on iris leaves, 00:05:14.585 --> 00:05:15.960 and we wanted to see if you could 00:05:15.960 --> 00:05:17.560 show that they behave mechanically, 00:05:17.560 --> 00:05:19.210 like a sandwich beam. 00:05:19.210 --> 00:05:22.030 So you remember that we had that equation for the deflection 00:05:22.030 --> 00:05:23.570 of the sandwich beam. 00:05:23.570 --> 00:05:24.990 There were two terms. 00:05:24.990 --> 00:05:32.800 There was a bending term, and then there was a shearing term. 00:05:37.810 --> 00:05:40.530 And so we took some little sandwich beams. 00:05:40.530 --> 00:05:43.222 We cut little kind of rectangular beams. 00:05:43.222 --> 00:05:44.180 We hung little weights. 00:05:44.180 --> 00:05:45.707 We measured how much they deflected, 00:05:45.707 --> 00:05:47.790 and we wanted to see if we could use this equation 00:05:47.790 --> 00:05:50.445 to predict their stiffness and how much they deflected. 00:05:50.445 --> 00:05:52.570 So to do that, we needed to know a bunch of things. 00:05:52.570 --> 00:05:55.160 We needed to know some of the geometrical parameters. 00:05:55.160 --> 00:05:58.820 So we needed to know what volume fraction of the face 00:05:58.820 --> 00:06:02.630 is those solid ribs, how thick's the core, how thick's the face? 00:06:02.630 --> 00:06:05.780 And so we measured a bunch of these geometrical parameters. 00:06:05.780 --> 00:06:10.030 We tested it like a cantilever so we knew what B1 and B2 were 00:06:10.030 --> 00:06:11.800 for the cantilever. 00:06:11.800 --> 00:06:15.220 We knew how long the beam was, so we know what l is. 00:06:15.220 --> 00:06:17.920 We knew what loads we applied, so we knew what P was. 00:06:17.920 --> 00:06:19.610 But we needed to make some estimate 00:06:19.610 --> 00:06:22.350 of what the face modulus was and what the core shear 00:06:22.350 --> 00:06:23.850 modulus was, too. 00:06:23.850 --> 00:06:26.950 And so we made some estimates of that. 00:06:26.950 --> 00:06:29.710 So this table here just shows some 00:06:29.710 --> 00:06:31.570 of the dimensions of the leaf. 00:06:31.570 --> 00:06:34.270 The leaf tapers, and this is at the thin end, 00:06:34.270 --> 00:06:36.760 so here's the face thickness. 00:06:36.760 --> 00:06:38.845 Here's the sort of length of this. 00:06:38.845 --> 00:06:40.610 Some square cells in the face. 00:06:40.610 --> 00:06:42.912 This is the core thickness here. 00:06:42.912 --> 00:06:44.620 This is the dimensions of the core cells. 00:06:44.620 --> 00:06:47.120 This is the diameter of the ribs, the spacing of the ribs, 00:06:47.120 --> 00:06:49.041 the volume fraction of solids in the ribs. 00:06:49.041 --> 00:06:50.540 And we did that at different lengths 00:06:50.540 --> 00:06:53.700 along the different positions along the length of the rib, 00:06:53.700 --> 00:06:55.710 or length of the leaf. 00:06:55.710 --> 00:06:57.260 So we had the geometrical parameters, 00:06:57.260 --> 00:07:02.010 but we needed to get this E of the face and G of the core. 00:07:02.010 --> 00:07:04.590 And to do that, we looked at the literature. 00:07:04.590 --> 00:07:07.775 And people had done tests on the fiber parts of leaves. 00:07:07.775 --> 00:07:09.150 They'd done little tensile tests, 00:07:09.150 --> 00:07:11.500 and they'd measured modulii between about two 00:07:11.500 --> 00:07:13.330 and 20 gigapascals. 00:07:13.330 --> 00:07:15.960 And then we did some tension tests on the iris leaf. 00:07:15.960 --> 00:07:17.460 And in tension, those ribs are going 00:07:17.460 --> 00:07:19.340 to take most of the stress. 00:07:19.340 --> 00:07:21.340 And if you know the volume fraction of the ribs, 00:07:21.340 --> 00:07:24.520 you can back out what the stiffness of the ribs 00:07:24.520 --> 00:07:25.187 must have been. 00:07:25.187 --> 00:07:26.770 If you know the stiffness of the ribs, 00:07:26.770 --> 00:07:28.644 you can figure out the stiffness of the face. 00:07:28.644 --> 00:07:31.940 So we calculated that, and then we looked at the literature. 00:07:31.940 --> 00:07:34.510 And people have done tests on parenchyma cells 00:07:34.510 --> 00:07:37.320 and different types of tissue on things like apples and potatoes 00:07:37.320 --> 00:07:38.420 and carrots. 00:07:38.420 --> 00:07:41.010 And these are the values for the Young's modulus they get. 00:07:41.010 --> 00:07:47.850 They're between about 1, and the highest one was 14 megapascals. 00:07:47.850 --> 00:07:49.970 But most of these values for the Young's modulus 00:07:49.970 --> 00:07:51.570 are around about four. 00:07:51.570 --> 00:07:53.540 And the shear modulus is roughly about half 00:07:53.540 --> 00:07:54.710 of the Young's modulus. 00:07:54.710 --> 00:07:56.820 So we said the shear modulus was around two. 00:07:56.820 --> 00:08:00.500 So we have these values we could plug it in and then calculate 00:08:00.500 --> 00:08:04.300 what the stiffness would be for the iris leaf. 00:08:04.300 --> 00:08:06.030 And so this was a little analysis we did. 00:08:06.030 --> 00:08:08.030 So this was the measured beam stiffness up here. 00:08:08.030 --> 00:08:11.130 We had four beams, and they were different stiffnesses. 00:08:11.130 --> 00:08:12.630 They all had the same length. 00:08:12.630 --> 00:08:14.910 They all the same face thickness. 00:08:14.910 --> 00:08:16.484 The core thickness varied. 00:08:16.484 --> 00:08:17.650 They all had the same width. 00:08:17.650 --> 00:08:20.090 We cut them to have the same width so we could 00:08:20.090 --> 00:08:21.700 calculate a flexural rigidity. 00:08:21.700 --> 00:08:24.130 That's the EI equivalent. 00:08:24.130 --> 00:08:27.050 We could calculate the bending deflection term, the shear 00:08:27.050 --> 00:08:28.290 deflection term. 00:08:28.290 --> 00:08:30.690 And this is the calculated beam stiffness. 00:08:30.690 --> 00:08:32.539 And then this is the ratio of the calculated 00:08:32.539 --> 00:08:33.590 over the measured. 00:08:33.590 --> 00:08:35.450 So it's not exactly right. 00:08:35.450 --> 00:08:38.120 Obviously, there's some difference here. 00:08:38.120 --> 00:08:39.929 But it's in the same order of magnitude. 00:08:39.929 --> 00:08:41.357 It's in the same ballpark. 00:08:41.357 --> 00:08:43.440 And one of the complications that we didn't really 00:08:43.440 --> 00:08:46.240 try to take into account was that the leaf isn't 00:08:46.240 --> 00:08:47.630 a nice rectangular structure. 00:08:47.630 --> 00:08:50.630 The leaf has this kind of curved cross-section to it. 00:08:50.630 --> 00:08:52.920 And we made a bit of an approximation to that, 00:08:52.920 --> 00:08:54.389 but it wasn't that close, really. 00:08:54.389 --> 00:08:56.180 We could have probably done better on that. 00:09:00.400 --> 00:09:04.790 But I think the idea that the iris behaves like a sandwich is 00:09:04.790 --> 00:09:06.330 a reasonable one. 00:09:06.330 --> 00:09:08.570 So that was the iris leaf. 00:09:08.570 --> 00:09:11.220 And then I wanted to show you some other structures in nature 00:09:11.220 --> 00:09:12.760 that are sandwiches. 00:09:12.760 --> 00:09:15.800 So this is a seakelp, help like a seaweed thing, 00:09:15.800 --> 00:09:17.760 in New Zealand. 00:09:17.760 --> 00:09:20.150 This is the largest intertidal seaweed. 00:09:20.150 --> 00:09:23.930 The fronds, the sort of long pieces of it, 00:09:23.930 --> 00:09:25.330 are up to 12 meters long. 00:09:25.330 --> 00:09:26.960 So that's almost 40 feet. 00:09:26.960 --> 00:09:29.340 So 40 feet is probably like from one side of this room 00:09:29.340 --> 00:09:30.590 to the other side of the room. 00:09:30.590 --> 00:09:31.720 It's quite long. 00:09:31.720 --> 00:09:34.700 And you can see, if you look at this section here, 00:09:34.700 --> 00:09:37.910 this is all like a honeycomb-type section here. 00:09:37.910 --> 00:09:42.430 And the honeycomb is like a honeycomb in a sandwich, 00:09:42.430 --> 00:09:44.190 and the top and the bottom faces are 00:09:44.190 --> 00:09:45.471 like the face of the sandwich. 00:09:45.471 --> 00:09:46.970 So this would be like the face here. 00:09:46.970 --> 00:09:48.345 That would be the honeycomb core. 00:09:48.345 --> 00:09:51.570 And that would be the other face on the other side over there. 00:09:51.570 --> 00:09:53.880 And those honeycomb-like cores, apparently, 00:09:53.880 --> 00:09:57.390 have some gas-filled pockets that then provide buoyancy 00:09:57.390 --> 00:09:58.790 to keep the whole thing floating. 00:09:58.790 --> 00:10:00.630 So it photosynthesizes. 00:10:00.630 --> 00:10:02.270 So one of the things about these leaves 00:10:02.270 --> 00:10:04.392 is that they have multiple functions. 00:10:04.392 --> 00:10:06.725 It's not just that they have to have a certain stiffness 00:10:06.725 --> 00:10:08.930 so they don't fall over. 00:10:08.930 --> 00:10:10.630 The plant wants to photosynthesize, 00:10:10.630 --> 00:10:12.760 so you want to maximize the surface area as well, 00:10:12.760 --> 00:10:14.790 and you want to have exposure to the sunlight. 00:10:14.790 --> 00:10:16.998 So there's a number of things that the plant's trying 00:10:16.998 --> 00:10:19.770 to do in having this structure. 00:10:19.770 --> 00:10:22.820 So that seakelp is one example. 00:10:22.820 --> 00:10:25.410 These are skulls from birds. 00:10:25.410 --> 00:10:27.160 And so this is a pigeon here. 00:10:27.160 --> 00:10:28.680 This is a magpie. 00:10:28.680 --> 00:10:30.950 If you come from the West you see magpies out West. 00:10:30.950 --> 00:10:32.490 You see them in Europe as well. 00:10:32.490 --> 00:10:34.190 And this is a long-eared owl. 00:10:34.190 --> 00:10:37.420 This long-eared owl's around here. 00:10:37.420 --> 00:10:40.540 And I brought in a couple of bird skulls as well. 00:10:40.540 --> 00:10:42.880 And you can see that all of those birds skulls 00:10:42.880 --> 00:10:44.450 are sandwich structures. 00:10:44.450 --> 00:10:48.690 The one for the pigeon has sort of a foam-like core here. 00:10:48.690 --> 00:10:50.960 And you can see that the two faces 00:10:50.960 --> 00:10:53.470 aren't sort of concentric for the pigeon skull. 00:10:53.470 --> 00:10:56.820 They sort of not following each other. 00:10:56.820 --> 00:11:00.440 But here, this would be, say, on the top shell 00:11:00.440 --> 00:11:04.680 of the magpie, where the two, the inner and outer face, 00:11:04.680 --> 00:11:06.080 are sort of concentric. 00:11:06.080 --> 00:11:08.800 Then you get these kind of little ribs of trabecular bone 00:11:08.800 --> 00:11:11.410 in between them, and then the same with a long-eared owl. 00:11:11.410 --> 00:11:13.390 You get these little ribs in between them. 00:11:13.390 --> 00:11:15.887 And so you can see that there's a sandwich structure there. 00:11:15.887 --> 00:11:17.470 And obviously, birds want to be light. 00:11:17.470 --> 00:11:20.290 They have to be light to fly, to take off, 00:11:20.290 --> 00:11:22.300 and so they want to be light. 00:11:22.300 --> 00:11:24.857 So I've got two skulls here. 00:11:24.857 --> 00:11:25.940 And I'll pass them around. 00:11:25.940 --> 00:11:28.064 Please be careful because they're kind of delicate. 00:11:28.064 --> 00:11:31.170 This one is from a screech owl, and you see screech owls 00:11:31.170 --> 00:11:31.710 around here. 00:11:31.710 --> 00:11:36.350 This was a screech owl that had an intersection with a car. 00:11:36.350 --> 00:11:38.780 Yeah, so the skull fractured, but you can see the sandwich 00:11:38.780 --> 00:11:39.280 right there. 00:11:39.280 --> 00:11:41.030 You see the two little bits? 00:11:41.030 --> 00:11:43.610 So you can see the inner plate and the outer plate 00:11:43.610 --> 00:11:46.206 and the foam, the trabecular bone. 00:11:46.206 --> 00:11:49.580 So that's the screech owl. 00:11:49.580 --> 00:11:52.110 And this is a red tail hawk. 00:11:52.110 --> 00:11:54.385 So you can't really see the shell and the sandwich 00:11:54.385 --> 00:11:55.010 structure here. 00:11:55.010 --> 00:11:56.077 But I want to pass it around just 00:11:56.077 --> 00:11:57.368 so you can see how light it is. 00:11:57.368 --> 00:11:58.580 So it's amazingly light. 00:11:58.580 --> 00:12:01.470 So a red tail hawk is probably about this big, 00:12:01.470 --> 00:12:02.700 something like that. 00:12:02.700 --> 00:12:09.490 And this is one of the things that makes them very light. 00:12:09.490 --> 00:12:10.929 So those are the bird skulls. 00:12:10.929 --> 00:12:12.970 Oh, yes, so now I have to tell you about the owl. 00:12:12.970 --> 00:12:15.178 So I think the people in 3032 have heard this before. 00:12:15.178 --> 00:12:16.960 But the other people haven't. 00:12:16.960 --> 00:12:19.064 So one of the things about the owl 00:12:19.064 --> 00:12:20.480 is if you look at the whole skull, 00:12:20.480 --> 00:12:22.970 if you look at this picture here, one of the things 00:12:22.970 --> 00:12:26.210 is that this bone here is not symmetrical with that bone 00:12:26.210 --> 00:12:26.810 there. 00:12:26.810 --> 00:12:29.290 Normally, when you think of a body, 00:12:29.290 --> 00:12:31.250 you think of the bones being symmetrical. 00:12:31.250 --> 00:12:32.770 But those bones are not symmetrical, 00:12:32.770 --> 00:12:35.660 and those bones are near where the ear is. 00:12:35.660 --> 00:12:38.140 And it turns out on owls, at least on some owls, 00:12:38.140 --> 00:12:41.490 the ears are at different heights on their heads. 00:12:41.490 --> 00:12:44.060 And people think that one of the things that 00:12:44.060 --> 00:12:47.660 allows the owls to do is it allows their hearing 00:12:47.660 --> 00:12:50.090 to sort of pinpoint where something is. 00:12:50.090 --> 00:12:53.440 And owls can catch little creatures at night, 00:12:53.440 --> 00:12:56.100 but they can also catch little creatures underneath the snow. 00:12:56.100 --> 00:12:58.420 So they can catch things that they can't even see. 00:12:58.420 --> 00:13:01.400 And they have a number of adaptations 00:13:01.400 --> 00:13:03.660 to improve their hearing, but this is one of them. 00:13:03.660 --> 00:13:08.100 So here's a little owl Allison Curtis is a Canadian friend who 00:13:08.100 --> 00:13:10.460 lives in northern Ontario, and this is looking out 00:13:10.460 --> 00:13:11.900 of her living room window. 00:13:11.900 --> 00:13:12.994 And that's a barred owl. 00:13:12.994 --> 00:13:14.410 And you can see the barred owl has 00:13:14.410 --> 00:13:16.156 caught this little vole here. 00:13:16.156 --> 00:13:17.530 And you can see in the background 00:13:17.530 --> 00:13:18.910 it's winter in Canada. 00:13:18.910 --> 00:13:20.860 and there's snow all over the place. 00:13:20.860 --> 00:13:22.980 So this owl has probably caught that little vole 00:13:22.980 --> 00:13:24.520 underneath the snow. 00:13:24.520 --> 00:13:26.840 And then it's come to eat it. 00:13:26.840 --> 00:13:28.490 And this is another picture of-- you 00:13:28.490 --> 00:13:31.960 can see this is where an owl landed in the snow. 00:13:31.960 --> 00:13:36.290 It's wings hit the snow, trying to catch something underneath. 00:13:36.290 --> 00:13:39.280 And this is another kind of beautiful print 00:13:39.280 --> 00:13:44.150 of the owl's wings hitting the snow in the winter time. 00:13:44.150 --> 00:13:46.427 So did I show you the fox video? 00:13:46.427 --> 00:13:47.760 Should I show you the fox video? 00:13:50.850 --> 00:13:51.600 You saw it, right? 00:13:51.600 --> 00:13:53.472 I think I showed it last time in 3032. 00:13:53.472 --> 00:13:54.680 But you guys haven't seen it. 00:13:54.680 --> 00:13:56.697 Let me show you the fox video because foxes 00:13:56.697 --> 00:13:57.780 do the same kind of thing. 00:13:57.780 --> 00:13:59.420 Their ears are the same as ours. 00:13:59.420 --> 00:14:01.190 They're in the same position. 00:14:04.537 --> 00:14:05.870 But they have this-- let me see. 00:14:05.870 --> 00:14:06.870 Where's the sound thing? 00:14:06.870 --> 00:14:08.590 We don't really need the sound for this, 00:14:08.590 --> 00:14:11.210 but there's BBC sound. 00:14:11.210 --> 00:14:14.445 So we get this music, even though the fox 00:14:14.445 --> 00:14:16.680 can't hear the music. 00:14:16.680 --> 00:14:18.610 Here we go, fox no drive. 00:14:18.610 --> 00:14:21.340 Check this out. 00:14:21.340 --> 00:14:22.436 Is it going to come up? 00:14:26.635 --> 00:14:27.810 Is that going to play? 00:14:27.810 --> 00:14:28.310 OK 00:14:28.310 --> 00:14:29.684 [VIDEO PLAYBACK] 00:14:29.684 --> 00:14:32.890 -It listens for the tiny sounds of its prey moving about below. 00:14:32.890 --> 00:14:34.723 PROFESSOR: So you see how it cocks its head, 00:14:34.723 --> 00:14:36.496 and it does this with its head? 00:14:36.496 --> 00:14:38.245 It's putting its ears at different heights 00:14:38.245 --> 00:14:39.200 when it does that. 00:14:58.120 --> 00:14:59.140 So check this out. 00:14:59.140 --> 00:15:01.380 And look carefully, you can see the little animal 00:15:01.380 --> 00:15:03.557 it's got in its mouth when it comes out. 00:15:03.557 --> 00:15:04.473 There's a little tail. 00:15:07.290 --> 00:15:10.690 So part of the reason dogs and foxes and coyotes 00:15:10.690 --> 00:15:12.510 do that thing, I think, is because they 00:15:12.510 --> 00:15:14.010 put their ears at different heights, 00:15:14.010 --> 00:15:17.230 and it helps them pinpoint where something is. 00:15:17.230 --> 00:15:17.989 [END PLAYBACK] 00:15:17.989 --> 00:15:19.780 You know I love these Nature videos, right? 00:15:19.780 --> 00:15:20.779 So that's the fox video. 00:15:20.779 --> 00:15:23.115 Let me see if I can stop that. 00:15:26.256 --> 00:15:28.380 So that's one of the interesting things about owls. 00:15:33.860 --> 00:15:35.965 Let me go back to my little PowerPoints. 00:15:39.010 --> 00:15:42.570 So here's another example of a creature that 00:15:42.570 --> 00:15:44.430 has a sandwich-type structures. 00:15:44.430 --> 00:15:45.810 So here's the sandwich here. 00:15:45.810 --> 00:15:49.100 Here is the ever so charming looking cuttlefish. 00:15:49.100 --> 00:15:52.040 And the cuttlefish is not actually a fish. 00:15:52.040 --> 00:15:53.570 It's a mollusk. 00:15:53.570 --> 00:15:56.090 So it's related to things like octopus, things like that, 00:15:56.090 --> 00:15:57.480 and squids. 00:15:57.480 --> 00:16:00.870 It's a cephalopod. 00:16:00.870 --> 00:16:03.040 And you can't see it so well in this picture, 00:16:03.040 --> 00:16:04.400 but I'm going to show you something else and you see it. 00:16:04.400 --> 00:16:05.691 It's got like little tentacles. 00:16:05.691 --> 00:16:08.140 These things here are actually separate little tentacles. 00:16:08.140 --> 00:16:11.220 And because it's not a fish, it doesn't have like fins 00:16:11.220 --> 00:16:12.780 that can kind of swim with. 00:16:12.780 --> 00:16:15.370 And it's got this thing called the cuttlefish bone. 00:16:15.370 --> 00:16:17.670 And this is a cuttlefish bone here. 00:16:17.670 --> 00:16:20.262 And that bone has the sandwich structure here. 00:16:20.262 --> 00:16:21.470 And it's not actually a bone. 00:16:21.470 --> 00:16:22.790 It's really a shell. 00:16:22.790 --> 00:16:27.160 It's a calcium carbonate thing, not a calcium phosphate thing. 00:16:27.160 --> 00:16:29.600 But the cuttlefish can control how much air 00:16:29.600 --> 00:16:31.010 goes into those little pockets. 00:16:31.010 --> 00:16:34.120 And it can control its buoyancy by controlling how much air 00:16:34.120 --> 00:16:35.650 goes into those little pockets. 00:16:35.650 --> 00:16:39.680 And I brought with me a cuttlefish bone. 00:16:39.680 --> 00:16:41.970 Have you ever owned like, I don't know, 00:16:41.970 --> 00:16:44.880 like a parrot or a pet bird? 00:16:44.880 --> 00:16:47.150 Apparently, pet birds love to sharpen their beaks 00:16:47.150 --> 00:16:48.700 on this cuttlefish bone. 00:16:48.700 --> 00:16:51.700 So if you go to a pet store, you can buy this stuff. 00:16:51.700 --> 00:16:54.370 So you won't be able to see the little sandwich 00:16:54.370 --> 00:16:56.695 structure because it's a very small length scale. 00:16:56.695 --> 00:16:59.490 But you can kind of see there's a sort 00:16:59.490 --> 00:17:01.390 of different material on the inside 00:17:01.390 --> 00:17:04.410 than there is on the outside of that. 00:17:04.410 --> 00:17:07.530 So do people know the other thing 00:17:07.530 --> 00:17:09.950 that cuttlefish are famous for, besides the bone? 00:17:09.950 --> 00:17:10.923 Change colors. 00:17:10.923 --> 00:17:13.089 Can I show you a video of cuttlefish changing color? 00:17:13.089 --> 00:17:14.837 Yeah, of course. 00:17:14.837 --> 00:17:16.170 So let me get rid of this again. 00:17:16.170 --> 00:17:18.869 Go back to this. 00:17:18.869 --> 00:17:21.589 Let's see, somewhere-- where's the cuttlefish? 00:17:21.589 --> 00:17:22.099 Here we go. 00:17:27.210 --> 00:17:27.719 Did I do it? 00:17:27.719 --> 00:17:29.760 Is it thinking? 00:17:29.760 --> 00:17:30.260 Here we go. 00:17:30.260 --> 00:17:31.190 Where's the cuttlefish? 00:17:31.190 --> 00:17:33.106 So this is another one of these Science Friday 00:17:33.106 --> 00:17:37.944 videos from National Public Radio with Flora Lichtman. 00:17:37.944 --> 00:17:38.610 [VIDEO PLAYBACK] 00:17:38.610 --> 00:17:39.650 -OK, let's play a game. 00:17:39.650 --> 00:17:42.608 [GAME SHOW MUSIC PLAYING] 00:17:42.608 --> 00:17:44.670 [APPLAUSE] 00:17:44.670 --> 00:17:45.420 PROFESSOR: See it? 00:17:48.720 --> 00:17:51.290 -Biologist Sarah Zielinski took these shots. 00:17:51.290 --> 00:17:54.860 And if you needed a helping hand to find the cuttlefish, 00:17:54.860 --> 00:17:55.559 don't feel bad. 00:17:55.559 --> 00:17:57.850 -I've certainly taken photos in the past then come back 00:17:57.850 --> 00:18:00.420 to look at them and gone, I'm sure there was a cuttlefish 00:18:00.420 --> 00:18:02.762 in there somewhere! 00:18:02.762 --> 00:18:06.160 -These cephalopods are master camouflagers. 00:18:06.160 --> 00:18:07.690 But while they're hiding their body, 00:18:07.690 --> 00:18:10.590 they're revealing something about their mind, 00:18:10.590 --> 00:18:12.236 or at least their visual system. 00:18:12.236 --> 00:18:13.860 -In very simple terms, they can tell us 00:18:13.860 --> 00:18:15.944 what they can see by the body patterns they 00:18:15.944 --> 00:18:16.860 produce on their skin. 00:18:16.860 --> 00:18:18.330 -They produce these body patterns 00:18:18.330 --> 00:18:21.010 by expanding or contracting chromatophores, 00:18:21.010 --> 00:18:22.820 these little ink sacks on their skin. 00:18:22.820 --> 00:18:25.070 And they use different displays for different reasons, 00:18:25.070 --> 00:18:27.130 like for male-to-male combat. 00:18:27.130 --> 00:18:28.920 -Two males will turn into each other 00:18:28.920 --> 00:18:31.950 and pass these kind of waves of dark chromatophores 00:18:31.950 --> 00:18:35.840 over a really bright sort of iridescent stripey body pattern 00:18:35.840 --> 00:18:39.140 and somehow solve these combats. 00:18:39.140 --> 00:18:43.110 Eventually, one male gives up and goes away. 00:18:43.110 --> 00:18:44.971 -And then there's this unsolved mystery. 00:18:48.780 --> 00:18:51.170 It changes color when it grabs a snack. 00:18:51.170 --> 00:18:53.240 -That doesn't make perfect sense because it seems 00:18:53.240 --> 00:18:54.440 to make it very conspicuous. 00:18:54.440 --> 00:18:58.240 So one theory is that it's just a happy signal 00:18:58.240 --> 00:18:59.920 of how excited it is to have caught 00:18:59.920 --> 00:19:02.980 something, some response that it doesn't have any control over. 00:19:02.980 --> 00:19:04.810 -But most of the time they seem to be 00:19:04.810 --> 00:19:07.320 using their chromatophores more intentionally, 00:19:07.320 --> 00:19:08.796 primarily to blend in. 00:19:08.796 --> 00:19:10.920 -Because otherwise they're more likely to be eaten, 00:19:10.920 --> 00:19:13.050 so it's very important they don't make mistakes 00:19:13.050 --> 00:19:15.240 about ambiguous visual information. 00:19:15.240 --> 00:19:16.970 -And ambiguous visual information 00:19:16.970 --> 00:19:20.360 is specifically what Zielinski's interested in. 00:19:20.360 --> 00:19:21.980 So here's the experimental setup. 00:19:21.980 --> 00:19:24.910 Print out laminated patterns, like this checkerboard, 00:19:24.910 --> 00:19:26.310 and stick them in a tank. 00:19:26.310 --> 00:19:29.000 -And we place the animals in the tank. 00:19:29.000 --> 00:19:31.140 And we record the body patterns that they produce. 00:19:31.140 --> 00:19:33.690 -You're seeing them on squares, but they do the same thing 00:19:33.690 --> 00:19:35.330 on top of circles. 00:19:35.330 --> 00:19:36.030 They produce-- 00:19:36.030 --> 00:19:38.610 - --the disruptive pattern, where you get these blocky 00:19:38.610 --> 00:19:40.700 components of high-contrast components. 00:19:40.700 --> 00:19:43.765 -But when you put a cuttlefish over squiggles, it produces-- 00:19:43.765 --> 00:19:46.140 - --a sort of mottley pattern, where you get these little 00:19:46.140 --> 00:19:48.870 groups of dark spots showing across the body. 00:19:48.870 --> 00:19:51.690 -So what happens when you put a cuttlefish on something 00:19:51.690 --> 00:19:57.240 in between, when you put them on incomplete circles? 00:19:57.240 --> 00:19:59.930 When we see something like this, our visual system 00:19:59.930 --> 00:20:03.660 likes to fill in the blanks, something we do constantly, 00:20:03.660 --> 00:20:04.570 Zielinski says. 00:20:04.570 --> 00:20:07.350 -The reason why cartoons and sketches work 00:20:07.350 --> 00:20:09.270 is because we can recognize objects 00:20:09.270 --> 00:20:10.630 based on their edges alone. 00:20:10.630 --> 00:20:13.310 -And we can identify objects even if they're broken up or-- 00:20:13.310 --> 00:20:15.679 - --have an object that is occluded by another object. 00:20:15.679 --> 00:20:16.720 That's no problem for us. 00:20:16.720 --> 00:20:19.430 We can still work out what the object is most of the time. 00:20:19.430 --> 00:20:21.460 And I was interested to know whether cuttlefish 00:20:21.460 --> 00:20:23.690 can solve similar problems. 00:20:23.690 --> 00:20:26.380 -And Zielinski and colleagues report this week that 00:20:26.380 --> 00:20:28.230 cuttlefish do seem to-- 00:20:28.230 --> 00:20:31.920 - --fill in those gaps and interpret those little segments 00:20:31.920 --> 00:20:33.440 as a whole circle. 00:20:33.440 --> 00:20:36.500 -Or anyway, the broken circles prompted the same camo pattern 00:20:36.500 --> 00:20:37.690 as full circles. 00:20:37.690 --> 00:20:41.140 So if you're wondering, uh, I see these as circles, too. 00:20:41.140 --> 00:20:43.020 What's the big deal? 00:20:43.020 --> 00:20:47.360 The weird thing here is that there's no reason why 00:20:47.360 --> 00:20:48.763 cuttlefish, which are-- 00:20:48.763 --> 00:20:51.820 - --invertebrates, and they're in the same group as slugs 00:20:51.820 --> 00:20:52.450 and snails. 00:20:52.450 --> 00:20:55.080 - --should see the world the way we do. 00:20:55.080 --> 00:20:57.162 -Yes, it's like they're alien, but we also 00:20:57.162 --> 00:20:58.870 seem to have so much in common with them. 00:20:58.870 --> 00:21:00.120 -So the next step? 00:21:00.120 --> 00:21:02.410 -Because we can't share the perceptive experience 00:21:02.410 --> 00:21:05.190 of a cuttlefish, it's hard to know 00:21:05.190 --> 00:21:09.660 exactly what it is that they're doing to fill in that missing 00:21:09.660 --> 00:21:10.340 information. 00:21:10.340 --> 00:21:12.298 And I want to try to get a better grasp on that 00:21:12.298 --> 00:21:14.070 and also see whether they actually respond 00:21:14.070 --> 00:21:15.760 to true illusory contours. 00:21:15.760 --> 00:21:19.630 -So you're going to show optical illusions to cuttlefish? 00:21:19.630 --> 00:21:22.676 -(LAUGHING) That's what I'm hoping to do, yes. 00:21:22.676 --> 00:21:27.010 [END PLAYBACK] 00:21:29.760 --> 00:21:32.400 PROFESSOR: So let's go back to sandwiches. 00:21:32.400 --> 00:21:36.160 I think I have-- do I have one more? 00:21:36.160 --> 00:21:37.870 There we go. 00:21:37.870 --> 00:21:39.930 So horseshoe crab shells, so different sorts 00:21:39.930 --> 00:21:42.390 of arthropods, the shells are sandwiched too. 00:21:42.390 --> 00:21:44.649 This is from Mark Myers' work. 00:21:44.649 --> 00:21:46.190 So we're looking at the cross-section 00:21:46.190 --> 00:21:47.692 of a horseshoe crab shell. 00:21:47.692 --> 00:21:49.650 So again, it's the same idea-- the animal wants 00:21:49.650 --> 00:21:51.066 to minimize the amount of material 00:21:51.066 --> 00:21:54.160 or minimize the weight, and this is a way of doing that. 00:21:54.160 --> 00:21:57.540 And I went to the Galapagos about a year ago. 00:21:57.540 --> 00:22:01.530 And there was a place where they had these giant Galapagos 00:22:01.530 --> 00:22:02.632 tortoise shells. 00:22:02.632 --> 00:22:04.090 And one of them was broken, and you 00:22:04.090 --> 00:22:06.465 could see there was a sandwich structure in the Galapagos 00:22:06.465 --> 00:22:07.260 tortoise shells. 00:22:07.260 --> 00:22:10.377 These Galapagos tortoises, their shell is like this big. 00:22:10.377 --> 00:22:11.085 They're gigantic. 00:22:11.085 --> 00:22:12.560 They're huge. 00:22:12.560 --> 00:22:16.920 So those are my examples of sandwich panels and beams 00:22:16.920 --> 00:22:18.710 and shells and whatnot in nature. 00:22:18.710 --> 00:22:20.800 So the idea is that nature too wants 00:22:20.800 --> 00:22:24.140 to minimize weight and minimize the amount of material, 00:22:24.140 --> 00:22:27.181 and the sandwich structure is a way of doing that. 00:22:27.181 --> 00:22:29.430 So I have one more thing I wanted to talk about today. 00:22:29.430 --> 00:22:31.490 So this isn't quite sandwich structures, 00:22:31.490 --> 00:22:34.780 but it's looking at another kind of natural structure 00:22:34.780 --> 00:22:38.340 that is designed to reduce the weight of plant stems, 00:22:38.340 --> 00:22:40.160 in this case, palm stems. 00:22:40.160 --> 00:22:42.590 And there's a couple of interesting things about this. 00:22:42.590 --> 00:22:44.910 So when you look at palms, like let's pretend 00:22:44.910 --> 00:22:45.840 we're not in Boston. 00:22:45.840 --> 00:22:48.120 We're in California, where they have palms. 00:22:48.120 --> 00:22:50.370 And we're in LA, and they don't have winter. 00:22:50.370 --> 00:22:53.860 And if you look at the palms growing, when the palm's short, 00:22:53.860 --> 00:22:55.590 it's about this big in diameter. 00:22:55.590 --> 00:22:56.966 And as it gets taller and taller, 00:22:56.966 --> 00:22:58.423 the diameter doesn't really change. 00:22:58.423 --> 00:23:00.020 It gets taller and taller and taller, 00:23:00.020 --> 00:23:02.970 but the diameter doesn't change, at least in some species. 00:23:02.970 --> 00:23:04.554 Whereas if you think of a tree, a tree 00:23:04.554 --> 00:23:06.261 starts out with a little skinny diameter. 00:23:06.261 --> 00:23:08.560 And as the tree gets taller, the diameter gets bigger. 00:23:08.560 --> 00:23:10.630 And it sort of tapers and does that whole thing. 00:23:10.630 --> 00:23:11.700 So palms don't do that. 00:23:11.700 --> 00:23:13.040 And palms are not trees. 00:23:13.040 --> 00:23:16.510 They're a botanically different thing from trees. 00:23:16.510 --> 00:23:18.450 So here's a coconut palm. 00:23:18.450 --> 00:23:22.090 And so the question is, as the stem gets taller and taller, 00:23:22.090 --> 00:23:23.934 how does it resist the bending loads that 00:23:23.934 --> 00:23:24.850 get bigger and bigger? 00:23:24.850 --> 00:23:27.790 So probably, the main load on these sorts of things 00:23:27.790 --> 00:23:29.330 is from the wind. 00:23:29.330 --> 00:23:31.735 And often these plants are in areas 00:23:31.735 --> 00:23:32.860 where they have hurricanes. 00:23:32.860 --> 00:23:34.318 And you see them in hurricanes, you 00:23:34.318 --> 00:23:37.930 see the pictures of the palm stem blowing way over. 00:23:37.930 --> 00:23:41.110 And so how do they resist the larger internal stresses 00:23:41.110 --> 00:23:43.740 as they get taller and taller, if the diameter doesn't 00:23:43.740 --> 00:23:44.990 get bigger and bigger? 00:23:44.990 --> 00:23:48.760 And the way they do that is that they deposit additional layers 00:23:48.760 --> 00:23:51.650 of cell wall as the plant ages. 00:23:51.650 --> 00:23:54.040 So if you think of a tree, when a tree grows, 00:23:54.040 --> 00:23:55.884 it just deposits more and more cells. 00:23:55.884 --> 00:23:57.800 And the cells have roughly the same thickness. 00:23:57.800 --> 00:23:59.880 So there's ones that are deposited in the spring have 00:23:59.880 --> 00:24:00.410 thinner walls. 00:24:00.410 --> 00:24:02.409 Then the summer and the fall have thicker walls. 00:24:02.409 --> 00:24:04.620 But more or less, it's similar. 00:24:04.620 --> 00:24:06.710 Whereas the palm, it deposit cells, 00:24:06.710 --> 00:24:08.780 and then as the trunk of the palm 00:24:08.780 --> 00:24:10.540 gets taller, as the stem gets taller, 00:24:10.540 --> 00:24:13.550 it deposits more layers on the cell wall. 00:24:13.550 --> 00:24:15.300 So this is an example in an SCM. 00:24:15.300 --> 00:24:18.340 You can see here this is a young cell, 00:24:18.340 --> 00:24:21.760 and it's got-- this one that's not marked is a primary cell 00:24:21.760 --> 00:24:24.420 wall, and then this is the first layer of the secondary cell 00:24:24.420 --> 00:24:25.450 wall. 00:24:25.450 --> 00:24:27.360 And then this is an older palm. 00:24:27.360 --> 00:24:29.250 And you can see here it's got more layers, 00:24:29.250 --> 00:24:31.800 and so the cell wall itself has gotten thicker. 00:24:31.800 --> 00:24:33.800 So that means that the density of the tissue 00:24:33.800 --> 00:24:36.310 changes as the palm ages. 00:24:36.310 --> 00:24:39.120 And it does so in a very kind of clever way. 00:24:39.120 --> 00:24:41.550 If you think of the palm as being like a cantilever that's 00:24:41.550 --> 00:24:45.510 vertical and it's bending in the wind, when we have a cantilever 00:24:45.510 --> 00:24:47.094 beam or any kind of beam, the stresses 00:24:47.094 --> 00:24:49.093 are going to be biggest on the periphery, right? 00:24:49.093 --> 00:24:51.040 They're going to be biggest on the outside. 00:24:51.040 --> 00:24:52.920 And if you think of the palm as having 00:24:52.920 --> 00:24:56.299 a circular cross-section, that outer periphery 00:24:56.299 --> 00:24:57.840 is going to see the biggest stresses. 00:24:57.840 --> 00:25:00.570 So it would make the most sense if that was the densest tissue. 00:25:00.570 --> 00:25:02.659 And that's exactly what the palm does. 00:25:02.659 --> 00:25:04.700 So there was a nice study done by Paul Rich quite 00:25:04.700 --> 00:25:06.010 a number of years ago. 00:25:06.010 --> 00:25:07.920 And he studied palms in Central America 00:25:07.920 --> 00:25:09.787 and looked at the density and measured 00:25:09.787 --> 00:25:10.870 the mechanical properties. 00:25:10.870 --> 00:25:13.190 And I'm going to talk about his stuff today. 00:25:13.190 --> 00:25:14.830 So the white is the low density. 00:25:14.830 --> 00:25:17.060 The gray's the medium, and the black's the high. 00:25:17.060 --> 00:25:18.976 So you can see the low density's on the middle 00:25:18.976 --> 00:25:21.320 of the young stem, and just at the very base 00:25:21.320 --> 00:25:23.870 and then the periphery is the dense tissue. 00:25:23.870 --> 00:25:26.450 But as the stem gets taller and gets older, 00:25:26.450 --> 00:25:30.110 then stuff that was low density is now high density. 00:25:30.110 --> 00:25:33.584 And only the very middle here is the low density. 00:25:33.584 --> 00:25:35.250 And that some stuff that was low density 00:25:35.250 --> 00:25:36.459 has turned to middle density. 00:25:36.459 --> 00:25:37.916 And some stuff that was low density 00:25:37.916 --> 00:25:39.140 has turned to high density. 00:25:39.140 --> 00:25:41.670 So it's done this by adding more and more layers to the cell 00:25:41.670 --> 00:25:43.400 wall, making the cell wall thicker 00:25:43.400 --> 00:25:46.410 and making the cells themselves denser. 00:25:46.410 --> 00:25:49.060 So this is looking just at a single palm. 00:25:49.060 --> 00:25:52.370 So each one of these lines is a single palm. 00:25:52.370 --> 00:25:54.810 And this is looking at how the density changes 00:25:54.810 --> 00:25:57.540 from the periphery to the center of the palm. 00:25:57.540 --> 00:26:00.140 So if you cut the palm down and, say, 00:26:00.140 --> 00:26:04.480 we take a little sample radially from the middle to the outside 00:26:04.480 --> 00:26:06.910 or from the outside to the middle, 00:26:06.910 --> 00:26:08.570 he then measured the density. 00:26:08.570 --> 00:26:11.911 And it's probably easiest to think about the dry ones 00:26:11.911 --> 00:26:14.160 because that's kind of what you would compare wood to. 00:26:14.160 --> 00:26:17.240 So the dry densities varied from about one gram per CC, 00:26:17.240 --> 00:26:20.080 that's about 1,000 kilograms per cubic meter, 00:26:20.080 --> 00:26:23.020 down to almost zero in this particular species 00:26:23.020 --> 00:26:25.222 here, probably like 50 or something like that. 00:26:25.222 --> 00:26:26.680 And if you compare this with woods, 00:26:26.680 --> 00:26:30.520 this little arrow here is the density of most common woods. 00:26:30.520 --> 00:26:33.840 So if you looked at pine and spruce an oak and maple 00:26:33.840 --> 00:26:36.930 and ash and hickory, they would all be in that little range 00:26:36.930 --> 00:26:37.580 there. 00:26:37.580 --> 00:26:40.680 So a single palm stem can have a bigger range 00:26:40.680 --> 00:26:44.400 of densities than many different species of wood. 00:26:44.400 --> 00:26:47.825 So it has this kind of profile of the density. 00:26:47.825 --> 00:26:49.200 And the thing I was interested in 00:26:49.200 --> 00:26:51.030 is seeing how mechanically efficient 00:26:51.030 --> 00:26:54.010 that was to put the denser material at the outside. 00:26:54.010 --> 00:26:56.310 So I looked at the stiffness of the palm, 00:26:56.310 --> 00:26:59.120 and I also looked at the strength. 00:26:59.120 --> 00:27:03.880 So I just replotted that data on this slightly different axes 00:27:03.880 --> 00:27:04.560 here. 00:27:04.560 --> 00:27:08.020 So this is the radial position relative to the outer radius, 00:27:08.020 --> 00:27:09.290 and this is the density. 00:27:09.290 --> 00:27:12.700 And I subtracted off the minimum and then took the range. 00:27:12.700 --> 00:27:14.830 And for this species here, the minimum density 00:27:14.830 --> 00:27:15.600 was almost zero. 00:27:15.600 --> 00:27:18.420 So this expression simplifies to something like that. 00:27:18.420 --> 00:27:20.332 And just because it's mathematically simpler, 00:27:20.332 --> 00:27:21.790 that's what we're going to look at. 00:27:21.790 --> 00:27:26.720 So the density goes roughly as the radius squared. 00:27:26.720 --> 00:27:30.030 And Paul Rich also did a lot of mechanical tests on the palm, 00:27:30.030 --> 00:27:32.530 and he took out little beams of different densities. 00:27:32.530 --> 00:27:35.420 And he measured the stiffness and the strength of the beams. 00:27:35.420 --> 00:27:39.100 So he measured the modulus of elasticity here versus density. 00:27:39.100 --> 00:27:41.550 And he measured the modulus of rupture here. 00:27:41.550 --> 00:27:43.410 And these are all along the grain. 00:27:43.410 --> 00:27:47.450 And he found that the Young's modulus varied with the density 00:27:47.450 --> 00:27:50.390 to the 2.5 power, and the strength 00:27:50.390 --> 00:27:53.020 varied as the density squared. 00:27:53.020 --> 00:27:53.810 And if the-- 00:27:53.810 --> 00:27:54.560 [BUZZING SOUND] 00:27:54.560 --> 00:27:55.110 Oh, hello. 00:27:55.110 --> 00:27:57.194 [LAUGHTER] 00:27:57.194 --> 00:27:59.110 So these were just sorts of empirical findings 00:27:59.110 --> 00:28:00.540 that he made. 00:28:00.540 --> 00:28:03.180 If you have prismatic cells and you deform them axially, 00:28:03.180 --> 00:28:07.110 and the cell wall was the same in the different specimens, 00:28:07.110 --> 00:28:09.260 then the solid modulus would be a constant. 00:28:09.260 --> 00:28:11.530 And you would expect that the modulus of the beam 00:28:11.530 --> 00:28:14.720 would go just linearly with the density, sort 00:28:14.720 --> 00:28:16.600 of like a honeycomb loaded [? at a ?] plane. 00:28:16.600 --> 00:28:20.000 But what he measured was that the modulus and the strength 00:28:20.000 --> 00:28:22.024 varied with some power of the density. 00:28:22.024 --> 00:28:23.440 And the reason for that really was 00:28:23.440 --> 00:28:27.760 that the cell walls of the denser material 00:28:27.760 --> 00:28:29.090 had more layers. 00:28:29.090 --> 00:28:32.214 And in the additional layers, the cellulose microfibular 00:28:32.214 --> 00:28:34.630 angle was probably different, so that the different layers 00:28:34.630 --> 00:28:36.230 had different stiffnesses. 00:28:36.230 --> 00:28:38.370 And if you have layers of differences, 00:28:38.370 --> 00:28:42.090 then you're going to get this power relationship. 00:28:42.090 --> 00:28:44.990 So what I then did was I took his data, 00:28:44.990 --> 00:28:48.190 and I tried to see how efficient that would be in bending. 00:28:48.190 --> 00:28:51.600 So he had found that the density varied with the radius raised 00:28:51.600 --> 00:28:52.300 to some power. 00:28:52.300 --> 00:28:54.550 This power n was 2, but I wanted to do it just 00:28:54.550 --> 00:28:56.760 for a general case, so I said I was just n. 00:28:56.760 --> 00:28:59.000 And he said that he found that the modulus varied 00:28:59.000 --> 00:29:02.392 with the density raised to some other power m. 00:29:02.392 --> 00:29:05.131 And for him, m was 2 and 1/2. 00:29:05.131 --> 00:29:06.880 And so I could write just another equation 00:29:06.880 --> 00:29:10.800 saying that the modulus goes as the radius to the mn power. 00:29:10.800 --> 00:29:12.550 And then you could do a little calculation 00:29:12.550 --> 00:29:14.884 where you work out with the equivalent flexural rigidity 00:29:14.884 --> 00:29:15.383 is. 00:29:15.383 --> 00:29:16.620 So you have to integrate up. 00:29:16.620 --> 00:29:18.370 You kind of say you have a little band 00:29:18.370 --> 00:29:19.400 at a certain radius. 00:29:19.400 --> 00:29:22.480 That radius has a certain modulus. 00:29:22.480 --> 00:29:24.360 And you can figure out the moment of inertia 00:29:24.360 --> 00:29:25.943 that goes with that particular radius. 00:29:25.943 --> 00:29:28.230 And then if you integrate it up over the whole thing, 00:29:28.230 --> 00:29:29.950 you can say that the flexural rigidity 00:29:29.950 --> 00:29:33.370 for the gradient density is some constant times 00:29:33.370 --> 00:29:36.640 pi times the outer radius to the fourth power divided 00:29:36.640 --> 00:29:39.370 by those two powers mn plus 4. 00:29:39.370 --> 00:29:41.310 So m was the power here for the modulus. 00:29:41.310 --> 00:29:43.826 And n was the power there for the density. 00:29:43.826 --> 00:29:46.200 And then you could compare that with having the same mass 00:29:46.200 --> 00:29:49.560 just uniformly distributed over the whole cross-section. 00:29:49.560 --> 00:29:53.060 And then if you take the ratio of the flexural rigidity 00:29:53.060 --> 00:29:56.630 for the density gradient versus the flexural rigidity 00:29:56.630 --> 00:29:59.390 for the uniform density, you can show 00:29:59.390 --> 00:30:01.240 that it's this equation here. 00:30:01.240 --> 00:30:03.510 And then if you plug in these measured values 00:30:03.510 --> 00:30:05.720 for those exponents for n and m, you 00:30:05.720 --> 00:30:09.270 find that the flexural rigidity with the gradient density 00:30:09.270 --> 00:30:12.400 relative to the uniform density is a factor of 2 and 1/2. 00:30:12.400 --> 00:30:14.560 So the stem is 2 and 1/2 times stiffer 00:30:14.560 --> 00:30:16.450 by having that density profile. 00:30:16.450 --> 00:30:18.670 So there's a huge sort of mechanical advantage 00:30:18.670 --> 00:30:19.580 to doing that. 00:30:19.580 --> 00:30:21.100 And just sort of physically, if you 00:30:21.100 --> 00:30:24.330 know the stresses our biggest on the outside, 00:30:24.330 --> 00:30:27.211 it would make sense to put the denser material on the outside. 00:30:27.211 --> 00:30:28.710 And then the other thing I looked at 00:30:28.710 --> 00:30:32.250 was the strength of the palm. 00:30:32.250 --> 00:30:34.640 So imagine this is our very schematic palm here, 00:30:34.640 --> 00:30:36.800 and then there's a circular cross section. 00:30:36.800 --> 00:30:39.270 So I wanted to compare the bending stress distribution 00:30:39.270 --> 00:30:41.650 with the bending strength distribution. 00:30:41.650 --> 00:30:45.625 So the stress goes as the modulus times the strain, 00:30:45.625 --> 00:30:47.100 just Hooke's law. 00:30:47.100 --> 00:30:50.650 And here we're assuming that plane sections remain plane, 00:30:50.650 --> 00:30:53.450 like that's the standard assumption of bending. 00:30:53.450 --> 00:30:55.730 So if you assume plane sections remain plane, 00:30:55.730 --> 00:30:59.140 then the strain goes with the curvature times the distance y 00:30:59.140 --> 00:31:01.460 from the neutral axis, the distance from the middle. 00:31:01.460 --> 00:31:03.585 So this distance here would be the dis-- [? same ?] 00:31:03.585 --> 00:31:05.390 at loaded with a loaded p here. 00:31:05.390 --> 00:31:07.404 That distance would be y there. 00:31:07.404 --> 00:31:09.070 And then I can plug in some things here. 00:31:09.070 --> 00:31:11.340 So instead of E, I'm going to plug-in my relationship 00:31:11.340 --> 00:31:14.060 with the radius to that mn power. 00:31:14.060 --> 00:31:15.920 And here's my curvature, and instead of y, 00:31:15.920 --> 00:31:17.420 if I say that some radius, I'm going 00:31:17.420 --> 00:31:19.840 to say y is our r cos theta. 00:31:19.840 --> 00:31:21.930 And so I'm going to say that the stress goes-- 00:31:21.930 --> 00:31:22.430 [SNEEZE] 00:31:22.430 --> 00:31:23.450 Bless you. 00:31:23.450 --> 00:31:27.430 Goes as radius raised to some power mn plus 1. 00:31:27.430 --> 00:31:30.380 And again, for the species I know what n and m are, 00:31:30.380 --> 00:31:34.280 so the stress goes as the radius to the sixth power. 00:31:34.280 --> 00:31:37.090 And then I can also compare with what Paul Rich had 00:31:37.090 --> 00:31:38.270 found for the strength. 00:31:38.270 --> 00:31:41.380 He found that the strength-- so sigma star is the strength-- 00:31:41.380 --> 00:31:44.320 was proportional to the density raised to some power q, 00:31:44.320 --> 00:31:48.600 and that power was 2 in the measurements that he made. 00:31:48.600 --> 00:31:50.550 And so I can say that the strength 00:31:50.550 --> 00:31:55.150 goes as the radius to this power nq, so to the fourth power. 00:31:55.150 --> 00:31:59.170 And then if I plot the stress distribution and the strength 00:31:59.170 --> 00:32:02.230 distribution-- so imagine, this is through the cross-section 00:32:02.230 --> 00:32:02.730 here. 00:32:02.730 --> 00:32:06.950 So this is the diameter of the stem. 00:32:06.950 --> 00:32:09.400 And this is the neutral axis here in the middle. 00:32:09.400 --> 00:32:15.280 The strength goes as that solid line there. 00:32:15.280 --> 00:32:17.380 It goes as the fourth power. 00:32:17.380 --> 00:32:19.490 And the stress goes as that dashed line there, 00:32:19.490 --> 00:32:21.160 as the sixth power. 00:32:21.160 --> 00:32:23.190 So they're not exactly on top of each other, 00:32:23.190 --> 00:32:25.430 but they're very close to being on top of each other. 00:32:25.430 --> 00:32:27.260 So basically what the palm has done 00:32:27.260 --> 00:32:29.850 is it's arranged the material in such a way 00:32:29.850 --> 00:32:32.040 that the strength matches the stresses that 00:32:32.040 --> 00:32:33.140 are applied to it. 00:32:33.140 --> 00:32:37.090 So if I just had a constant density, 00:32:37.090 --> 00:32:39.880 my stress profile would look like that. 00:32:39.880 --> 00:32:42.290 And if I had a constant density, the strength profile 00:32:42.290 --> 00:32:43.460 would kind of like that. 00:32:43.460 --> 00:32:46.220 So the strength here would be a constant, 00:32:46.220 --> 00:32:48.554 and this would be the stress here. 00:32:48.554 --> 00:32:50.470 So the stuff in the middle, it's much stronger 00:32:50.470 --> 00:32:51.460 than it needs to be. 00:32:51.460 --> 00:32:53.930 Whereas the palm has arranged things so that it's got 00:32:53.930 --> 00:32:57.890 just the right amount of strength for the stress, 00:32:57.890 --> 00:32:59.490 as a function of the radial position. 00:32:59.490 --> 00:33:01.130 So it's kind of a clever thing. 00:33:01.130 --> 00:33:03.180 So that's kind of a beautiful thing. 00:33:03.180 --> 00:33:04.850 And I think that is it. 00:33:04.850 --> 00:33:07.380 I think that's-- yeah, that's the end of it. 00:33:07.380 --> 00:33:11.260 So all these images came from this other book that we wrote. 00:33:11.260 --> 00:33:12.930 And if you wanted to get the sources, 00:33:12.930 --> 00:33:14.330 you could get them from there. 00:33:14.330 --> 00:33:16.470 So that all I wanted to talk about today 00:33:16.470 --> 00:33:20.130 was some examples of sort of efficient mechanical design 00:33:20.130 --> 00:33:22.940 in nature and the sandwich panel structures as one, 00:33:22.940 --> 00:33:26.230 and these radial density gradients is another. 00:33:26.230 --> 00:33:28.620 We have a project on bamboo right now, 00:33:28.620 --> 00:33:31.120 and the bamboo also has a radial density gradient, 00:33:31.120 --> 00:33:32.120 and it's the same thing. 00:33:32.120 --> 00:33:33.703 The densest material's on the outside, 00:33:33.703 --> 00:33:36.280 and the least dense is on the inside. 00:33:36.280 --> 00:33:39.750 So I think I'm going to stop there for today. 00:33:39.750 --> 00:33:41.790 So what I was going to do on Monday 00:33:41.790 --> 00:33:45.690 is talk a little bit about bio-mimicking. 00:33:45.690 --> 00:33:47.960 And that won't take the whole class at all. 00:33:47.960 --> 00:33:50.043 And I thought we could spend the rest of the class 00:33:50.043 --> 00:33:51.380 on Monday just doing a review. 00:33:51.380 --> 00:33:53.410 So the test's on Wednesday. 00:33:53.410 --> 00:33:55.050 So if you want to bring questions, 00:33:55.050 --> 00:33:58.020 that would be a beautiful thing. 00:33:58.020 --> 00:34:00.510 I can't really can I review the whole last six weeks 00:34:00.510 --> 00:34:03.390 or something in an hour and a half or something. 00:34:03.390 --> 00:34:05.430 So if you want to bring questions, I'll be here 00:34:05.430 --> 00:34:07.280 and we can just go over questions. 00:34:07.280 --> 00:34:09.310 Does that sound good?