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 --> 00:00:10.680 continue to offer high quality educational resources for free. 00:00:10.680 --> 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. 00:00:26.540 --> 00:00:29.100 LORNA GIBSON: All right, so last time we 00:00:29.100 --> 00:00:31.560 started talking about energy absorption, 00:00:31.560 --> 00:00:33.920 and I wanted to try to finish that up today. 00:00:33.920 --> 00:00:36.460 And then next week we would talk about sandwich panels 00:00:36.460 --> 00:00:39.990 and using honeycombs and foams in sandwich panels. 00:00:39.990 --> 00:00:42.140 So I think we got as far as the idea 00:00:42.140 --> 00:00:45.470 of introducing what these energy absorption diagrams are. 00:00:45.470 --> 00:00:48.180 So let me run through this little sequence again, 00:00:48.180 --> 00:00:50.480 and then I'll put the notes up on the board. 00:00:50.480 --> 00:00:54.350 So the idea is that you have your compressive stress strain 00:00:54.350 --> 00:00:57.140 curve-- so here's a series of curves for different densities 00:00:57.140 --> 00:00:58.230 of a foam. 00:00:58.230 --> 00:01:00.500 And we would do these all at the same strain 00:01:00.500 --> 00:01:03.170 rate and temperature, so that those aren't variables. 00:01:03.170 --> 00:01:06.370 And then what we would do is we could turn those into energy 00:01:06.370 --> 00:01:07.720 absorption diagrams. 00:01:07.720 --> 00:01:10.200 So notice here, this is a log plot. 00:01:10.200 --> 00:01:12.250 So here's that energy absorption here. 00:01:12.250 --> 00:01:14.650 Here's the peak stress here-- so that's 00:01:14.650 --> 00:01:18.620 the peak stress up to some level of energy that you've absorbed. 00:01:18.620 --> 00:01:22.470 And we've normalized both of those by the solid modulus. 00:01:22.470 --> 00:01:25.160 So say we look at one density here, say we look at the lowest 00:01:25.160 --> 00:01:26.540 density-- 0.01. 00:01:26.540 --> 00:01:30.410 So here's our curve here for the test. 00:01:30.410 --> 00:01:33.000 If I go up to some stress level that's 00:01:33.000 --> 00:01:35.120 still in the linear elastic region, 00:01:35.120 --> 00:01:38.570 then that's going to translate into somewhere along here 00:01:38.570 --> 00:01:40.165 on the energy absorption curve. 00:01:40.165 --> 00:01:41.540 And one of the things we're going 00:01:41.540 --> 00:01:43.850 to do today-- I'm going to show you how you draw these, 00:01:43.850 --> 00:01:46.410 and how you can set them up. 00:01:46.410 --> 00:01:48.810 And you can either get them from experiments-- 00:01:48.810 --> 00:01:52.290 so this is, say the top curve were experiments, doing it 00:01:52.290 --> 00:01:57.020 from experiments-- or you can use the models for the foams 00:01:57.020 --> 00:01:57.930 to do it, as well. 00:01:57.930 --> 00:02:00.150 So we'll see how you can do from both ways. 00:02:00.150 --> 00:02:02.150 So this would be the linear elastic bit here. 00:02:02.150 --> 00:02:04.720 This vertical part-- where the energy is increasing, 00:02:04.720 --> 00:02:07.050 but the peak stress isn't increasing-- that corresponds 00:02:07.050 --> 00:02:08.940 to the plateau here. 00:02:08.940 --> 00:02:11.700 And then this part here, where the energy is not 00:02:11.700 --> 00:02:13.670 increasing very much, but the stress increases 00:02:13.670 --> 00:02:18.010 a lot-- that corresponds to the densification part over there. 00:02:18.010 --> 00:02:20.330 So what you would do is you would do tests 00:02:20.330 --> 00:02:23.340 on foams of different densities, and from the test data, 00:02:23.340 --> 00:02:25.170 you could draw an energy absorption 00:02:25.170 --> 00:02:27.150 curve for each density. 00:02:27.150 --> 00:02:29.590 So you plot-- there's four different densities here, 00:02:29.590 --> 00:02:32.446 so it forms a family of these curves. 00:02:32.446 --> 00:02:33.820 And then what you do is you say-- 00:02:33.820 --> 00:02:35.810 and I think we talked with this last time-- 00:02:35.810 --> 00:02:38.630 that the place you want to be is at this shoulder point. 00:02:38.630 --> 00:02:41.770 You want to be absorbing as much energy as possible 00:02:41.770 --> 00:02:43.344 at that plateau stress. 00:02:43.344 --> 00:02:45.760 So you want to be at the point just before it turns around 00:02:45.760 --> 00:02:47.730 to the densification regime. 00:02:47.730 --> 00:02:50.330 So you can mark that little shoulder point 00:02:50.330 --> 00:02:51.130 for each density. 00:02:51.130 --> 00:02:54.390 So here's like 0.01, here's 0.03, and so on. 00:02:54.390 --> 00:02:57.320 And then those points can be connected by a line-- 00:02:57.320 --> 00:03:00.470 so that heavy line then connects those shoulder points, 00:03:00.470 --> 00:03:02.350 or those optimum points. 00:03:02.350 --> 00:03:06.010 And then what you can do is then repeat this whole process 00:03:06.010 --> 00:03:07.670 for different strain rates. 00:03:07.670 --> 00:03:11.260 So this family of lines here is at different strain rates-- 00:03:11.260 --> 00:03:15.166 so this set that goes this way, corresponds to this line here. 00:03:15.166 --> 00:03:17.040 And if you do them at different strain rates, 00:03:17.040 --> 00:03:20.730 where the shoulder appears at a slightly different point-- 00:03:20.730 --> 00:03:22.900 and so if you mark those shorter points, 00:03:22.900 --> 00:03:25.690 you can draw these lines here that connect up 00:03:25.690 --> 00:03:27.680 for one relative density. 00:03:27.680 --> 00:03:30.820 So this line on the left hand side here, 00:03:30.820 --> 00:03:33.450 these are all relative densities of 0.01, 00:03:33.450 --> 00:03:36.020 these ones are all relative densities of 0.03. 00:03:36.020 --> 00:03:38.800 So this diagram down here, doesn't really 00:03:38.800 --> 00:03:40.360 look like this at all-- it doesn't 00:03:40.360 --> 00:03:42.990 look like the basic energy absorption diagram. 00:03:42.990 --> 00:03:44.950 But it actually has information for what 00:03:44.950 --> 00:03:47.620 the optimum would be for a range of densities 00:03:47.620 --> 00:03:49.700 and a range of strain rates. 00:03:49.700 --> 00:03:52.500 So typically, these foams are viscoelastic 00:03:52.500 --> 00:03:54.300 and they have some strain rate sensitivity. 00:03:54.300 --> 00:03:57.200 So you'd like to get the strain rate sensitivity into it. 00:03:57.200 --> 00:03:58.870 And it's not shown here, but you could 00:03:58.870 --> 00:04:00.840 do the same thing at a constant strain rate 00:04:00.840 --> 00:04:02.240 and varying the temperature, too. 00:04:02.240 --> 00:04:04.198 So if you had things at different temperatures, 00:04:04.198 --> 00:04:05.910 you could do the same kind of idea. 00:04:05.910 --> 00:04:08.730 OK-- so are we good with how this works? 00:04:08.730 --> 00:04:11.140 Because now I'm going to write some notes on the board 00:04:11.140 --> 00:04:13.335 so you have it in your notes. 00:04:37.560 --> 00:04:41.300 So the idea is that you turn your stress strain curve 00:04:41.300 --> 00:04:44.860 to look something like that, into an energy absorption 00:04:44.860 --> 00:04:46.070 diagram. 00:04:46.070 --> 00:04:56.130 And you can plot on log log scales, the energy 00:04:56.130 --> 00:04:57.520 versus the peak stress. 00:04:57.520 --> 00:04:59.380 And you get something like that. 00:04:59.380 --> 00:05:02.666 And this point here, I'm going to call the shoulder point. 00:05:07.970 --> 00:05:10.920 And that would use the material in the most efficient way-- 00:05:10.920 --> 00:05:13.530 you get the most energy absorption without getting 00:05:13.530 --> 00:05:15.147 higher than that plateau stress. 00:05:18.490 --> 00:05:24.390 So we can say at this stress plateau, the energy increases 00:05:24.390 --> 00:05:26.345 without much increase in the peak stress. 00:05:44.670 --> 00:05:50.680 And then as the foam densifies, then you 00:05:50.680 --> 00:05:56.010 get an increase in that peak stress, 00:05:56.010 --> 00:05:58.190 with little increase in the energy absorbed. 00:06:07.890 --> 00:06:10.210 And so ideally, you want to be at that shoulder point. 00:06:25.350 --> 00:06:28.160 So to construct these energy diagrams, 00:06:28.160 --> 00:06:32.220 you can test the series of foams at different relative densities 00:06:32.220 --> 00:06:35.320 and constant strain rate and temperature. 00:06:56.140 --> 00:06:59.950 And then you make that plot of the energy absorbed 00:06:59.950 --> 00:07:06.170 normalized by the solid modulus, versus the peak stress 00:07:06.170 --> 00:07:09.020 normalized by the solid modulus for each curve. 00:07:14.880 --> 00:07:17.720 And typically what people do is they would take 00:07:17.720 --> 00:07:22.776 the solid modulus at a constant strain rate and temperature, 00:07:22.776 --> 00:07:24.651 so you don't have to introduce that, as well. 00:07:34.054 --> 00:07:36.470 Then you would mark the density for each of those shoulder 00:07:36.470 --> 00:07:41.010 points, and then you would connect them. 00:07:53.070 --> 00:07:55.000 And then you could repeat this whole process 00:07:55.000 --> 00:07:56.320 for different strain rates. 00:08:06.360 --> 00:08:08.870 And then you would draw the final diagram 00:08:08.870 --> 00:08:11.390 at the bottom, where you have this family of lines that 00:08:11.390 --> 00:08:14.486 describes the shoulder points for different densities 00:08:14.486 --> 00:08:15.610 and different strain rates. 00:08:45.542 --> 00:08:48.000 And you could treat different temperatures in the same way, 00:08:48.000 --> 00:08:48.790 if you wanted to. 00:08:48.790 --> 00:08:50.456 You would hold the strain rate constant, 00:08:50.456 --> 00:08:53.240 and vary the temperature. 00:08:53.240 --> 00:08:54.990 so it's kind of a nice way of just putting 00:08:54.990 --> 00:08:56.490 a lot of information in one diagram. 00:08:58.780 --> 00:09:00.900 So one of the things about this is 00:09:00.900 --> 00:09:04.240 that, because we're normalizing by Es, 00:09:04.240 --> 00:09:08.210 and if you think of elastomeric foams, elastomeric foams, 00:09:08.210 --> 00:09:10.960 both the Young's modulus depends on Es, 00:09:10.960 --> 00:09:13.500 and the plateau stress depends Es. 00:09:13.500 --> 00:09:16.290 So the Young's modulus depends on the stiffness of the solid, 00:09:16.290 --> 00:09:18.155 and also because the plateau stress 00:09:18.155 --> 00:09:20.200 is related to elastic buckling, it also 00:09:20.200 --> 00:09:22.820 depends on the modulus of the solid. 00:09:22.820 --> 00:09:27.010 So for elastomeric foams-- it's because you normalized it 00:09:27.010 --> 00:09:29.690 with respect to Es-- one of these diagrams 00:09:29.690 --> 00:09:32.487 will represent all elastomeric foams. 00:09:32.487 --> 00:09:34.070 So that's rather a nice thing-- so you 00:09:34.070 --> 00:09:35.960 can have different elastomeric foams, 00:09:35.960 --> 00:09:38.550 but one of those diagrams is going to represent all of them. 00:09:46.640 --> 00:09:49.730 So we can say, elastomeric foams can all 00:09:49.730 --> 00:09:53.030 be plotted on one plot, or one curve, 00:09:53.030 --> 00:09:55.275 since both the modulus and the plateau stress 00:09:55.275 --> 00:09:56.495 are related to Es. 00:10:38.390 --> 00:10:40.962 So if we look at this next figure here-- 00:10:40.962 --> 00:10:43.336 maybe I'll just wait a minute for people to stop writing. 00:10:50.060 --> 00:10:51.601 Some people write faster than others. 00:11:00.140 --> 00:11:02.230 So if we look at this next plot here, 00:11:02.230 --> 00:11:04.770 here's a compressive stress and strain. 00:11:04.770 --> 00:11:06.450 These tests are done for one density, 00:11:06.450 --> 00:11:08.283 but at different strain rates-- so it's kind 00:11:08.283 --> 00:11:10.170 of the other version of this. 00:11:10.170 --> 00:11:12.370 But here's the stress strain curves here, 00:11:12.370 --> 00:11:14.830 and here's the energy absorption diagram that's 00:11:14.830 --> 00:11:16.260 derived from those. 00:11:16.260 --> 00:11:19.580 And then here's a summary diagram 00:11:19.580 --> 00:11:22.210 that has the different strain rates, and that would 00:11:22.210 --> 00:11:24.130 have different densities here. 00:11:24.130 --> 00:11:26.220 And the idea is this diagram here 00:11:26.220 --> 00:11:28.870 could represent all elastomeric foams. 00:11:28.870 --> 00:11:31.090 So this has been put together for polyurethane, 00:11:31.090 --> 00:11:34.210 but it should be able to represent other sorts 00:11:34.210 --> 00:11:40.980 of flexible elastomeric foams. 00:11:40.980 --> 00:11:41.994 Sorry? 00:11:41.994 --> 00:11:44.602 AUDIENCE: In those diagrams, then, 00:11:44.602 --> 00:11:46.320 the intersection of this strain rate 00:11:46.320 --> 00:11:48.350 line and your relative density line 00:11:48.350 --> 00:11:50.330 should be the shoulder position? 00:11:50.330 --> 00:11:51.590 LORNA GIBSON: Yeah, exactly. 00:11:51.590 --> 00:11:56.520 And so this line here is for 0.01, and that one's for 0.03. 00:11:56.520 --> 00:11:58.370 So 0.02 is going to be-- you'd have 00:11:58.370 --> 00:12:01.530 to interpolate somewhere in between there. 00:12:01.530 --> 00:12:03.586 So we've just put on certain values, 00:12:03.586 --> 00:12:05.710 because we're not going to put on a million values. 00:12:05.710 --> 00:12:09.700 We just put on certain ones, and then you 00:12:09.700 --> 00:12:11.820 can estimate where other densities would 00:12:11.820 --> 00:12:12.840 appear on there. 00:12:12.840 --> 00:12:14.710 OK? 00:12:14.710 --> 00:12:17.430 So here's another example here-- these are 00:12:17.430 --> 00:12:19.020 curves for two different foams. 00:12:19.020 --> 00:12:21.130 So here's a polyurethane a polyethylene, 00:12:21.130 --> 00:12:22.790 so these are both elastomers. 00:12:22.790 --> 00:12:25.690 And one is the dashed line, and one is the solid line. 00:12:25.690 --> 00:12:28.530 And you can kind of see how the lines mesh up. 00:12:28.530 --> 00:12:32.970 So here's a density of 0.01 for the polyurethane. 00:12:32.970 --> 00:12:35.760 Here's 0.05 for the polyurethane. 00:12:35.760 --> 00:12:38.250 And here's 0.06 for the polyethylene. 00:12:38.250 --> 00:12:40.460 And you can see how the 0.06 and 0.05-- 00:12:40.460 --> 00:12:42.220 they're not quite on top of each other, 00:12:42.220 --> 00:12:44.553 but they're pretty close to coming on top of each other. 00:12:44.553 --> 00:12:47.910 And then 0.1, 0.12-- and so you get a family of them 00:12:47.910 --> 00:12:50.480 for the different densities. 00:12:50.480 --> 00:12:53.150 And you can also do this for materials 00:12:53.150 --> 00:12:56.500 that have a yield point, so polymethacrylimid has a yield 00:12:56.500 --> 00:12:59.940 point, so you do exactly the same kind of thing. 00:12:59.940 --> 00:13:01.840 So here's the energy absorption diagram 00:13:01.840 --> 00:13:04.480 that's been developed from the stress strain curves. 00:13:04.480 --> 00:13:07.870 But now this curve here, or this set of curves here, 00:13:07.870 --> 00:13:11.740 is really just valid for one ratio of sigma [? ys ?] 00:13:11.740 --> 00:13:15.996 to Es-- so the solid yield strength of the solid modulus. 00:13:15.996 --> 00:13:17.370 So it's valid for whatever it was 00:13:17.370 --> 00:13:24.230 for that particular type of foam-- the polymethacrylimid. 00:13:28.330 --> 00:13:35.200 So I'll just say, if we have foams 00:13:35.200 --> 00:13:37.846 that are made from a material with a yield point-- 00:13:37.846 --> 00:13:43.220 and so they have a plastic collapse stress-- then 00:13:43.220 --> 00:13:53.450 the curve will be valid for foams 00:13:53.450 --> 00:13:55.790 with the same ratio of [? sigma ys ?] to Es. 00:14:06.210 --> 00:14:09.730 So in that case there, for the polymethacrylimid, 00:14:09.730 --> 00:14:14.230 that ratio is about equal to 1 over 30. 00:14:14.230 --> 00:14:17.660 So that plot would probably give not a bad description 00:14:17.660 --> 00:14:24.860 of other foams, with the same value of sigma ys over Es. 00:14:24.860 --> 00:14:26.490 So the idea here is we can generate 00:14:26.490 --> 00:14:30.379 these diagrams either from data-- the way 00:14:30.379 --> 00:14:32.337 those ones have been done-- or from the models. 00:15:35.410 --> 00:15:39.130 So another way to generate these is to think about the models 00:15:39.130 --> 00:15:41.674 that we have for the foams, and the foam behavior. 00:15:41.674 --> 00:15:44.090 So we have an equation that describes the Young's modulus, 00:15:44.090 --> 00:15:46.880 we have equations that describe the plateau stresses, 00:15:46.880 --> 00:15:50.570 we have an empirical equation for the densification strain. 00:15:50.570 --> 00:15:53.500 And we can use those to generate these diagrams. 00:15:53.500 --> 00:15:55.180 And they're kind of useful, because they 00:15:55.180 --> 00:15:59.320 show you what's going on a sort of mechanistic basis. 00:15:59.320 --> 00:16:02.590 So this is a diagram here that's been generated for open cell 00:16:02.590 --> 00:16:04.140 elastomeric foams. 00:16:04.140 --> 00:16:06.050 Here's our energy absorbed, here's 00:16:06.050 --> 00:16:07.870 our peak stress down here. 00:16:07.870 --> 00:16:11.650 This little inset is sort of a schematic of the idealized foam 00:16:11.650 --> 00:16:12.150 behavior. 00:16:12.150 --> 00:16:13.790 So here's the Young's modulus, here's 00:16:13.790 --> 00:16:15.580 the elastic [? collapse ?] stress, here's 00:16:15.580 --> 00:16:17.770 the densification over here. 00:16:17.770 --> 00:16:21.480 So obviously it's kind of a very idealized set-up. 00:16:21.480 --> 00:16:23.274 But we can generate this diagram-- 00:16:23.274 --> 00:16:25.190 and I'm going to go through the equations that 00:16:25.190 --> 00:16:26.860 will let us do that. 00:16:26.860 --> 00:16:32.260 So one thing to note is here's the curves for each density. 00:16:32.260 --> 00:16:35.340 Here is this line that connects the shoulder points. 00:16:35.340 --> 00:16:37.050 There's a couple of other lines on here 00:16:37.050 --> 00:16:39.550 that I just wanted to mention something about. 00:16:39.550 --> 00:16:42.240 If you think about the densities-- like that's 0.01, 00:16:42.240 --> 00:16:44.430 this is 0.03, that's 0.1-- if you 00:16:44.430 --> 00:16:48.540 had a fully dense solid that was made of the same elastomer, 00:16:48.540 --> 00:16:51.040 you could plot the curve for that, 00:16:51.040 --> 00:16:52.890 and that is going to show up over here. 00:16:52.890 --> 00:16:54.580 So this is kind of an upper bound. 00:16:54.580 --> 00:16:57.520 It can't get any more from that. 00:16:57.520 --> 00:17:01.030 And we've also got a dotted line here, 00:17:01.030 --> 00:17:03.870 which takes into account fluid flow within the cells. 00:17:03.870 --> 00:17:05.901 So there can be some fluid flow, and because we 00:17:05.901 --> 00:17:08.359 haven't talked about that, we're not going to go into that. 00:17:08.359 --> 00:17:10.619 So we can just ignore that dotted line for now. 00:17:13.380 --> 00:17:18.690 So let me go through how we can do the modeling. 00:17:18.690 --> 00:17:21.030 So we're going to divide the stress strain curve up 00:17:21.030 --> 00:17:23.530 into bits, and I'm going to write equations 00:17:23.530 --> 00:17:26.300 for the energy absorbed for each bit. 00:17:26.300 --> 00:17:30.102 So we're going to start with a linear elastic behavior. 00:17:33.030 --> 00:17:37.860 And I'm going to-- let's see-- yeah, 00:17:37.860 --> 00:17:41.570 so let me just note here that this is the densification 00:17:41.570 --> 00:17:43.070 strain out here. 00:17:43.070 --> 00:17:45.650 And this strain, epsilon naught, corresponds 00:17:45.650 --> 00:17:48.870 to the strain at which we first reach the stress plateau. 00:17:48.870 --> 00:17:51.600 So here, for the linear elastic part, 00:17:51.600 --> 00:17:55.670 I'm going to say that the strain is less than that. 00:17:55.670 --> 00:17:57.940 So the strain is less than absolute naught. 00:17:57.940 --> 00:18:02.200 And then I can say, the energy absorbed-- 00:18:02.200 --> 00:18:03.700 so if you just remember from Hooke's 00:18:03.700 --> 00:18:06.830 law on linear elasticity, energy under the stress strain 00:18:06.830 --> 00:18:08.360 curve for the linear elastic part 00:18:08.360 --> 00:18:11.810 is 1/2 of sigma squared over E. So I'm 00:18:11.810 --> 00:18:14.510 going to call sigma-- whatever the stress is going to be, 00:18:14.510 --> 00:18:16.510 the peak stress that we get to. 00:18:16.510 --> 00:18:18.980 And now we're going to divide by E of the foam-- 00:18:18.980 --> 00:18:21.100 because these were our foams here. 00:18:21.100 --> 00:18:30.070 And I can use our model here to say-- 00:18:30.070 --> 00:18:31.740 and now I've got to divide that by Es, 00:18:31.740 --> 00:18:33.220 because I've normalized here. 00:18:40.680 --> 00:18:42.830 So because I know from my modeling 00:18:42.830 --> 00:18:44.850 that the Young's modulus of the foam 00:18:44.850 --> 00:18:47.500 is just equal to Es times the relative density squared 00:18:47.500 --> 00:18:49.390 for the open celled foam, that means 00:18:49.390 --> 00:18:52.230 I've now got an Es squared in the denominator, 00:18:52.230 --> 00:18:54.310 so I've got a sigma p over Es squared. 00:18:54.310 --> 00:18:59.790 And then I've got a 1 over the relative density squared term. 00:18:59.790 --> 00:19:04.610 So that factor there, that equation there, 00:19:04.610 --> 00:19:07.340 gives you these first set of lines here. 00:19:07.340 --> 00:19:10.370 Gives you that bit, and this bit, and that bit. 00:19:10.370 --> 00:19:13.143 So it gives you those first parts of the energy absorption 00:19:13.143 --> 00:19:13.643 diagram. 00:19:21.410 --> 00:19:23.810 And then if we look at the stress plateau-- 00:19:23.810 --> 00:19:27.300 so here we're going to say that epsilon naught is less 00:19:27.300 --> 00:19:30.940 than epsilon is less than the densification strain-- 00:19:30.940 --> 00:19:33.420 so we're on the plateau somewhere. 00:19:33.420 --> 00:19:36.560 And now the energy absorbed is just 00:19:36.560 --> 00:19:40.320 going to be our plateau stress times the amount of strain 00:19:40.320 --> 00:19:43.360 we've got. 00:19:43.360 --> 00:19:46.290 So that's epsilon minus epsilon naught. 00:19:46.290 --> 00:19:50.080 And if I normalized with respect the solid modulus, 00:19:50.080 --> 00:19:59.300 I can write down that my plateau stress is 0.05 times 00:19:59.300 --> 00:20:01.510 the relative density squared, and then 00:20:01.510 --> 00:20:05.125 multiply that times epsilon minus epsilon naught. 00:20:08.900 --> 00:20:11.000 So that equation then corresponds 00:20:11.000 --> 00:20:14.510 to these vertical parts-- so this part here, that part 00:20:14.510 --> 00:20:16.090 there, this part here. 00:20:16.090 --> 00:20:19.070 It corresponds to those vertical lines on the figure. 00:20:34.020 --> 00:20:36.090 Vertical lines on the diagram. 00:20:36.090 --> 00:20:38.110 And then the plateau stress is going 00:20:38.110 --> 00:20:40.490 to end at the densification strain. 00:20:45.830 --> 00:20:47.753 And at that point, the energy diagram 00:20:47.753 --> 00:20:49.128 is just going to become vertical. 00:21:37.120 --> 00:21:39.114 OK, and then the last part-- I'll 00:21:39.114 --> 00:21:40.613 try to rub this off a little better. 00:21:47.130 --> 00:21:48.870 And then the last part is when we're 00:21:48.870 --> 00:22:01.930 at the end of this stress plateau, 00:22:01.930 --> 00:22:06.180 and the strain is equal to that densification strain. 00:22:06.180 --> 00:22:08.360 And so the amount of energy we absorb here 00:22:08.360 --> 00:22:09.776 is really going to be the maximum. 00:22:35.504 --> 00:22:36.920 So this is the energy that's going 00:22:36.920 --> 00:22:38.740 to correspond to that shoulder point 00:22:38.740 --> 00:22:40.790 that I've been talking about. 00:22:40.790 --> 00:22:46.360 So I'm going to call that W max, and normalize that with respect 00:22:46.360 --> 00:22:47.810 to Es. 00:22:47.810 --> 00:22:52.800 And that's then going to be our plateau stress 00:22:52.800 --> 00:22:56.960 times the densification strain. 00:22:56.960 --> 00:23:02.246 And the densification strain was just 1 minus 1.4 times 00:23:02.246 --> 00:23:03.120 the relative density. 00:23:11.330 --> 00:23:17.780 So here I'm assuming that the densification strain 00:23:17.780 --> 00:23:20.580 is very much bigger than the strain at which 00:23:20.580 --> 00:23:23.000 the buckling first occurs, and I'm neglecting 00:23:23.000 --> 00:23:24.415 that linear elastic part. 00:23:34.800 --> 00:23:39.890 So then we could say that the optimum foam 00:23:39.890 --> 00:23:41.860 is at that shoulder point. 00:23:54.880 --> 00:23:57.020 And I can say that the peak stress at that point 00:23:57.020 --> 00:23:58.933 is just equal to the plateau stress. 00:24:03.370 --> 00:24:08.590 And what I want to do is get an equation for that solid line 00:24:08.590 --> 00:24:11.430 up here that connects all those shoulder points. 00:24:11.430 --> 00:24:13.780 So I want an equation, in terms of the energy, 00:24:13.780 --> 00:24:16.700 and the peak stress, instead of in terms of the density. 00:24:16.700 --> 00:24:19.130 So what I'm going to do a solve this for the density, 00:24:19.130 --> 00:24:20.867 and then plug that back into there. 00:24:34.287 --> 00:24:36.120 So I get that the relative density is, then, 00:24:36.120 --> 00:24:40.067 20 times the peak stress over the solid modulus, 00:24:40.067 --> 00:24:41.525 and I take the square root of that. 00:24:49.600 --> 00:24:54.612 And now I can substitute this up here for the relative density. 00:24:54.612 --> 00:24:55.820 I think I need another board. 00:25:29.710 --> 00:25:32.680 So then I've got-- this is my peak stress, or my plateau 00:25:32.680 --> 00:25:39.670 stress, over Es, and this is all just the densification strain. 00:25:39.670 --> 00:25:42.454 And that's just 1 minus 1.4 times the relative density. 00:25:42.454 --> 00:25:44.120 But now I'm putting the relative density 00:25:44.120 --> 00:25:47.085 in terms of the peak stress, or the plateau stress. 00:25:57.290 --> 00:26:00.830 If I just simplify that slightly with the constant, 00:26:00.830 --> 00:26:08.312 it's 1 minus 6.26 times sigma p over Es to the 1/2 power. 00:26:11.930 --> 00:26:18.270 So that equation there describes the-- oops, no more updates. 00:26:18.270 --> 00:26:19.390 No updates. 00:26:19.390 --> 00:26:21.494 Go away. 00:26:21.494 --> 00:26:25.870 Ah, so that equation there describes this line here that 00:26:25.870 --> 00:26:28.367 connects those shoulder points. 00:26:28.367 --> 00:26:30.450 And that's the line you're the most interested in, 00:26:30.450 --> 00:26:32.250 because each of those shoulder points 00:26:32.250 --> 00:26:34.100 is a point where the foam is being 00:26:34.100 --> 00:26:37.355 used in the most efficient way, or the optimum way. 00:26:48.509 --> 00:26:50.300 And then, let's see-- is that going to fit? 00:26:50.300 --> 00:26:51.714 No-- let me try the other board. 00:26:55.505 --> 00:26:56.880 And then the last thing we can do 00:26:56.880 --> 00:26:59.910 is calculate that line that corresponds to the dense solid. 00:26:59.910 --> 00:27:02.072 Yeah? 00:27:02.072 --> 00:27:04.055 AUDIENCE: On those ones over there, 00:27:04.055 --> 00:27:06.554 it says it corresponds to the vertical lines on the diagram. 00:27:06.554 --> 00:27:08.554 And then later it says then it becomes vertical. 00:27:08.554 --> 00:27:11.050 Is that referring to two different diagrams? 00:27:11.050 --> 00:27:14.020 LORNA GIBSON: So this stress plateau equation 00:27:14.020 --> 00:27:18.320 here corresponds to these vertical lines here. 00:27:18.320 --> 00:27:23.220 So for relative density of 0.01, it corresponds to that part. 00:27:23.220 --> 00:27:25.340 For 0.03 it's this part. 00:27:25.340 --> 00:27:27.560 And your 0.01 it's that part. 00:27:27.560 --> 00:27:29.522 AUDIENCE: But then some of the [INAUDIBLE] 00:27:29.522 --> 00:27:32.246 it says, then w [? versus ?] sigma becomes vertical. 00:27:32.246 --> 00:27:33.400 Should that-- 00:27:33.400 --> 00:27:35.120 LORNA GIBSON: So, well the plateau stress 00:27:35.120 --> 00:27:36.920 ends at the densification strain. 00:27:36.920 --> 00:27:39.200 So the plateau stress ends here. 00:27:39.200 --> 00:27:41.810 Oh, let's see-- and then it becomes-- should be horizontal. 00:27:41.810 --> 00:27:42.310 Sorry. 00:27:56.850 --> 00:27:58.140 OK, sorry. 00:27:58.140 --> 00:27:58.640 Happy? 00:28:01.657 --> 00:28:03.240 And now I'm going to rub that all off. 00:28:15.230 --> 00:28:16.560 OK, did everybody get this? 00:28:16.560 --> 00:28:17.268 I can rub it off? 00:28:36.050 --> 00:28:45.350 OK, so then the last part is what happens 00:28:45.350 --> 00:28:48.540 when the foam is densified. 00:28:48.540 --> 00:28:50.540 And if it was fully dense-- and you never really 00:28:50.540 --> 00:28:52.200 can get to this point-- but if it was fully dense, 00:28:52.200 --> 00:28:53.658 you would get rid of all the pores, 00:28:53.658 --> 00:28:55.040 and it would just be a solid. 00:28:55.040 --> 00:28:56.750 And then the energy absorption curve 00:28:56.750 --> 00:29:00.200 would be the curve for the solid. 00:29:00.200 --> 00:29:09.142 So I'll just say, when fully densified, 00:29:09.142 --> 00:29:13.095 I'm going to say a curve approaches that for the solid. 00:29:19.450 --> 00:29:24.695 And for the solid, you would just have that W over Es 00:29:24.695 --> 00:29:29.885 is equal to 1/2 the peak stress squared over Es. 00:29:33.410 --> 00:29:36.650 So this model curve, the curves have the same shape 00:29:36.650 --> 00:29:40.070 as when you get the diagrams from the experiments. 00:29:40.070 --> 00:29:42.190 And you can see how the different mechanisms 00:29:42.190 --> 00:29:45.422 of deformation and failure contribute to the diagram, 00:29:45.422 --> 00:29:46.630 where the diagram comes from. 00:29:48.884 --> 00:29:50.300 And I guess one other point is you 00:29:50.300 --> 00:29:53.120 can see that the foams are always going to be a lot better 00:29:53.120 --> 00:29:54.260 than the solid. 00:29:54.260 --> 00:29:56.050 And remember this is a log log curve, 00:29:56.050 --> 00:30:01.010 so that a foam that has a density of 3% here, there's 00:30:01.010 --> 00:30:03.460 a huge difference in the peak stress. 00:30:03.460 --> 00:30:07.740 So say you wanted to absorb this amount of energy up here, 00:30:07.740 --> 00:30:10.640 for a foam that was 0.03 dense, the peak stress 00:30:10.640 --> 00:30:13.900 would be a little less than 10 to the minus 4, 00:30:13.900 --> 00:30:15.520 normalized by the modulus. 00:30:15.520 --> 00:30:17.870 And for the solid, it would be 10 to the minus 2-- 00:30:17.870 --> 00:30:19.630 so it's orders of magnitude better to have 00:30:19.630 --> 00:30:23.040 the foam rather than the solid. 00:30:23.040 --> 00:30:27.030 All right, now let's see what else we have. 00:30:27.030 --> 00:30:29.890 So we could do a similar thing for closed-cell foams, 00:30:29.890 --> 00:30:32.066 and you get diagrams that look like this. 00:30:32.066 --> 00:30:34.440 One of the differences with the closed-cell foams, if you 00:30:34.440 --> 00:30:37.950 assume that the faces don't rupture, the plateau stresses 00:30:37.950 --> 00:30:41.160 and horizontals-- remember we had that gas contribution, 00:30:41.160 --> 00:30:43.270 and you can take that into account? 00:30:43.270 --> 00:30:46.410 So I'm not going to go over the details of that. 00:30:46.410 --> 00:30:47.960 The next one I wanted to talk about 00:30:47.960 --> 00:30:51.500 was looking at foams that have a yield point. 00:30:51.500 --> 00:30:54.200 And again, you can generate a similar kind of diagram, 00:30:54.200 --> 00:30:57.480 but now, instead of having an elastic failure here, 00:30:57.480 --> 00:31:00.810 you've got a plastic failure-- you form plastic hinges. 00:31:00.810 --> 00:31:02.670 And then again, this diagram is less 00:31:02.670 --> 00:31:06.000 general than the one for elastomeric foams, 00:31:06.000 --> 00:31:10.150 so this diagram would be valid for whatever ratio of sigma ys 00:31:10.150 --> 00:31:11.810 over Es you've the calculation for. 00:31:11.810 --> 00:31:14.730 So this one here is for 0.01. 00:31:14.730 --> 00:31:17.590 So let me just run through the same kind of calculation 00:31:17.590 --> 00:31:19.930 for the plastic foams. 00:31:25.414 --> 00:31:26.830 Can I rub this off, and then I can 00:31:26.830 --> 00:31:28.280 use this board to start here? 00:32:01.960 --> 00:32:07.980 OK, so the linear elastic part is just the same 00:32:07.980 --> 00:32:10.970 as for the elastomeric foams. 00:32:10.970 --> 00:32:16.956 So you get W over Es is 1/2. 00:32:16.956 --> 00:32:21.970 Sigma p over Es squared times 1 over the relative density 00:32:21.970 --> 00:32:24.700 squared, so it's just the same thing. 00:32:24.700 --> 00:32:34.370 And the stress plateau-- you get w over Es 00:32:34.370 --> 00:32:43.010 is just the plastic collapse strength times the strain range 00:32:43.010 --> 00:32:44.960 that you go up to. 00:32:44.960 --> 00:32:46.980 So if you remember the plastic collapse strength 00:32:46.980 --> 00:32:55.260 was 0.3 sigma ys times the relative density to the 3/2 00:32:55.260 --> 00:32:57.590 power, and then times the strain range. 00:33:06.820 --> 00:33:09.290 And then at the end of the stress plateau, 00:33:09.290 --> 00:33:13.310 you've got the maximum energy absorbed. 00:33:13.310 --> 00:33:16.420 So normalize that by Es. 00:33:16.420 --> 00:33:20.300 And that's going to be your peak stress over Es 00:33:20.300 --> 00:33:22.395 times the densification strain again. 00:33:26.870 --> 00:33:31.674 So this bit here is the densification strain. 00:33:37.000 --> 00:33:38.530 And then you can do a similar thing 00:33:38.530 --> 00:33:40.363 to figure out the equation of that line that 00:33:40.363 --> 00:33:41.590 joins the shoulder points. 00:34:04.220 --> 00:34:08.155 So the first step is to solve for the relative density there. 00:34:24.130 --> 00:34:27.810 So if this part here-- 0.3 sigma ys times the relative density 00:34:27.810 --> 00:34:31.719 to the 3/2 power is the plastic collapse stress, 00:34:31.719 --> 00:34:35.760 then at the densification point, the relative density, 00:34:35.760 --> 00:34:38.690 you just rewrite that and it comes out to the 2/3 power, 00:34:38.690 --> 00:34:40.580 because you turn the power around. 00:34:40.580 --> 00:34:42.870 And then you just substitute this up in here. 00:35:17.280 --> 00:35:20.070 So you get that the maximum energy absorbed, 00:35:20.070 --> 00:35:23.310 normalized by the solid modulus, is your peak stress, times 00:35:23.310 --> 00:35:27.290 1 minus 1.4 times this thing in brackets to the 2/3 power-- 00:35:27.290 --> 00:35:30.350 the 3.3 times the peak stress over the yield 00:35:30.350 --> 00:35:31.930 strength of the solid. 00:35:31.930 --> 00:35:40.830 And then if I just rearrange that, and get the constants, 00:35:40.830 --> 00:35:51.890 it's 1 minus 3.1 times our ratio of the stresses there. 00:35:57.060 --> 00:35:59.610 So maybe I'll just put over here-- 00:35:59.610 --> 00:36:04.465 the curves are less general than for elastomeric foams. 00:36:31.100 --> 00:36:33.280 So each family of curves would be 00:36:33.280 --> 00:36:36.400 for a particular ratio of the solid yield strength 00:36:36.400 --> 00:36:37.453 to the solid modulus. 00:37:22.590 --> 00:37:23.490 So you get the idea? 00:37:23.490 --> 00:37:25.880 It's fairly straightforward. 00:37:25.880 --> 00:37:27.690 So I wanted to finish up this topic 00:37:27.690 --> 00:37:31.280 by giving you a few examples of how you can use these curves. 00:37:31.280 --> 00:37:33.560 So the next thing is to look at the selection of foams 00:37:33.560 --> 00:37:35.080 for impact protection. 00:37:35.080 --> 00:37:37.750 And typically, you're given some information about the objects-- 00:37:37.750 --> 00:37:39.850 so typically you want to protect some object. 00:37:39.850 --> 00:37:42.230 It could be a computer, it could be your head, 00:37:42.230 --> 00:37:43.650 some part of your body. 00:37:43.650 --> 00:37:45.650 So typically you know something about the object 00:37:45.650 --> 00:37:46.680 you want to protect. 00:37:46.680 --> 00:37:50.350 So you might know its mass, you might know the area of contact, 00:37:50.350 --> 00:37:52.280 you might say, well, if it's my computer, 00:37:52.280 --> 00:37:53.890 I want to make sure it doesn't break if I drop it 00:37:53.890 --> 00:37:54.890 from a height of a meter. 00:37:54.890 --> 00:37:56.550 Or you could say whatever, [? maybe it's ?] 2 meters. 00:37:56.550 --> 00:37:58.010 But you pick something. 00:37:58.010 --> 00:37:59.820 And so there's a certain amount of energy 00:37:59.820 --> 00:38:01.410 you know that you need to absorb. 00:38:01.410 --> 00:38:04.310 And you may know that whatever the component is, 00:38:04.310 --> 00:38:06.280 or the body part, or whatever-- there's 00:38:06.280 --> 00:38:09.427 some maximum acceleration you can tolerate. 00:38:09.427 --> 00:38:11.010 So you might say, well, I want to make 00:38:11.010 --> 00:38:14.180 sure my computer doesn't break under acceleration of so much. 00:38:14.180 --> 00:38:16.399 So you're given the acceleration. 00:38:16.399 --> 00:38:18.440 And so if you know the mass and the acceleration, 00:38:18.440 --> 00:38:19.814 and you know the area of contact, 00:38:19.814 --> 00:38:22.300 you can figure out a force over an area, 00:38:22.300 --> 00:38:24.140 and that gives you the peak stress. 00:38:24.140 --> 00:38:26.940 So typically, you know those things in the problem. 00:38:26.940 --> 00:38:29.700 And typically the problem involves choosing a material, 00:38:29.700 --> 00:38:31.810 or choosing-- like choosing what kind of material 00:38:31.810 --> 00:38:34.390 do you want to make the foam out of, and what density of foam 00:38:34.390 --> 00:38:35.800 do you want to use, what thickness of foam 00:38:35.800 --> 00:38:36.810 do you want to use? 00:38:36.810 --> 00:38:38.830 So I've got a couple of examples just 00:38:38.830 --> 00:38:40.580 to show you how this works. 00:38:40.580 --> 00:38:43.094 So let me just write down a couple notes, and then 00:38:43.094 --> 00:38:45.677 the rest of it I think I'm just going to take from the slides. 00:39:09.140 --> 00:39:12.410 So typically, you know what it is you want to protect, 00:39:12.410 --> 00:39:13.850 and you know something about it. 00:39:20.714 --> 00:39:22.380 So if you know what it is, typically you 00:39:22.380 --> 00:39:23.557 know what the mass is. 00:39:28.700 --> 00:39:31.090 You might know what the contact area would be. 00:39:41.300 --> 00:39:49.279 Say a maximum drop height, maximum tolerable acceleration. 00:39:53.870 --> 00:39:55.750 So say if you're worried about brain injury-- 00:39:55.750 --> 00:39:59.230 and making a helmet-- you might know what the maximum tolerable 00:39:59.230 --> 00:40:00.482 acceleration would be. 00:40:06.870 --> 00:40:09.720 So typically, you know what the peak allowable stress is, just 00:40:09.720 --> 00:40:11.770 from whatever the object itself is. 00:40:11.770 --> 00:40:15.700 And the variables that you have to play around 00:40:15.700 --> 00:40:25.530 with-- variables-- are things like the foam material, 00:40:25.530 --> 00:40:28.965 the foam density, and the foam thickness. 00:40:32.420 --> 00:40:34.030 So I have a couple of examples that 00:40:34.030 --> 00:40:37.910 have different setups here. 00:40:37.910 --> 00:40:41.610 And we'll just see how the thing works out here. 00:40:41.610 --> 00:40:45.520 So the first example, we're told the mass of the packaged object 00:40:45.520 --> 00:40:47.210 is 1/2 kilogram. 00:40:47.210 --> 00:40:49.870 We're told the area of contact between the foam 00:40:49.870 --> 00:40:51.370 and the object is going to be point. 00:40:51.370 --> 00:40:53.190 0.01 of 1 meter squared. 00:40:53.190 --> 00:40:54.700 And we're told that it's supposed 00:40:54.700 --> 00:40:57.830 to be designed to withstand a drop of 1 meter-- 00:40:57.830 --> 00:40:59.790 so if the drop height is 1 meter, 00:40:59.790 --> 00:41:03.670 then the velocity is just the square root of 2gh. 00:41:03.670 --> 00:41:06.620 So g is gravity, so you can work out the velocity on impact 00:41:06.620 --> 00:41:09.184 would be 4.5 meters per second. 00:41:09.184 --> 00:41:11.350 And if you have the velocity on impact and the mass, 00:41:11.350 --> 00:41:13.387 you can figure out the energy to be absorbed. 00:41:13.387 --> 00:41:14.970 You can say mv squared screwed over 2, 00:41:14.970 --> 00:41:17.280 or you could say it's mgh-- either way. 00:41:17.280 --> 00:41:20.430 So here it's going to work out to 5 joules. 00:41:20.430 --> 00:41:25.100 And in this case, we're told that the maximum deceleration 00:41:25.100 --> 00:41:29.300 is 10g-- so then if that's 10g, the maximum force is the mass 00:41:29.300 --> 00:41:30.900 times the acceleration. 00:41:30.900 --> 00:41:32.920 That works out to 50 Newtons. 00:41:32.920 --> 00:41:34.800 And then that gives us a peak stress, 00:41:34.800 --> 00:41:36.240 the maximum allowable peak stress 00:41:36.240 --> 00:41:39.060 of the force over the area it's 5 kiloNewtons per meter 00:41:39.060 --> 00:41:40.270 squared. 00:41:40.270 --> 00:41:42.240 And in this case, we're told that the foam is 00:41:42.240 --> 00:41:44.400 going to be a flexible polyurethane, 00:41:44.400 --> 00:41:47.550 and it has a solid modulus of 50 megapascals. 00:41:47.550 --> 00:41:49.920 And so we can calculate this normalized peak stress. 00:41:49.920 --> 00:41:53.110 So the normalized peak stress here is 10 to the minus 4. 00:41:53.110 --> 00:41:56.350 So in this problem here, we need to figure out 00:41:56.350 --> 00:41:58.020 what's the foam density, and what's 00:41:58.020 --> 00:42:01.450 the thickness of the foam to protect the object? 00:42:01.450 --> 00:42:05.024 And so that last slide is just summarized here. 00:42:05.024 --> 00:42:07.190 And I realized that when I was going to put this up, 00:42:07.190 --> 00:42:08.773 the font is going to be kind of small, 00:42:08.773 --> 00:42:10.680 so I blew it up a little. 00:42:10.680 --> 00:42:12.980 So we have figured out that we're 00:42:12.980 --> 00:42:15.850 at sigma p over Es-- the peak stress normalized 00:42:15.850 --> 00:42:18.372 by the solid modulus is 10 to the minus 4. 00:42:18.372 --> 00:42:19.830 And we know that we're going to use 00:42:19.830 --> 00:42:22.840 a flexible elastomeric polyurethane, 00:42:22.840 --> 00:42:26.330 so we pull out our diagram for elastomeric foams. 00:42:26.330 --> 00:42:28.660 And this sort of hashed band here 00:42:28.660 --> 00:42:30.940 corresponds to all the different strain rates, and all 00:42:30.940 --> 00:42:31.990 the different densities. 00:42:31.990 --> 00:42:33.900 So I haven't plotted each individual line, 00:42:33.900 --> 00:42:37.970 we've just got this band that represents the whole thing. 00:42:37.970 --> 00:42:39.510 So we know that our normalized peak 00:42:39.510 --> 00:42:43.060 stress is going to be somewhere along this line here. 00:42:43.060 --> 00:42:44.620 That's from everything that's given, 00:42:44.620 --> 00:42:46.220 and what we can calculate. 00:42:46.220 --> 00:42:48.220 And we want to know what density of foam to use, 00:42:48.220 --> 00:42:49.610 and what thickness. 00:42:49.610 --> 00:42:52.300 So the way you approach this is the thickness 00:42:52.300 --> 00:42:53.759 is going to affect the strain rate. 00:42:53.759 --> 00:42:56.299 So the strain rate's just going to be the velocity on impact, 00:42:56.299 --> 00:42:58.590 divided by the thickness-- or it's an approximation 00:42:58.590 --> 00:42:59.960 for the strain rate. 00:42:59.960 --> 00:43:02.380 So we don't know if we're at this point down here, 00:43:02.380 --> 00:43:03.950 or if we're at this point up there, 00:43:03.950 --> 00:43:06.190 because we don't know where we are in the strain rate 00:43:06.190 --> 00:43:07.580 end of things. 00:43:07.580 --> 00:43:10.506 So the way you solve this is you just guess a thickness. 00:43:10.506 --> 00:43:11.880 And if you guess a thickness, you 00:43:11.880 --> 00:43:13.237 can calculate a strain rate. 00:43:13.237 --> 00:43:14.820 Then if you calculate the strain rate, 00:43:14.820 --> 00:43:16.650 you know where in this band you are. 00:43:16.650 --> 00:43:19.370 You can figure out a value of W over Es. 00:43:19.370 --> 00:43:21.970 And you can use an iterative process. 00:43:21.970 --> 00:43:23.690 And the way this is set up is we've 00:43:23.690 --> 00:43:27.090 chosen two very different initial thicknesses, 00:43:27.090 --> 00:43:29.130 and the point of doing that is to show you 00:43:29.130 --> 00:43:31.190 that it converges very quickly. 00:43:31.190 --> 00:43:33.410 So the first iteration on this side 00:43:33.410 --> 00:43:35.540 here, we've chosen the thickness of a meter, which 00:43:35.540 --> 00:43:38.590 is probably unlikely that we need a meter of foam. 00:43:38.590 --> 00:43:41.450 And on the side here, we've chosen a millimeter-- 0.001 00:43:41.450 --> 00:43:41.950 meters. 00:43:41.950 --> 00:43:43.620 So probably, we need more than that. 00:43:43.620 --> 00:43:45.078 So we probably need to be somewhere 00:43:45.078 --> 00:43:46.570 between those two bounds. 00:43:46.570 --> 00:43:49.600 So if the thickness was a meter, then the strain rate 00:43:49.600 --> 00:43:52.300 turns out to be 4.5 per second. 00:43:52.300 --> 00:43:54.940 And then we know where we are in this diagram, 00:43:54.940 --> 00:43:57.970 and we can read off a value of W over Es. 00:43:57.970 --> 00:44:00.350 So we know we're on this line here, 00:44:00.350 --> 00:44:02.220 and for a particular strain rate, 00:44:02.220 --> 00:44:04.580 we can read off the W over Es. 00:44:04.580 --> 00:44:08.660 So here's the value-- 5.25 times 10 to the minus 5. 00:44:08.660 --> 00:44:10.840 And if we know Es, which we do, we 00:44:10.840 --> 00:44:13.579 can then calculate the actual energy 00:44:13.579 --> 00:44:14.620 absorbed per unit volume. 00:44:14.620 --> 00:44:19.190 We get W-- so W is [? 2620 ?] joules per cubic meter. 00:44:19.190 --> 00:44:21.550 And we can use that value-- because that's 00:44:21.550 --> 00:44:24.904 an energy per unit volume-- we know the area of contact, 00:44:24.904 --> 00:44:27.320 and we can use that to get another value of the thickness. 00:44:27.320 --> 00:44:30.160 So we use that to calculate the next iteration 00:44:30.160 --> 00:44:31.580 of the thickness. 00:44:31.580 --> 00:44:34.190 So U is the total energy in joules, 00:44:34.190 --> 00:44:36.600 and W is the energy per unit volume. 00:44:36.600 --> 00:44:38.930 So U, the energy in joules, is going 00:44:38.930 --> 00:44:41.410 to equal the energy unit volume times the area 00:44:41.410 --> 00:44:42.746 times the thickness. 00:44:42.746 --> 00:44:44.120 So we know what the area is, too. 00:44:44.120 --> 00:44:46.270 We can then calculate a new thickness. 00:44:46.270 --> 00:44:49.320 So now our new thickness is 0.19 meters. 00:44:49.320 --> 00:44:50.790 We can use that to get a new strain 00:44:50.790 --> 00:44:53.790 rate-- that's 24 per second, and go through the whole thing 00:44:53.790 --> 00:44:54.390 again. 00:44:54.390 --> 00:44:58.320 And we end up with a revised energy of 3,300 joules 00:44:58.320 --> 00:45:00.032 per cubic meter. 00:45:00.032 --> 00:45:01.490 Now if we started at the other end, 00:45:01.490 --> 00:45:05.410 if we started with the first guess was a millimeter, then 00:45:05.410 --> 00:45:09.890 the strain rate is 4.5 times 10 to the minus 3 per second. 00:45:09.890 --> 00:45:12.270 That gives us a different value that we read off here 00:45:12.270 --> 00:45:15.780 for W over Es, and a different value for W. 00:45:15.780 --> 00:45:17.950 And then we use this value here for W 00:45:17.950 --> 00:45:20.230 to make another guess for the thickness. 00:45:20.230 --> 00:45:22.707 So that value is 0.14. 00:45:22.707 --> 00:45:24.290 And then we go through the whole thing 00:45:24.290 --> 00:45:27.580 again-- we get a revised strain rate a revised W over Es, 00:45:27.580 --> 00:45:31.510 and a revised W. And you can see after just two iterations, 00:45:31.510 --> 00:45:33.449 these two things are almost exactly the same. 00:45:33.449 --> 00:45:34.990 And then on the third iteration, they 00:45:34.990 --> 00:45:38.730 both would give you a thickness of point 0.15 meters. 00:45:38.730 --> 00:45:42.620 So even though you can pick wildly wrong first iterations, 00:45:42.620 --> 00:45:46.120 it converges very quickly, and it's a fairly simple 00:45:46.120 --> 00:45:48.310 calculation to do. 00:45:48.310 --> 00:45:51.210 So you know the thickness that you want is in here, 00:45:51.210 --> 00:45:54.180 and then you can get the optimum density here. 00:45:54.180 --> 00:45:58.540 So you know that your sigma p over Es is along this line 00:45:58.540 --> 00:46:00.970 of 10 to the minus 4--we're somewhere in here. 00:46:00.970 --> 00:46:03.210 These two strain rates here-- one was 24, 00:46:03.210 --> 00:46:06.400 one was 32-- so the final value is going 00:46:06.400 --> 00:46:08.210 to be somewhere around 30. 00:46:08.210 --> 00:46:10.550 And if you look on this thing here, 00:46:10.550 --> 00:46:12.830 you can see there's a line that corresponds to 10, 00:46:12.830 --> 00:46:14.624 there's a line that corresponds to 100. 00:46:14.624 --> 00:46:16.290 We're going to be right around in there. 00:46:16.290 --> 00:46:20.180 So the relative density is going to be right around 0.01. 00:46:20.180 --> 00:46:22.280 So you can use the diagram to get the thickness 00:46:22.280 --> 00:46:24.660 and to get the density. 00:46:24.660 --> 00:46:26.220 OK, are we good? 00:46:26.220 --> 00:46:28.320 We're good? 00:46:28.320 --> 00:46:31.190 So I've written some notes, and I'll just scan those 00:46:31.190 --> 00:46:34.370 and I'll put them in the Stellar site. 00:46:34.370 --> 00:46:37.700 So here's another example here-- and in this example, 00:46:37.700 --> 00:46:40.190 it's set up a little bit differently. 00:46:40.190 --> 00:46:44.212 So in this example here, we're not told the material, 00:46:44.212 --> 00:46:45.920 but we're told the thickness of the foam. 00:46:45.920 --> 00:46:47.910 So this time we want to get the material, 00:46:47.910 --> 00:46:50.460 and we want to get the density of the foam. 00:46:50.460 --> 00:46:53.020 So here we've got the specification. 00:46:53.020 --> 00:46:55.920 We're told the mass is 2 and 1/2 kilograms. 00:46:55.920 --> 00:46:58.724 The area of contact is 0.025 meters squared. 00:46:58.724 --> 00:47:01.224 We're told the thickness-- here thickness is 20 millimeters. 00:47:02.540 --> 00:47:04.844 We've got a drop height of 1 meter again. 00:47:04.844 --> 00:47:06.260 And the velocity of impact is then 00:47:06.260 --> 00:47:08.784 going to be 4.5 meters per second again. 00:47:08.784 --> 00:47:11.200 And since we know T, we know that the strain rate is going 00:47:11.200 --> 00:47:15.960 to be around 225 per second. 00:47:15.960 --> 00:47:19.700 We can calculate the energy absorbed-- [? MGH-- ?] 00:47:19.700 --> 00:47:21.790 25 joules. 00:47:21.790 --> 00:47:24.154 We can calculate the energy absorbed per unit volume, 00:47:24.154 --> 00:47:26.070 because we've got the area and the thickness-- 00:47:26.070 --> 00:47:28.694 so I'm just going to divide that by the area and the thickness. 00:47:28.694 --> 00:47:33.300 Now we have 5 times 10 to the 4th joules per cubic meter. 00:47:33.300 --> 00:47:35.520 And we're told that we're supposed to design it 00:47:35.520 --> 00:47:40.260 so the package can withstand a deceleration of 100g-- 00:47:40.260 --> 00:47:42.530 and so that gives you a maximum force. 00:47:42.530 --> 00:47:45.520 And here we've got a maximum allowable peak stress of 10 00:47:45.520 --> 00:47:48.460 of the 5 Newtons per meter squared. 00:47:48.460 --> 00:47:51.327 So here we have our curve for the elastomeric foams again-- 00:47:51.327 --> 00:47:53.410 let's assume it's going to be an elastomeric foam, 00:47:53.410 --> 00:47:56.290 but we don't know what kind of foam. 00:47:56.290 --> 00:47:58.180 So the way you solve this problem 00:47:58.180 --> 00:48:01.050 is that you make a guess for what Es is. 00:48:01.050 --> 00:48:04.480 So remember, these diagrams are all normalized by Es. 00:48:04.480 --> 00:48:07.630 So to plot a point on there, we need to know what Es is. 00:48:07.630 --> 00:48:09.440 So here, we're going to make a guess, 00:48:09.440 --> 00:48:13.850 and we're going to assume that Es is 100 megapascals to start. 00:48:13.850 --> 00:48:17.670 And if we had that value of Es, we know W, up here, 00:48:17.670 --> 00:48:19.700 and we know sigma p there. 00:48:19.700 --> 00:48:22.960 So we just divide those values of W and sigma p by Es, 00:48:22.960 --> 00:48:24.990 and we get these two values here. 00:48:24.990 --> 00:48:28.200 And we plot those two values on the thing here. 00:48:28.200 --> 00:48:30.450 So here's our point A-- and that corresponds 00:48:30.450 --> 00:48:33.300 to that first guess of 100 mega Pascals 00:48:33.300 --> 00:48:36.010 for the modulus of the solid. 00:48:36.010 --> 00:48:38.200 So that's not necessarily the final answer, 00:48:38.200 --> 00:48:41.210 that's not the right answer-- that's just somewhere to start. 00:48:41.210 --> 00:48:44.877 So the thing to notice is, if we have that point there, 00:48:44.877 --> 00:48:46.960 the strain rate there is probably not quite right. 00:48:46.960 --> 00:48:50.580 This upper bound here is-- let's see. 00:48:50.580 --> 00:48:51.790 Got to get closer. 00:48:51.790 --> 00:48:54.770 Oh, let's see-- that's 10 to the minus 2, that's 10 to the 2. 00:48:54.770 --> 00:48:57.280 So the strain rate we want to be is closer up to here, 00:48:57.280 --> 00:48:59.830 it's not quite down there. 00:48:59.830 --> 00:49:02.240 So we're not at the right strain rate. 00:49:02.240 --> 00:49:05.650 But the thing to notice is that if we draw a line of slope 1-- 00:49:05.650 --> 00:49:08.090 so there's this dash line of slope 1-- 00:49:08.090 --> 00:49:11.895 when we move up and down that line, we're just changing Es. 00:49:11.895 --> 00:49:13.770 Because everything is normalized with respect 00:49:13.770 --> 00:49:16.310 to Es-- if that line has a slope of 1, 00:49:16.310 --> 00:49:20.040 then we're just moving up and down with respect to Es. 00:49:20.040 --> 00:49:22.300 So what we do is we scoot up the line 00:49:22.300 --> 00:49:25.700 to get to the point that's on the right strain rate. 00:49:25.700 --> 00:49:28.720 So if this was a strain rate of 100, or around 200, 00:49:28.720 --> 00:49:31.590 we want to be at point B. And then from point B, 00:49:31.590 --> 00:49:35.380 we can read off what's the value of W over Es, 00:49:35.380 --> 00:49:36.960 and sigma p over Es. 00:49:36.960 --> 00:49:39.650 And from that, we can back out what the solid modulus we want 00:49:39.650 --> 00:49:40.350 is. 00:49:40.350 --> 00:49:43.560 So these are the values that we read off the chart. 00:49:43.560 --> 00:49:46.930 This gives us an Es of 28 mega Pascals. 00:49:46.930 --> 00:49:50.240 And again, you can go to this more detailed diagram here, 00:49:50.240 --> 00:49:53.790 and if you read off the sigma p over Es, and the W over Es, 00:49:53.790 --> 00:49:56.370 the density you want is about 0.1. 00:49:56.370 --> 00:49:58.092 So it tells you the modulus of the solid, 00:49:58.092 --> 00:49:59.550 and from that you can pick a solid, 00:49:59.550 --> 00:50:02.060 and it tells you the density. 00:50:02.060 --> 00:50:04.232 Are we good? 00:50:04.232 --> 00:50:05.190 OK, so I have one more. 00:50:05.190 --> 00:50:08.154 So there's a slightly different way you can do it, too. 00:50:08.154 --> 00:50:10.320 So now I want to talk about bicycle helmets-- you're 00:50:10.320 --> 00:50:11.400 my bicycle helmet person. 00:50:14.040 --> 00:50:15.810 So this is another little case study 00:50:15.810 --> 00:50:18.990 that involves a slightly different way to do this. 00:50:18.990 --> 00:50:21.410 And this involves a slightly different diagram. 00:50:21.410 --> 00:50:24.859 So the idea here is to choose a material for a bicycle helmet. 00:50:24.859 --> 00:50:26.900 And as you probably all know, the bicycle helmets 00:50:26.900 --> 00:50:29.700 have a hard shell, and they have some sort of foamy liner. 00:50:29.700 --> 00:50:32.660 And the foam's usually around 20 millimeters thick. 00:50:32.660 --> 00:50:34.244 And you want something that's light, 00:50:34.244 --> 00:50:36.410 because you don't want your helmet to be too heavy-- 00:50:36.410 --> 00:50:38.035 but you want something that will absorb 00:50:38.035 --> 00:50:39.310 the energy from the impact. 00:50:39.310 --> 00:50:43.760 So I've set this up here-- so we assume the mass of the head 00:50:43.760 --> 00:50:45.610 is about 3 kilograms. 00:50:45.610 --> 00:50:47.170 And we assume that it can withstand 00:50:47.170 --> 00:50:50.120 a deceleration of something like 300g-- 00:50:50.120 --> 00:50:53.190 and so then you can get a force mass times the acceleration, 00:50:53.190 --> 00:50:54.460 because you have the force. 00:50:54.460 --> 00:50:56.460 And I've assumed an area of contact of something 00:50:56.460 --> 00:51:01.270 like 0.01 meters squared, so that gives you a peak stress. 00:51:01.270 --> 00:51:04.150 So this method here is based on the idea 00:51:04.150 --> 00:51:07.590 that you have these material selection charts for foams. 00:51:07.590 --> 00:51:09.770 Remember we talked about that earlier. 00:51:09.770 --> 00:51:12.660 And this is the compressive stress at 25% strain. 00:51:12.660 --> 00:51:14.350 So the idea is that axis there is 00:51:14.350 --> 00:51:16.590 meant to represent the plateau stress, 00:51:16.590 --> 00:51:20.060 and this axis here represents the densification strain. 00:51:20.060 --> 00:51:22.950 And these dashed lines here correspond 00:51:22.950 --> 00:51:26.090 to basically a value of W-- and energy 00:51:26.090 --> 00:51:28.290 absorbed per unit volume. 00:51:28.290 --> 00:51:30.380 So this is an energy absorbed per unit volume 00:51:30.380 --> 00:51:35.470 of 0.001 megajoules per cubic meter, 0.01, and so on. 00:51:35.470 --> 00:51:39.846 So if you know the peak stress that you can tolerate, 00:51:39.846 --> 00:51:41.470 for the numbers I gave you it works out 00:51:41.470 --> 00:51:45.220 to be 0.9 mega Pascals-- so here it's just a little less than 1. 00:51:45.220 --> 00:51:48.240 So that's the peak stress that you can tolerate there. 00:51:48.240 --> 00:51:51.800 And you can see that the material that's 00:51:51.800 --> 00:51:55.040 going to absorb the most energy-- so you're absorbing 00:51:55.040 --> 00:51:59.040 more energy as you move over this way on the curve 00:51:59.040 --> 00:52:01.820 on the plot-- so the material that's going to do the best 00:52:01.820 --> 00:52:05.480 is something like an expanded polystyrene that's 5% dense. 00:52:05.480 --> 00:52:07.440 So I've highlighted that in red-- expanded 00:52:07.440 --> 00:52:10.030 polystyrene that's 5% dense. 00:52:10.030 --> 00:52:13.060 And then this is the densification strain here. 00:52:13.060 --> 00:52:15.510 And you know that the lines of the energy absorption 00:52:15.510 --> 00:52:18.580 are just the stress times the strain. 00:52:18.580 --> 00:52:20.580 So you can basically just read off from here 00:52:20.580 --> 00:52:22.940 that expanded polystyrene that was 5% dense 00:52:22.940 --> 00:52:26.680 would be a good choice for a bicycle helmet foam. 00:52:26.680 --> 00:52:30.570 Would you like to add anything about bicycle helmet foams? 00:52:30.570 --> 00:52:33.850 I think that is exactly what they use, yes. 00:52:33.850 --> 00:52:36.180 So this is just another way to do this kind of thing. 00:52:36.180 --> 00:52:38.640 And I did one more little calculation here-- 00:52:38.640 --> 00:52:42.340 if you know the thickness of the foam is, say, 20 millimeters, 00:52:42.340 --> 00:52:45.110 and we've estimated the area of the contact, 00:52:45.110 --> 00:52:47.980 you can figure out what the energy absorbed is 00:52:47.980 --> 00:52:49.970 per unit volume, and from that you can back out 00:52:49.970 --> 00:52:53.020 the energy in terms of joules, and from that you can back out 00:52:53.020 --> 00:52:56.170 the velocity that's the maximum speed that one 00:52:56.170 --> 00:52:59.490 would want to get dinged at on your bicycle. 00:52:59.490 --> 00:53:02.540 And the maximum speed works out about 22 miles an hour. 00:53:02.540 --> 00:53:06.190 So that's just another example. 00:53:06.190 --> 00:53:07.750 Are we good? 00:53:07.750 --> 00:53:11.592 OK-- yeah, exactly, your head would 00:53:11.592 --> 00:53:13.300 be hitting the ground at 22 miles an hour 00:53:13.300 --> 00:53:14.730 which, would be ouchy. 00:53:14.730 --> 00:53:17.310 Which is why you want to wear your helmet, 00:53:17.310 --> 00:53:20.126 because your skull will not be happy if that happens. 00:53:20.126 --> 00:53:21.500 And your brain will not be happy. 00:53:21.500 --> 00:53:23.110 And you will not be happy. 00:53:23.110 --> 00:53:26.780 And your mom and dad will be really, really, really unhappy. 00:53:26.780 --> 00:53:29.470 So you don't want that to happen. 00:53:29.470 --> 00:53:31.540 so I have a few minutes left-- and I 00:53:31.540 --> 00:53:33.464 know I've done this for the people in 3032, 00:53:33.464 --> 00:53:35.630 but I was going to buy woodpecker talk, because it's 00:53:35.630 --> 00:53:37.420 about energy absorption. 00:53:37.420 --> 00:53:39.920 So if you don't want to watch it, if you've already seen it, 00:53:39.920 --> 00:53:40.572 you can go. 00:53:40.572 --> 00:53:42.780 But there are some people-- you guys haven't seen it, 00:53:42.780 --> 00:53:43.590 and you haven't seen it. 00:53:43.590 --> 00:53:45.215 There's a few people that haven't seen. 00:53:45.215 --> 00:53:47.222 And it's cute, involves birds. 00:53:47.222 --> 00:53:48.680 And it involves energy absorption-- 00:53:48.680 --> 00:53:50.576 so I thought I would do this woodpecker talk. 00:53:56.830 --> 00:53:58.510 So Barry, this is all just slides. 00:53:58.510 --> 00:54:01.310 I don't know if you want to do the lights differently. 00:54:01.310 --> 00:54:02.590 I'm not going to write anything on the board, 00:54:02.590 --> 00:54:03.440 I'm just going to talk. 00:54:03.440 --> 00:54:05.172 BARRY: Well, if it will help them see the slides better then 00:54:05.172 --> 00:54:05.550 certainly. 00:54:05.550 --> 00:54:07.050 LORNA GIBSON: Yeah, I think maybe we 00:54:07.050 --> 00:54:09.021 could turn the lights down a little, please. 00:54:16.210 --> 00:54:18.240 BARRY: Let's try this one. 00:54:18.240 --> 00:54:19.490 LORNA GIBSON: Oh, there we go. 00:54:19.490 --> 00:54:20.060 That's good. 00:54:20.060 --> 00:54:22.920 Yeah, now I don't feel like I'm looking in the spotlight 00:54:22.920 --> 00:54:23.420 so much. 00:54:23.420 --> 00:54:24.510 That's good. 00:54:24.510 --> 00:54:28.380 OK, so you guys know that I like to watch birds. 00:54:28.380 --> 00:54:31.150 And you know that I work on foams. 00:54:31.150 --> 00:54:34.040 And if you look at bird books, sometimes the bird books 00:54:34.040 --> 00:54:37.940 say that woodpeckers can withstand the impact 00:54:37.940 --> 00:54:40.590 from pecking because they have a special material 00:54:40.590 --> 00:54:42.550 between their skulls and their brains. 00:54:42.550 --> 00:54:44.550 And I thought, oh, well I study foams, 00:54:44.550 --> 00:54:46.850 and I'm interested in woodpeckers-- I should find out 00:54:46.850 --> 00:54:48.440 what this special material is. 00:54:48.440 --> 00:54:49.980 So I started looking into this. 00:54:49.980 --> 00:54:52.180 And it turns out there is no special material. 00:54:52.180 --> 00:54:55.160 People have looked at the anatomy of woodpecker brains 00:54:55.160 --> 00:54:57.660 and skulls, and there is no special material. 00:54:57.660 --> 00:55:00.020 But it turns out there were also a group of neurologists 00:55:00.020 --> 00:55:02.740 in the late 1970s who got interested in why woodpeckers 00:55:02.740 --> 00:55:05.610 don't get brain injury, and they took high speed video 00:55:05.610 --> 00:55:06.710 of a woodpecker pecking. 00:55:06.710 --> 00:55:09.110 And it was kind of amazing what they found out. 00:55:09.110 --> 00:55:11.230 So it turns out the woodpeckers can withstand 00:55:11.230 --> 00:55:14.810 incredibly high decelerations-- much higher than our brains 00:55:14.810 --> 00:55:15.684 could withstand. 00:55:15.684 --> 00:55:17.350 And so I kind of got interested in this, 00:55:17.350 --> 00:55:21.050 and I decided to try to figure out how it works. 00:55:21.050 --> 00:55:23.650 So here's an acorn woodpecker. 00:55:23.650 --> 00:55:27.590 And let's see-- I got a little video here. 00:55:27.590 --> 00:55:30.860 Wait a minute-- there we go. 00:55:30.860 --> 00:55:31.420 There we go. 00:55:31.420 --> 00:55:32.920 So here's a little acorn woodpecker. 00:55:32.920 --> 00:55:34.160 These live in California. 00:55:34.160 --> 00:55:35.510 Anybody from California? 00:55:35.510 --> 00:55:37.570 Yeah-- have you seen them? 00:55:37.570 --> 00:55:39.430 No, OK. 00:55:39.430 --> 00:55:41.230 Well you have not been looking carefully. 00:55:41.230 --> 00:55:44.810 So here's our little acorn-- and you can see they peck-- oh? 00:55:44.810 --> 00:55:46.240 Like around San Francisco. 00:55:46.240 --> 00:55:48.586 AUDIENCE: [INAUDIBLE]. 00:55:48.586 --> 00:55:50.520 [LAUGHS] 00:55:50.520 --> 00:55:52.010 LORNA GIBSON: So they're pecking, 00:55:52.010 --> 00:55:54.760 and when they're pecking-- they don't just go bonk. 00:55:54.760 --> 00:55:58.190 They do this repeatedly-- they can peck at 10 or 20 times 00:55:58.190 --> 00:55:59.300 per second. 00:55:59.300 --> 00:56:03.450 So the question is, why don't they get brain injury? 00:56:03.450 --> 00:56:05.720 So, first of all, why do they peck? 00:56:05.720 --> 00:56:08.520 So as we in that little video, that woodpecker 00:56:08.520 --> 00:56:10.860 was foraging-- it was trying to get little things out 00:56:10.860 --> 00:56:11.470 of the bark. 00:56:11.470 --> 00:56:16.320 And woodpeckers eat insects, and so the bird books 00:56:16.320 --> 00:56:18.890 say that they can actually hear insects scurrying around 00:56:18.890 --> 00:56:21.300 under the bark, and they'll peck at the bark 00:56:21.300 --> 00:56:23.607 and forage to try to get insects. 00:56:23.607 --> 00:56:25.940 And there's one other anatomical feature of woodpeckers, 00:56:25.940 --> 00:56:28.601 which is kind of amazing-- and you can see it in this picture 00:56:28.601 --> 00:56:29.100 here. 00:56:29.100 --> 00:56:31.094 So this is the woodpecker tongue, 00:56:31.094 --> 00:56:32.760 and the tongue is connected to something 00:56:32.760 --> 00:56:34.210 called the hyoid process. 00:56:34.210 --> 00:56:37.736 And the hyoid process wraps around their eyeballs. 00:56:37.736 --> 00:56:39.110 And then when they peck-- I mean, 00:56:39.110 --> 00:56:41.840 the idea is they're making a hole in the tree, 00:56:41.840 --> 00:56:43.930 and they've got to get their tongue into the hole 00:56:43.930 --> 00:56:44.950 to get the bug. 00:56:44.950 --> 00:56:47.610 And the end of their tongue has little barbs on it. 00:56:47.610 --> 00:56:50.150 And when they contract this thing here, 00:56:50.150 --> 00:56:53.280 their tongue scoots out and gets the little bugs. 00:56:53.280 --> 00:56:56.020 So they pick partly to forage, but they also 00:56:56.020 --> 00:56:58.220 build something called cavity nests. 00:56:58.220 --> 00:57:01.000 So they'll find a tree that's started to rot, 00:57:01.000 --> 00:57:03.500 and they'll drill a sort of horizontal hole, 00:57:03.500 --> 00:57:05.542 and then they'll drill a cup underneath that, 00:57:05.542 --> 00:57:07.250 and they lay the eggs and have their nest 00:57:07.250 --> 00:57:08.577 at the bottom of the cup. 00:57:08.577 --> 00:57:11.160 And then they also-- especially at this time of year, in fact, 00:57:11.160 --> 00:57:13.600 today I heard woodpeckers drumming-- 00:57:13.600 --> 00:57:16.890 so it's one of these mating things, one of these courtship 00:57:16.890 --> 00:57:17.390 things. 00:57:17.390 --> 00:57:21.210 So woodpeckers will peck on a hollow branch or a hollow tree, 00:57:21.210 --> 00:57:23.400 just to make a big loud noise to say, 00:57:23.400 --> 00:57:28.150 here I am, looking for sex, I'm ready, this is my territory. 00:57:28.150 --> 00:57:30.200 And so in the spring-- so this time of year 00:57:30.200 --> 00:57:31.780 you hear woodpeckers drumming. 00:57:31.780 --> 00:57:35.380 And I think naturally they do this on hollow trees 00:57:35.380 --> 00:57:36.880 to try to make a big sound, but they 00:57:36.880 --> 00:57:40.380 have adapted to metal downspouts, which 00:57:40.380 --> 00:57:43.350 are also very effective for making this loud noise. 00:57:43.350 --> 00:57:45.660 And people who've-- I wrote a paper on this-- 00:57:45.660 --> 00:57:48.202 people who have read my paper sometimes email me and say, oh, 00:57:48.202 --> 00:57:49.951 I heard you know about woodpecker pecking. 00:57:49.951 --> 00:57:52.180 How can I get them to stop drumming on my downspout? 00:57:52.180 --> 00:57:53.360 Because it's kind of annoying, if you're 00:57:53.360 --> 00:57:54.850 the human inside the house. 00:57:54.850 --> 00:57:57.470 So anyway, they peck for these reasons. 00:57:57.470 --> 00:57:59.990 And then acorn woodpeckers are special-- acorn woodpeckers 00:57:59.990 --> 00:58:03.320 are what I think of as the champions of pecking. 00:58:03.320 --> 00:58:05.260 And they do one more behavior-- so 00:58:05.260 --> 00:58:08.510 here's from David Sibley's beautiful Guide to Birds, 00:58:08.510 --> 00:58:10.160 here's the acorn woodpecker. 00:58:10.160 --> 00:58:12.850 They store acorns in what's called a granary, 00:58:12.850 --> 00:58:18.360 and they look at old tree trunks that are beginning to rot, 00:58:18.360 --> 00:58:20.560 and they pick holes in the tree trunk 00:58:20.560 --> 00:58:22.530 and they store the acorns in the holes. 00:58:22.530 --> 00:58:25.510 So see all those little dark dots on that trunk? 00:58:25.510 --> 00:58:29.310 Those are all holes that the acorn woodpecker has pecked. 00:58:29.310 --> 00:58:31.430 And they'll do this-- they live in social groups, 00:58:31.430 --> 00:58:34.530 so there might be like 10 or 20 of them living together, 00:58:34.530 --> 00:58:38.210 and they'll peck like 10,000 holes into their granary. 00:58:38.210 --> 00:58:40.960 There will be thousands and thousands of these holes. 00:58:40.960 --> 00:58:42.550 And here we have the acorn woodpecker 00:58:42.550 --> 00:58:46.390 with the acorn in its beak, and you can see some of these holes 00:58:46.390 --> 00:58:48.120 have acorns, and some of them are empty. 00:58:48.120 --> 00:58:51.350 So here is the acorn woodpecker in action. 00:58:51.350 --> 00:58:53.940 And here's the little video again-- I won't play the video. 00:58:53.940 --> 00:58:56.140 So I often give this talk for non-engineers, 00:58:56.140 --> 00:58:58.290 so I'm going to explain some things-- there's 00:58:58.290 --> 00:58:59.370 going to be some writing on the slides 00:58:59.370 --> 00:59:00.660 that you guys already know. 00:59:00.660 --> 00:59:03.180 So the impact force depends on the deceleration-- 00:59:03.180 --> 00:59:06.969 how quickly the brain stops when the beak hits the tree. 00:59:06.969 --> 00:59:09.260 And I should mention, these videos are from the Cornell 00:59:09.260 --> 00:59:13.420 Lab of Ornithology-- they have an amazing collection of bird 00:59:13.420 --> 00:59:17.890 audio, like bird calls, bird songs, and bird photographs 00:59:17.890 --> 00:59:18.600 and videos. 00:59:18.600 --> 00:59:22.730 It's incredible, the collection that they've got. 00:59:22.730 --> 00:59:24.320 And then I explain what acceleration 00:59:24.320 --> 00:59:26.650 is-- so I'm going to put acceleration 00:59:26.650 --> 00:59:27.740 in terms of gravity. 00:59:27.740 --> 00:59:29.720 And when the beak hits the tree, there's 00:59:29.720 --> 00:59:32.250 going to be a deceleration on impact. 00:59:32.250 --> 00:59:34.790 And just as a comparison, human brain injury 00:59:34.790 --> 00:59:37.500 occurs roughly at about 100g. 00:59:37.500 --> 00:59:40.200 And so the question is, how much deceleration 00:59:40.200 --> 00:59:42.350 can the woodpecker brain take? 00:59:42.350 --> 00:59:45.820 And that's where the neurologists in the Bay Area 00:59:45.820 --> 00:59:47.230 come into the picture. 00:59:47.230 --> 00:59:49.910 They found out that there was a park 00:59:49.910 --> 00:59:53.110 ranger-- I think maybe at Point Reyes, just north 00:59:53.110 --> 00:59:54.440 of San Francisco. 00:59:54.440 --> 00:59:56.702 And he had an acorn woodpecker that, I don't, had 00:59:56.702 --> 00:59:57.910 an injured wing or something. 00:59:57.910 --> 01:00:01.810 Anyway, he had this acorn woodpecker that he kept. 01:00:01.810 --> 01:00:05.440 And they were able to use this acorn woodpecker, 01:00:05.440 --> 01:00:08.760 and they took high-speed video of the woodpecker pecking. 01:00:08.760 --> 01:00:11.523 So from the high-speed video, the video that they took 01:00:11.523 --> 01:00:14.260 went at something like 2,000 frames a second. 01:00:14.260 --> 01:00:17.420 So they have a picture of where the head is every 2,000th 01:00:17.420 --> 01:00:18.459 of a second. 01:00:18.459 --> 01:00:20.250 So if you know the position at these times, 01:00:20.250 --> 01:00:23.900 you can get the velocity, and you can get the deceleration. 01:00:23.900 --> 01:00:25.510 So they measured the deceleration, 01:00:25.510 --> 01:00:27.470 and they measured some amazing things. 01:00:27.470 --> 01:00:30.510 So they measured that on impact, the woodpecker's bill 01:00:30.510 --> 01:00:33.090 was going something like 15 miles an hour. 01:00:33.090 --> 01:00:35.570 And the decelerations were up to 1,500g-- 01:00:35.570 --> 01:00:39.450 so many times more than what we can withstand. 01:00:39.450 --> 01:00:41.240 And they also measured the stopping time-- 01:00:41.240 --> 01:00:45.190 and they thought it was between about 1/500th to 1/1,000th 01:00:45.190 --> 01:00:45.970 of a second. 01:00:45.970 --> 01:00:48.889 And that's going to be important later on. 01:00:48.889 --> 01:00:50.680 So one of the interesting things about this 01:00:50.680 --> 01:00:52.810 was how they got this whole thing set up. 01:00:52.810 --> 01:00:55.150 So I don't know how many of you do UROPs-- but you know, 01:00:55.150 --> 01:00:56.960 part of the thing in doing UROPs, and doing experiments 01:00:56.960 --> 01:00:58.950 in the lab is just how do you do the experiments? 01:00:58.950 --> 01:01:01.241 So you know, the park rangers got the acorn woodpecker, 01:01:01.241 --> 01:01:02.332 that's all very good. 01:01:02.332 --> 01:01:03.790 But they have to get the woodpecker 01:01:03.790 --> 01:01:05.340 to peck in front of a camera, and they 01:01:05.340 --> 01:01:06.714 have to get the camera to turn on 01:01:06.714 --> 01:01:09.890 as it's pecking-- so there's some experimental challenges. 01:01:09.890 --> 01:01:11.710 So the important thing, the critical thing, 01:01:11.710 --> 01:01:12.960 is the date of the paper. 01:01:12.960 --> 01:01:15.780 This was written in 1979, which meant they probably 01:01:15.780 --> 01:01:17.770 did the experiments in 1978. 01:01:17.770 --> 01:01:19.960 And I was a graduate student in 1978. 01:01:19.960 --> 01:01:24.010 And I can report there were no Apple computers in 1978-- 01:01:24.010 --> 01:01:25.360 there were no laptops. 01:01:25.360 --> 01:01:28.280 You couldn't just kind of do your little PowerPoint slides. 01:01:28.280 --> 01:01:31.530 And most offices had something called an IBM Selectric 01:01:31.530 --> 01:01:34.240 typewriter-- I don't know if you've ever seen the old IBM 01:01:34.240 --> 01:01:35.089 typewriters. 01:01:35.089 --> 01:01:37.380 But the typewriters, when you typed on the typewriters, 01:01:37.380 --> 01:01:39.730 they made these noises, and it sounded kind of 01:01:39.730 --> 01:01:41.180 like a woodpecker pecking. 01:01:41.180 --> 01:01:44.410 And the ranger had one of these typewriters in his office, 01:01:44.410 --> 01:01:46.786 and he had discovered that if he typed on the typewriter, 01:01:46.786 --> 01:01:49.076 the woodpecker thought, oh, there's another woodpecker. 01:01:49.076 --> 01:01:49.990 I'll start pecking. 01:01:49.990 --> 01:01:51.700 And so they used the typewriter as a way 01:01:51.700 --> 01:01:53.310 to get the woodpeckers to peck. 01:01:53.310 --> 01:01:54.810 And I think they had some old stump, 01:01:54.810 --> 01:01:56.620 and I don't know if they put nuts or peanut butter 01:01:56.620 --> 01:01:58.390 or something into the stump to get the woodpecker 01:01:58.390 --> 01:01:59.350 to peck at it-- because they needed 01:01:59.350 --> 01:02:01.724 to peck at a particular spot, so they have the camera all 01:02:01.724 --> 01:02:02.310 set up. 01:02:02.310 --> 01:02:04.530 So anyway, they had this whole arrangement 01:02:04.530 --> 01:02:10.230 to do this high-speed video of the woodpecker pecking. 01:02:10.230 --> 01:02:12.190 OK, so it goes that up to 1,500g, 01:02:12.190 --> 01:02:13.380 which is kind of amazing. 01:02:13.380 --> 01:02:15.900 And then, remember also, they do this repeatedly-- 01:02:15.900 --> 01:02:19.185 they do it at like 10 or 20 times a second. 01:02:19.185 --> 01:02:20.560 Then this is just explaining what 01:02:20.560 --> 01:02:22.560 stress is-- but you already know what stress is, 01:02:22.560 --> 01:02:24.580 so I'm going to skip over that. 01:02:24.580 --> 01:02:26.520 And so the way you can think about this 01:02:26.520 --> 01:02:29.420 is to think about it in terms of a scaling argument. 01:02:29.420 --> 01:02:31.610 So imagine there's the brain and there's the skull, 01:02:31.610 --> 01:02:34.450 and when the head hits the tree, the brain's going 01:02:34.450 --> 01:02:37.010 to accelerate, and the brain and the skull 01:02:37.010 --> 01:02:38.790 are both going to decelerate. 01:02:38.790 --> 01:02:43.470 And you can think of the stress as the force over the area. 01:02:43.470 --> 01:02:46.680 So the force is the mass times the deceleration over the area. 01:02:46.680 --> 01:02:50.470 So that value for the woodpecker, you can say, 01:02:50.470 --> 01:02:54.460 is roughly equal to the same values, but for the human. 01:02:54.460 --> 01:02:58.290 So what that argument relies on is the idea 01:02:58.290 --> 01:03:01.300 that the stress to cause damage in the woodpecker brain 01:03:01.300 --> 01:03:03.910 is similar to the stress to cause damage 01:03:03.910 --> 01:03:05.320 in the human brain. 01:03:05.320 --> 01:03:08.310 And that's not totally unreasonable. 01:03:08.310 --> 01:03:10.201 So if you look at bone, for example, 01:03:10.201 --> 01:03:12.450 like when you measure the strength of the whale bones, 01:03:12.450 --> 01:03:14.100 it's not going to be that different from what you 01:03:14.100 --> 01:03:15.630 would measure from human bones. 01:03:15.630 --> 01:03:18.850 So when you look at a particular type of tissue, 01:03:18.850 --> 01:03:21.692 and you look at the strength of it in different species, 01:03:21.692 --> 01:03:23.900 the properties aren't that different from one species 01:03:23.900 --> 01:03:24.810 to another. 01:03:24.810 --> 01:03:27.470 So let's say the brain tissue gets 01:03:27.470 --> 01:03:31.010 damaged at the same stress in the two species. 01:03:31.010 --> 01:03:33.250 So we can write this sort of equation down. 01:03:33.250 --> 01:03:39.310 And the mass is going to depend on the density of the brain 01:03:39.310 --> 01:03:41.750 tissue times the volume-- and the volume 01:03:41.750 --> 01:03:43.380 goes as the radius cubed. 01:03:43.380 --> 01:03:46.035 And the density is going to be the same for the woodpecker, 01:03:46.035 --> 01:03:48.290 or for the human-- so assume the brain tissue has 01:03:48.290 --> 01:03:50.380 the same kind of basic stuff. 01:03:50.380 --> 01:03:53.760 So the mass goes as the radius cubed, and the area of contact 01:03:53.760 --> 01:03:55.880 is going to go as the radius squared. 01:03:55.880 --> 01:03:57.790 And so there's a radius term. 01:03:57.790 --> 01:03:59.870 So you can say the radius times the deceleration 01:03:59.870 --> 01:04:02.290 in the woodpecker should be equal to the radius 01:04:02.290 --> 01:04:04.470 times the deceleration of the human. 01:04:04.470 --> 01:04:06.000 And obviously, the woodpecker radius 01:04:06.000 --> 01:04:09.104 is going to be a lot smaller, so the woodpecker deceleration 01:04:09.104 --> 01:04:10.270 is going to be a lot bigger. 01:04:10.270 --> 01:04:13.930 So part of the thing is the brain is just a lot smaller. 01:04:13.930 --> 01:04:16.510 Then there's another factor that comes into it-- 01:04:16.510 --> 01:04:20.390 these are photographs of an acorn woodpecker 01:04:20.390 --> 01:04:22.740 skull and a human skull that I got 01:04:22.740 --> 01:04:25.790 from the Museum of Comparative Zoology at Harvard. 01:04:25.790 --> 01:04:27.490 So this is looking down on the top, 01:04:27.490 --> 01:04:29.866 and this is an elevation view. 01:04:29.866 --> 01:04:32.490 And if you think of the brain as roughly a hemisphere-- I mean, 01:04:32.490 --> 01:04:33.850 obviously it's not a perfect hemisphere, 01:04:33.850 --> 01:04:35.558 but let's say it's roughly a hemisphere-- 01:04:35.558 --> 01:04:37.750 the orientation of the brain in the skull 01:04:37.750 --> 01:04:40.309 is slightly different in the birds and in the human. 01:04:40.309 --> 01:04:42.100 So if you think of it as being this way on, 01:04:42.100 --> 01:04:45.540 and in the woodpecker it's turned roughly this way on, 01:04:45.540 --> 01:04:48.480 and the contact area-- think of this as the contact area. 01:04:48.480 --> 01:04:51.590 The projected area would be a full circle, and in the human, 01:04:51.590 --> 01:04:53.240 the brain is more this way on. 01:04:53.240 --> 01:04:56.800 And then the projected contact area is a semicircle. 01:04:56.800 --> 01:04:58.540 So there's a factor of 2 difference, 01:04:58.540 --> 01:05:01.910 just because of the orientation of the brain. 01:05:01.910 --> 01:05:04.970 And so I've put the factor of 2 that accounts for that. 01:05:04.970 --> 01:05:06.470 So then I could say the deceleration 01:05:06.470 --> 01:05:08.800 that the woodpecker can take is twice 01:05:08.800 --> 01:05:11.940 the ratio of the radii of the human and the woodpecker brain, 01:05:11.940 --> 01:05:13.730 times the deceleration the human can take. 01:05:13.730 --> 01:05:16.080 And this was around 100g, remember. 01:05:16.080 --> 01:05:18.440 So then I wanted to know what the ratio of the sizes 01:05:18.440 --> 01:05:19.910 was, and I thought, oh geez-- I'm 01:05:19.910 --> 01:05:22.190 going to have to mess around with skulls, 01:05:22.190 --> 01:05:23.940 and try to make some sort of measurements, 01:05:23.940 --> 01:05:25.320 and this is going to be a drag. 01:05:25.320 --> 01:05:27.630 And then I found this paper-- I couldn't believe it-- 01:05:27.630 --> 01:05:29.830 I found this paper called "Brain Size in Birds." 01:05:29.830 --> 01:05:31.700 And this guy had table after table 01:05:31.700 --> 01:05:34.910 after table of the mass of the brain in different birds-- 01:05:34.910 --> 01:05:37.720 and he had the acorn woodpecker, lucky for me. 01:05:37.720 --> 01:05:40.804 So if you just assume that the brain is roughly a hemisphere, 01:05:40.804 --> 01:05:42.720 if you have the mass, you can work out roughly 01:05:42.720 --> 01:05:44.030 what the radius is. 01:05:44.030 --> 01:05:45.880 So it turns out there's a factor of 8 01:05:45.880 --> 01:05:48.600 difference between the radii. 01:05:48.600 --> 01:05:51.880 And so the human brain is about eight times the size 01:05:51.880 --> 01:05:53.030 of the woodpecker. 01:05:53.030 --> 01:05:55.292 And then if you take into account this factor of 2, 01:05:55.292 --> 01:05:56.750 that means the woodpecker should be 01:05:56.750 --> 01:06:01.655 able to tolerate a deceleration of 16 times what the human can. 01:06:01.655 --> 01:06:03.030 So remember, I said the human can 01:06:03.030 --> 01:06:06.490 take about 100-- so this would get the woodpecker up to 1,600. 01:06:06.490 --> 01:06:07.960 But they measured 1,500. 01:06:07.960 --> 01:06:10.280 And I'm a civil engineer, originally, 01:06:10.280 --> 01:06:12.430 I like big factors of safety-- that's a little too 01:06:12.430 --> 01:06:14.630 close for comfort for me. 01:06:14.630 --> 01:06:18.360 And so it turns out there's one more factor that matters. 01:06:18.360 --> 01:06:21.690 People have studied human brain injury pretty extensively, 01:06:21.690 --> 01:06:23.350 and one of the things they've looked at 01:06:23.350 --> 01:06:27.500 is how much acceleration you can tolerate without injury, 01:06:27.500 --> 01:06:29.730 relative to the duration of the impact. 01:06:29.730 --> 01:06:33.337 So this is from a car crash conference-- so here's 01:06:33.337 --> 01:06:34.920 the tolerable acceleration, and here's 01:06:34.920 --> 01:06:36.560 the duration of the impact. 01:06:36.560 --> 01:06:38.480 And typically, for human head impacts, 01:06:38.480 --> 01:06:41.320 the deceleration occurs over a few milliseconds-- 01:06:41.320 --> 01:06:43.950 like over 3 to 10 milliseconds. 01:06:43.950 --> 01:06:46.810 So if this is the duration of the typical head 01:06:46.810 --> 01:06:49.960 impact for a human, here's the range of the tolerable 01:06:49.960 --> 01:06:53.080 accelerations between about 80g and 160g-- so you know, 01:06:53.080 --> 01:06:54.490 I said around 100. 01:06:54.490 --> 01:06:57.650 So we can take this curve, and now we have this factor of 16, 01:06:57.650 --> 01:06:59.760 and we can just scale it up by our factor of 16 01:06:59.760 --> 01:07:01.070 for the woodpecker. 01:07:01.070 --> 01:07:04.660 So if I scale it up by the factor of 16, we're there. 01:07:04.660 --> 01:07:08.264 But the duration of the impacts was more around 1/2 01:07:08.264 --> 01:07:09.930 a millisecond, to a millisecond, so I've 01:07:09.930 --> 01:07:11.730 extrapolated this a little bit. 01:07:11.730 --> 01:07:14.610 And the duration of them is up in here. 01:07:14.610 --> 01:07:16.190 So this is saying the woodpecker can 01:07:16.190 --> 01:07:19.550 take these sorts of decelerations here, 01:07:19.550 --> 01:07:22.180 and that adds on another factor of 4. 01:07:22.180 --> 01:07:25.130 And these were the measured decelerations-- 01:07:25.130 --> 01:07:27.320 1,500 was about the biggest, and I think it 01:07:27.320 --> 01:07:30.510 went to about a few hundred g. 01:07:30.510 --> 01:07:31.935 So there's really three factors-- 01:07:31.935 --> 01:07:33.560 one is the small brain size, so there's 01:07:33.560 --> 01:07:35.470 this sort of scaling factor. 01:07:35.470 --> 01:07:37.140 One is the orientation of the brain, 01:07:37.140 --> 01:07:38.440 that was another factor of 2. 01:07:38.440 --> 01:07:40.148 And then there's this duration of impact, 01:07:40.148 --> 01:07:41.650 which is a factor of 4. 01:07:41.650 --> 01:07:44.377 And so that's how you can get this huge decelerations 01:07:44.377 --> 01:07:46.210 that they've measured in the woodpecker when 01:07:46.210 --> 01:07:48.250 they're pecking. 01:07:48.250 --> 01:07:51.320 So now I have just a couple more slides. 01:07:51.320 --> 01:07:54.640 So woodpeckers have various adaptations to pecking, too. 01:07:54.640 --> 01:07:56.910 So one of the things is they have amazingly stiff tail 01:07:56.910 --> 01:07:58.760 feathers-- you see the tails here? 01:07:58.760 --> 01:08:01.176 You can't quite see it because this didn't reproduce quite 01:08:01.176 --> 01:08:03.750 properly, but the woodpecker is perched on a tree here, 01:08:03.750 --> 01:08:06.197 and the tail is pressed up against the tree. 01:08:06.197 --> 01:08:08.030 And if you think about pecking, like imagine 01:08:08.030 --> 01:08:10.071 if its tail was not pressed up against the tree-- 01:08:10.071 --> 01:08:12.080 it would be kind of grabbing on with its feet, 01:08:12.080 --> 01:08:14.666 and it would be trying to peck, and it would be hard to push. 01:08:14.666 --> 01:08:16.540 You know, you need something to push against. 01:08:16.540 --> 01:08:19.164 And so it's got these stiff tail feathers, which make it easier 01:08:19.164 --> 01:08:22.149 to push against the tree. 01:08:22.149 --> 01:08:24.750 And so here's the stiff tail feathers here. 01:08:24.750 --> 01:08:26.840 It's also got kind of unusual feet 01:08:26.840 --> 01:08:30.011 for birds-- it's got two toes forward and two toes back. 01:08:30.011 --> 01:08:31.760 And again, if it's grabbing with its feet, 01:08:31.760 --> 01:08:35.260 that helps it get some purchase to push against. 01:08:35.260 --> 01:08:38.939 That's called zygodactyl in the bird world. 01:08:38.939 --> 01:08:40.934 So it's got these adaptations, the pecking. 01:08:40.934 --> 01:08:42.600 And then finally, I just like this slide 01:08:42.600 --> 01:08:44.080 here from The New Yorker, because it's 01:08:44.080 --> 01:08:45.760 a woodpecker pecking out a woodpecker, 01:08:45.760 --> 01:08:47.540 so it seemed kind of cute. 01:08:47.540 --> 01:08:50.279 And several people helped me with this project. 01:08:50.279 --> 01:08:52.740 Trey Crisco studies head injury at Brown. 01:08:52.740 --> 01:08:57.520 He actually does work for the NFL on football brain injuries, 01:08:57.520 --> 01:08:58.790 and looks at football helmets. 01:08:58.790 --> 01:09:00.410 Sharon Swartz is a friend of mine at Brown, 01:09:00.410 --> 01:09:01.229 who's a biologist. 01:09:01.229 --> 01:09:02.310 She studies bat flight. 01:09:02.310 --> 01:09:04.720 And she just thought this was kind of a cool project. 01:09:04.720 --> 01:09:09.380 So, in fact, I was walking the dog last week, a few days ago, 01:09:09.380 --> 01:09:11.899 and I saw bats flying around overhead at night. 01:09:11.899 --> 01:09:14.069 And it was so great to see the little bats. 01:09:14.069 --> 01:09:15.979 So I had to immediately email Sharon, 01:09:15.979 --> 01:09:18.240 and say, bats-- there's bats in my neighborhood. 01:09:18.240 --> 01:09:21.470 Andy Biewener runs the Concord Field Station, 01:09:21.470 --> 01:09:23.970 and studies animal locomotion, and I talked to him about it. 01:09:23.970 --> 01:09:26.270 Jeremy Trimble was the one who gave me the skull pictures, 01:09:26.270 --> 01:09:27.770 and Matt Dawson was a student helped 01:09:27.770 --> 01:09:29.840 me do some of the images. 01:09:29.840 --> 01:09:32.120 So that's my woodpecker talk. 01:09:32.120 --> 01:09:33.890 So that's the end of energy absorption, 01:09:33.890 --> 01:09:36.180 I just thought that was kind of amusing. 01:09:36.180 --> 01:09:39.120 So next time, we'll start talking about sandwich panels. 01:09:39.120 --> 01:09:41.170 So, let's see-- Monday's a holiday. 01:09:41.170 --> 01:09:43.754 I will be in Toronto on Monday, seeing my family. 01:09:43.754 --> 01:09:45.920 In fact, I'm going to see one of my old professors-- 01:09:45.920 --> 01:09:48.211 I'm going to my old fluid mechanics professor on Monday 01:09:48.211 --> 01:09:48.880 and have lunch. 01:09:48.880 --> 01:09:50.689 I'll see my family on the weekend. 01:09:50.689 --> 01:09:53.850 And so we'll meet Wednesday next week, 01:09:53.850 --> 01:09:56.550 and I'll start the bit on sandwich panels. 01:09:56.550 --> 01:09:59.860 So I think there's two lectures on engineering sandwich panels, 01:09:59.860 --> 01:10:03.930 and then there's a lecture on natural sandwich panels-- 01:10:03.930 --> 01:10:06.630 so bird skulls, for example, are natural sandwich panels. 01:10:06.630 --> 01:10:07.890 So I'll talk about that. 01:10:07.890 --> 01:10:09.720 And then I think the last lecture-- 01:10:09.720 --> 01:10:12.080 there's only a handful of lectures left-- the last one I 01:10:12.080 --> 01:10:14.475 think I talk about natural materials, because you know, 01:10:14.475 --> 01:10:15.270 I like that. 01:10:15.270 --> 01:10:17.890 So I just do that for fun.