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LORNA GIBSON: All
right, so last time we

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00:00:29,100 --> 00:00:31,560
started talking about
energy absorption,

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00:00:31,560 --> 00:00:33,920
and I wanted to try to
finish that up today.

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00:00:33,920 --> 00:00:36,460
And then next week we would
talk about sandwich panels

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00:00:36,460 --> 00:00:39,990
and using honeycombs and
foams in sandwich panels.

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00:00:39,990 --> 00:00:42,140
So I think we got
as far as the idea

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00:00:42,140 --> 00:00:45,470
of introducing what these
energy absorption diagrams are.

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00:00:45,470 --> 00:00:48,180
So let me run through this
little sequence again,

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00:00:48,180 --> 00:00:50,480
and then I'll put the
notes up on the board.

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00:00:50,480 --> 00:00:54,350
So the idea is that you have
your compressive stress strain

18
00:00:54,350 --> 00:00:57,140
curve-- so here's a series of
curves for different densities

19
00:00:57,140 --> 00:00:58,230
of a foam.

20
00:00:58,230 --> 00:01:00,500
And we would do these
all at the same strain

21
00:01:00,500 --> 00:01:03,170
rate and temperature, so
that those aren't variables.

22
00:01:03,170 --> 00:01:06,370
And then what we would do is
we could turn those into energy

23
00:01:06,370 --> 00:01:07,720
absorption diagrams.

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00:01:07,720 --> 00:01:10,200
So notice here,
this is a log plot.

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00:01:10,200 --> 00:01:12,250
So here's that energy
absorption here.

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00:01:12,250 --> 00:01:14,650
Here's the peak stress
here-- so that's

27
00:01:14,650 --> 00:01:18,620
the peak stress up to some level
of energy that you've absorbed.

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00:01:18,620 --> 00:01:22,470
And we've normalized both of
those by the solid modulus.

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00:01:22,470 --> 00:01:25,160
So say we look at one density
here, say we look at the lowest

30
00:01:25,160 --> 00:01:26,540
density-- 0.01.

31
00:01:26,540 --> 00:01:30,410
So here's our curve
here for the test.

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00:01:30,410 --> 00:01:33,000
If I go up to some
stress level that's

33
00:01:33,000 --> 00:01:35,120
still in the linear
elastic region,

34
00:01:35,120 --> 00:01:38,570
then that's going to translate
into somewhere along here

35
00:01:38,570 --> 00:01:40,165
on the energy absorption curve.

36
00:01:40,165 --> 00:01:41,540
And one of the
things we're going

37
00:01:41,540 --> 00:01:43,850
to do today-- I'm going to
show you how you draw these,

38
00:01:43,850 --> 00:01:46,410
and how you can set them up.

39
00:01:46,410 --> 00:01:48,810
And you can either get
them from experiments--

40
00:01:48,810 --> 00:01:52,290
so this is, say the top curve
were experiments, doing it

41
00:01:52,290 --> 00:01:57,020
from experiments-- or you can
use the models for the foams

42
00:01:57,020 --> 00:01:57,930
to do it, as well.

43
00:01:57,930 --> 00:02:00,150
So we'll see how you
can do from both ways.

44
00:02:00,150 --> 00:02:02,150
So this would be the
linear elastic bit here.

45
00:02:02,150 --> 00:02:04,720
This vertical part-- where
the energy is increasing,

46
00:02:04,720 --> 00:02:07,050
but the peak stress isn't
increasing-- that corresponds

47
00:02:07,050 --> 00:02:08,940
to the plateau here.

48
00:02:08,940 --> 00:02:11,700
And then this part here,
where the energy is not

49
00:02:11,700 --> 00:02:13,670
increasing very much,
but the stress increases

50
00:02:13,670 --> 00:02:18,010
a lot-- that corresponds to the
densification part over there.

51
00:02:18,010 --> 00:02:20,330
So what you would do
is you would do tests

52
00:02:20,330 --> 00:02:23,340
on foams of different densities,
and from the test data,

53
00:02:23,340 --> 00:02:25,170
you could draw an
energy absorption

54
00:02:25,170 --> 00:02:27,150
curve for each density.

55
00:02:27,150 --> 00:02:29,590
So you plot-- there's four
different densities here,

56
00:02:29,590 --> 00:02:32,446
so it forms a family
of these curves.

57
00:02:32,446 --> 00:02:33,820
And then what you
do is you say--

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00:02:33,820 --> 00:02:35,810
and I think we talked
with this last time--

59
00:02:35,810 --> 00:02:38,630
that the place you want to
be is at this shoulder point.

60
00:02:38,630 --> 00:02:41,770
You want to be absorbing
as much energy as possible

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00:02:41,770 --> 00:02:43,344
at that plateau stress.

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00:02:43,344 --> 00:02:45,760
So you want to be at the point
just before it turns around

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00:02:45,760 --> 00:02:47,730
to the densification regime.

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00:02:47,730 --> 00:02:50,330
So you can mark that
little shoulder point

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00:02:50,330 --> 00:02:51,130
for each density.

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00:02:51,130 --> 00:02:54,390
So here's like 0.01,
here's 0.03, and so on.

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00:02:54,390 --> 00:02:57,320
And then those points can
be connected by a line--

68
00:02:57,320 --> 00:03:00,470
so that heavy line then
connects those shoulder points,

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00:03:00,470 --> 00:03:02,350
or those optimum points.

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00:03:02,350 --> 00:03:06,010
And then what you can do is
then repeat this whole process

71
00:03:06,010 --> 00:03:07,670
for different strain rates.

72
00:03:07,670 --> 00:03:11,260
So this family of lines here
is at different strain rates--

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00:03:11,260 --> 00:03:15,166
so this set that goes this way,
corresponds to this line here.

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00:03:15,166 --> 00:03:17,040
And if you do them at
different strain rates,

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00:03:17,040 --> 00:03:20,730
where the shoulder appears at
a slightly different point--

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00:03:20,730 --> 00:03:22,900
and so if you mark
those shorter points,

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00:03:22,900 --> 00:03:25,690
you can draw these lines
here that connect up

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00:03:25,690 --> 00:03:27,680
for one relative density.

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00:03:27,680 --> 00:03:30,820
So this line on the
left hand side here,

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00:03:30,820 --> 00:03:33,450
these are all relative
densities of 0.01,

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00:03:33,450 --> 00:03:36,020
these ones are all
relative densities of 0.03.

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00:03:36,020 --> 00:03:38,800
So this diagram down
here, doesn't really

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00:03:38,800 --> 00:03:40,360
look like this at
all-- it doesn't

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00:03:40,360 --> 00:03:42,990
look like the basic
energy absorption diagram.

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00:03:42,990 --> 00:03:44,950
But it actually has
information for what

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00:03:44,950 --> 00:03:47,620
the optimum would be
for a range of densities

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00:03:47,620 --> 00:03:49,700
and a range of strain rates.

88
00:03:49,700 --> 00:03:52,500
So typically, these
foams are viscoelastic

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00:03:52,500 --> 00:03:54,300
and they have some
strain rate sensitivity.

90
00:03:54,300 --> 00:03:57,200
So you'd like to get the strain
rate sensitivity into it.

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00:03:57,200 --> 00:03:58,870
And it's not shown
here, but you could

92
00:03:58,870 --> 00:04:00,840
do the same thing at
a constant strain rate

93
00:04:00,840 --> 00:04:02,240
and varying the
temperature, too.

94
00:04:02,240 --> 00:04:04,198
So if you had things at
different temperatures,

95
00:04:04,198 --> 00:04:05,910
you could do the
same kind of idea.

96
00:04:05,910 --> 00:04:08,730
OK-- so are we good
with how this works?

97
00:04:08,730 --> 00:04:11,140
Because now I'm going to
write some notes on the board

98
00:04:11,140 --> 00:04:13,335
so you have it in your notes.

99
00:04:37,560 --> 00:04:41,300
So the idea is that you turn
your stress strain curve

100
00:04:41,300 --> 00:04:44,860
to look something like that,
into an energy absorption

101
00:04:44,860 --> 00:04:46,070
diagram.

102
00:04:46,070 --> 00:04:56,130
And you can plot on log
log scales, the energy

103
00:04:56,130 --> 00:04:57,520
versus the peak stress.

104
00:04:57,520 --> 00:04:59,380
And you get something like that.

105
00:04:59,380 --> 00:05:02,666
And this point here, I'm going
to call the shoulder point.

106
00:05:07,970 --> 00:05:10,920
And that would use the material
in the most efficient way--

107
00:05:10,920 --> 00:05:13,530
you get the most energy
absorption without getting

108
00:05:13,530 --> 00:05:15,147
higher than that plateau stress.

109
00:05:18,490 --> 00:05:24,390
So we can say at this stress
plateau, the energy increases

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00:05:24,390 --> 00:05:26,345
without much increase
in the peak stress.

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00:05:44,670 --> 00:05:50,680
And then as the foam
densifies, then you

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00:05:50,680 --> 00:05:56,010
get an increase in
that peak stress,

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00:05:56,010 --> 00:05:58,190
with little increase
in the energy absorbed.

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00:06:07,890 --> 00:06:10,210
And so ideally, you want to
be at that shoulder point.

115
00:06:25,350 --> 00:06:28,160
So to construct these
energy diagrams,

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00:06:28,160 --> 00:06:32,220
you can test the series of foams
at different relative densities

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00:06:32,220 --> 00:06:35,320
and constant strain
rate and temperature.

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00:06:56,140 --> 00:06:59,950
And then you make that
plot of the energy absorbed

119
00:06:59,950 --> 00:07:06,170
normalized by the solid
modulus, versus the peak stress

120
00:07:06,170 --> 00:07:09,020
normalized by the solid
modulus for each curve.

121
00:07:14,880 --> 00:07:17,720
And typically what people
do is they would take

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00:07:17,720 --> 00:07:22,776
the solid modulus at a constant
strain rate and temperature,

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00:07:22,776 --> 00:07:24,651
so you don't have to
introduce that, as well.

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00:07:34,054 --> 00:07:36,470
Then you would mark the density
for each of those shoulder

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00:07:36,470 --> 00:07:41,010
points, and then you
would connect them.

126
00:07:53,070 --> 00:07:55,000
And then you could
repeat this whole process

127
00:07:55,000 --> 00:07:56,320
for different strain rates.

128
00:08:06,360 --> 00:08:08,870
And then you would
draw the final diagram

129
00:08:08,870 --> 00:08:11,390
at the bottom, where you have
this family of lines that

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00:08:11,390 --> 00:08:14,486
describes the shoulder points
for different densities

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00:08:14,486 --> 00:08:15,610
and different strain rates.

132
00:08:45,542 --> 00:08:48,000
And you could treat different
temperatures in the same way,

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00:08:48,000 --> 00:08:48,790
if you wanted to.

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00:08:48,790 --> 00:08:50,456
You would hold the
strain rate constant,

135
00:08:50,456 --> 00:08:53,240
and vary the temperature.

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00:08:53,240 --> 00:08:54,990
so it's kind of a nice
way of just putting

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00:08:54,990 --> 00:08:56,490
a lot of information
in one diagram.

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00:08:58,780 --> 00:09:00,900
So one of the
things about this is

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00:09:00,900 --> 00:09:04,240
that, because we're
normalizing by Es,

140
00:09:04,240 --> 00:09:08,210
and if you think of elastomeric
foams, elastomeric foams,

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00:09:08,210 --> 00:09:10,960
both the Young's
modulus depends on Es,

142
00:09:10,960 --> 00:09:13,500
and the plateau
stress depends Es.

143
00:09:13,500 --> 00:09:16,290
So the Young's modulus depends
on the stiffness of the solid,

144
00:09:16,290 --> 00:09:18,155
and also because
the plateau stress

145
00:09:18,155 --> 00:09:20,200
is related to elastic
buckling, it also

146
00:09:20,200 --> 00:09:22,820
depends on the
modulus of the solid.

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00:09:22,820 --> 00:09:27,010
So for elastomeric foams--
it's because you normalized it

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00:09:27,010 --> 00:09:29,690
with respect to Es--
one of these diagrams

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00:09:29,690 --> 00:09:32,487
will represent all
elastomeric foams.

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00:09:32,487 --> 00:09:34,070
So that's rather a
nice thing-- so you

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00:09:34,070 --> 00:09:35,960
can have different
elastomeric foams,

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00:09:35,960 --> 00:09:38,550
but one of those diagrams is
going to represent all of them.

153
00:09:46,640 --> 00:09:49,730
So we can say,
elastomeric foams can all

154
00:09:49,730 --> 00:09:53,030
be plotted on one
plot, or one curve,

155
00:09:53,030 --> 00:09:55,275
since both the modulus
and the plateau stress

156
00:09:55,275 --> 00:09:56,495
are related to Es.

157
00:10:38,390 --> 00:10:40,962
So if we look at this
next figure here--

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00:10:40,962 --> 00:10:43,336
maybe I'll just wait a minute
for people to stop writing.

159
00:10:50,060 --> 00:10:51,601
Some people write
faster than others.

160
00:11:00,140 --> 00:11:02,230
So if we look at
this next plot here,

161
00:11:02,230 --> 00:11:04,770
here's a compressive
stress and strain.

162
00:11:04,770 --> 00:11:06,450
These tests are done
for one density,

163
00:11:06,450 --> 00:11:08,283
but at different strain
rates-- so it's kind

164
00:11:08,283 --> 00:11:10,170
of the other version of this.

165
00:11:10,170 --> 00:11:12,370
But here's the stress
strain curves here,

166
00:11:12,370 --> 00:11:14,830
and here's the energy
absorption diagram that's

167
00:11:14,830 --> 00:11:16,260
derived from those.

168
00:11:16,260 --> 00:11:19,580
And then here's
a summary diagram

169
00:11:19,580 --> 00:11:22,210
that has the different
strain rates, and that would

170
00:11:22,210 --> 00:11:24,130
have different densities here.

171
00:11:24,130 --> 00:11:26,220
And the idea is
this diagram here

172
00:11:26,220 --> 00:11:28,870
could represent all
elastomeric foams.

173
00:11:28,870 --> 00:11:31,090
So this has been put
together for polyurethane,

174
00:11:31,090 --> 00:11:34,210
but it should be able
to represent other sorts

175
00:11:34,210 --> 00:11:40,980
of flexible elastomeric foams.

176
00:11:40,980 --> 00:11:41,994
Sorry?

177
00:11:41,994 --> 00:11:44,602
AUDIENCE: In those
diagrams, then,

178
00:11:44,602 --> 00:11:46,320
the intersection
of this strain rate

179
00:11:46,320 --> 00:11:48,350
line and your
relative density line

180
00:11:48,350 --> 00:11:50,330
should be the shoulder position?

181
00:11:50,330 --> 00:11:51,590
LORNA GIBSON: Yeah, exactly.

182
00:11:51,590 --> 00:11:56,520
And so this line here is for
0.01, and that one's for 0.03.

183
00:11:56,520 --> 00:11:58,370
So 0.02 is going
to be-- you'd have

184
00:11:58,370 --> 00:12:01,530
to interpolate somewhere
in between there.

185
00:12:01,530 --> 00:12:03,586
So we've just put
on certain values,

186
00:12:03,586 --> 00:12:05,710
because we're not going to
put on a million values.

187
00:12:05,710 --> 00:12:09,700
We just put on certain
ones, and then you

188
00:12:09,700 --> 00:12:11,820
can estimate where
other densities would

189
00:12:11,820 --> 00:12:12,840
appear on there.

190
00:12:12,840 --> 00:12:14,710
OK?

191
00:12:14,710 --> 00:12:17,430
So here's another
example here-- these are

192
00:12:17,430 --> 00:12:19,020
curves for two different foams.

193
00:12:19,020 --> 00:12:21,130
So here's a polyurethane
a polyethylene,

194
00:12:21,130 --> 00:12:22,790
so these are both elastomers.

195
00:12:22,790 --> 00:12:25,690
And one is the dashed line,
and one is the solid line.

196
00:12:25,690 --> 00:12:28,530
And you can kind of see
how the lines mesh up.

197
00:12:28,530 --> 00:12:32,970
So here's a density of
0.01 for the polyurethane.

198
00:12:32,970 --> 00:12:35,760
Here's 0.05 for
the polyurethane.

199
00:12:35,760 --> 00:12:38,250
And here's 0.06 for
the polyethylene.

200
00:12:38,250 --> 00:12:40,460
And you can see how
the 0.06 and 0.05--

201
00:12:40,460 --> 00:12:42,220
they're not quite on
top of each other,

202
00:12:42,220 --> 00:12:44,553
but they're pretty close to
coming on top of each other.

203
00:12:44,553 --> 00:12:47,910
And then 0.1, 0.12-- and
so you get a family of them

204
00:12:47,910 --> 00:12:50,480
for the different densities.

205
00:12:50,480 --> 00:12:53,150
And you can also do
this for materials

206
00:12:53,150 --> 00:12:56,500
that have a yield point, so
polymethacrylimid has a yield

207
00:12:56,500 --> 00:12:59,940
point, so you do exactly
the same kind of thing.

208
00:12:59,940 --> 00:13:01,840
So here's the energy
absorption diagram

209
00:13:01,840 --> 00:13:04,480
that's been developed from
the stress strain curves.

210
00:13:04,480 --> 00:13:07,870
But now this curve here,
or this set of curves here,

211
00:13:07,870 --> 00:13:11,740
is really just valid for
one ratio of sigma [? ys ?]

212
00:13:11,740 --> 00:13:15,996
to Es-- so the solid yield
strength of the solid modulus.

213
00:13:15,996 --> 00:13:17,370
So it's valid for
whatever it was

214
00:13:17,370 --> 00:13:24,230
for that particular type of
foam-- the polymethacrylimid.

215
00:13:28,330 --> 00:13:35,200
So I'll just say,
if we have foams

216
00:13:35,200 --> 00:13:37,846
that are made from a
material with a yield point--

217
00:13:37,846 --> 00:13:43,220
and so they have a plastic
collapse stress-- then

218
00:13:43,220 --> 00:13:53,450
the curve will be
valid for foams

219
00:13:53,450 --> 00:13:55,790
with the same ratio of
[? sigma ys ?] to Es.

220
00:14:06,210 --> 00:14:09,730
So in that case there,
for the polymethacrylimid,

221
00:14:09,730 --> 00:14:14,230
that ratio is about
equal to 1 over 30.

222
00:14:14,230 --> 00:14:17,660
So that plot would probably
give not a bad description

223
00:14:17,660 --> 00:14:24,860
of other foams, with the same
value of sigma ys over Es.

224
00:14:24,860 --> 00:14:26,490
So the idea here
is we can generate

225
00:14:26,490 --> 00:14:30,379
these diagrams either
from data-- the way

226
00:14:30,379 --> 00:14:32,337
those ones have been
done-- or from the models.

227
00:15:35,410 --> 00:15:39,130
So another way to generate these
is to think about the models

228
00:15:39,130 --> 00:15:41,674
that we have for the foams,
and the foam behavior.

229
00:15:41,674 --> 00:15:44,090
So we have an equation that
describes the Young's modulus,

230
00:15:44,090 --> 00:15:46,880
we have equations that
describe the plateau stresses,

231
00:15:46,880 --> 00:15:50,570
we have an empirical equation
for the densification strain.

232
00:15:50,570 --> 00:15:53,500
And we can use those to
generate these diagrams.

233
00:15:53,500 --> 00:15:55,180
And they're kind of
useful, because they

234
00:15:55,180 --> 00:15:59,320
show you what's going on a
sort of mechanistic basis.

235
00:15:59,320 --> 00:16:02,590
So this is a diagram here that's
been generated for open cell

236
00:16:02,590 --> 00:16:04,140
elastomeric foams.

237
00:16:04,140 --> 00:16:06,050
Here's our energy
absorbed, here's

238
00:16:06,050 --> 00:16:07,870
our peak stress down here.

239
00:16:07,870 --> 00:16:11,650
This little inset is sort of a
schematic of the idealized foam

240
00:16:11,650 --> 00:16:12,150
behavior.

241
00:16:12,150 --> 00:16:13,790
So here's the Young's
modulus, here's

242
00:16:13,790 --> 00:16:15,580
the elastic [? collapse ?]
stress, here's

243
00:16:15,580 --> 00:16:17,770
the densification over here.

244
00:16:17,770 --> 00:16:21,480
So obviously it's kind of
a very idealized set-up.

245
00:16:21,480 --> 00:16:23,274
But we can generate
this diagram--

246
00:16:23,274 --> 00:16:25,190
and I'm going to go
through the equations that

247
00:16:25,190 --> 00:16:26,860
will let us do that.

248
00:16:26,860 --> 00:16:32,260
So one thing to note is here's
the curves for each density.

249
00:16:32,260 --> 00:16:35,340
Here is this line that
connects the shoulder points.

250
00:16:35,340 --> 00:16:37,050
There's a couple of
other lines on here

251
00:16:37,050 --> 00:16:39,550
that I just wanted to
mention something about.

252
00:16:39,550 --> 00:16:42,240
If you think about the
densities-- like that's 0.01,

253
00:16:42,240 --> 00:16:44,430
this is 0.03,
that's 0.1-- if you

254
00:16:44,430 --> 00:16:48,540
had a fully dense solid that
was made of the same elastomer,

255
00:16:48,540 --> 00:16:51,040
you could plot the
curve for that,

256
00:16:51,040 --> 00:16:52,890
and that is going to
show up over here.

257
00:16:52,890 --> 00:16:54,580
So this is kind
of an upper bound.

258
00:16:54,580 --> 00:16:57,520
It can't get any more from that.

259
00:16:57,520 --> 00:17:01,030
And we've also got
a dotted line here,

260
00:17:01,030 --> 00:17:03,870
which takes into account
fluid flow within the cells.

261
00:17:03,870 --> 00:17:05,901
So there can be some
fluid flow, and because we

262
00:17:05,901 --> 00:17:08,359
haven't talked about that,
we're not going to go into that.

263
00:17:08,359 --> 00:17:10,619
So we can just ignore
that dotted line for now.

264
00:17:13,380 --> 00:17:18,690
So let me go through how
we can do the modeling.

265
00:17:18,690 --> 00:17:21,030
So we're going to divide
the stress strain curve up

266
00:17:21,030 --> 00:17:23,530
into bits, and I'm
going to write equations

267
00:17:23,530 --> 00:17:26,300
for the energy
absorbed for each bit.

268
00:17:26,300 --> 00:17:30,102
So we're going to start with
a linear elastic behavior.

269
00:17:33,030 --> 00:17:37,860
And I'm going to--
let's see-- yeah,

270
00:17:37,860 --> 00:17:41,570
so let me just note here that
this is the densification

271
00:17:41,570 --> 00:17:43,070
strain out here.

272
00:17:43,070 --> 00:17:45,650
And this strain, epsilon
naught, corresponds

273
00:17:45,650 --> 00:17:48,870
to the strain at which we
first reach the stress plateau.

274
00:17:48,870 --> 00:17:51,600
So here, for the
linear elastic part,

275
00:17:51,600 --> 00:17:55,670
I'm going to say that the
strain is less than that.

276
00:17:55,670 --> 00:17:57,940
So the strain is less
than absolute naught.

277
00:17:57,940 --> 00:18:02,200
And then I can say,
the energy absorbed--

278
00:18:02,200 --> 00:18:03,700
so if you just
remember from Hooke's

279
00:18:03,700 --> 00:18:06,830
law on linear elasticity,
energy under the stress strain

280
00:18:06,830 --> 00:18:08,360
curve for the
linear elastic part

281
00:18:08,360 --> 00:18:11,810
is 1/2 of sigma
squared over E. So I'm

282
00:18:11,810 --> 00:18:14,510
going to call sigma-- whatever
the stress is going to be,

283
00:18:14,510 --> 00:18:16,510
the peak stress that we get to.

284
00:18:16,510 --> 00:18:18,980
And now we're going to
divide by E of the foam--

285
00:18:18,980 --> 00:18:21,100
because these were
our foams here.

286
00:18:21,100 --> 00:18:30,070
And I can use our
model here to say--

287
00:18:30,070 --> 00:18:31,740
and now I've got to
divide that by Es,

288
00:18:31,740 --> 00:18:33,220
because I've normalized here.

289
00:18:40,680 --> 00:18:42,830
So because I know
from my modeling

290
00:18:42,830 --> 00:18:44,850
that the Young's
modulus of the foam

291
00:18:44,850 --> 00:18:47,500
is just equal to Es times
the relative density squared

292
00:18:47,500 --> 00:18:49,390
for the open celled
foam, that means

293
00:18:49,390 --> 00:18:52,230
I've now got an Es squared
in the denominator,

294
00:18:52,230 --> 00:18:54,310
so I've got a sigma
p over Es squared.

295
00:18:54,310 --> 00:18:59,790
And then I've got a 1 over the
relative density squared term.

296
00:18:59,790 --> 00:19:04,610
So that factor there,
that equation there,

297
00:19:04,610 --> 00:19:07,340
gives you these first
set of lines here.

298
00:19:07,340 --> 00:19:10,370
Gives you that bit, and
this bit, and that bit.

299
00:19:10,370 --> 00:19:13,143
So it gives you those first
parts of the energy absorption

300
00:19:13,143 --> 00:19:13,643
diagram.

301
00:19:21,410 --> 00:19:23,810
And then if we look at
the stress plateau--

302
00:19:23,810 --> 00:19:27,300
so here we're going to say
that epsilon naught is less

303
00:19:27,300 --> 00:19:30,940
than epsilon is less than
the densification strain--

304
00:19:30,940 --> 00:19:33,420
so we're on the
plateau somewhere.

305
00:19:33,420 --> 00:19:36,560
And now the energy
absorbed is just

306
00:19:36,560 --> 00:19:40,320
going to be our plateau stress
times the amount of strain

307
00:19:40,320 --> 00:19:43,360
we've got.

308
00:19:43,360 --> 00:19:46,290
So that's epsilon
minus epsilon naught.

309
00:19:46,290 --> 00:19:50,080
And if I normalized with
respect the solid modulus,

310
00:19:50,080 --> 00:19:59,300
I can write down that my
plateau stress is 0.05 times

311
00:19:59,300 --> 00:20:01,510
the relative density
squared, and then

312
00:20:01,510 --> 00:20:05,125
multiply that times epsilon
minus epsilon naught.

313
00:20:08,900 --> 00:20:11,000
So that equation
then corresponds

314
00:20:11,000 --> 00:20:14,510
to these vertical parts--
so this part here, that part

315
00:20:14,510 --> 00:20:16,090
there, this part here.

316
00:20:16,090 --> 00:20:19,070
It corresponds to those
vertical lines on the figure.

317
00:20:34,020 --> 00:20:36,090
Vertical lines on the diagram.

318
00:20:36,090 --> 00:20:38,110
And then the plateau
stress is going

319
00:20:38,110 --> 00:20:40,490
to end at the
densification strain.

320
00:20:45,830 --> 00:20:47,753
And at that point,
the energy diagram

321
00:20:47,753 --> 00:20:49,128
is just going to
become vertical.

322
00:21:37,120 --> 00:21:39,114
OK, and then the
last part-- I'll

323
00:21:39,114 --> 00:21:40,613
try to rub this off
a little better.

324
00:21:47,130 --> 00:21:48,870
And then the last
part is when we're

325
00:21:48,870 --> 00:22:01,930
at the end of this
stress plateau,

326
00:22:01,930 --> 00:22:06,180
and the strain is equal to
that densification strain.

327
00:22:06,180 --> 00:22:08,360
And so the amount of
energy we absorb here

328
00:22:08,360 --> 00:22:09,776
is really going
to be the maximum.

329
00:22:35,504 --> 00:22:36,920
So this is the
energy that's going

330
00:22:36,920 --> 00:22:38,740
to correspond to
that shoulder point

331
00:22:38,740 --> 00:22:40,790
that I've been talking about.

332
00:22:40,790 --> 00:22:46,360
So I'm going to call that W max,
and normalize that with respect

333
00:22:46,360 --> 00:22:47,810
to Es.

334
00:22:47,810 --> 00:22:52,800
And that's then going
to be our plateau stress

335
00:22:52,800 --> 00:22:56,960
times the densification strain.

336
00:22:56,960 --> 00:23:02,246
And the densification strain
was just 1 minus 1.4 times

337
00:23:02,246 --> 00:23:03,120
the relative density.

338
00:23:11,330 --> 00:23:17,780
So here I'm assuming that
the densification strain

339
00:23:17,780 --> 00:23:20,580
is very much bigger
than the strain at which

340
00:23:20,580 --> 00:23:23,000
the buckling first
occurs, and I'm neglecting

341
00:23:23,000 --> 00:23:24,415
that linear elastic part.

342
00:23:34,800 --> 00:23:39,890
So then we could say
that the optimum foam

343
00:23:39,890 --> 00:23:41,860
is at that shoulder point.

344
00:23:54,880 --> 00:23:57,020
And I can say that the
peak stress at that point

345
00:23:57,020 --> 00:23:58,933
is just equal to
the plateau stress.

346
00:24:03,370 --> 00:24:08,590
And what I want to do is get
an equation for that solid line

347
00:24:08,590 --> 00:24:11,430
up here that connects all
those shoulder points.

348
00:24:11,430 --> 00:24:13,780
So I want an equation,
in terms of the energy,

349
00:24:13,780 --> 00:24:16,700
and the peak stress, instead
of in terms of the density.

350
00:24:16,700 --> 00:24:19,130
So what I'm going to do a
solve this for the density,

351
00:24:19,130 --> 00:24:20,867
and then plug that
back into there.

352
00:24:34,287 --> 00:24:36,120
So I get that the
relative density is, then,

353
00:24:36,120 --> 00:24:40,067
20 times the peak stress
over the solid modulus,

354
00:24:40,067 --> 00:24:41,525
and I take the
square root of that.

355
00:24:49,600 --> 00:24:54,612
And now I can substitute this up
here for the relative density.

356
00:24:54,612 --> 00:24:55,820
I think I need another board.

357
00:25:29,710 --> 00:25:32,680
So then I've got-- this is
my peak stress, or my plateau

358
00:25:32,680 --> 00:25:39,670
stress, over Es, and this is all
just the densification strain.

359
00:25:39,670 --> 00:25:42,454
And that's just 1 minus 1.4
times the relative density.

360
00:25:42,454 --> 00:25:44,120
But now I'm putting
the relative density

361
00:25:44,120 --> 00:25:47,085
in terms of the peak stress,
or the plateau stress.

362
00:25:57,290 --> 00:26:00,830
If I just simplify that
slightly with the constant,

363
00:26:00,830 --> 00:26:08,312
it's 1 minus 6.26 times sigma
p over Es to the 1/2 power.

364
00:26:11,930 --> 00:26:18,270
So that equation there describes
the-- oops, no more updates.

365
00:26:18,270 --> 00:26:19,390
No updates.

366
00:26:19,390 --> 00:26:21,494
Go away.

367
00:26:21,494 --> 00:26:25,870
Ah, so that equation there
describes this line here that

368
00:26:25,870 --> 00:26:28,367
connects those shoulder points.

369
00:26:28,367 --> 00:26:30,450
And that's the line you're
the most interested in,

370
00:26:30,450 --> 00:26:32,250
because each of
those shoulder points

371
00:26:32,250 --> 00:26:34,100
is a point where
the foam is being

372
00:26:34,100 --> 00:26:37,355
used in the most efficient
way, or the optimum way.

373
00:26:48,509 --> 00:26:50,300
And then, let's see--
is that going to fit?

374
00:26:50,300 --> 00:26:51,714
No-- let me try the other board.

375
00:26:55,505 --> 00:26:56,880
And then the last
thing we can do

376
00:26:56,880 --> 00:26:59,910
is calculate that line that
corresponds to the dense solid.

377
00:26:59,910 --> 00:27:02,072
Yeah?

378
00:27:02,072 --> 00:27:04,055
AUDIENCE: On those
ones over there,

379
00:27:04,055 --> 00:27:06,554
it says it corresponds to the
vertical lines on the diagram.

380
00:27:06,554 --> 00:27:08,554
And then later it says
then it becomes vertical.

381
00:27:08,554 --> 00:27:11,050
Is that referring to
two different diagrams?

382
00:27:11,050 --> 00:27:14,020
LORNA GIBSON: So this
stress plateau equation

383
00:27:14,020 --> 00:27:18,320
here corresponds to these
vertical lines here.

384
00:27:18,320 --> 00:27:23,220
So for relative density of 0.01,
it corresponds to that part.

385
00:27:23,220 --> 00:27:25,340
For 0.03 it's this part.

386
00:27:25,340 --> 00:27:27,560
And your 0.01 it's that part.

387
00:27:27,560 --> 00:27:29,522
AUDIENCE: But then
some of the [INAUDIBLE]

388
00:27:29,522 --> 00:27:32,246
it says, then w [? versus ?]
sigma becomes vertical.

389
00:27:32,246 --> 00:27:33,400
Should that--

390
00:27:33,400 --> 00:27:35,120
LORNA GIBSON: So, well
the plateau stress

391
00:27:35,120 --> 00:27:36,920
ends at the
densification strain.

392
00:27:36,920 --> 00:27:39,200
So the plateau stress ends here.

393
00:27:39,200 --> 00:27:41,810
Oh, let's see-- and then it
becomes-- should be horizontal.

394
00:27:41,810 --> 00:27:42,310
Sorry.

395
00:27:56,850 --> 00:27:58,140
OK, sorry.

396
00:27:58,140 --> 00:27:58,640
Happy?

397
00:28:01,657 --> 00:28:03,240
And now I'm going
to rub that all off.

398
00:28:15,230 --> 00:28:16,560
OK, did everybody get this?

399
00:28:16,560 --> 00:28:17,268
I can rub it off?

400
00:28:36,050 --> 00:28:45,350
OK, so then the last
part is what happens

401
00:28:45,350 --> 00:28:48,540
when the foam is densified.

402
00:28:48,540 --> 00:28:50,540
And if it was fully dense--
and you never really

403
00:28:50,540 --> 00:28:52,200
can get to this point--
but if it was fully dense,

404
00:28:52,200 --> 00:28:53,658
you would get rid
of all the pores,

405
00:28:53,658 --> 00:28:55,040
and it would just be a solid.

406
00:28:55,040 --> 00:28:56,750
And then the energy
absorption curve

407
00:28:56,750 --> 00:29:00,200
would be the curve
for the solid.

408
00:29:00,200 --> 00:29:09,142
So I'll just say,
when fully densified,

409
00:29:09,142 --> 00:29:13,095
I'm going to say a curve
approaches that for the solid.

410
00:29:19,450 --> 00:29:24,695
And for the solid, you would
just have that W over Es

411
00:29:24,695 --> 00:29:29,885
is equal to 1/2 the peak
stress squared over Es.

412
00:29:33,410 --> 00:29:36,650
So this model curve, the
curves have the same shape

413
00:29:36,650 --> 00:29:40,070
as when you get the diagrams
from the experiments.

414
00:29:40,070 --> 00:29:42,190
And you can see how the
different mechanisms

415
00:29:42,190 --> 00:29:45,422
of deformation and failure
contribute to the diagram,

416
00:29:45,422 --> 00:29:46,630
where the diagram comes from.

417
00:29:48,884 --> 00:29:50,300
And I guess one
other point is you

418
00:29:50,300 --> 00:29:53,120
can see that the foams are
always going to be a lot better

419
00:29:53,120 --> 00:29:54,260
than the solid.

420
00:29:54,260 --> 00:29:56,050
And remember this
is a log log curve,

421
00:29:56,050 --> 00:30:01,010
so that a foam that has a
density of 3% here, there's

422
00:30:01,010 --> 00:30:03,460
a huge difference
in the peak stress.

423
00:30:03,460 --> 00:30:07,740
So say you wanted to absorb
this amount of energy up here,

424
00:30:07,740 --> 00:30:10,640
for a foam that was 0.03
dense, the peak stress

425
00:30:10,640 --> 00:30:13,900
would be a little less
than 10 to the minus 4,

426
00:30:13,900 --> 00:30:15,520
normalized by the modulus.

427
00:30:15,520 --> 00:30:17,870
And for the solid, it would
be 10 to the minus 2--

428
00:30:17,870 --> 00:30:19,630
so it's orders of
magnitude better to have

429
00:30:19,630 --> 00:30:23,040
the foam rather than the solid.

430
00:30:23,040 --> 00:30:27,030
All right, now let's
see what else we have.

431
00:30:27,030 --> 00:30:29,890
So we could do a similar
thing for closed-cell foams,

432
00:30:29,890 --> 00:30:32,066
and you get diagrams
that look like this.

433
00:30:32,066 --> 00:30:34,440
One of the differences with
the closed-cell foams, if you

434
00:30:34,440 --> 00:30:37,950
assume that the faces don't
rupture, the plateau stresses

435
00:30:37,950 --> 00:30:41,160
and horizontals-- remember
we had that gas contribution,

436
00:30:41,160 --> 00:30:43,270
and you can take
that into account?

437
00:30:43,270 --> 00:30:46,410
So I'm not going to go
over the details of that.

438
00:30:46,410 --> 00:30:47,960
The next one I
wanted to talk about

439
00:30:47,960 --> 00:30:51,500
was looking at foams
that have a yield point.

440
00:30:51,500 --> 00:30:54,200
And again, you can generate
a similar kind of diagram,

441
00:30:54,200 --> 00:30:57,480
but now, instead of having
an elastic failure here,

442
00:30:57,480 --> 00:31:00,810
you've got a plastic failure--
you form plastic hinges.

443
00:31:00,810 --> 00:31:02,670
And then again,
this diagram is less

444
00:31:02,670 --> 00:31:06,000
general than the one
for elastomeric foams,

445
00:31:06,000 --> 00:31:10,150
so this diagram would be valid
for whatever ratio of sigma ys

446
00:31:10,150 --> 00:31:11,810
over Es you've the
calculation for.

447
00:31:11,810 --> 00:31:14,730
So this one here is for 0.01.

448
00:31:14,730 --> 00:31:17,590
So let me just run through
the same kind of calculation

449
00:31:17,590 --> 00:31:19,930
for the plastic foams.

450
00:31:25,414 --> 00:31:26,830
Can I rub this
off, and then I can

451
00:31:26,830 --> 00:31:28,280
use this board to start here?

452
00:32:01,960 --> 00:32:07,980
OK, so the linear elastic
part is just the same

453
00:32:07,980 --> 00:32:10,970
as for the elastomeric foams.

454
00:32:10,970 --> 00:32:16,956
So you get W over Es is 1/2.

455
00:32:16,956 --> 00:32:21,970
Sigma p over Es squared times
1 over the relative density

456
00:32:21,970 --> 00:32:24,700
squared, so it's
just the same thing.

457
00:32:24,700 --> 00:32:34,370
And the stress plateau--
you get w over Es

458
00:32:34,370 --> 00:32:43,010
is just the plastic collapse
strength times the strain range

459
00:32:43,010 --> 00:32:44,960
that you go up to.

460
00:32:44,960 --> 00:32:46,980
So if you remember the
plastic collapse strength

461
00:32:46,980 --> 00:32:55,260
was 0.3 sigma ys times the
relative density to the 3/2

462
00:32:55,260 --> 00:32:57,590
power, and then times
the strain range.

463
00:33:06,820 --> 00:33:09,290
And then at the end
of the stress plateau,

464
00:33:09,290 --> 00:33:13,310
you've got the maximum
energy absorbed.

465
00:33:13,310 --> 00:33:16,420
So normalize that by Es.

466
00:33:16,420 --> 00:33:20,300
And that's going to be
your peak stress over Es

467
00:33:20,300 --> 00:33:22,395
times the densification
strain again.

468
00:33:26,870 --> 00:33:31,674
So this bit here is the
densification strain.

469
00:33:37,000 --> 00:33:38,530
And then you can
do a similar thing

470
00:33:38,530 --> 00:33:40,363
to figure out the
equation of that line that

471
00:33:40,363 --> 00:33:41,590
joins the shoulder points.

472
00:34:04,220 --> 00:34:08,155
So the first step is to solve
for the relative density there.

473
00:34:24,130 --> 00:34:27,810
So if this part here-- 0.3 sigma
ys times the relative density

474
00:34:27,810 --> 00:34:31,719
to the 3/2 power is the
plastic collapse stress,

475
00:34:31,719 --> 00:34:35,760
then at the densification
point, the relative density,

476
00:34:35,760 --> 00:34:38,690
you just rewrite that and it
comes out to the 2/3 power,

477
00:34:38,690 --> 00:34:40,580
because you turn
the power around.

478
00:34:40,580 --> 00:34:42,870
And then you just
substitute this up in here.

479
00:35:17,280 --> 00:35:20,070
So you get that the
maximum energy absorbed,

480
00:35:20,070 --> 00:35:23,310
normalized by the solid modulus,
is your peak stress, times

481
00:35:23,310 --> 00:35:27,290
1 minus 1.4 times this thing
in brackets to the 2/3 power--

482
00:35:27,290 --> 00:35:30,350
the 3.3 times the peak
stress over the yield

483
00:35:30,350 --> 00:35:31,930
strength of the solid.

484
00:35:31,930 --> 00:35:40,830
And then if I just rearrange
that, and get the constants,

485
00:35:40,830 --> 00:35:51,890
it's 1 minus 3.1 times our
ratio of the stresses there.

486
00:35:57,060 --> 00:35:59,610
So maybe I'll just
put over here--

487
00:35:59,610 --> 00:36:04,465
the curves are less general
than for elastomeric foams.

488
00:36:31,100 --> 00:36:33,280
So each family of
curves would be

489
00:36:33,280 --> 00:36:36,400
for a particular ratio of
the solid yield strength

490
00:36:36,400 --> 00:36:37,453
to the solid modulus.

491
00:37:22,590 --> 00:37:23,490
So you get the idea?

492
00:37:23,490 --> 00:37:25,880
It's fairly straightforward.

493
00:37:25,880 --> 00:37:27,690
So I wanted to
finish up this topic

494
00:37:27,690 --> 00:37:31,280
by giving you a few examples of
how you can use these curves.

495
00:37:31,280 --> 00:37:33,560
So the next thing is to look
at the selection of foams

496
00:37:33,560 --> 00:37:35,080
for impact protection.

497
00:37:35,080 --> 00:37:37,750
And typically, you're given some
information about the objects--

498
00:37:37,750 --> 00:37:39,850
so typically you want
to protect some object.

499
00:37:39,850 --> 00:37:42,230
It could be a computer,
it could be your head,

500
00:37:42,230 --> 00:37:43,650
some part of your body.

501
00:37:43,650 --> 00:37:45,650
So typically you know
something about the object

502
00:37:45,650 --> 00:37:46,680
you want to protect.

503
00:37:46,680 --> 00:37:50,350
So you might know its mass, you
might know the area of contact,

504
00:37:50,350 --> 00:37:52,280
you might say, well,
if it's my computer,

505
00:37:52,280 --> 00:37:53,890
I want to make sure it
doesn't break if I drop it

506
00:37:53,890 --> 00:37:54,890
from a height of a meter.

507
00:37:54,890 --> 00:37:56,550
Or you could say whatever,
[? maybe it's ?] 2 meters.

508
00:37:56,550 --> 00:37:58,010
But you pick something.

509
00:37:58,010 --> 00:37:59,820
And so there's a
certain amount of energy

510
00:37:59,820 --> 00:38:01,410
you know that you
need to absorb.

511
00:38:01,410 --> 00:38:04,310
And you may know that
whatever the component is,

512
00:38:04,310 --> 00:38:06,280
or the body part, or
whatever-- there's

513
00:38:06,280 --> 00:38:09,427
some maximum acceleration
you can tolerate.

514
00:38:09,427 --> 00:38:11,010
So you might say,
well, I want to make

515
00:38:11,010 --> 00:38:14,180
sure my computer doesn't break
under acceleration of so much.

516
00:38:14,180 --> 00:38:16,399
So you're given
the acceleration.

517
00:38:16,399 --> 00:38:18,440
And so if you know the
mass and the acceleration,

518
00:38:18,440 --> 00:38:19,814
and you know the
area of contact,

519
00:38:19,814 --> 00:38:22,300
you can figure out a
force over an area,

520
00:38:22,300 --> 00:38:24,140
and that gives you
the peak stress.

521
00:38:24,140 --> 00:38:26,940
So typically, you know
those things in the problem.

522
00:38:26,940 --> 00:38:29,700
And typically the problem
involves choosing a material,

523
00:38:29,700 --> 00:38:31,810
or choosing-- like choosing
what kind of material

524
00:38:31,810 --> 00:38:34,390
do you want to make the foam
out of, and what density of foam

525
00:38:34,390 --> 00:38:35,800
do you want to use,
what thickness of foam

526
00:38:35,800 --> 00:38:36,810
do you want to use?

527
00:38:36,810 --> 00:38:38,830
So I've got a couple
of examples just

528
00:38:38,830 --> 00:38:40,580
to show you how this works.

529
00:38:40,580 --> 00:38:43,094
So let me just write down
a couple notes, and then

530
00:38:43,094 --> 00:38:45,677
the rest of it I think I'm just
going to take from the slides.

531
00:39:09,140 --> 00:39:12,410
So typically, you know what
it is you want to protect,

532
00:39:12,410 --> 00:39:13,850
and you know something about it.

533
00:39:20,714 --> 00:39:22,380
So if you know what
it is, typically you

534
00:39:22,380 --> 00:39:23,557
know what the mass is.

535
00:39:28,700 --> 00:39:31,090
You might know what the
contact area would be.

536
00:39:41,300 --> 00:39:49,279
Say a maximum drop height,
maximum tolerable acceleration.

537
00:39:53,870 --> 00:39:55,750
So say if you're worried
about brain injury--

538
00:39:55,750 --> 00:39:59,230
and making a helmet-- you might
know what the maximum tolerable

539
00:39:59,230 --> 00:40:00,482
acceleration would be.

540
00:40:06,870 --> 00:40:09,720
So typically, you know what the
peak allowable stress is, just

541
00:40:09,720 --> 00:40:11,770
from whatever the
object itself is.

542
00:40:11,770 --> 00:40:15,700
And the variables that
you have to play around

543
00:40:15,700 --> 00:40:25,530
with-- variables-- are things
like the foam material,

544
00:40:25,530 --> 00:40:28,965
the foam density, and
the foam thickness.

545
00:40:32,420 --> 00:40:34,030
So I have a couple
of examples that

546
00:40:34,030 --> 00:40:37,910
have different setups here.

547
00:40:37,910 --> 00:40:41,610
And we'll just see how
the thing works out here.

548
00:40:41,610 --> 00:40:45,520
So the first example, we're told
the mass of the packaged object

549
00:40:45,520 --> 00:40:47,210
is 1/2 kilogram.

550
00:40:47,210 --> 00:40:49,870
We're told the area of
contact between the foam

551
00:40:49,870 --> 00:40:51,370
and the object is
going to be point.

552
00:40:51,370 --> 00:40:53,190
0.01 of 1 meter squared.

553
00:40:53,190 --> 00:40:54,700
And we're told
that it's supposed

554
00:40:54,700 --> 00:40:57,830
to be designed to withstand
a drop of 1 meter--

555
00:40:57,830 --> 00:40:59,790
so if the drop
height is 1 meter,

556
00:40:59,790 --> 00:41:03,670
then the velocity is just
the square root of 2gh.

557
00:41:03,670 --> 00:41:06,620
So g is gravity, so you can
work out the velocity on impact

558
00:41:06,620 --> 00:41:09,184
would be 4.5 meters per second.

559
00:41:09,184 --> 00:41:11,350
And if you have the velocity
on impact and the mass,

560
00:41:11,350 --> 00:41:13,387
you can figure out the
energy to be absorbed.

561
00:41:13,387 --> 00:41:14,970
You can say mv squared
screwed over 2,

562
00:41:14,970 --> 00:41:17,280
or you could say it's
mgh-- either way.

563
00:41:17,280 --> 00:41:20,430
So here it's going to
work out to 5 joules.

564
00:41:20,430 --> 00:41:25,100
And in this case, we're told
that the maximum deceleration

565
00:41:25,100 --> 00:41:29,300
is 10g-- so then if that's 10g,
the maximum force is the mass

566
00:41:29,300 --> 00:41:30,900
times the acceleration.

567
00:41:30,900 --> 00:41:32,920
That works out to 50 Newtons.

568
00:41:32,920 --> 00:41:34,800
And then that gives
us a peak stress,

569
00:41:34,800 --> 00:41:36,240
the maximum
allowable peak stress

570
00:41:36,240 --> 00:41:39,060
of the force over the area
it's 5 kiloNewtons per meter

571
00:41:39,060 --> 00:41:40,270
squared.

572
00:41:40,270 --> 00:41:42,240
And in this case, we're
told that the foam is

573
00:41:42,240 --> 00:41:44,400
going to be a
flexible polyurethane,

574
00:41:44,400 --> 00:41:47,550
and it has a solid
modulus of 50 megapascals.

575
00:41:47,550 --> 00:41:49,920
And so we can calculate
this normalized peak stress.

576
00:41:49,920 --> 00:41:53,110
So the normalized peak stress
here is 10 to the minus 4.

577
00:41:53,110 --> 00:41:56,350
So in this problem here,
we need to figure out

578
00:41:56,350 --> 00:41:58,020
what's the foam
density, and what's

579
00:41:58,020 --> 00:42:01,450
the thickness of the foam
to protect the object?

580
00:42:01,450 --> 00:42:05,024
And so that last slide
is just summarized here.

581
00:42:05,024 --> 00:42:07,190
And I realized that when I
was going to put this up,

582
00:42:07,190 --> 00:42:08,773
the font is going
to be kind of small,

583
00:42:08,773 --> 00:42:10,680
so I blew it up a little.

584
00:42:10,680 --> 00:42:12,980
So we have figured
out that we're

585
00:42:12,980 --> 00:42:15,850
at sigma p over Es-- the
peak stress normalized

586
00:42:15,850 --> 00:42:18,372
by the solid modulus
is 10 to the minus 4.

587
00:42:18,372 --> 00:42:19,830
And we know that
we're going to use

588
00:42:19,830 --> 00:42:22,840
a flexible elastomeric
polyurethane,

589
00:42:22,840 --> 00:42:26,330
so we pull out our diagram
for elastomeric foams.

590
00:42:26,330 --> 00:42:28,660
And this sort of
hashed band here

591
00:42:28,660 --> 00:42:30,940
corresponds to all the
different strain rates, and all

592
00:42:30,940 --> 00:42:31,990
the different densities.

593
00:42:31,990 --> 00:42:33,900
So I haven't plotted
each individual line,

594
00:42:33,900 --> 00:42:37,970
we've just got this band that
represents the whole thing.

595
00:42:37,970 --> 00:42:39,510
So we know that
our normalized peak

596
00:42:39,510 --> 00:42:43,060
stress is going to be
somewhere along this line here.

597
00:42:43,060 --> 00:42:44,620
That's from everything
that's given,

598
00:42:44,620 --> 00:42:46,220
and what we can calculate.

599
00:42:46,220 --> 00:42:48,220
And we want to know what
density of foam to use,

600
00:42:48,220 --> 00:42:49,610
and what thickness.

601
00:42:49,610 --> 00:42:52,300
So the way you approach
this is the thickness

602
00:42:52,300 --> 00:42:53,759
is going to affect
the strain rate.

603
00:42:53,759 --> 00:42:56,299
So the strain rate's just going
to be the velocity on impact,

604
00:42:56,299 --> 00:42:58,590
divided by the thickness--
or it's an approximation

605
00:42:58,590 --> 00:42:59,960
for the strain rate.

606
00:42:59,960 --> 00:43:02,380
So we don't know if we're
at this point down here,

607
00:43:02,380 --> 00:43:03,950
or if we're at this
point up there,

608
00:43:03,950 --> 00:43:06,190
because we don't know where
we are in the strain rate

609
00:43:06,190 --> 00:43:07,580
end of things.

610
00:43:07,580 --> 00:43:10,506
So the way you solve this is
you just guess a thickness.

611
00:43:10,506 --> 00:43:11,880
And if you guess
a thickness, you

612
00:43:11,880 --> 00:43:13,237
can calculate a strain rate.

613
00:43:13,237 --> 00:43:14,820
Then if you calculate
the strain rate,

614
00:43:14,820 --> 00:43:16,650
you know where in
this band you are.

615
00:43:16,650 --> 00:43:19,370
You can figure out a
value of W over Es.

616
00:43:19,370 --> 00:43:21,970
And you can use an
iterative process.

617
00:43:21,970 --> 00:43:23,690
And the way this
is set up is we've

618
00:43:23,690 --> 00:43:27,090
chosen two very different
initial thicknesses,

619
00:43:27,090 --> 00:43:29,130
and the point of doing
that is to show you

620
00:43:29,130 --> 00:43:31,190
that it converges very quickly.

621
00:43:31,190 --> 00:43:33,410
So the first
iteration on this side

622
00:43:33,410 --> 00:43:35,540
here, we've chosen the
thickness of a meter, which

623
00:43:35,540 --> 00:43:38,590
is probably unlikely that
we need a meter of foam.

624
00:43:38,590 --> 00:43:41,450
And on the side here, we've
chosen a millimeter-- 0.001

625
00:43:41,450 --> 00:43:41,950
meters.

626
00:43:41,950 --> 00:43:43,620
So probably, we
need more than that.

627
00:43:43,620 --> 00:43:45,078
So we probably need
to be somewhere

628
00:43:45,078 --> 00:43:46,570
between those two bounds.

629
00:43:46,570 --> 00:43:49,600
So if the thickness was a
meter, then the strain rate

630
00:43:49,600 --> 00:43:52,300
turns out to be 4.5 per second.

631
00:43:52,300 --> 00:43:54,940
And then we know where
we are in this diagram,

632
00:43:54,940 --> 00:43:57,970
and we can read off
a value of W over Es.

633
00:43:57,970 --> 00:44:00,350
So we know we're
on this line here,

634
00:44:00,350 --> 00:44:02,220
and for a particular
strain rate,

635
00:44:02,220 --> 00:44:04,580
we can read off the W over Es.

636
00:44:04,580 --> 00:44:08,660
So here's the value-- 5.25
times 10 to the minus 5.

637
00:44:08,660 --> 00:44:10,840
And if we know Es,
which we do, we

638
00:44:10,840 --> 00:44:13,579
can then calculate
the actual energy

639
00:44:13,579 --> 00:44:14,620
absorbed per unit volume.

640
00:44:14,620 --> 00:44:19,190
We get W-- so W is [? 2620 ?]
joules per cubic meter.

641
00:44:19,190 --> 00:44:21,550
And we can use that
value-- because that's

642
00:44:21,550 --> 00:44:24,904
an energy per unit volume--
we know the area of contact,

643
00:44:24,904 --> 00:44:27,320
and we can use that to get
another value of the thickness.

644
00:44:27,320 --> 00:44:30,160
So we use that to calculate
the next iteration

645
00:44:30,160 --> 00:44:31,580
of the thickness.

646
00:44:31,580 --> 00:44:34,190
So U is the total
energy in joules,

647
00:44:34,190 --> 00:44:36,600
and W is the energy
per unit volume.

648
00:44:36,600 --> 00:44:38,930
So U, the energy
in joules, is going

649
00:44:38,930 --> 00:44:41,410
to equal the energy unit
volume times the area

650
00:44:41,410 --> 00:44:42,746
times the thickness.

651
00:44:42,746 --> 00:44:44,120
So we know what
the area is, too.

652
00:44:44,120 --> 00:44:46,270
We can then calculate
a new thickness.

653
00:44:46,270 --> 00:44:49,320
So now our new thickness
is 0.19 meters.

654
00:44:49,320 --> 00:44:50,790
We can use that to
get a new strain

655
00:44:50,790 --> 00:44:53,790
rate-- that's 24 per second,
and go through the whole thing

656
00:44:53,790 --> 00:44:54,390
again.

657
00:44:54,390 --> 00:44:58,320
And we end up with a revised
energy of 3,300 joules

658
00:44:58,320 --> 00:45:00,032
per cubic meter.

659
00:45:00,032 --> 00:45:01,490
Now if we started
at the other end,

660
00:45:01,490 --> 00:45:05,410
if we started with the first
guess was a millimeter, then

661
00:45:05,410 --> 00:45:09,890
the strain rate is 4.5 times
10 to the minus 3 per second.

662
00:45:09,890 --> 00:45:12,270
That gives us a different
value that we read off here

663
00:45:12,270 --> 00:45:15,780
for W over Es, and a
different value for W.

664
00:45:15,780 --> 00:45:17,950
And then we use this
value here for W

665
00:45:17,950 --> 00:45:20,230
to make another guess
for the thickness.

666
00:45:20,230 --> 00:45:22,707
So that value is 0.14.

667
00:45:22,707 --> 00:45:24,290
And then we go through
the whole thing

668
00:45:24,290 --> 00:45:27,580
again-- we get a revised strain
rate a revised W over Es,

669
00:45:27,580 --> 00:45:31,510
and a revised W. And you can
see after just two iterations,

670
00:45:31,510 --> 00:45:33,449
these two things are
almost exactly the same.

671
00:45:33,449 --> 00:45:34,990
And then on the
third iteration, they

672
00:45:34,990 --> 00:45:38,730
both would give you a
thickness of point 0.15 meters.

673
00:45:38,730 --> 00:45:42,620
So even though you can pick
wildly wrong first iterations,

674
00:45:42,620 --> 00:45:46,120
it converges very quickly,
and it's a fairly simple

675
00:45:46,120 --> 00:45:48,310
calculation to do.

676
00:45:48,310 --> 00:45:51,210
So you know the thickness
that you want is in here,

677
00:45:51,210 --> 00:45:54,180
and then you can get the
optimum density here.

678
00:45:54,180 --> 00:45:58,540
So you know that your sigma
p over Es is along this line

679
00:45:58,540 --> 00:46:00,970
of 10 to the minus
4--we're somewhere in here.

680
00:46:00,970 --> 00:46:03,210
These two strain rates
here-- one was 24,

681
00:46:03,210 --> 00:46:06,400
one was 32-- so the
final value is going

682
00:46:06,400 --> 00:46:08,210
to be somewhere around 30.

683
00:46:08,210 --> 00:46:10,550
And if you look on
this thing here,

684
00:46:10,550 --> 00:46:12,830
you can see there's a line
that corresponds to 10,

685
00:46:12,830 --> 00:46:14,624
there's a line that
corresponds to 100.

686
00:46:14,624 --> 00:46:16,290
We're going to be
right around in there.

687
00:46:16,290 --> 00:46:20,180
So the relative density is
going to be right around 0.01.

688
00:46:20,180 --> 00:46:22,280
So you can use the diagram
to get the thickness

689
00:46:22,280 --> 00:46:24,660
and to get the density.

690
00:46:24,660 --> 00:46:26,220
OK, are we good?

691
00:46:26,220 --> 00:46:28,320
We're good?

692
00:46:28,320 --> 00:46:31,190
So I've written some notes,
and I'll just scan those

693
00:46:31,190 --> 00:46:34,370
and I'll put them
in the Stellar site.

694
00:46:34,370 --> 00:46:37,700
So here's another example
here-- and in this example,

695
00:46:37,700 --> 00:46:40,190
it's set up a little
bit differently.

696
00:46:40,190 --> 00:46:44,212
So in this example here,
we're not told the material,

697
00:46:44,212 --> 00:46:45,920
but we're told the
thickness of the foam.

698
00:46:45,920 --> 00:46:47,910
So this time we want
to get the material,

699
00:46:47,910 --> 00:46:50,460
and we want to get the
density of the foam.

700
00:46:50,460 --> 00:46:53,020
So here we've got
the specification.

701
00:46:53,020 --> 00:46:55,920
We're told the mass is
2 and 1/2 kilograms.

702
00:46:55,920 --> 00:46:58,724
The area of contact is
0.025 meters squared.

703
00:46:58,724 --> 00:47:01,224
We're told the thickness-- here
thickness is 20 millimeters.

704
00:47:02,540 --> 00:47:04,844
We've got a drop height
of 1 meter again.

705
00:47:04,844 --> 00:47:06,260
And the velocity
of impact is then

706
00:47:06,260 --> 00:47:08,784
going to be 4.5 meters
per second again.

707
00:47:08,784 --> 00:47:11,200
And since we know T, we know
that the strain rate is going

708
00:47:11,200 --> 00:47:15,960
to be around 225 per second.

709
00:47:15,960 --> 00:47:19,700
We can calculate the energy
absorbed-- [? MGH-- ?]

710
00:47:19,700 --> 00:47:21,790
25 joules.

711
00:47:21,790 --> 00:47:24,154
We can calculate the energy
absorbed per unit volume,

712
00:47:24,154 --> 00:47:26,070
because we've got the
area and the thickness--

713
00:47:26,070 --> 00:47:28,694
so I'm just going to divide that
by the area and the thickness.

714
00:47:28,694 --> 00:47:33,300
Now we have 5 times 10 to the
4th joules per cubic meter.

715
00:47:33,300 --> 00:47:35,520
And we're told that we're
supposed to design it

716
00:47:35,520 --> 00:47:40,260
so the package can withstand
a deceleration of 100g--

717
00:47:40,260 --> 00:47:42,530
and so that gives
you a maximum force.

718
00:47:42,530 --> 00:47:45,520
And here we've got a maximum
allowable peak stress of 10

719
00:47:45,520 --> 00:47:48,460
of the 5 Newtons
per meter squared.

720
00:47:48,460 --> 00:47:51,327
So here we have our curve for
the elastomeric foams again--

721
00:47:51,327 --> 00:47:53,410
let's assume it's going
to be an elastomeric foam,

722
00:47:53,410 --> 00:47:56,290
but we don't know
what kind of foam.

723
00:47:56,290 --> 00:47:58,180
So the way you
solve this problem

724
00:47:58,180 --> 00:48:01,050
is that you make a
guess for what Es is.

725
00:48:01,050 --> 00:48:04,480
So remember, these diagrams
are all normalized by Es.

726
00:48:04,480 --> 00:48:07,630
So to plot a point on there,
we need to know what Es is.

727
00:48:07,630 --> 00:48:09,440
So here, we're going
to make a guess,

728
00:48:09,440 --> 00:48:13,850
and we're going to assume that
Es is 100 megapascals to start.

729
00:48:13,850 --> 00:48:17,670
And if we had that value
of Es, we know W, up here,

730
00:48:17,670 --> 00:48:19,700
and we know sigma p there.

731
00:48:19,700 --> 00:48:22,960
So we just divide those
values of W and sigma p by Es,

732
00:48:22,960 --> 00:48:24,990
and we get these
two values here.

733
00:48:24,990 --> 00:48:28,200
And we plot those two
values on the thing here.

734
00:48:28,200 --> 00:48:30,450
So here's our point A--
and that corresponds

735
00:48:30,450 --> 00:48:33,300
to that first guess
of 100 mega Pascals

736
00:48:33,300 --> 00:48:36,010
for the modulus of the solid.

737
00:48:36,010 --> 00:48:38,200
So that's not necessarily
the final answer,

738
00:48:38,200 --> 00:48:41,210
that's not the right answer--
that's just somewhere to start.

739
00:48:41,210 --> 00:48:44,877
So the thing to notice is,
if we have that point there,

740
00:48:44,877 --> 00:48:46,960
the strain rate there is
probably not quite right.

741
00:48:46,960 --> 00:48:50,580
This upper bound
here is-- let's see.

742
00:48:50,580 --> 00:48:51,790
Got to get closer.

743
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.

744
00:48:54,770 --> 00:48:57,280
So the strain rate we want
to be is closer up to here,

745
00:48:57,280 --> 00:48:59,830
it's not quite down there.

746
00:48:59,830 --> 00:49:02,240
So we're not at the
right strain rate.

747
00:49:02,240 --> 00:49:05,650
But the thing to notice is that
if we draw a line of slope 1--

748
00:49:05,650 --> 00:49:08,090
so there's this dash
line of slope 1--

749
00:49:08,090 --> 00:49:11,895
when we move up and down that
line, we're just changing Es.

750
00:49:11,895 --> 00:49:13,770
Because everything is
normalized with respect

751
00:49:13,770 --> 00:49:16,310
to Es-- if that line
has a slope of 1,

752
00:49:16,310 --> 00:49:20,040
then we're just moving up
and down with respect to Es.

753
00:49:20,040 --> 00:49:22,300
So what we do is we
scoot up the line

754
00:49:22,300 --> 00:49:25,700
to get to the point that's
on the right strain rate.

755
00:49:25,700 --> 00:49:28,720
So if this was a strain
rate of 100, or around 200,

756
00:49:28,720 --> 00:49:31,590
we want to be at point
B. And then from point B,

757
00:49:31,590 --> 00:49:35,380
we can read off what's
the value of W over Es,

758
00:49:35,380 --> 00:49:36,960
and sigma p over Es.

759
00:49:36,960 --> 00:49:39,650
And from that, we can back out
what the solid modulus we want

760
00:49:39,650 --> 00:49:40,350
is.

761
00:49:40,350 --> 00:49:43,560
So these are the values
that we read off the chart.

762
00:49:43,560 --> 00:49:46,930
This gives us an Es
of 28 mega Pascals.

763
00:49:46,930 --> 00:49:50,240
And again, you can go to this
more detailed diagram here,

764
00:49:50,240 --> 00:49:53,790
and if you read off the sigma
p over Es, and the W over Es,

765
00:49:53,790 --> 00:49:56,370
the density you
want is about 0.1.

766
00:49:56,370 --> 00:49:58,092
So it tells you the
modulus of the solid,

767
00:49:58,092 --> 00:49:59,550
and from that you
can pick a solid,

768
00:49:59,550 --> 00:50:02,060
and it tells you the density.

769
00:50:02,060 --> 00:50:04,232
Are we good?

770
00:50:04,232 --> 00:50:05,190
OK, so I have one more.

771
00:50:05,190 --> 00:50:08,154
So there's a slightly different
way you can do it, too.

772
00:50:08,154 --> 00:50:10,320
So now I want to talk about
bicycle helmets-- you're

773
00:50:10,320 --> 00:50:11,400
my bicycle helmet person.

774
00:50:14,040 --> 00:50:15,810
So this is another
little case study

775
00:50:15,810 --> 00:50:18,990
that involves a slightly
different way to do this.

776
00:50:18,990 --> 00:50:21,410
And this involves a
slightly different diagram.

777
00:50:21,410 --> 00:50:24,859
So the idea here is to choose a
material for a bicycle helmet.

778
00:50:24,859 --> 00:50:26,900
And as you probably all
know, the bicycle helmets

779
00:50:26,900 --> 00:50:29,700
have a hard shell, and they
have some sort of foamy liner.

780
00:50:29,700 --> 00:50:32,660
And the foam's usually
around 20 millimeters thick.

781
00:50:32,660 --> 00:50:34,244
And you want something
that's light,

782
00:50:34,244 --> 00:50:36,410
because you don't want your
helmet to be too heavy--

783
00:50:36,410 --> 00:50:38,035
but you want something
that will absorb

784
00:50:38,035 --> 00:50:39,310
the energy from the impact.

785
00:50:39,310 --> 00:50:43,760
So I've set this up here-- so
we assume the mass of the head

786
00:50:43,760 --> 00:50:45,610
is about 3 kilograms.

787
00:50:45,610 --> 00:50:47,170
And we assume that
it can withstand

788
00:50:47,170 --> 00:50:50,120
a deceleration of
something like 300g--

789
00:50:50,120 --> 00:50:53,190
and so then you can get a force
mass times the acceleration,

790
00:50:53,190 --> 00:50:54,460
because you have the force.

791
00:50:54,460 --> 00:50:56,460
And I've assumed an area
of contact of something

792
00:50:56,460 --> 00:51:01,270
like 0.01 meters squared, so
that gives you a peak stress.

793
00:51:01,270 --> 00:51:04,150
So this method here
is based on the idea

794
00:51:04,150 --> 00:51:07,590
that you have these material
selection charts for foams.

795
00:51:07,590 --> 00:51:09,770
Remember we talked
about that earlier.

796
00:51:09,770 --> 00:51:12,660
And this is the compressive
stress at 25% strain.

797
00:51:12,660 --> 00:51:14,350
So the idea is
that axis there is

798
00:51:14,350 --> 00:51:16,590
meant to represent
the plateau stress,

799
00:51:16,590 --> 00:51:20,060
and this axis here represents
the densification strain.

800
00:51:20,060 --> 00:51:22,950
And these dashed
lines here correspond

801
00:51:22,950 --> 00:51:26,090
to basically a value
of W-- and energy

802
00:51:26,090 --> 00:51:28,290
absorbed per unit volume.

803
00:51:28,290 --> 00:51:30,380
So this is an energy
absorbed per unit volume

804
00:51:30,380 --> 00:51:35,470
of 0.001 megajoules per
cubic meter, 0.01, and so on.

805
00:51:35,470 --> 00:51:39,846
So if you know the peak
stress that you can tolerate,

806
00:51:39,846 --> 00:51:41,470
for the numbers I
gave you it works out

807
00:51:41,470 --> 00:51:45,220
to be 0.9 mega Pascals-- so here
it's just a little less than 1.

808
00:51:45,220 --> 00:51:48,240
So that's the peak stress
that you can tolerate there.

809
00:51:48,240 --> 00:51:51,800
And you can see that
the material that's

810
00:51:51,800 --> 00:51:55,040
going to absorb the most
energy-- so you're absorbing

811
00:51:55,040 --> 00:51:59,040
more energy as you move
over this way on the curve

812
00:51:59,040 --> 00:52:01,820
on the plot-- so the material
that's going to do the best

813
00:52:01,820 --> 00:52:05,480
is something like an expanded
polystyrene that's 5% dense.

814
00:52:05,480 --> 00:52:07,440
So I've highlighted
that in red-- expanded

815
00:52:07,440 --> 00:52:10,030
polystyrene that's 5% dense.

816
00:52:10,030 --> 00:52:13,060
And then this is the
densification strain here.

817
00:52:13,060 --> 00:52:15,510
And you know that the lines
of the energy absorption

818
00:52:15,510 --> 00:52:18,580
are just the stress
times the strain.

819
00:52:18,580 --> 00:52:20,580
So you can basically
just read off from here

820
00:52:20,580 --> 00:52:22,940
that expanded polystyrene
that was 5% dense

821
00:52:22,940 --> 00:52:26,680
would be a good choice
for a bicycle helmet foam.

822
00:52:26,680 --> 00:52:30,570
Would you like to add anything
about bicycle helmet foams?

823
00:52:30,570 --> 00:52:33,850
I think that is exactly
what they use, yes.

824
00:52:33,850 --> 00:52:36,180
So this is just another way
to do this kind of thing.

825
00:52:36,180 --> 00:52:38,640
And I did one more
little calculation here--

826
00:52:38,640 --> 00:52:42,340
if you know the thickness of the
foam is, say, 20 millimeters,

827
00:52:42,340 --> 00:52:45,110
and we've estimated the
area of the contact,

828
00:52:45,110 --> 00:52:47,980
you can figure out what
the energy absorbed is

829
00:52:47,980 --> 00:52:49,970
per unit volume, and from
that you can back out

830
00:52:49,970 --> 00:52:53,020
the energy in terms of joules,
and from that you can back out

831
00:52:53,020 --> 00:52:56,170
the velocity that's the
maximum speed that one

832
00:52:56,170 --> 00:52:59,490
would want to get dinged
at on your bicycle.

833
00:52:59,490 --> 00:53:02,540
And the maximum speed works
out about 22 miles an hour.

834
00:53:02,540 --> 00:53:06,190
So that's just another example.

835
00:53:06,190 --> 00:53:07,750
Are we good?

836
00:53:07,750 --> 00:53:11,592
OK-- yeah, exactly,
your head would

837
00:53:11,592 --> 00:53:13,300
be hitting the ground
at 22 miles an hour

838
00:53:13,300 --> 00:53:14,730
which, would be ouchy.

839
00:53:14,730 --> 00:53:17,310
Which is why you want
to wear your helmet,

840
00:53:17,310 --> 00:53:20,126
because your skull will not
be happy if that happens.

841
00:53:20,126 --> 00:53:21,500
And your brain
will not be happy.

842
00:53:21,500 --> 00:53:23,110
And you will not be happy.

843
00:53:23,110 --> 00:53:26,780
And your mom and dad will be
really, really, really unhappy.

844
00:53:26,780 --> 00:53:29,470
So you don't want
that to happen.

845
00:53:29,470 --> 00:53:31,540
so I have a few
minutes left-- and I

846
00:53:31,540 --> 00:53:33,464
know I've done this
for the people in 3032,

847
00:53:33,464 --> 00:53:35,630
but I was going to buy
woodpecker talk, because it's

848
00:53:35,630 --> 00:53:37,420
about energy absorption.

849
00:53:37,420 --> 00:53:39,920
So if you don't want to watch
it, if you've already seen it,

850
00:53:39,920 --> 00:53:40,572
you can go.

851
00:53:40,572 --> 00:53:42,780
But there are some people--
you guys haven't seen it,

852
00:53:42,780 --> 00:53:43,590
and you haven't seen it.

853
00:53:43,590 --> 00:53:45,215
There's a few people
that haven't seen.

854
00:53:45,215 --> 00:53:47,222
And it's cute, involves birds.

855
00:53:47,222 --> 00:53:48,680
And it involves
energy absorption--

856
00:53:48,680 --> 00:53:50,576
so I thought I would do
this woodpecker talk.

857
00:53:56,830 --> 00:53:58,510
So Barry, this is
all just slides.

858
00:53:58,510 --> 00:54:01,310
I don't know if you want to
do the lights differently.

859
00:54:01,310 --> 00:54:02,590
I'm not going to write
anything on the board,

860
00:54:02,590 --> 00:54:03,440
I'm just going to talk.

861
00:54:03,440 --> 00:54:05,172
BARRY: Well, if it will help
them see the slides better then

862
00:54:05,172 --> 00:54:05,550
certainly.

863
00:54:05,550 --> 00:54:07,050
LORNA GIBSON: Yeah,
I think maybe we

864
00:54:07,050 --> 00:54:09,021
could turn the lights
down a little, please.

865
00:54:16,210 --> 00:54:18,240
BARRY: Let's try this one.

866
00:54:18,240 --> 00:54:19,490
LORNA GIBSON: Oh, there we go.

867
00:54:19,490 --> 00:54:20,060
That's good.

868
00:54:20,060 --> 00:54:22,920
Yeah, now I don't feel like
I'm looking in the spotlight

869
00:54:22,920 --> 00:54:23,420
so much.

870
00:54:23,420 --> 00:54:24,510
That's good.

871
00:54:24,510 --> 00:54:28,380
OK, so you guys know that
I like to watch birds.

872
00:54:28,380 --> 00:54:31,150
And you know that
I work on foams.

873
00:54:31,150 --> 00:54:34,040
And if you look at bird books,
sometimes the bird books

874
00:54:34,040 --> 00:54:37,940
say that woodpeckers
can withstand the impact

875
00:54:37,940 --> 00:54:40,590
from pecking because they
have a special material

876
00:54:40,590 --> 00:54:42,550
between their skulls
and their brains.

877
00:54:42,550 --> 00:54:44,550
And I thought, oh,
well I study foams,

878
00:54:44,550 --> 00:54:46,850
and I'm interested in
woodpeckers-- I should find out

879
00:54:46,850 --> 00:54:48,440
what this special material is.

880
00:54:48,440 --> 00:54:49,980
So I started looking into this.

881
00:54:49,980 --> 00:54:52,180
And it turns out there
is no special material.

882
00:54:52,180 --> 00:54:55,160
People have looked at the
anatomy of woodpecker brains

883
00:54:55,160 --> 00:54:57,660
and skulls, and there
is no special material.

884
00:54:57,660 --> 00:55:00,020
But it turns out there were
also a group of neurologists

885
00:55:00,020 --> 00:55:02,740
in the late 1970s who got
interested in why woodpeckers

886
00:55:02,740 --> 00:55:05,610
don't get brain injury, and
they took high speed video

887
00:55:05,610 --> 00:55:06,710
of a woodpecker pecking.

888
00:55:06,710 --> 00:55:09,110
And it was kind of amazing
what they found out.

889
00:55:09,110 --> 00:55:11,230
So it turns out the
woodpeckers can withstand

890
00:55:11,230 --> 00:55:14,810
incredibly high decelerations--
much higher than our brains

891
00:55:14,810 --> 00:55:15,684
could withstand.

892
00:55:15,684 --> 00:55:17,350
And so I kind of got
interested in this,

893
00:55:17,350 --> 00:55:21,050
and I decided to try to
figure out how it works.

894
00:55:21,050 --> 00:55:23,650
So here's an acorn woodpecker.

895
00:55:23,650 --> 00:55:27,590
And let's see-- I got
a little video here.

896
00:55:27,590 --> 00:55:30,860
Wait a minute-- there we go.

897
00:55:30,860 --> 00:55:31,420
There we go.

898
00:55:31,420 --> 00:55:32,920
So here's a little
acorn woodpecker.

899
00:55:32,920 --> 00:55:34,160
These live in California.

900
00:55:34,160 --> 00:55:35,510
Anybody from California?

901
00:55:35,510 --> 00:55:37,570
Yeah-- have you seen them?

902
00:55:37,570 --> 00:55:39,430
No, OK.

903
00:55:39,430 --> 00:55:41,230
Well you have not been
looking carefully.

904
00:55:41,230 --> 00:55:44,810
So here's our little acorn--
and you can see they peck-- oh?

905
00:55:44,810 --> 00:55:46,240
Like around San Francisco.

906
00:55:46,240 --> 00:55:48,586
AUDIENCE: [INAUDIBLE].

907
00:55:48,586 --> 00:55:50,520
[LAUGHS]

908
00:55:50,520 --> 00:55:52,010
LORNA GIBSON: So
they're pecking,

909
00:55:52,010 --> 00:55:54,760
and when they're pecking--
they don't just go bonk.

910
00:55:54,760 --> 00:55:58,190
They do this repeatedly-- they
can peck at 10 or 20 times

911
00:55:58,190 --> 00:55:59,300
per second.

912
00:55:59,300 --> 00:56:03,450
So the question is, why
don't they get brain injury?

913
00:56:03,450 --> 00:56:05,720
So, first of all,
why do they peck?

914
00:56:05,720 --> 00:56:08,520
So as we in that little
video, that woodpecker

915
00:56:08,520 --> 00:56:10,860
was foraging-- it was trying
to get little things out

916
00:56:10,860 --> 00:56:11,470
of the bark.

917
00:56:11,470 --> 00:56:16,320
And woodpeckers eat insects,
and so the bird books

918
00:56:16,320 --> 00:56:18,890
say that they can actually
hear insects scurrying around

919
00:56:18,890 --> 00:56:21,300
under the bark, and
they'll peck at the bark

920
00:56:21,300 --> 00:56:23,607
and forage to try
to get insects.

921
00:56:23,607 --> 00:56:25,940
And there's one other anatomical
feature of woodpeckers,

922
00:56:25,940 --> 00:56:28,601
which is kind of amazing-- and
you can see it in this picture

923
00:56:28,601 --> 00:56:29,100
here.

924
00:56:29,100 --> 00:56:31,094
So this is the
woodpecker tongue,

925
00:56:31,094 --> 00:56:32,760
and the tongue is
connected to something

926
00:56:32,760 --> 00:56:34,210
called the hyoid process.

927
00:56:34,210 --> 00:56:37,736
And the hyoid process wraps
around their eyeballs.

928
00:56:37,736 --> 00:56:39,110
And then when they
peck-- I mean,

929
00:56:39,110 --> 00:56:41,840
the idea is they're
making a hole in the tree,

930
00:56:41,840 --> 00:56:43,930
and they've got to get
their tongue into the hole

931
00:56:43,930 --> 00:56:44,950
to get the bug.

932
00:56:44,950 --> 00:56:47,610
And the end of their tongue
has little barbs on it.

933
00:56:47,610 --> 00:56:50,150
And when they contract
this thing here,

934
00:56:50,150 --> 00:56:53,280
their tongue scoots out
and gets the little bugs.

935
00:56:53,280 --> 00:56:56,020
So they pick partly to
forage, but they also

936
00:56:56,020 --> 00:56:58,220
build something
called cavity nests.

937
00:56:58,220 --> 00:57:01,000
So they'll find a tree
that's started to rot,

938
00:57:01,000 --> 00:57:03,500
and they'll drill a
sort of horizontal hole,

939
00:57:03,500 --> 00:57:05,542
and then they'll drill
a cup underneath that,

940
00:57:05,542 --> 00:57:07,250
and they lay the eggs
and have their nest

941
00:57:07,250 --> 00:57:08,577
at the bottom of the cup.

942
00:57:08,577 --> 00:57:11,160
And then they also-- especially
at this time of year, in fact,

943
00:57:11,160 --> 00:57:13,600
today I heard
woodpeckers drumming--

944
00:57:13,600 --> 00:57:16,890
so it's one of these mating
things, one of these courtship

945
00:57:16,890 --> 00:57:17,390
things.

946
00:57:17,390 --> 00:57:21,210
So woodpeckers will peck on a
hollow branch or a hollow tree,

947
00:57:21,210 --> 00:57:23,400
just to make a big
loud noise to say,

948
00:57:23,400 --> 00:57:28,150
here I am, looking for sex, I'm
ready, this is my territory.

949
00:57:28,150 --> 00:57:30,200
And so in the spring--
so this time of year

950
00:57:30,200 --> 00:57:31,780
you hear woodpeckers drumming.

951
00:57:31,780 --> 00:57:35,380
And I think naturally they
do this on hollow trees

952
00:57:35,380 --> 00:57:36,880
to try to make a
big sound, but they

953
00:57:36,880 --> 00:57:40,380
have adapted to metal
downspouts, which

954
00:57:40,380 --> 00:57:43,350
are also very effective
for making this loud noise.

955
00:57:43,350 --> 00:57:45,660
And people who've-- I
wrote a paper on this--

956
00:57:45,660 --> 00:57:48,202
people who have read my paper
sometimes email me and say, oh,

957
00:57:48,202 --> 00:57:49,951
I heard you know about
woodpecker pecking.

958
00:57:49,951 --> 00:57:52,180
How can I get them to stop
drumming on my downspout?

959
00:57:52,180 --> 00:57:53,360
Because it's kind of
annoying, if you're

960
00:57:53,360 --> 00:57:54,850
the human inside the house.

961
00:57:54,850 --> 00:57:57,470
So anyway, they peck
for these reasons.

962
00:57:57,470 --> 00:57:59,990
And then acorn woodpeckers are
special-- acorn woodpeckers

963
00:57:59,990 --> 00:58:03,320
are what I think of as
the champions of pecking.

964
00:58:03,320 --> 00:58:05,260
And they do one
more behavior-- so

965
00:58:05,260 --> 00:58:08,510
here's from David Sibley's
beautiful Guide to Birds,

966
00:58:08,510 --> 00:58:10,160
here's the acorn woodpecker.

967
00:58:10,160 --> 00:58:12,850
They store acorns in
what's called a granary,

968
00:58:12,850 --> 00:58:18,360
and they look at old tree trunks
that are beginning to rot,

969
00:58:18,360 --> 00:58:20,560
and they pick holes
in the tree trunk

970
00:58:20,560 --> 00:58:22,530
and they store the
acorns in the holes.

971
00:58:22,530 --> 00:58:25,510
So see all those little
dark dots on that trunk?

972
00:58:25,510 --> 00:58:29,310
Those are all holes that the
acorn woodpecker has pecked.

973
00:58:29,310 --> 00:58:31,430
And they'll do this-- they
live in social groups,

974
00:58:31,430 --> 00:58:34,530
so there might be like 10 or
20 of them living together,

975
00:58:34,530 --> 00:58:38,210
and they'll peck like 10,000
holes into their granary.

976
00:58:38,210 --> 00:58:40,960
There will be thousands and
thousands of these holes.

977
00:58:40,960 --> 00:58:42,550
And here we have
the acorn woodpecker

978
00:58:42,550 --> 00:58:46,390
with the acorn in its beak, and
you can see some of these holes

979
00:58:46,390 --> 00:58:48,120
have acorns, and some
of them are empty.

980
00:58:48,120 --> 00:58:51,350
So here is the acorn
woodpecker in action.

981
00:58:51,350 --> 00:58:53,940
And here's the little video
again-- I won't play the video.

982
00:58:53,940 --> 00:58:56,140
So I often give this
talk for non-engineers,

983
00:58:56,140 --> 00:58:58,290
so I'm going to explain
some things-- there's

984
00:58:58,290 --> 00:58:59,370
going to be some
writing on the slides

985
00:58:59,370 --> 00:59:00,660
that you guys already know.

986
00:59:00,660 --> 00:59:03,180
So the impact force depends
on the deceleration--

987
00:59:03,180 --> 00:59:06,969
how quickly the brain stops
when the beak hits the tree.

988
00:59:06,969 --> 00:59:09,260
And I should mention, these
videos are from the Cornell

989
00:59:09,260 --> 00:59:13,420
Lab of Ornithology-- they have
an amazing collection of bird

990
00:59:13,420 --> 00:59:17,890
audio, like bird calls, bird
songs, and bird photographs

991
00:59:17,890 --> 00:59:18,600
and videos.

992
00:59:18,600 --> 00:59:22,730
It's incredible, the
collection that they've got.

993
00:59:22,730 --> 00:59:24,320
And then I explain
what acceleration

994
00:59:24,320 --> 00:59:26,650
is-- so I'm going
to put acceleration

995
00:59:26,650 --> 00:59:27,740
in terms of gravity.

996
00:59:27,740 --> 00:59:29,720
And when the beak
hits the tree, there's

997
00:59:29,720 --> 00:59:32,250
going to be a
deceleration on impact.

998
00:59:32,250 --> 00:59:34,790
And just as a comparison,
human brain injury

999
00:59:34,790 --> 00:59:37,500
occurs roughly at about 100g.

1000
00:59:37,500 --> 00:59:40,200
And so the question is,
how much deceleration

1001
00:59:40,200 --> 00:59:42,350
can the woodpecker brain take?

1002
00:59:42,350 --> 00:59:45,820
And that's where the
neurologists in the Bay Area

1003
00:59:45,820 --> 00:59:47,230
come into the picture.

1004
00:59:47,230 --> 00:59:49,910
They found out that
there was a park

1005
00:59:49,910 --> 00:59:53,110
ranger-- I think maybe at
Point Reyes, just north

1006
00:59:53,110 --> 00:59:54,440
of San Francisco.

1007
00:59:54,440 --> 00:59:56,702
And he had an acorn
woodpecker that, I don't, had

1008
00:59:56,702 --> 00:59:57,910
an injured wing or something.

1009
00:59:57,910 --> 01:00:01,810
Anyway, he had this acorn
woodpecker that he kept.

1010
01:00:01,810 --> 01:00:05,440
And they were able to use
this acorn woodpecker,

1011
01:00:05,440 --> 01:00:08,760
and they took high-speed video
of the woodpecker pecking.

1012
01:00:08,760 --> 01:00:11,523
So from the high-speed video,
the video that they took

1013
01:00:11,523 --> 01:00:14,260
went at something like
2,000 frames a second.

1014
01:00:14,260 --> 01:00:17,420
So they have a picture of
where the head is every 2,000th

1015
01:00:17,420 --> 01:00:18,459
of a second.

1016
01:00:18,459 --> 01:00:20,250
So if you know the
position at these times,

1017
01:00:20,250 --> 01:00:23,900
you can get the velocity, and
you can get the deceleration.

1018
01:00:23,900 --> 01:00:25,510
So they measured
the deceleration,

1019
01:00:25,510 --> 01:00:27,470
and they measured
some amazing things.

1020
01:00:27,470 --> 01:00:30,510
So they measured that on
impact, the woodpecker's bill

1021
01:00:30,510 --> 01:00:33,090
was going something
like 15 miles an hour.

1022
01:00:33,090 --> 01:00:35,570
And the decelerations
were up to 1,500g--

1023
01:00:35,570 --> 01:00:39,450
so many times more than
what we can withstand.

1024
01:00:39,450 --> 01:00:41,240
And they also measured
the stopping time--

1025
01:00:41,240 --> 01:00:45,190
and they thought it was between
about 1/500th to 1/1,000th

1026
01:00:45,190 --> 01:00:45,970
of a second.

1027
01:00:45,970 --> 01:00:48,889
And that's going to
be important later on.

1028
01:00:48,889 --> 01:00:50,680
So one of the interesting
things about this

1029
01:00:50,680 --> 01:00:52,810
was how they got this
whole thing set up.

1030
01:00:52,810 --> 01:00:55,150
So I don't know how many of
you do UROPs-- but you know,

1031
01:00:55,150 --> 01:00:56,960
part of the thing in doing
UROPs, and doing experiments

1032
01:00:56,960 --> 01:00:58,950
in the lab is just how do
you do the experiments?

1033
01:00:58,950 --> 01:01:01,241
So you know, the park rangers
got the acorn woodpecker,

1034
01:01:01,241 --> 01:01:02,332
that's all very good.

1035
01:01:02,332 --> 01:01:03,790
But they have to
get the woodpecker

1036
01:01:03,790 --> 01:01:05,340
to peck in front of
a camera, and they

1037
01:01:05,340 --> 01:01:06,714
have to get the
camera to turn on

1038
01:01:06,714 --> 01:01:09,890
as it's pecking-- so there's
some experimental challenges.

1039
01:01:09,890 --> 01:01:11,710
So the important thing,
the critical thing,

1040
01:01:11,710 --> 01:01:12,960
is the date of the paper.

1041
01:01:12,960 --> 01:01:15,780
This was written in 1979,
which meant they probably

1042
01:01:15,780 --> 01:01:17,770
did the experiments in 1978.

1043
01:01:17,770 --> 01:01:19,960
And I was a graduate
student in 1978.

1044
01:01:19,960 --> 01:01:24,010
And I can report there were
no Apple computers in 1978--

1045
01:01:24,010 --> 01:01:25,360
there were no laptops.

1046
01:01:25,360 --> 01:01:28,280
You couldn't just kind of do
your little PowerPoint slides.

1047
01:01:28,280 --> 01:01:31,530
And most offices had something
called an IBM Selectric

1048
01:01:31,530 --> 01:01:34,240
typewriter-- I don't know if
you've ever seen the old IBM

1049
01:01:34,240 --> 01:01:35,089
typewriters.

1050
01:01:35,089 --> 01:01:37,380
But the typewriters, when
you typed on the typewriters,

1051
01:01:37,380 --> 01:01:39,730
they made these noises,
and it sounded kind of

1052
01:01:39,730 --> 01:01:41,180
like a woodpecker pecking.

1053
01:01:41,180 --> 01:01:44,410
And the ranger had one of these
typewriters in his office,

1054
01:01:44,410 --> 01:01:46,786
and he had discovered that if
he typed on the typewriter,

1055
01:01:46,786 --> 01:01:49,076
the woodpecker thought, oh,
there's another woodpecker.

1056
01:01:49,076 --> 01:01:49,990
I'll start pecking.

1057
01:01:49,990 --> 01:01:51,700
And so they used the
typewriter as a way

1058
01:01:51,700 --> 01:01:53,310
to get the woodpeckers to peck.

1059
01:01:53,310 --> 01:01:54,810
And I think they
had some old stump,

1060
01:01:54,810 --> 01:01:56,620
and I don't know if they
put nuts or peanut butter

1061
01:01:56,620 --> 01:01:58,390
or something into the
stump to get the woodpecker

1062
01:01:58,390 --> 01:01:59,350
to peck at it--
because they needed

1063
01:01:59,350 --> 01:02:01,724
to peck at a particular spot,
so they have the camera all

1064
01:02:01,724 --> 01:02:02,310
set up.

1065
01:02:02,310 --> 01:02:04,530
So anyway, they had
this whole arrangement

1066
01:02:04,530 --> 01:02:10,230
to do this high-speed video
of the woodpecker pecking.

1067
01:02:10,230 --> 01:02:12,190
OK, so it goes
that up to 1,500g,

1068
01:02:12,190 --> 01:02:13,380
which is kind of amazing.

1069
01:02:13,380 --> 01:02:15,900
And then, remember also,
they do this repeatedly--

1070
01:02:15,900 --> 01:02:19,185
they do it at like 10
or 20 times a second.

1071
01:02:19,185 --> 01:02:20,560
Then this is just
explaining what

1072
01:02:20,560 --> 01:02:22,560
stress is-- but you already
know what stress is,

1073
01:02:22,560 --> 01:02:24,580
so I'm going to skip over that.

1074
01:02:24,580 --> 01:02:26,520
And so the way you
can think about this

1075
01:02:26,520 --> 01:02:29,420
is to think about it in
terms of a scaling argument.

1076
01:02:29,420 --> 01:02:31,610
So imagine there's the
brain and there's the skull,

1077
01:02:31,610 --> 01:02:34,450
and when the head hits the
tree, the brain's going

1078
01:02:34,450 --> 01:02:37,010
to accelerate, and the
brain and the skull

1079
01:02:37,010 --> 01:02:38,790
are both going to decelerate.

1080
01:02:38,790 --> 01:02:43,470
And you can think of the stress
as the force over the area.

1081
01:02:43,470 --> 01:02:46,680
So the force is the mass times
the deceleration over the area.

1082
01:02:46,680 --> 01:02:50,470
So that value for the
woodpecker, you can say,

1083
01:02:50,470 --> 01:02:54,460
is roughly equal to the same
values, but for the human.

1084
01:02:54,460 --> 01:02:58,290
So what that argument
relies on is the idea

1085
01:02:58,290 --> 01:03:01,300
that the stress to cause
damage in the woodpecker brain

1086
01:03:01,300 --> 01:03:03,910
is similar to the
stress to cause damage

1087
01:03:03,910 --> 01:03:05,320
in the human brain.

1088
01:03:05,320 --> 01:03:08,310
And that's not
totally unreasonable.

1089
01:03:08,310 --> 01:03:10,201
So if you look at
bone, for example,

1090
01:03:10,201 --> 01:03:12,450
like when you measure the
strength of the whale bones,

1091
01:03:12,450 --> 01:03:14,100
it's not going to be that
different from what you

1092
01:03:14,100 --> 01:03:15,630
would measure from human bones.

1093
01:03:15,630 --> 01:03:18,850
So when you look at a
particular type of tissue,

1094
01:03:18,850 --> 01:03:21,692
and you look at the strength
of it in different species,

1095
01:03:21,692 --> 01:03:23,900
the properties aren't that
different from one species

1096
01:03:23,900 --> 01:03:24,810
to another.

1097
01:03:24,810 --> 01:03:27,470
So let's say the
brain tissue gets

1098
01:03:27,470 --> 01:03:31,010
damaged at the same
stress in the two species.

1099
01:03:31,010 --> 01:03:33,250
So we can write this
sort of equation down.

1100
01:03:33,250 --> 01:03:39,310
And the mass is going to depend
on the density of the brain

1101
01:03:39,310 --> 01:03:41,750
tissue times the
volume-- and the volume

1102
01:03:41,750 --> 01:03:43,380
goes as the radius cubed.

1103
01:03:43,380 --> 01:03:46,035
And the density is going to be
the same for the woodpecker,

1104
01:03:46,035 --> 01:03:48,290
or for the human-- so
assume the brain tissue has

1105
01:03:48,290 --> 01:03:50,380
the same kind of basic stuff.

1106
01:03:50,380 --> 01:03:53,760
So the mass goes as the radius
cubed, and the area of contact

1107
01:03:53,760 --> 01:03:55,880
is going to go as
the radius squared.

1108
01:03:55,880 --> 01:03:57,790
And so there's a radius term.

1109
01:03:57,790 --> 01:03:59,870
So you can say the radius
times the deceleration

1110
01:03:59,870 --> 01:04:02,290
in the woodpecker should
be equal to the radius

1111
01:04:02,290 --> 01:04:04,470
times the deceleration
of the human.

1112
01:04:04,470 --> 01:04:06,000
And obviously, the
woodpecker radius

1113
01:04:06,000 --> 01:04:09,104
is going to be a lot smaller,
so the woodpecker deceleration

1114
01:04:09,104 --> 01:04:10,270
is going to be a lot bigger.

1115
01:04:10,270 --> 01:04:13,930
So part of the thing is the
brain is just a lot smaller.

1116
01:04:13,930 --> 01:04:16,510
Then there's another
factor that comes into it--

1117
01:04:16,510 --> 01:04:20,390
these are photographs
of an acorn woodpecker

1118
01:04:20,390 --> 01:04:22,740
skull and a human
skull that I got

1119
01:04:22,740 --> 01:04:25,790
from the Museum of Comparative
Zoology at Harvard.

1120
01:04:25,790 --> 01:04:27,490
So this is looking
down on the top,

1121
01:04:27,490 --> 01:04:29,866
and this is an elevation view.

1122
01:04:29,866 --> 01:04:32,490
And if you think of the brain as
roughly a hemisphere-- I mean,

1123
01:04:32,490 --> 01:04:33,850
obviously it's not a
perfect hemisphere,

1124
01:04:33,850 --> 01:04:35,558
but let's say it's
roughly a hemisphere--

1125
01:04:35,558 --> 01:04:37,750
the orientation of
the brain in the skull

1126
01:04:37,750 --> 01:04:40,309
is slightly different in
the birds and in the human.

1127
01:04:40,309 --> 01:04:42,100
So if you think of it
as being this way on,

1128
01:04:42,100 --> 01:04:45,540
and in the woodpecker it's
turned roughly this way on,

1129
01:04:45,540 --> 01:04:48,480
and the contact area-- think
of this as the contact area.

1130
01:04:48,480 --> 01:04:51,590
The projected area would be a
full circle, and in the human,

1131
01:04:51,590 --> 01:04:53,240
the brain is more this way on.

1132
01:04:53,240 --> 01:04:56,800
And then the projected
contact area is a semicircle.

1133
01:04:56,800 --> 01:04:58,540
So there's a factor
of 2 difference,

1134
01:04:58,540 --> 01:05:01,910
just because of the
orientation of the brain.

1135
01:05:01,910 --> 01:05:04,970
And so I've put the factor
of 2 that accounts for that.

1136
01:05:04,970 --> 01:05:06,470
So then I could say
the deceleration

1137
01:05:06,470 --> 01:05:08,800
that the woodpecker
can take is twice

1138
01:05:08,800 --> 01:05:11,940
the ratio of the radii of the
human and the woodpecker brain,

1139
01:05:11,940 --> 01:05:13,730
times the deceleration
the human can take.

1140
01:05:13,730 --> 01:05:16,080
And this was around
100g, remember.

1141
01:05:16,080 --> 01:05:18,440
So then I wanted to know
what the ratio of the sizes

1142
01:05:18,440 --> 01:05:19,910
was, and I thought,
oh geez-- I'm

1143
01:05:19,910 --> 01:05:22,190
going to have to mess
around with skulls,

1144
01:05:22,190 --> 01:05:23,940
and try to make some
sort of measurements,

1145
01:05:23,940 --> 01:05:25,320
and this is going to be a drag.

1146
01:05:25,320 --> 01:05:27,630
And then I found this paper--
I couldn't believe it--

1147
01:05:27,630 --> 01:05:29,830
I found this paper called
"Brain Size in Birds."

1148
01:05:29,830 --> 01:05:31,700
And this guy had
table after table

1149
01:05:31,700 --> 01:05:34,910
after table of the mass of
the brain in different birds--

1150
01:05:34,910 --> 01:05:37,720
and he had the acorn
woodpecker, lucky for me.

1151
01:05:37,720 --> 01:05:40,804
So if you just assume that the
brain is roughly a hemisphere,

1152
01:05:40,804 --> 01:05:42,720
if you have the mass,
you can work out roughly

1153
01:05:42,720 --> 01:05:44,030
what the radius is.

1154
01:05:44,030 --> 01:05:45,880
So it turns out
there's a factor of 8

1155
01:05:45,880 --> 01:05:48,600
difference between the radii.

1156
01:05:48,600 --> 01:05:51,880
And so the human brain is
about eight times the size

1157
01:05:51,880 --> 01:05:53,030
of the woodpecker.

1158
01:05:53,030 --> 01:05:55,292
And then if you take into
account this factor of 2,

1159
01:05:55,292 --> 01:05:56,750
that means the
woodpecker should be

1160
01:05:56,750 --> 01:06:01,655
able to tolerate a deceleration
of 16 times what the human can.

1161
01:06:01,655 --> 01:06:03,030
So remember, I
said the human can

1162
01:06:03,030 --> 01:06:06,490
take about 100-- so this would
get the woodpecker up to 1,600.

1163
01:06:06,490 --> 01:06:07,960
But they measured 1,500.

1164
01:06:07,960 --> 01:06:10,280
And I'm a civil
engineer, originally,

1165
01:06:10,280 --> 01:06:12,430
I like big factors of
safety-- that's a little too

1166
01:06:12,430 --> 01:06:14,630
close for comfort for me.

1167
01:06:14,630 --> 01:06:18,360
And so it turns out there's
one more factor that matters.

1168
01:06:18,360 --> 01:06:21,690
People have studied human brain
injury pretty extensively,

1169
01:06:21,690 --> 01:06:23,350
and one of the things
they've looked at

1170
01:06:23,350 --> 01:06:27,500
is how much acceleration you
can tolerate without injury,

1171
01:06:27,500 --> 01:06:29,730
relative to the
duration of the impact.

1172
01:06:29,730 --> 01:06:33,337
So this is from a car crash
conference-- so here's

1173
01:06:33,337 --> 01:06:34,920
the tolerable
acceleration, and here's

1174
01:06:34,920 --> 01:06:36,560
the duration of the impact.

1175
01:06:36,560 --> 01:06:38,480
And typically, for
human head impacts,

1176
01:06:38,480 --> 01:06:41,320
the deceleration occurs
over a few milliseconds--

1177
01:06:41,320 --> 01:06:43,950
like over 3 to 10 milliseconds.

1178
01:06:43,950 --> 01:06:46,810
So if this is the duration
of the typical head

1179
01:06:46,810 --> 01:06:49,960
impact for a human, here's
the range of the tolerable

1180
01:06:49,960 --> 01:06:53,080
accelerations between about
80g and 160g-- so you know,

1181
01:06:53,080 --> 01:06:54,490
I said around 100.

1182
01:06:54,490 --> 01:06:57,650
So we can take this curve, and
now we have this factor of 16,

1183
01:06:57,650 --> 01:06:59,760
and we can just scale it
up by our factor of 16

1184
01:06:59,760 --> 01:07:01,070
for the woodpecker.

1185
01:07:01,070 --> 01:07:04,660
So if I scale it up by the
factor of 16, we're there.

1186
01:07:04,660 --> 01:07:08,264
But the duration of the
impacts was more around 1/2

1187
01:07:08,264 --> 01:07:09,930
a millisecond, to a
millisecond, so I've

1188
01:07:09,930 --> 01:07:11,730
extrapolated this a little bit.

1189
01:07:11,730 --> 01:07:14,610
And the duration of
them is up in here.

1190
01:07:14,610 --> 01:07:16,190
So this is saying
the woodpecker can

1191
01:07:16,190 --> 01:07:19,550
take these sorts of
decelerations here,

1192
01:07:19,550 --> 01:07:22,180
and that adds on
another factor of 4.

1193
01:07:22,180 --> 01:07:25,130
And these were the
measured decelerations--

1194
01:07:25,130 --> 01:07:27,320
1,500 was about the
biggest, and I think it

1195
01:07:27,320 --> 01:07:30,510
went to about a few hundred g.

1196
01:07:30,510 --> 01:07:31,935
So there's really
three factors--

1197
01:07:31,935 --> 01:07:33,560
one is the small
brain size, so there's

1198
01:07:33,560 --> 01:07:35,470
this sort of scaling factor.

1199
01:07:35,470 --> 01:07:37,140
One is the orientation
of the brain,

1200
01:07:37,140 --> 01:07:38,440
that was another factor of 2.

1201
01:07:38,440 --> 01:07:40,148
And then there's this
duration of impact,

1202
01:07:40,148 --> 01:07:41,650
which is a factor of 4.

1203
01:07:41,650 --> 01:07:44,377
And so that's how you can
get this huge decelerations

1204
01:07:44,377 --> 01:07:46,210
that they've measured
in the woodpecker when

1205
01:07:46,210 --> 01:07:48,250
they're pecking.

1206
01:07:48,250 --> 01:07:51,320
So now I have just a
couple more slides.

1207
01:07:51,320 --> 01:07:54,640
So woodpeckers have various
adaptations to pecking, too.

1208
01:07:54,640 --> 01:07:56,910
So one of the things is they
have amazingly stiff tail

1209
01:07:56,910 --> 01:07:58,760
feathers-- you see
the tails here?

1210
01:07:58,760 --> 01:08:01,176
You can't quite see it because
this didn't reproduce quite

1211
01:08:01,176 --> 01:08:03,750
properly, but the woodpecker
is perched on a tree here,

1212
01:08:03,750 --> 01:08:06,197
and the tail is pressed
up against the tree.

1213
01:08:06,197 --> 01:08:08,030
And if you think about
pecking, like imagine

1214
01:08:08,030 --> 01:08:10,071
if its tail was not pressed
up against the tree--

1215
01:08:10,071 --> 01:08:12,080
it would be kind of
grabbing on with its feet,

1216
01:08:12,080 --> 01:08:14,666
and it would be trying to peck,
and it would be hard to push.

1217
01:08:14,666 --> 01:08:16,540
You know, you need
something to push against.

1218
01:08:16,540 --> 01:08:19,164
And so it's got these stiff tail
feathers, which make it easier

1219
01:08:19,164 --> 01:08:22,149
to push against the tree.

1220
01:08:22,149 --> 01:08:24,750
And so here's the stiff
tail feathers here.

1221
01:08:24,750 --> 01:08:26,840
It's also got kind
of unusual feet

1222
01:08:26,840 --> 01:08:30,011
for birds-- it's got two toes
forward and two toes back.

1223
01:08:30,011 --> 01:08:31,760
And again, if it's
grabbing with its feet,

1224
01:08:31,760 --> 01:08:35,260
that helps it get some
purchase to push against.

1225
01:08:35,260 --> 01:08:38,939
That's called zygodactyl
in the bird world.

1226
01:08:38,939 --> 01:08:40,934
So it's got these
adaptations, the pecking.

1227
01:08:40,934 --> 01:08:42,600
And then finally, I
just like this slide

1228
01:08:42,600 --> 01:08:44,080
here from The New
Yorker, because it's

1229
01:08:44,080 --> 01:08:45,760
a woodpecker pecking
out a woodpecker,

1230
01:08:45,760 --> 01:08:47,540
so it seemed kind of cute.

1231
01:08:47,540 --> 01:08:50,279
And several people helped
me with this project.

1232
01:08:50,279 --> 01:08:52,740
Trey Crisco studies
head injury at Brown.

1233
01:08:52,740 --> 01:08:57,520
He actually does work for the
NFL on football brain injuries,

1234
01:08:57,520 --> 01:08:58,790
and looks at football helmets.

1235
01:08:58,790 --> 01:09:00,410
Sharon Swartz is a
friend of mine at Brown,

1236
01:09:00,410 --> 01:09:01,229
who's a biologist.

1237
01:09:01,229 --> 01:09:02,310
She studies bat flight.

1238
01:09:02,310 --> 01:09:04,720
And she just thought this
was kind of a cool project.

1239
01:09:04,720 --> 01:09:09,380
So, in fact, I was walking the
dog last week, a few days ago,

1240
01:09:09,380 --> 01:09:11,899
and I saw bats flying
around overhead at night.

1241
01:09:11,899 --> 01:09:14,069
And it was so great to
see the little bats.

1242
01:09:14,069 --> 01:09:15,979
So I had to immediately
email Sharon,

1243
01:09:15,979 --> 01:09:18,240
and say, bats-- there's
bats in my neighborhood.

1244
01:09:18,240 --> 01:09:21,470
Andy Biewener runs the
Concord Field Station,

1245
01:09:21,470 --> 01:09:23,970
and studies animal locomotion,
and I talked to him about it.

1246
01:09:23,970 --> 01:09:26,270
Jeremy Trimble was the one who
gave me the skull pictures,

1247
01:09:26,270 --> 01:09:27,770
and Matt Dawson was
a student helped

1248
01:09:27,770 --> 01:09:29,840
me do some of the images.

1249
01:09:29,840 --> 01:09:32,120
So that's my woodpecker talk.

1250
01:09:32,120 --> 01:09:33,890
So that's the end of
energy absorption,

1251
01:09:33,890 --> 01:09:36,180
I just thought that
was kind of amusing.

1252
01:09:36,180 --> 01:09:39,120
So next time, we'll start
talking about sandwich panels.

1253
01:09:39,120 --> 01:09:41,170
So, let's see--
Monday's a holiday.

1254
01:09:41,170 --> 01:09:43,754
I will be in Toronto on
Monday, seeing my family.

1255
01:09:43,754 --> 01:09:45,920
In fact, I'm going to see
one of my old professors--

1256
01:09:45,920 --> 01:09:48,211
I'm going to my old fluid
mechanics professor on Monday

1257
01:09:48,211 --> 01:09:48,880
and have lunch.

1258
01:09:48,880 --> 01:09:50,689
I'll see my family
on the weekend.

1259
01:09:50,689 --> 01:09:53,850
And so we'll meet
Wednesday next week,

1260
01:09:53,850 --> 01:09:56,550
and I'll start the bit
on sandwich panels.

1261
01:09:56,550 --> 01:09:59,860
So I think there's two lectures
on engineering sandwich panels,

1262
01:09:59,860 --> 01:10:03,930
and then there's a lecture
on natural sandwich panels--

1263
01:10:03,930 --> 01:10:06,630
so bird skulls, for example,
are natural sandwich panels.

1264
01:10:06,630 --> 01:10:07,890
So I'll talk about that.

1265
01:10:07,890 --> 01:10:09,720
And then I think
the last lecture--

1266
01:10:09,720 --> 01:10:12,080
there's only a handful of
lectures left-- the last one I

1267
01:10:12,080 --> 01:10:14,475
think I talk about natural
materials, because you know,

1268
01:10:14,475 --> 01:10:15,270
I like that.

1269
01:10:15,270 --> 01:10:17,890
So I just do that for fun.