# Re: Airbagged(was Dive!Dive!Dive!)

```On Wed, 6 Nov 1996, Jeffrey Martz wrote:

>       Correct me if I am wrong (or if what I am saying makes no sense at
> all), but I don't think that the relationship between bone strength w.
> thickness and the mass of an animal is linear.  In other
> words, if the strength of a bone related to is a certain proportion between
> the thickness of a bone and the size of the animal, I don't think keeping
> that proportion canstant as you increase the mass on the animal (by
> increasing bone thickness) will mean the animal can still do the same
> things because the bone will be just as strong relative to the mass of
> the animal.
>      In other words, if T.rex weighed as much as a person it might be
> able to roll around, and a scapula that large RELATIVE to body size
> might be usefull in breaking the fall, but for a six tonne animal, it is
> more likely to break the scaluplae.
>      To put it another way:  You can build a minerature skyscraper out
> of toothpicks that have a certain relative thickness to the overall size
> of the skyscraper, but if you were to built an 80 story version of the
> same building, it wouldn't work to use humongous toothpicks that were to
> the same scale.  Wood as a building material has practical limitations
> as you increase size, and so I suspect does bone.

>      Can anyone provide a little information about the relative increases
> in mass and bone strength?  I also can't answer questions about how much
> support the interior of a bone (as opposed to the cortical exterior)
> provides in different animals.

You're correct, they're not linear.
Way back when, Galileo figured all this out- clever guy. The
strength of a beam, support, bone, whatever, is directly proportional to
its *cross-sectional* area. That is, the linear dimension squared. The
mass and volume of an animal are directly proportional to the linear
dimension CUBED which means mass, and hence all your stresses, become much
larger much faster than does strength (assuming all body proportions are
identical)!
Animals do compensate for this, and so you'll see that the larger
an animal, in general, the more robust the bone is relatively- it must
increase it's cross-section. Even with this compensation, however, the
overall strength ratio is not as high- this is why mice can take falls
that will break a horse's leg. So a larger animal needs thicker bones, but
it has limits to how much it can compensate.
One partial solution of this is to only put the bone where it
is most needed- basically put it where stress and strain are the
greatest, eliminating it elsewhere. This is the design principle
behind I-beams. The middle of the beam is subjected to much less
severe forces than the upper and lower edges, so you just eliminate
the middle. Sauropods do something similar, I think, with their
pleurocoelous vertebrae- eliminating the material in the middle, where
it doesn't do much good. T. rex did the same thing with it's femur. So
while the cortical bone may be the same amount as in an elephant, its
placement may mean that the bone was stronger overall. Again, maybe
not by a whole lot, but it could be significant if the paper didn't

Now, the surface area thing rears it's head anytime a volume/mass
to surface area problem comes up. Like birds, which gain lift from surface
area- that's why they have size limits, eventually they have less and less
surface area per pound body mass as they get bigger. That's why dinos have
heat problems ( at least, in theory)- surface area being the only way to
lose heat, and a 20-ton Apatosaurus not having a lot of it. That's why we
have multicellular animals instead of giant amoebas- "The Blob" wouldn't
have enough surface area to exchange gas, waste, etc. with its
environment. That's why polar animals tend to be bigger- less surface
area, less heat loss. It's why we have lungs (surface area) really long
coiled intestines with lots of little villi (surface area) etc. etc.

```