throopw@rtp47.UUCP (Wayne Throop) (09/13/85)
I apparently was a little unclear in my posting about Sauropods and powerlifting. I'll try to clarify my points here. > > Wrong. The problem introduced by the square-cube disparity is not > > "power", as in muscular power, but structural strength. > > Don't take my word for this one, Wayne. Consider "On Size and Life", a > Scientific American Library book, 1983 by Thomas A. McMahan and John > Bonner. On pages 55 and 56 it states: > > "..The figure shows that the weight lifted in each of the > body-weight classes up to 198 lbs is quite precisely proportional to > the .67 power of body weight as would be predicted by an argument > that muscle stress is invariant to body size, so that muscle force, > and therefore total weight-lifting ability is proportional to the > cross-sectional area of the body (that is, the 2/3 power of body > weight in animals scaled by isometry)." No conflict here. I didn't say that the square-cube problem didn't exist, just that it wasn't a problem of *power*, but a problem of *stress*. The given article agrees with this. There are two issues here. The first is that a simple weight^.67 scaling applies to "muscle stress", not to available muscle power. The second is that this only appies to "scaling by isometry". The problem is this. The amount of force (not power) that can be applied is limited by the structural strength of the muscles, tendons, bones, and so on. This is in turn limited by the smallest cross-section that this force must be applied through. Thus a correct limit is obtained by finding where the most stress is placed on the limb (often the narrowest cross section), and finding how much tension can be supported there. The limit in humans is in the knees, not the thighs (or so I think... I'm a little rusty on anatomy... the limit *might* be in the ankle). Now, before you go and scale up a human knee, remember the bit about "scaling by isometry". The amount of force placed on a given knee is *not* totally determined by the weight of the body supported by the knee. There is also the geometry of the knee to be considered. A thicker knee (in relation to limb length), in addition to supporting more stress by the square-cube principle, requires less force to move a given load, since it has more leverage. So, the scaling you gave *didn't* give all the appropriate advantages to the Sauropod. You neglected leverage, you scaled power rather than stress, and you scaled the wrong part of the leg. Now, I can't do the arithmetic, since I don't know the various factors that apply to the Sauropod. But such calculations are bread and butter for (some) paleontoligists, and I have a fair amount of confidence that the folks quoted by Stanley got it right. In other cases where I've read such calculations, they (seem to have) got it right, and I have no reason to suspect they screwed up this time. > you might try watching ants carrying leaves 20 times their own weight > for awhile An interesting example. If you apply scaling of an ant in the same way you scaled a human, you can easily "prove" that *humans* can't exist, since an ant the size of a human would break it's legs just standing up, and would suffocate due to an inadequate oxegen supply. It just goes to show, you *shouldn't* do "scaling by isometry" when you scale between an ant and a human, or a human and a Sauropod, because the compared things aren't isometric. > >Wrong. Human muscle tissue, even in trained athletes, is quite a bit > >weaker than "equivalent" muscle tissue from most animals. > > If you believe this, Wayne, you should move to Roanoke and join > Falwell's flock tommorrow; you've just told me that man was created > separately from the lower animals and could not possibly be descended > from any of them. Not at all. To conclude unique-ness of humanity, I would have also had to state that humans are the *only* animals with this mass/strength ratio, and that there is a large gap between humans and the nearest "competitor" for weakest muscles. I intended to point out that humans and animals may have a wide range of mass/strength ratios, and that the assumption that human muscle tissue is as strong as any in the world is not well founded without further evidence. Upon re-reading, I find that my original statement could be taken to imply the two things above, but I didn't intend this implication. I only intended stating that *some* animals are stronger than humans (mass for mass) by fairly great margins. (Also, where I said "most animals", I meant "most primates".) The tests I am thinking of are tests of grip strength that were published in Scientific American some time ago (if my memory serves me right). Other primates did much better (per mass) than humans in these tests, and so I concluded that their muscles were more efficent. On the other hand, it *could* be that they had some other advantage, and the comparison could have been against "average" people (though I recall that the comparisons were to athletes). So it could well be correct that maximally trained and drugged human muscle tissue is the strongest in the world. However, this assertion would have to be better supported to convince me of it as a fact, and is not central to the issue of whether Sauropods could walk around or not in any event. Now, as to whether an adult Gorilla could deadlift 5 reps of 1000 lbs... well, that *is* impressive, and upon reflection, I'm not sure that a 350 lb Gorilla could do it. Maybe if we put him on steroids :-). Does anybody else know more about strength/mass ratios of various animals? And lastly, as to mass-for-mass strength, your example of the ant shows that at least *one* "animal" can lift 20 times it's weight and cary it around fairly briskly. Show me a human who can do *that*. -- Wayne Throop at Data General, RTP, NC <the-known-world>!mcnc!rti-sel!rtp47!throopw