throopw@rtp47.UUCP (Wayne Throop) (09/14/85)
I'd like to sort of reason-test a simple-minded scale-up from human size to "Ultrasaur" size. Basically, in a simple-minded scale up, horizontal distances scale by F^1.5, while vertical distances scale by F, where F is H1/H2, the ratio of height after to height before. Now, in the case of the Ultrasaur, Ted Holden gives figures of 30 feet high at the shoulder, and 300,000 pounds. A human (when you turn one into a quadroped), is about 3 feet high at the shoulder, and 250 pounds. Thus, the vertical scale factor F is 10, and the horizontal scale factor is (gasp) 31.6! (I note in passing that the weight scales about right also: 250*10^3 ~= 300,000. Why did I give our starting quadroped a weight of 250 pounds? Because I turned the arms of a 200 pound, 6-foot man into legs to match the hind ones.) Well, this is indeed ridiculous, since it means that the poor reptile would need knees more than twelve feet thick! However, this simple-minded scale-up is (so far) overlooking some important factors. First, this scale up would allow the mumble-saur to have loading factors on its limbs similar to those of a human. Second, I am ignoring the advantages of leverage gained in having thicker limbs. I'll estimate leverage factors and additional loads, and back off of the 30-times horizontal factor a little. Now, a human knee, (just looking at an example here), is applying muscle power on an arm 2.5 inches, delivering power to an arm ~20 inches long. Our initial scale up has the mumble-saur applying on a 6-foot arm, and delivering power to a 15-foot (or less) arm. This is about a 3-to-4 times increase in force due to leverage. Can we reduce the diameter of the knee by a factor of (say) 3, and still not exceed the tearing limit of muscle and ligament? This would make the knee 4 feet across, handling 9 times as much force as the human knee. The wear-and-tear on the knee would be that of a human weighing (hmmm, four human-designed knees, supporting 250 pounds, so over two times 9) 1125 pounds (or a human knee working in 4.5 Gs). Now this borders on the impossible, but doesn't seem to me to be out of the question. There are still some factors favoring the mumble-saur that we haven't addressed. For example, our mumble-saur wouldn't be in any *muscular* distress. The problem is strictly one of the ability of his bones and skeleton handling the stress without breaking. And I haven't addressed the actual geometry of the mumble-saur knee. I simply used human geometry and scaled it. An actual mumble-saur could get a fair extra margin from altered application of stress to the limb by varying the geometry (for example, humans balance weight on top of the leg, while the sauropod slings the weight between, leading to much smaller legs, as seen in existing quadropeds). Now, this back-of-an-envelope scaling excersise points up the fact that the Ultrasaur is an impressive beast, and that the larger sauropods are pushing the limits of possible size in a 1-G gravity, but it *doesn't* show that it is impossible. On the contrary, I'd say it shows that it is (just barely) possible. -- Wayne Throop at Data General, RTP, NC <the-known-world>!mcnc!rti-sel!rtp47!throopw
throopw@rtp47.UUCP (Wayne Throop) (09/15/85)
(remove foot from mouth, proceed to type) My previous article of this title contained a ridiculous error. In essence, I left out a paragraph just after the paragraph that adjusted the scaling operation for leverage. The leverage adjustment given there was supposed to be just one of (at least) two possible adjustments. Picking up where that paragraph left off, I took back *all* the leverage advantage gained by enlarging the joints, and showed that the stress on the animal was at least thinkable. Imeant to add that a more realistic scenario was to calculate how much room was under the mumble-saur for knees, calculate the extra stress caused by fitting the legs into this space, and the extra leverage that would result. There should be at least 15 feet side-to-side room under a mumble-saur. That means that knees *could* be as much as 7 feet in diameter. This would cause leverage advantage that would cut about 1/2 of the stress to the knee. Since the knee is about half as wide as it "should be" when scaled from human dimensions, this means that there is 4 times the stress, or twice the stress experienced by a human. And *this* is well within the range of reasonability. The point of the paragraph that appeared originally was that *even* with essentially *no* leverage advantage, a mumble-saur should be able to at least stand up. Sorry for the confusion. -- Wayne Throop at Data General, RTP, NC <the-known-world>!mcnc!rti-sel!rtp47!throopw