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The really large terrestrial animals are all extinct, but we still have elephants and rhinos for a bit of insight into this problem. Think of the last time you went to the zoo. True, there was a fence around the elephant compound, but a moment's reflection will convince you that the fence can't be meant to keep the elephants in--all they would have to do is lean against the fence to bring it down. No, the fence is there to keep you out. What really keeps the elephants in is the dry moat around their compound; a fall of half a dozen feet would shatter the bones in the elephants' legs and the elephants know that very well indeed. One of the major flaws of all the Kong movies is that the giant apes are just too active, leaping and crashing around as if they were monkeys, protected by their small size. Remember the elephants, and look on these antics with a bit more skepticism.
A second, more subtle, problem pervades the Kong movies. The strength of a bone is approximately proportional to its cross-sectional area; this is simply another way of saying that there is a maximum mechanical stress, or force per unit area, that a bone (or any other material object, for that matter) can withstand. The load the bone must bear is proportional to the mass of an animal. With an increase in size but no change in shape, the load on the bone will increase in proportion to the increase in volume (length cubed), but the cross-sectional area of the bone will only increase as length squared. Eventually, the animal's bones will break under its own weight.
enlargeGalileo sketched the change in shape necessary for a bone to support a larger animal.
One way around this problem is to change the shape of the bone as size increases, so that the cross-sectional area better follows the increase in the animal's mass. This is a widespread trend in biology--larger animals have proportionally stouter, thicker bones. Compare the skeletons of a cat to a lion or that of a deer to a moose. This observation is not exactly hot news--both the trend and its explanation were given by Galileo in Two New Sciences (1638).
But my colleague Andrew Biewener (formerly at the University of Chicago, now at Harvard's Concord Field Station) has revisited this question with surprising results. At least for the long bones in the limbs of mammals, the changes in shape that accompany evolutionary changes in size are not sufficient to compensate for the increased loads. Since all bone has virtually the same breaking stress, this implies that larger animals increasingly push the limits of their own skeletons' strength. However, Biewener's direct measurements of bone deformations as an animal walks or runs show that the safety factor (the ratio of breaking stress to working stress) only ranges from three to five. This is remarkably risky design--most things that humans build have safety factors from ten to several hundred. Biewener has looked at animals from chipmunks to elephants and finds that the safety factor is constant across this 25,000-fold size range--scaling has been sidestepped. This result is achieved by a combination of the shape changes in the bones described by Galileo and changes in the behaviors of the animals, particularly adjustments in posture to ensure that the loads the bone must bear are directed along the bones to minimize bending.
Andrew Biewener
Chart of peak bone stress
The chart at right describes Biewener's findings. On the horizontal axis is body mass, running from a tenth of a kilogram (about three ounces) on the left to 5,000 kilograms (about 5 tons) on the right. The vertical scale is stress, measured in force per unit area. The strength of bone does not vary from one mammal to another: for all mammals, bone breaks when the stress it carries exceeds about 200 megapascals (Mpa)--the hatched region in the middle of the graph. Say you had an animal the size of a chipmunk (body mass about 0.1 kg). Its bones have been measured to carry a stress of about 50 Mpa during routine locomotion. What if that chipmunk got bigger, either through evolution or the effects of consuming radioactive tomatoes, as in so many of these movies? If the chipmunk's bones simply enlarged proportionally with no change in shape, stress in the bone would follow the solid curve on the left, with stress increasing as the cube root of body mass. Note that at about 10-20 kg body mass (about 20-40 pounds), that line intersects the hatched region. The implication is that at that size, our hypertrophied rodent cannot move--even routine locomotion would generate high enough stresses to break its bones.
But clearly there are mammals larger than 10-20 kilograms--you and I, to name two. Indeed, empirical measurements of the working stresses in bones indicate a very different story. The bars on the graph indicate the working stress levels in the bones of a variety of mammals from mice to elephants; hatched bars are indirect estimates from the measures of the forces the animal exerts on the ground, white bars are direct measurements from strain gauges directly attached to the animals' long bones. As is apparent, bone stress does not grow as the cube root of body mass. Indeed, the working stress in the bones seems to be independent of body size, running about a fourth to a third the breaking stress for all mammals. In a sense, what we have here is nature's "design principle" for mainstream skeletons: all have evolved to have a safety factor of three to five.
enlargeUpright posture allows animals to support greater weight.
As mentioned above, this is achieved by changes in posture. Small mammals run with their limbs bent; large mammals always run with their limbs straight. If you've ever seen a slow-motion movie of a horse running, you may have noticed that the horse's leg is perfectly straight when it contacts the ground and it stays straight as long as it's bearing the horse's weight. This behavior is even more obvious in elephants.
Back to King Kong. Based on some measurements from stills from the original movie, at the beginning of the movie Kong is about 22 feet tall, but by the time he climbs the Empire State Building, he appears to be 50 percent bigger, presumably because he was allowed bananas ad libitum. At 22 feet tall, Kong is about four to five times the size of your garden-variety lowland gorilla. A fivefold increase in height implies a 25-fold increase in bone cross-sectional area and a 125-fold increase in body mass; the stress on the bones thus should be about five times greater than the stress on a normal gorilla's bones. But, remember, according to Andy Biewener's data, a safety factor of five is extreme for mammals; Kong's excessive body size should have exhausted the safety factor. True, Kong stands a bit straighter than the average gorilla so he may gain a bit of the safety factor back, but it's clear that he's pushing the envelope. Is that why he has such a short fuse and is always roaring and bashing things? Not only does he continually run the risk of breaking his legs, but undoubtedly his feet hurt.
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