This column is reproduced from the June 2002 issue

A Weighty Matter

At nearly seven tons, Tyrannosaurus rex would have simply been too heavy to run fast.

By Adam Summers ~ Illustrations by Sally J. Bensusen (www.visualsciencestudio.com)

Oblong, milk-chocolate slabs of rock, dappled with darker footprints, hang from the walls and cover trestle tables in the Pratt Museum at Amherst College. While assembling and cataloging this collection of rocks about a century and a half ago, geologist Edward Hitchcock identified more than a hundred species of animals on the basis of the size, shape, and spacing of the footprints and trails they’d left behind in the Triassic mud. Among the raindrop craters, the worm trails, and the bulldozer tracks of armored invertebrates are the three-toed prints of small dinosaurs and the deeper tracks of bigger, heavier animals.

	Comparisons with living animals suggest that about 25 percent of T. rex’s body mass was locked up in leg muscle. This would have capped the dinosaur’s top speed at somewhere between 10 and 25 miles per hour.
	Some scientists have proposed a more crouched running posture for T. rex, as well as speeds of up to 45 miles per hour. For such a huge dinosaur to run this fast, however, its leg muscles would have to take up 85 percent of its body mass, with little left over for the rest of the body. The result would be a scary looking, but not very probable, creature.

Data from trackways like these, along with detailed measurements of skeletons and computer-generated models, are giving paleontologists with a biomechanical bent new insight into the real world of Jurassic Park. (For the record, few of the interspecific encounters in Steven Spielberg’s movie could ever have taken place, because the actual creatures lived in several geological periods: the Cretaceous as well as the Triassic and Jurassic.)

Researchers use the length and width of fossil footprints to estimate the size, including leg length, of the beast that left them. The spacing of the prints reveals whether the animal was ambling along or sprinting. Fossil trackways indicate that bipedal dinosaurs weighing up to 4,000 pounds could sprint, while larger dinosaurs could move no faster than a swift walk. Yet this evidence hasn’t stopped some scientists from speculating that a charismatic megacarnivore like Tyrannosaurus rex, which weighed roughly 13,000 pounds, could race along at forty-five miles per hour after its prey. And they are right not to have been intimidated, for in the world of fossils, the absence of evidence is not the same as evidence of absence. However, recent research suggests why no one has found any tracks of big running dinosaurs: the largest species just didn’t have the muscle power required to run fast.

A running biped bounces up and down, its center of mass dropping down as the body is supported on one bent leg and then rebounding as the leg straightens. The force with which a running foot strikes the ground has been measured for a number of species, over a broad range of body sizes, and is surprisingly consistent: at least two and a half times the body weight. A 200-pound human running down Central Park West in New York City thus hits the ground with about 500 pounds of force at each step. At its lowest point, the body is in a sort of equilibrium—the leg in contact with the ground is bent at the hip, knee, and ankle, with its muscles having exerted enough force to counteract the downward momentum and begin the upward, straightening acceleration.

Amazingly, a given cross-sectional area of muscle generates about the same amount of force regardless of what animal (at least what vertebrate) it comes from. This fact is very handy, because if you know the size of a muscle—whether it belongs to Arnold Schwarzenegger or a hummingbird—you can make a pretty good guess about how much force it can exert.

This relationship between force and cross-sectional area is at the heart of the problem, not only for T. rex but for every other large critter. While available muscle force increases as the square of muscle size, the weight of the muscle (and, indeed, of the whole animal) increases as the cube of its size—that is, as its volume increases. The force that a running animal must overcome is proportional to its body weight; beyond a certain weight, the animal won’t have the strength to keep from crashing to the ground.

To determine the minimal amount of muscle a Tyrannosaurus would need to run fast, John Hutchinson and Mariano Garcia, of the University of California, Berkeley, used a two-dimensional computer model of a T. rex skeleton to look at the key moment in the running stride: just before the animal bounces back up. They tried out various postures, from an improbably upright one to a more scientifically fashionable crouch. Their simulations determined that the mass of the leg-straightening muscles ranged from 25 percent of body mass for the straight-legged pose to a whopping 85 percent for the crouching sprinter. To see how these percentages would compare with those of a living animal, the researchers applied the model to the chicken, which is a strong runner. They found that, according to the model, a chicken should be able to run with as little as 10 percent of its body weight tied up in leg-straightening muscles.

Living animals devote at most half their body weight to muscles, including heart, biceps, and abdominal muscles, as well as those used for walking or running. In chickens and other strong two-legged runners, about 20 percent of the body mass is in the leg straighteners—about twice as much as Hutchinson and Garcia’s model says is needed. To run quickly, Tyrannosaurus would have required more leg muscle than any living animal has. In fact, a T. rex that adopted a crouched posture while running would have had to devote so much body mass to leg muscle that there would have been almost nothing left for skin and bones.

So, how quickly could a huge carnivorous dinosaur move? Given its long legs, probably more than ten miles per hour. It may even have gotten up to twenty-five—swift enough to run down most humans, but not fast enough to catch an SUV speeding through Jurassic Park.

Adam Summers (asummers@uci.edu) is an assistant professor of ecology and evolutionary biology at the University of California, Irvine.

Copyright © Natural History Magazine, Inc., 2002