Mar. 4, 2002 King of the Cretaceous, Tyrannosaurus rex stood on two powerful hind limbs and terrorized potential prey with its elephantine size and lethal jaws. The dinosaur was big and bad. But was it fast?
That's long been a topic of scientific debate, with some paleontologists arguing T. rex ran at a zippy top speed of 45 miles per hour and others suggesting a more moderate 25 miles per hour. Both estimates seemed fast to John Hutchinson of Stanford, who as a graduate student at the University of California-Berkeley set out with help from postdoctoral researcher Mariano Garcia, now of Borg-Warner Automotive, to test them using principles of biomechanics.
The researchers created a computer model to calculate how much leg muscle a land animal would need to support running fast. In the Feb. 28 issue of the journal Nature, they report that T. rex probably could not run quickly. In fact, hindered by its size, it may not have been able to run at all. Though not enough is known to give an exact speed limit for T. rex, a range of 10 to 25 miles per hour is possible, according to the authors.
"When you get down to the science of how animals move, relatively speaking, big things really don't move fast," says Hutchinson, a National Science Foundation postdoctoral research fellow. At Stanford since September, he studies the evolution of anatomy and locomotion. When small animals move quickly - rabbits jump, monkeys climb, birds fly, cheetahs sprint - they endure high physical forces for their body weights. Such forces are biomechanically impossible for large animals. Aquatic animals, such as whales, are less limited than land animals, such as elephants, because water buoys them.
Skeletal muscle is built similarly in all vertebrate animals. The force that it can exert depends on its cross-sectional area - that is, two factors: muscle length and muscle width. But an animal's weight, or body mass, depends on three factors: length, width and height. The math behind that physical reality results in limitations.
"That's why as animals get really enormous, eventually to support their weight, their muscles have to be bigger and bigger and bigger," Hutchinson says. "But as they get bigger, they add more mass. So you run up against a problem as animals grow larger in that they need to be adding more muscle cross-sectional area to support their own weight, but the mere fact of adding that muscle adds weight. Eventually, something's got to give."
Says Hutchinson: "No one's really ever tried to look at, or barely thought about, how much muscle a huge animal like a T. rex would need in order to run quickly. A lot of discussion has been over the bones - were they strong enough? - or other lines of evidence. But the main question to me is, could the muscles generate enough force to support the body during running?"
Finding an answer was tricky, as the researchers were studying something they couldn't observe directly. "We're looking at extinct animals, which we know very little about, and we're trying to understand their locomotion, which we have almost no evidence of directly," says Hutchinson. While fossils provide evidence of small dinosaurs moving fast, none indicates that big dinosaurs could do the same.
Models of the extant and the extinct
Garcia and Hutchinson created a computer program to analyze animal motion. Their model has a firm foundation in anatomy but emphasizes biomechanics. By varying different biomechanical parameters - posture, center of mass, leg weight and total weight - the researchers can quickly quantify the physical forces exerted during movement and the amount of muscle needed to support various postures and speeds. They can create two-dimensional stick figures to show how animals move and study conditions at each moving joint.
To gain expertise in biomechanics, Hutchinson as a graduate student worked with Associate Professor Scott Delp, co-chair of Stanford's Biomechanical Engineering Division. Delp's computer model of human movement accurately predicts how moving a tendon during surgery will affect a patient's gait, for example. But Delp's model is also a great tool for studying any animal with muscles and joints, says Hutchinson, who currently uses such 3-D models. Researchers around the world have used it to study biomechanics in cockroaches, frogs, monkeys and more.
A key part of Hutchinson's calculations involve knowing the torque, or twisting force, that muscles need to apply about the joints, says Garcia, who wrote the programs that do these calculations. As a graduate student in the lab of Cornell's Andy Ruina and as a postdoctoral researcher in the lab of Berkeley's Bob Full, Garcia had created similar programs to model the biomechanics of walking robots and multi-legged creatures.
"It has been known for a long time that as things get bigger, they don't move as fast relative to their size, and in fact as they get really, really big, they can't run at all," Garcia says. "But until now, no one that I know of has tried to predict the cutoffs, which is what we are doing."
According to Professor Kevin Padian of Berkeley, a curator in the University of California-Berkeley Museum of Paleontology, Hutchinson and Garcia's paper is "setting a standard for how this kind of work will have to be done in the future. It's the first study to use this kind of computer analysis and to build in sensitivity. What that means is John can check each value and see if a difference in each value can make a difference to the overall model - and that's a big thing to do when projecting models."
Hutchinson and Garcia tested the accuracy of their model with data from living animals that are distant cousins of T. rex - alligators and birds - as well as from humans.
Asking the model to calculate how much muscle each of these animals would need to run quickly, the researchers got values that made sense, Hutchinson says. "Chickens and humans have almost twice as much leg muscle as they need for bipedal running, whereas an alligator has only half the muscle mass it needs to run. Thus, humans can chase chickens around the barnyard, whereas alligators don't run around on their hind legs."
Then the researchers turned to dinosaurs. Using dinosaur data from Hutchinson's doctoral dissertation, they tried the model on two small dinosaurs and a big adult tyrannosaur. It turned out that the smaller dinosaurs needed much less muscle mass to run than did the adult T. rex.
To run 45 miles per hour, the adult T. rex in a crouched posture would need almost 43 percent of its weight in each leg as supportive muscles, the model showed. "It might have needed 86 percent of its body weight to be leg muscles," says Hutchinson. "That is ridiculous, because it would leave very little room for anything else in the body - a skeleton, other muscles, et cetera!"
Even a T. rex in a nearly straight-legged stance - biomechanically the best - still needed 13 percent of its weight as supportive muscle in each leg. That's an extreme amount compared to living animals: Good runners typically have 5 to 10 percent of their body weight as supportive muscle in each leg, and bad runners have less than 5 percent.
"Our model shows that these really fast speeds of 50 miles an hour and probably down to even 25 miles an hour just don't hold up when you really scrutinize them and look at the physics," Hutchinson says. "It doesn't make a lot of sense that these animals could go that fast. There's really no good evidence that they could."
This doesn't mean T. rex was too slow to prey on large herbivores such as horn-faced Triceratops or duck-billed Edmontosaurus. All were elephant-sized, and all were likely poor runners. Remains indicate T. rex ate those animals, but whether it killed or scavenged them is still a mystery.
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To further illustrate that size limits speed, Garcia and Hutchinson used their model to scale up a chicken to the size of a T. rex - 13,228 pounds (6,000 kilograms) - to see if it would be able to run.
"We know from a lot of fossil evidence that birds actually are the descendants of dinosaurs, so we thought, we should look at one of the descendants of dinosaurs to see how it moves today," reasons Hutchinson. "A chicken is a two-legged animal. We know how they move. We can study them in the laboratory or in the barnyard or anywhere. We can go out and buy a recently dead chicken and dissect it to understand its anatomy. So a chicken was a logical choice for many reasons in terms of limb design, evolution and anatomy."
According to the model, could a giant chicken run? "Very clearly no, no matter what," Hutchinson says.
To run, a normal-sized chicken needs about 5 percent of its body mass in each leg to be muscle, Hutchinson says. It has almost 10 percent of its body mass in each leg as muscle, however, so it's "overbuilt" for running. The model showed that a giant cicken would need about 99 percent of its body mass in each leg as muscle to run quickly. "That's far more than is possible," Hutchinson says. "A giant chicken could not even walk."
That explains why elephants and hippos don't move like gazelles. Hutchinson recalls a high school physics teacher using a similar example to explain why Godzilla and King Kong are physical impossibilities: "That really struck home to me. That was probably the first moment where I thought in [terms of] biomechanics and applied it to big things like dinosaurs."
Relevant Web URLs:
* Stanford University Neuromuscular Biomechanics Lab -- http://www.stanford.edu/group/nmbl/
* University of California-Berkeley Museum of Paleontology -- http://www.ucmp.berkeley.edu/
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