How Fast Could Dinosaurs Run? Trackways, Leg Bones and Computer Models

A trackway records an animal moving, and in 1976 the British zoologist Robert McNeill Alexander published a formula, derived from living animals, that estimates speed from the length of the stride and the height of the hip, which can be taken as roughly four times the length of the footprint. A short stride for a given hip height is a walk and a long one a run, and the ratio gives a figure. Applied to the thousands of dinosaur trackways known, the method gives mostly walking speeds of four to eight kilometres an hour, which is what animals do most of the time, with a small number of running tracks: a set in Texas gives a medium-sized theropod about 30, and the fastest known dinosaur trackway, from La Rioja in Spain, indicates around 45. No trackway of a very large theropod shows running at all.

The second approach compares proportions with living animals. Fast runners have long lower legs relative to the thigh, a long foot, a short femur with a large area for muscle attachment, and light extremities; slow heavy animals have the reverse, as an elephant does. On those measures the ornithomimids, the ostrich dinosaurs, are the fastest-looking animals in the fossil record, with proportions closer to a modern ostrich than to anything else, and the small dromaeosaurs and troodontids are quick. Tyrannosaurus is the awkward case, since its lower leg is long for a large animal, which suggested to some researchers that it was built for speed, while its sheer mass argues against; the same bones have been used to support 30 and 70 kilometres an hour, which is why a third method was wanted.

From 2002 a series of studies has built digital dinosaurs with skeletons, estimated muscle masses and the physics of loading, and asked how fast they could go before something failed. John Hutchinson and Mariano Garcia calculated that for Tyrannosaurus to run at the speeds in the film it would have needed leg muscles amounting to more than 80 percent of its body mass, which is impossible, and later models that let the animal choose its own gait to minimise effort have converged on about 20 kilometres an hour, a fast walk to a gentle run, with the constraint being not muscle but bone: a 2017 study found that a six-tonne animal running would break its own leg bones. The picture that has emerged:

• •Ornithomimids and small theropods: 50 to 65 kilometres an hour, the sprinters
• •Medium theropods such as Allosaurus: 30 to 40
• •Tyrannosaurus and other giants: about 17 to 27, unable to truly run
• •Hadrosaurs and ceratopsians: 15 to 25, enough to outpace a tyrannosaur
• •Sauropods: 10 to 20 at most, and probably a walk, since a thirty-tonne animal that stumbles does not get up
• •Stegosaurs and ankylosaurs: slow, which is what the armour was for

The reason is geometry. Muscle strength grows with the cross-sectional area of the muscle, which scales with the square of an animal's linear size, while weight grows with volume, the cube, so that a body twice as long is eight times as heavy and only four times as strong; the same relationship limits the bones, whose strength depends on their cross-section. Beyond a certain mass, an animal cannot accelerate its own legs fast enough or survive the impact of landing on one, and the fastest living land animals are middle-sized, the cheetah at 60 kilograms rather than the elephant at six tonnes. Tyrannosaurus was six tonnes, and the physics that keeps an elephant from galloping kept it from sprinting.

A Tyrannosaurus that moved at 20 kilometres an hour could still catch most of what it ate, since the duck-billed and horned dinosaurs of its world were no faster, and a predator does not need to beat a jeep. The finding has also reshaped the picture of how it hunted, toward ambush and short pursuit rather than a chase, and toward the possibility that juveniles, which were lighter and long-legged, did the running while the adults did the killing. The film's chase, meanwhile, could be outrun by a person on a bicycle, which the researchers who produced the numbers have been explaining ever since.

Dinosaur speeds are estimated from trackways, which give mostly walking and a maximum around 45 kilometres an hour, from limb proportions, which make the ostrich-like ornithomimids the fastest, and from computer models of muscle and bone, which cap the largest predators at roughly 20 because muscle and bone strength grow with area while weight grows with volume. Tyrannosaurus could not run in the sense of leaving the ground, and it did not need to, since its prey was no quicker.