The incredibly powerful, long-legged Tyrannosaurus was slow for the same mathematical reason its demise in the mine shaft was so eruptive. Like surface area, bone strength only squares in strength as volume cubes. The result is that as an animal increases in size, it requires proportionally more muscle and leg bone to stand, move, and run. Beyond a certain size, the latter becomes physically impossible. For all its muscular bulk, the Tyrannosaurus rex’s leg bones would have shattered under anything more than the stress of a brisk jog. Judging by its mass, muscle, and bones, Snively doesn’t believe an adult Tyrannosaurus rex could have moved faster than 12 or 13 miles per hour. (Though 12 miles per hour approaches the top speed of a typical human, depending on conditioning—it equates to a 20-second 100 meter dash or a 5-minute mile—the T. rex’s slow acceleration and inspiring teeth would give the average runner a reasonable chance of outsprinting or outmaneuvering the lumbering predator.)1
1 Admittedly, there is some concerning speculation that T. rex hunted in packs, which would complicate your escape. Thankfully, the best current evidence suggests that, though they may have killed in packs like crocodiles, they did not coordinate their pursuits like wolves.
Of course, the Tyrannosaurus rex would hardly be your only concern. Numerous meat-eating dinosaurs of various sizes might take an interest in snacking on you, and whether you could outrun them again depends on their weight.
Three years ago the biologist Myriam Hirt, who studies animal movement at the German Centre for Biodiversity Research, asked a seemingly simple question: Why is it that the biggest, most powerful animals—the whales, elephants, and rhinoceroses—are not the fastest, while the smallest—the mice, minnows, and millipedes—are some of the slowest? Is the implication that there is an optimum size for speed?
The answer, Hirt found, is yes. If you were designing an animal for speed, that animal should weigh approximately 200 pounds. A bit heavier for a swimmer, and a bit lighter for a flyer.
Hirt found a precise parabolic relationship between size and speed that not only suggests you need to fear the midsize dinosaurs most but also that you shouldn’t fear the largest at all. The reason, she tells me, is a result of the interplay between power, acceleration, and the metabolism that fuels both.
An animal’s top speed, Hirt found, is the meeting point of two factors. The first is an animal’s total muscle power, which scales proportionally to its mass. But the second is its ability to accelerate that mass, which does not scale. Acceleration is reliant on the anaerobic muscle power or stored ATP energy in the muscle fibers. These so-called fast-twitch muscles produce the rapid, powerful contractions needed for acceleration, but they quickly deplete. And their capacity is determined by metabolism.
For reasons that aren’t totally understood, an animal’s energy production (metabolism) decreases proportional to its mass (more precisely, it decreases to the power of 0.75). If we had the metabolism proportional to that of a mouse, we’d have to eat around 25 pounds of food per day. Instead, we eat only around four. Larger animals are thus stronger and more efficient but produce proportionally less energy to accelerate and overcome their inertia.
By creating a simple formula that represents this balance, Hirt predicted the speeds of animals based upon nothing but their weight. When she placed it on a graph alongside the measured speeds of modern animals, the result looked something like this: