Previous work in this area, led by Myriam Hirt of the German Center for Integrative Biodiversity Research, found that the key to speed had to do with an animal’s metabolism, the process by which the body converts nutrients into fuel, a finite amount of which is stored in the muscle fibers for use when sprinting. Hirt’s team found that larger animals run out of this fuel more quickly than smaller animals do, because it takes them more time to accelerate their heavier bodies. This is known as muscle fatigue. It explains why, theoretically, a human could have outrun a Tyrannosaurus rex.
But Günther and his colleagues were skeptical. “I thought we might be able to give another explanation,” he says, one that used only the principles of classical physics to explain speed constraints. So they built a biomechanical model consisting of over 40 different parameters relating to body design, the geometry of running, and the balance of competing forces acting on the body.
“The basic idea is that two things limit maximum speed,” says Robert Rockenfeller, a mathematician at the University of Koblenz-Landau who coauthored the study. The first is air resistance, or drag, the opposing force acting on each leg as it tries to push the body forward. Since the effects of drag don’t increase with mass, it’s the dominating factor capping speed in smaller animals. “If you were infinitely heavy, you would run infinitely fast, according to air drag,” Rockenfeller says.
The second property at play, which does increase with greater mass, is called inertia, the resistance of an object to accelerate from a state of rest. When running, Rockenfeller says, there is a time limit for an animal to accelerate its own mass: It’s the duration between midstance, when the foot is flat on the ground, to liftoff, when the foot leaves the ground. This is especially limiting for larger animals—with more mass to push forward, it's harder to overcome inertia. So smaller bodies have the advantage here.
According to the team’s results, the sweet spot for overcoming air drag and inertia lies at around 110 pounds. Not coincidentally, that’s the average weight of both cheetahs and pronghorns.
Günther’s team was also able to predict theoretical speed maximums for different body designs at 100 kilograms, or about 220 pounds. A house cat this size could run up to 46 miles per hour; a giant spider, if its legs could somehow sustain its weight, would top out at 35 miles per hour. Unsurprisingly, the average human body design comes in last place here: At 100 kilograms, we can only reach about 24 miles per hour.
But body size isn’t the only feature that comes into play when maximizing speed. In the model, leg length also mattered. Animals with longer legs are able to push their bodies farther forward before their foot must leave the ground, prolonging the time they have to accelerate between midstance and liftoff.
As for why four-legged animals can run faster than humans, Günther says this isn’t because we only have two legs, but because our torsos are positioned upright and feel the full force of gravity. Bipedal creatures have evolved with much more rigid spinal structures to prioritize balance and stability over speed. Animals whose trunks are parallel to the ground, however, evolved with more flexible spines that are optimized for prolonged foot contact with the earth.
