# Is there a way to determine how far and how fast an animal can run for based on geometry?

I was looking at research and finding that drastically different animals can fall under the same brackets for how far and how fast they can run, or that similar animals can fall under different brackets. For instance, a kangaroo could hop at 40mph for a couple miles, meanwhile an elephant can also run about 40mph but for only a couple miles. They're very differently shaped animals, and yet have a similar ratio of their sustained run to their stamina.

Conversely, humans can run for a very long time but maybe no more than 20mph for those in great shape, though they can do it for many miles, over 20 miles which is longer than an elephant can run for. Bears have very similar legs and feet to humans as they are both larger plantigrade mammals, but they can run at 35mph for their top speed and otherwise don't have as much stamina as humans.

Felines and canines are often thought to be similar in many ways. Wolves are known for being able to run and walk for long distances, often having more stamina than their prey and moving 10-30 miles in a day. But, their top speed is only somewhere in the range of 20-35mph. Lions have very similarly shaped bodies and yet are more adapted to run short distances at around 50mph. Similarly, dogs can run for long distances, but cats can jump much higher and not just in proportion to their body length but in terms of absolute length, despite having very similarly shaped bodies.

The reasons for these differences must have something to do with the combination of the geometry of their vertebral column, legs and feet over which their muscles are shaped as well as the weight of an animal. If an elephant was lighter, it would surely run much faster, probably comparable to a horse as its feet are already ovaloid and digigrade. And, if a dog was lighter, it would probably be able to jump higher than a cat. If humans were more massive, then they probably wouldn't be able to run as far, but would probably as fast or faster due to increased muscle mass that compensates. A horse and other horse-like animals seem to have a very good ratio of geometric features to mass that lets them run both very far and very fast.

With all this diversity in mind, what common denominators can be found to account for how the geometry of an animal determines its speed for its given mass?

For instance just as a very crude estimate, I would say animals with particularly long legs that are more closely aligned with the angle of their vertebral column have a tendency to run the farthest, but also the slowest. This might have something to do with how the elasticity of longer muscles and tendons is more efficient for repetitive motion, but not necessarily for propelling a body forward by keeping the force transferred from feet perpendicular to the ground up the leg and in the direction of motion.

• Somewhat related: Why don't mammals have more than 4 limbs? – Remi.b Dec 14 '17 at 10:55
• At first thought, I'd imagine that anatomical geometry & stature would most heavily influence the initial acceleration of the organism, as well as top speeds. From there, the predominant muscle type (slow vs. fast twitch) in the legs of the organism, coupled with a consideration of the organism's metabolic rate, would reveal how far it can travel. If you're wanting to study the kinesiology itself, then, a wholesome response to the OP would probably be too complex for this medium of Q&A. It is a good question though.. – Charles Dec 14 '17 at 15:48
• Is there anything about the anatomy of a given animal that would suggest it has more slow or fast twitch fibers? – james Dec 14 '17 at 17:50
• It's not entirely a matter of geometry, but of differences in muscles, lungs, and circulation. For a good example, read about the extreme endurance of sled dogs. – jamesqf Dec 14 '17 at 19:53
• Couldn't those differences simply be attributed to training? I'm referring more to a purely elementary setting. – james Dec 14 '17 at 20:21