# Does maximum theoretical sprint speed increase in as extra legs are added and what is the top speed with optimal number of legs?

I read that for 4-legged animals, the cheetah moves close to the max possible speed -- if you tried to add more muscle, the weight of the muscles would start to take away from top sprint speed.

I can find nothing about adding more legs. I could see another pair allowing more power to be applied to ground but there seems like there might be a point of diminishing returns. On the other hand, why do centipedes have so many legs? I believe scaled up they move very fast.

It is very small animals which when scaling is used, move the fastest with cockroaches moving iirc at over 200 mph when scaled. But it is microorganisms that really move fast when scaled up.

But to clarify, I am looking at the maximum possible running speed in absolute terms, if we allow any number of legs. Perhaps 6 legs does not improve this speed much. Or if it does, is adding yet another pair help even more so that 8 etc. is better and what would that speed be?

If there is a limit to running speed, what causes this? Adding power only works to the point where the added muscle tissue starts to be a negative?

I would assume the ultimate limitation is how efficient muscle is -- the max power of a given mass of muscle is pretty easy to calculate.

If one had a creature that had a different kind of power source, that might change things. One thing that comes to mind is that fleas can accelerate amazingly by storing power in a spring-like structure, but this is not a repeatable process -- it is not used in running but for a single jump after which the spring has to be reset but I would guess the one-time speed of the jump, with something like 1000 gs acceleration translate into the highest speed when scaled up.

The maximum running speed has little to do with the number of legs, it all depends on how fast can the available legs be moved: in laymen terms, you can't run faster than the speed at which you can push your leg back.

Then there is the factor of mass: you want to have enough mass to give the needed power, but not more because it would just hamper speed. That's why cheetahs are so slender.

What limits the maximum running speed is the frequency at which the legs can be swung, which is again a function of their mass: at each cycle a leg has to go from 0 when hitting the ground to twice the running speed when lifted in the air and back to 0, the more mass it has the less frequently this cycle can happen.

• and yet the fastest sprinters by far are all four-legged -- by having four legs perhaps there is greater ability to apply the power of the legs? A human can only have one leg on the ground at a time. However, the ostrich is a very fast two-legged runner and scaled up, the roadrunner is, I bet, the very fastest chordate, so perhaps extra legs are not in fact necessary for speed. Commented Dec 20, 2022 at 5:29

The more legs the better.

The idea behind more legs, is that each leg can operate on a different cycle and reduce the wasted time.

When you run with 2 legs, you moving opposite to each other, ensuring you always have 1 foot in contact with the ground which will keep you accelerating.

With 4 legged animals, the front and back legs operate opposite to each other, with the back legs providing most of the acceleration and the front legs keeping the animal stable and in motion while the back legs move forward.

The only issue with this, is that as things get more legs and become bigger, it becomes harder or less efficient to move. That's why insects can move at 200x body lengths or jump 1000x their own height. If you scaled them up, their muscle mass would decrease this efficiency and many insects would just die under their own weight.

So what would your ideal creature look like? Well, it would be a ball of legs, with the legs all pointing outwards.

The more legs, the better. Why? Each leg would be able to provide running power when in contact with the ground. The more legs, the most consistent running power you have.

More legs also help to distribute your weight, so each leg doesn't require a huge amount of strong durable red muscles. You can have a lot of white muscles to allow each leg to twitch incredibly fast when in contact with the ground to help you get that extra speed.

And as you rotate, each muscle can recover and get ready for the next running motion. In fact, the rotational speed combined with gravity would help circulate the blood flow, helping to empty out the blood as the leg travels overhead and fill it with fresh blood as it comes back down.

Finally you want it to have long legs, so that you can leverage the muscles at the base of the leg to generate faster movement at the point of contact with the ground.

I'm not sure how many legs would be optimal, or how fast you could go. But this is how you would achieve a top running speed. Basically a giant tumble weed made out of giraffe legs.

Try different leg attachment

Four-legged mammal spines act like springs in all-out sprints, allowing its leg full length to push against the ground with each stride. But their legs are generally confined to 180* swing front and back for each stride. Hips are all ball-and-socket , and shoulders are generally also firmly connected (cats are an exception).

Disconnect them! See Philip Pullman's "His Dark Materials" series, including an intelligent species with mutualism with a hard seed to create an axle and spinning wheel.

Unlike Earth mammals which have to catch themselves with every sprinting step forward, if you have a front wheel, now the rear legs can just spin and the spine can be locked.

• i have read serious speculation about animals developing a natural wheel and why that has not occurred (although close, like rotifers I think have a ball that allows their "propellers" to spin). The problem with an actual wheel is blood circulation, but we have finger nails which do not require blood -- still hard to imagine how a wheel would naturally evolve. Commented Dec 22, 2022 at 7:03