# Acceleration of a legged animal (ie, humans)

1. Oct 10, 2009

### Omnirizon

What limits the acceleration of a runner? and how does this work?

my intuition is that it is primarily gravity. air resistance should have minimal influence. if this is the case, then it seems that humans (and most other legged animals) would reach their top speed almost immediately, since they are dealing with the constant of gravity limiting net acceleration, and not the exponentially increasing force of fluid resistance (ie air) sapping acceleration. for this to be the case, it would seem that as the runner's velocity increases, the acceleration of gravity towards the center of the planet would increase on the runner, to the point that the runner's net acceleration is zero.

Am I correct here? if this is the case, then is it complicated mechanics of moving legs and flexing muscles that cause whatever lapse between starting velocity and top speed of running animals? also, how would the reduction in acceleration due to gravity be modeled in a runner? some sort of trigonometry to account for the fact that runner's force is forward, while gravity is pulling downwards?

if it is trigonometry, would it be modeled as a right triangle, with the force the runner exerts as the tangent, and the effects of gravity one leg. then their top speed can be found by finding the length of the other leg (knowing the angle must be 90). just as an abstract model that is?

sorry for all the questions, I hope I am being clear enough. I am not a physics major, just a programmer attempting to find some computationally tractable model of simplified physics for a little game.

-Omni

2. Oct 10, 2009

### mgb_phys

Pretty much the same thing that limits a car's accelration = torque
Initial acceleration is mostly about muscle strength and the force it can use to accelerate a mass forward.

3. Oct 10, 2009

### Omnirizon

OK.

my issue is then what limits top speed? I do not thing for a runner it is simply torque. I thought about it like this: a human on a bicycle with one-to-one gearing can go much faster than a human on foot, yet they have the same torque (and the bicycle even has the extra overhead of the drive-train).

for a car, air resistance acts to limit the net acceleration provided by torque. after a point, the friction of air resistance completely cancels out the acceleration of the car. also, the efficiency of the drive train matters (for a runner, it is the efficiency of their 'drive train' that I think really matters).

so for a runner, air resistance doesn't factor in as much as it does with a car. knowing this, I was curious as to what is it that limits a runner's speed, and how is this modeled. I'm guessing now that it is simply the limits of the machinations of the runner's legs, and their ability to apply force and recover (their drive train). because this is the limit, and animals don't have gears to speak of, then a runner should achieve top speed very quickly (since air resistance doesn't become a huge factor until much faster than speeds most land animals can run, and they have much smaller frames than a car). gravity is not so much limiting forward motion of the runner, as it is limiting the runner's ability to move their legs.

in fact we see this, cheetahs accelerate much faster than any car. put a cheetah in an environment of double gravity, and acceleration would be reduced because there would be more weight on the legs and their activity-recovery cycles. this raises a question: would a car in a 2g environment accelerate more slowly, and why? would it be simply due to increased rolling resistance? or would the gravity act on all components of the car, decreasing all components ability to move.

4. Oct 10, 2009

### mgb_phys

Acceleration is different to final speed.
Initial acceleration is pretty much just leg muscle strength - so a sprinter can out accelerate a bike for the first few metres.

The final speed for a bike or a car is when the power you can put in is equal to the energy lost to wind resistance. For a bike on the flat this is around 30mph/50kmh.
For a runner it's a bit more complicated - the limit probably comes from the muscle strength need to accelerate the leg forward an then stop it on each stride.

5. Oct 11, 2009

### A.T.

6. Oct 11, 2009

### Omnirizon

7. Oct 11, 2009

### Cleonis

In athletics for disabled people special carbon fiber running devices have been developed for competitors who have lost, say, one foot.

Now, one competitor, who had one missing foot, had commisioned a pair of running feet that extended his legs. One was strapped on the angle stump of the leg that missed the foot, the other one was strapped on the foot and ankle of the normal leg.

I think that with the running feet that competitor stood 30 or 40 centimeters taller. Because of the difficulty of maintaining balance in the first steps he wasn't as fast out of the blocks, but at top speed he was flying. Other competitors protested, claiming that the leg lengthening devices gave an unfair advantage.

For one thing, the legs were made longer, so with the same leg frequency the strides were longer. And the elasticity of the carbon fiber running feet is such that much less energy is lost in the bounce. (Compare kangaroos, that have evolved tendons that on rebound give back almost all of the energy that was stored in them.)

Oscar Pistorius, who is a double amputee athlete, is on a mission to compete in the Olympics (not the paralympics.)

Cleonis