# Speed Limit to Running

1. Sep 9, 2009

### simpleton

Hi all,

I am doing a project on the speed limit on human sprinting. I was doing a thought experiment and then got myself confused, so I hope you guys can help me out.

I assumed that there is no air resistance, and that the coefficient of friction between the ground and the foot is sufficiently large such that no slipping will occur. Therefore, whenever the foot is on the ground, it will not move.

When one runs, one swings the foot backwards against the floor, and it is the friction that moves the person forward. Since the foot is not moving when it is on the floor, if the person swings the foot backwards at speed v relative to itself, I believe it is reasonable to say that the person will move forward at speed v relative to the ground too. In that case, if we ignore air resistance, doesn't that mean we can keep on increasing the speed and reach extremely extremely high speeds?

Also, I did a numerical simulation using excel, and found out that the drag force is actually not that big and rather insignificant because even Usain Bolt does not run fast enough for drag to become an important factor. Therefore, I would like to ask, why is it that humans run so slowly?

2. Sep 9, 2009

### A.T.

Mainly because the legs have inertia. You cannot swing them as fast as you want.

3. Sep 9, 2009

### simpleton

However, I think that if we neglect air resistance, then he is moving at constant velocity in the x-direction when he is off the ground. Therefore, I think we can take that as a inertial frame. And the swing of the leg is relative to yourself, not to the ground, so I think that if you just swing at a constant pace, your speed will keep on increasing.

4. Sep 9, 2009

### A.T.

No, you have to consider the stance phase too. To prevent breaking on heel strike you have to move your foot at least as fast, as the ground moves in your frame, which is faster and faster. Usually some breaking occurs in the begin of the stance phase, while acceleration occurs at the end of it, when the leg extends. But there is the same limit: you cannot extend your legs as fast as you want. Not only because of inertia but also muscle physiology.

Last edited: Sep 9, 2009
5. Sep 9, 2009

### simpleton

Oh right, I never thought of it that way. Thanks :)

6. Sep 23, 2009

### Molydood

interesting question, my instincts tell me that a human geared for ultimate top speed will not have as much power or accelerative ability, but due to a lighter build would have the ability to move legs at a higher rate than a bigger built human, and hence eek out a few extra m/s than others with heavier legs. If the air resistance really is not that significant then ultimate power, you would think, is for accelration only and not so much top speed. top speed appears to be governed by maximum leg speed, whereas acceleration appears to be more a force thing.

just instincts, I know this is not true as nealry all sprinters are big builds, and I imagine those at the top end of the 100m or 200m racing have the highest running speeds on the planet too.

so clearly my instincts are wrong, but I like the question :-)

7. Sep 23, 2009

### xxChrisxx

This is not Scooby Doo, people do not run like this, thats your first mistake.

People run by pushing into the floor at an angle. Friction is required to prevent slipping but past that, adding friction will not improve speed.

Before you bother going any further, try to develop a scenario that you can test that models someone running in a realisitc way.

8. Sep 26, 2009

### dimensionless

Because $$F = ma$$. In other words, because humans have to accelerate. By the time one accelerates to a certain speed, the blood O2 levels crash and heart can't keep up, that and it is stressful for the joints and leg muscles....also running means bouncing up and down. It's kind of like jumping up and down (think of what happens on a treadmill, where wind resistance is significantly less), and it becomes very exhausting.