# Walk the Line

See these guys? They’re racewalking. It’s like running in that you do it as fast as possible, but you’re not allowed to have both feet off the ground at any time. One foot has to be planted on the track at all times. The guy to the far right is slightly cheating – both his feet are off the ground.

But take a closer look at the foreground guy in the red, white, and blue. He illustrates the proper form very well. Think a little abstractly and imagine how the leg moves. The foot is planted and so the leg forms the radius of a circle. The hip therefore traces out part of that circular arc until at its forward point that foot comes off the ground and the same happens on the other leg.

And that’s uniform circular motion, which we know how to do. We’ll put the acceleration we need for circular motion on the right, and we’ll put the acceleration we actually get from gravity on the left:

Here g is not always pointed toward the center of the circle, so this equation is not quite right, but it’s pretty close. Solve for v:

Now let’s say the average person’s leg is a meter long. Plug in the figures, and I get a speed of 3.13 meters per second. You can’t walk any faster than that. Gravity won’t keep you held to the ground if you try to go faster than that.

But that’s only an 8.5 minute mile. Racewalkers can go faster than that. What gives? The answer is that they use a funky walk where they swivel their hips, flattening out the circle. That makes the effective r larger and lets the fastest racewalkers reach paces of a little over a six minute mile, or about 4.3 meters per second.

1. #1 Uncle Al
October 31, 2008

Construct a giant rotating banked track and observe how fast a racewalker can go before suffering structural failure.

2. #2 patrick
October 31, 2008

Uh, this calculation is completely incorrect. You can only use the equations for uniform circular motion in the absence of external forces, which clearly does not apply here.

3. #3 Matt Springer
October 31, 2008

It is true that we don’t have detailed knowledge of the internal forces, but we don’t need that to do the problem. The leg manifestly is in uniform circular motion aside from the small approximation I mentioned, and so we’re guaranteed that the forces must sum to mv^2/r, whatever they happen to be individually. We don’t know exactly how the forces distribute between gravity and the other forces in the hip joint, but all we need to know to do the problem is to say that in the aggregate the forces must produce the uniform circular motion force, and since gravity is the only force acting downward there’s no way to produce a v^2/r acceleration greater than g. This puts an upper limit on v.

4. #4 wokka
November 1, 2008

I’m kind of tired right now, but after thinking for a minute I think I understand what you are saying. When a walker takes a step, he cannot push only forward, but the vector is always pointing a little upwards. He cannot push so much that it will force the other foot off the ground, since that is against the walking rules, and therefore the motion is limited by the physics of uniform circular motion (leg planted on ground). This might not be immediately clear for every reader (I know from experience that I might think I’m slow, but there is always someone else who will take longer to understand…).

5. #5 Dave McGovern
November 3, 2008

Matt,

Two points that must be consider are the effects of hip rotation and ankle flexion. The lever that is the human leg grows considerably at the rearward portion of the stride as the hip rotates and as the ankle flexes behind the body. Although the lead walker (Francisco Fernandez of Spain, incidentally) is exhibiting a “flight phase,” his rear foot is demonstrating a degree of flexion the would add .1 to .15 meters to the stride even without the flight phase. He is also demonstrating pelvic rotation (notice his left butt cheek is visible from a side view. This would not be possible without a high degree of hip rotation.) This pelvic rotation will add another several (10 – 15) centimeters to the stride. These confounding factors must be worked into the equation. Good luck working that out!