# The Physics of Free Running

Before you leap, look to Newton

Check out this demo reel of Levi Meeuwenberg doing some jaw-dropping "free running". Free running is very similar to Parkour in the athleticism required and specific techniques and movements used, but while Parkour is about getting from one place to another in as efficient a manner as possible, free running is less directed and more creative in nature.

As mentioned in that ancient post, when performing either of these activities, in addition to spending years developing a formidable set of technical skills, balance, physical strength, and kamikaze attitude, it's important to be cognizant of some basic physics.

In order to lessen the impact upon landing after a fall, or to decrease the force upon a set of fingers while grabbing onto a wall, it is essential to reduce the acceleration during each collision as much as possible. This requires increasing the time of impact by smoothly bending, flexing, or rolling during impact.

Let's apply some of the physics by taking a quantitative example. During impact with the ground, there are essentially two forces acting on your body -- the downward force of gravity and the upward force of the ground.

Applying Newton's second law we get:

`Fnet = Fground \- mg = ma`

where `mg` is the weight force (a.k.a. the force of gravity) acting on your body. So let's say that Levi jumps from a height of 3.0 meters onto the ground. How much force is the ground going to exert on him during impact?

First, let's apply conservation of energy to determine Levi's speed just before contact.
The gravitational potential energy (mgh) due to his initial height relative to the ground is going to be converted into kinetic energy (½ mv2) just before landing. So

`Mgh = ½ mv2`

and `v = [2(9.8m/s2)(3.0m)]1/2 = 7.7m/s`

Now we have to bring him to a stop. Let's assume the lithe and wiry Levi has a mass of approximately 70 kg. Now because

`Fground = m(g + a) = 70 kg (9.8 m/s2 \+ a)`

we can see that the force of impact depends on the acceleration. But a = Δv/Δt and therefore depends on the time of impact. If he were to foolishly land on his heels with rigid locked knees this would result in a very small impact time -- as little as 0.01 or 0.02 seconds for this type of collision. The result?

`Fground = 70 kg (9.8 m/s2 \+ 7.7m/s/0.01s) = 55,000 N (or about 12,000 pounds).` Ouch!

However, by bending and rolling, the time of impact can be increased to as much as 0.3 or 0.4 seconds. By decreasing his velocity over this extended period of time, the force is substantially reduced. Applying the above calculation with an acceleration time of 0.4 seconds we now get Fground = 2000 N (460 pounds). It's still a significant force but as you can see in the video quite manageable for someone with the proper skill, strength and technique.

Speaking of landing on the heels, notice that Levi never does that. Impacts are always taken with the ball of the foot. Landing on the ball allows for an increased impact time and less compression on the legs. Now recall some previous posts on running shoes.

Did we not decide that the most efficient stride technique involved a mid- to fore-foot strike? It seems reasonable to propose that the most efficient stride is also the most natural stride for the running human, and might be expected to result in fewer injuries, relative to the much more jarring heel strike. Most running shoes have big padded heels, making it easy for the unwary jogger to strike with the heels. However, running barefoot, it's relatively impossible to do that. It's just too painful. You automatically impact on the front of the foot, much like Levi does when sticking a landing. Interesting. We've talked about a pair of shoes meant to simulate barefoot running. But what about the real thing? What about barefoot running itself?

To be continued...!

Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.