Saturday, December 1, 2012

Physics of Parkour

 By David Haimes

Parkour is the French art of movement, in which a traceur (someone who does parkour) moves in the most efficient way possible to get from point A to point B. Using our environment as an obstacle course, we use a variety of rolls, climbs, vaults and sometimes flips to traverse varying terrains. Since efficiency is so engrained in the very nature of parkour, the next logical step is clearly to study the physics of parkour to find ways traceurs can more efficiently perform movements and traverse an environment. I will analyze various movements and the related physics to see what patterns emerge and can make me a better traceur.

The roll and the flip – (roll demonstration: http://www.youtube.com/watch?v=5tJAyNxig_A)

A parkour roll is typically used to help lengthen the duration of an impact from jumping from a height. Both the parkour roll and the flip have very similar physics, as they are both rotational movements.

From our circular motion equations, we know the force of rotation is F = mv 2/r.

For a 72.5kg male, who must complete one rotation in order to land successfully, the main thing he can control is his radius by controlling the tightness of his tuck while rotating. A tighter tuck (smaller r) increases the force, allowing him to rotate faster. Using v=rw, estimating a very tight tuck of 2.5ft in diameter (r=.381m), we can approximate that the Force of rotation is mrω 2, or (72.5*.381*π2)=272.6N

The wall run – (http://www.youtube.com/watch?v=2OR6yon8VpQ)

The wall run is used to scale high walls by planting one’s foot and pushing against the wall. Thinking logically, we’ll get a different outcome if the force applied against the wall is at varying angles. If we push directly into the wall, the normal force will counter our force applied, and we will move only horizontally away from the wall, which won’t help us reach the top of the wall. Similarly, if our force applied is only vertical, we will just slip down the surface of the wall and fall down. The optimal angle that gives us both upward movement and prevents us from crashing face-first into the wall is 45 degrees.

This becomes a simple force problem to understand. To not crash into the wall, our Force applied in the x (Fa cos (45)) is equal to the normal force. Furthermore, the forces in the y direction are the force of friction opposing our downward applied force (and so is up), the force applied (Fa sin 45), and the force of gravity caused by our weight. Summing the forces:

Fa cos 45 = Fn

Ffr – Fg – Fa sin 45 = ma

(there is only acceleration in the y)

Plugging in,

µFa cos 45 – mg – Fa sin 45 = m a.
Estimating a coefficient of friction of .8 (we wear very grippy shoes), m = 72.5kg, and a final acceleration of positive 3 m/s2

One last simplification gives us

Fa = m(a+g) / (µcos 45 – sin 45). Using the estimations, we require a Fa of -2153N (down and into the wall) to give us an upward acceleration of 3 m/s2.

In the end, by looking at some physics equations, we can use our intuition and a few calculations to better traverse our environment in a more efficient way by using optimal angles, and tighter tucks in our rotations.

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