# Physics of Parkour, or how to run up a wall

Parkour: the act of running and jumping like a crazy superhero. I can’t do any of it. But I can analyze it. So, let me start with the wall-flip (or any kind of move that involves walking on vertical walls). This looks like a good example (there are a bajillion on youtube).

Pretty cool, huh? How do you run up a wall? Well, it has to do with friction. Remember, this is a fairly useful model for the magnitude of the frictional force on an object:

Where N is the force the surface exerts on the object (the normal force) and ?s is the coefficient of static friction. Note that this less than or equal to the frictional force. (here is much more about friction).

Let me start with a simple case. Suppose I take a book and push it horizontally so it stays on a vertical wall. Like this:

I was going to add a hand in the above diagram, but it just didn’t turn out right – oh well. Anyway, for this object, the forces must add up to the zero vector (if the object is at rest). Notice that the friction force is what acts in the opposite direction to the gravitational force.

This is sort of cool, but a wall-flipper doesn’t have someone pushing him or her up against the wall (except in a case like this)

This is Ninja Warrior Mark Witmer, and he is pushing himself against the wall to stay up. Of all the parkour stuff, this is probably the only thing I would have a small chance of being able to do. But for the wall flip move, how can there be a normal force on the person if there is nothing pushing the person? What if I re-draw the book diagram and remove the force from the hand?

If this were the case, the frictional force could be the opposite of gravity. However, the forces would not add to the zero vector in the horizontal direction. This would mean that the book would be accelerating to the left (which doesn’t mean it has to MOVE to the left). So, this is the key for the wall flip. The flipper (the person doing the flip), or would it be the parkourer, needs to accelerate in the direction opposite the wall. This could mean slowing down and speeding up.

For a book, this doesn’t seem very practical. For a person, however, it can be done. A person is not a rigid object. This means that the center of mass of the person can be acceleration while the feet stay in contact with the wall. Maybe I should just try a little video analysis on the above video.(mandatory Tracker Video Analysis link)

This is actually a pretty video for analysis. There only two problems. First, there is no scale. To compensate, I just completely guessed the the height of the guy while running was 1.5 meters. The other problem is that there are duplicate frames. I hate when that happens. But, to the credit of the creators, the camera is stationary and perpendicular to the motion of interest. The first thing I want to do is check how good my scale guess was. While the guy is falling back to the ground after leaving the wall, he should have an acceleration of around -9.8 m/s2. Here is the y-position plot from Tracker.

Here I just fit the parabola to the downward part of the motion. This gives an acceleration of around 10 m/s2, so that is good. And now, what about the horizontal acceleration while the guy is in contact with the wall. I will just assume that it is a constant acceleration (although clearly this doesn’t have to be true).

I admit this is not the best fit, but it will have to do. This gives a horizontal acceleration of 8.34 m/s2. If this is the only force in the horizontal (x) direction then:

If the guy is not accelerating in the vertical (y) direction, then:

Here I am assuming that the maximum friction is being applied (or I am solving for the minimum coefficient of static friction). Now I can put in my expression for the normal force and I get:

This gives a minimum coefficient of static friction of about 1.2. Seems high, but remember this is the coefficient between rubber (shoes) and brick. I would assume this could be very high. This site (the hypertextbook) gives the coefficient between concrete and rubber as up to 1.0 so maybe this is not too crazy.

Note: even if you understand the physics of wall flipping, I wouldn’t recommend trying it.

1. #1 Uncle Al
August 6, 2009

Ultra-high coefficient of friction TRAX rubber outsoles.

2. #2 david
August 16, 2009

Here’s some crazy parkour stuff I would love for you to analayze too.. Do you know Daniel Ilabaca of the WFPF (World Freerunning & Parkour Federation).. Check out him and some of his partners of the WFPF in this cool video shot in NYC this summer of 2009… yikes!!!! Phil Doyle, Daniel Arroyo, King David and Livewire too…….

3. #3 Rhett
August 17, 2009

@david

those guys are crazy. Why would you jump into a handstand on the edge of a building? I don’t get it.

4. #4 parkour anon
October 20, 2009

@Rhett
because it’s fun!

5. #5 chris
January 11, 2011

i am a free runner and a wallflip is a pretty easy movement.

6. #6 meg
March 2, 2011

im meg

7. #7 WHAT?
March 24, 2011

WHAT???