Is It Possible to Run Up a Wall? Sort of

A video shows a kid running up a wall in three steps -- but how, and is there a limit to the trick? Dot Physics blogger Rhett Allain crunches the numbers.

The short answer is: Yes, sort of. The guy above takes three steps running up a wall. Of course, he couldn't do this forever. So, how does this work?

Friction

Clearly, you need some friction to pull a stunt like a wall flip. In the simplest model for friction, the maximum magnitude of the frictional force is proportional to how hard to the two surfaces are pushed together. I can write that model like this:

Here, N is the force one surface pushes on the other (often called the normal force since it is perpendicular to the surface). The coefficient, μs, depends on the two types of materials rubbing together. One other thing, the direction of this frictional force is parallel to the surface.

Now for an example. Suppose I take a book and put it on a vertical wall. Could you push this book into the wall so that it stays put? Yes. If you want to try this, use a stick or something to push on the book. If you use your hand, you tend to also push up and into the wall. But if you pushed just into the wall, the forces on the book would look like this:

Untitled 1

For this case, the frictional force is pushing up on the book and essentially what keeps the book from falling. If there was no friction, it wouldn't matter how hard you push with your hand, it would fall.

Another Wall Climb

Before looking at running up a wall, here is another way to move up a vertical wall.

Untitled 3

This is former Ninja Warrior Mark Witmer. How does he stay on the wall? In this case, the friction force (on both his hands and feet) push up. The reason there is a frictional force at all is because he is pushing on two opposite walls. This move really isn't difficult. Oh, it's still hard, but lots of people can do this.

Wall Flip

Running up a wall is different. There is nothing pushing the person against the wall. This means that in order to have a frictional force, you would need a normal force like this.

Untitled 4

The only way you could have a normal force like this (without another force pushing to the right) would be if the object accelerated to the left. If there is a net force to the left, there has to be an acceleration to the left. This doesn't mean the object has to move to the left, it can move to the right and accelerate to the left.

This is exactly what happens with the wall flip. Here are the key steps:

  • Person runs toward wall (I will say to the right).
  • At the wall, the person puts a foot on the wall and pushes to the left. This does two things. First, this force creates an acceleration to slow the person down. Second, this force is the normal force that is needed for the upward frictional force.
  • During the move, the person must keep accelerating to the left. No acceleration means no normal force. No normal force means no friction. No friction means falling.
  • Eventually, the horizontal speed goes to zero and the person starts speeding up to the left. This is fine as long as the person doesn't get too far away from the wall to push on it. If you can't touch the wall, the wall can't push on you.
  • The move ends once the person is high enough to push off and end in a flip to land on the ground.

Maybe you prefer this as a diagram? Here you go. These images were created from this nice tutorial on performing the wall flip.

Untitled 6

How many steps can you take going up the wall? The guy in the top video does three. Pretty impressive. You want to take three steps? You don't have much time. Remember, the harder you push on the wall, the quicker you will slow down and move away from the wall. I wonder if someone could take four steps up the wall. Four real steps - not tiny little steps. Like I said, there isn't much time.

You might also notice that this is similar to the Warped Wall from Ninja Warrior. True, but different. In the warped wall, you want to finish the move by going up and the wall isn't straight. Of course, this will require another post - to come sometime in the future.

Perhaps I should add that this isn't a move you should just go try for yourself. You could really get hurt. Just do a YouTube search for "wall flip fail" and you will see what I mean.

Homework

There is just one homework question for this post. Find a nice wall flip video that shows the motion from the side. Use Tracker Video analysis or some other video analysis tool to measure the motion of the jump. Based on the horizontal acceleration, calculate the minimum coefficient of static friction for this wall flip to work.