Here is the video. Check it out. (Jed Mildon)

There are two important things in this jump (other than not crashing): time and rotation rate.

Time in the air

You need to be in the air long enough for the bike person to make three complete rotations. How do you do that? Go fast, and go high. The higher you go, the longer you are in the air. Suppose you launch straight up with an initial velocity v₀, how long would it take for you to get back to the same height? Here is your basic kinematic equation.

If the bike lands at the same starting height, then:

Notice that this is just the vertical velocity. Your horizontal velocity won’t really help too much. However, if you go straight up, you might not land in the correct location.

Rotation rate

How do you get the bike to rotate in the first place? Take a look at this frame where the bike leaves the ramp.

In order to change the rotational angular momentum of the person-bike, you need a torque about the center of mass. Notice how the person leans back so that the center of mass (represented by the dot) is behind the force the ramp exerts on the bike? This would start the bike rotating.

Just for comparison, here is a biker at the beginning of a front flip. Notice how the ramp pushes on the back tire behind the rider’s center of mass. This would cause an increase in angular momentum rotating forward.

Ok. So you are spinning. Great. But there is more than just spinning. You need to spin fast. There is only a short time in the air and spinning on the ground is called something different (in this part of the country, we call it crashing). How do you spin faster? There is nothing to push on to increase your spin rate.

The key here is that since there is nothing pushing on you, your angular momentum would be constant. But angular momentum is different than angular velocity. Look at this expression for angular momentum.

This is a simplified version of a much better representation for angular momentum, but it will work in this case. In the above equation, L is the angular momentum, ? is the angular velocity and I is the moment of inertia (see lots of links below about the moment of inertia).

Essentially the moment of inertia is a measure of how the mass is distributed around the axis of rotation. The closer the mass is to the axis, the lower the moment of inertia. So, if you change your position on your bike, you can reduce your moment of inertia. Since the angular momentum is constant, this means your angular velocity will increase. You can see this change in position while Jed Mildon is in the air.

Now, the next time you see some kind of jump listen to the announcers. You will often hear them talk about the jumper doing something to change his/her angular momentum. This is a mistake. As you can see above, the angular momentum is constant. It is the moment of inertia and the angular velocity that change.

Word of caution

Oh fine. Maybe you understand the physics involved in a jump like this. That doesn’t mean you should run down to your local ramp and try to break the record for back flips. Just don’t do it.

See Also: