The Sphere of Fear 
Hiding behind every amazing feat is a great application of physics. Many circus performances include something known as the sphere of fear, or circle of doom, or the Globe of Death. The basic design consists of a metal cage in the shape of a sphere that is big enough to allow a motorcycle or two to ride around inside. If the rider goes fast enough they can even ride upside-down or around the side of the sphere without falling. If you are interested in a bit of history about this thrill-show favorite, visit the HISTORY of the Sphear of Fear.
When examining the Sphere of Fear from a physics point of view, it becomes clear that there are two instances of concern. The first is how can the rider ride the vertical loop? The second is how can the rider ride the horizontal loop? Once these two concerns are addressed then we are safe in arguing that if a rider can ride both the vertical loop and the horizontal loop, they ought to be able to ride any loop that is a combination of the two.
The Vertical Loop
When riding the vertical loop, the three major forces that are acting on the cycle and rider combination are friction between the tires and the cage, the weight of the cycle & rider combination, and the normal force from the cage acting on the tires. In order for the cycle/rider to follow the circular path of the loop, these three forces must combine to produce the centripetal force (the force needed to keep an object in a specific circular path)
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What happens if the cycle is too slow?
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If the cycle is going too slow, then the weight (w)
ends up being greater than the force needed to keep in that path at that speed (the
centripetal force FC).
Since we have a force greater than the centripetal force needed, the cycle gets pulled
into a smaller circular path...it falls! The rider can not live with FC < w |
What happens if the speed is perfect?
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If the cycle is going just the right speed at the very top, then the
weight (w) will be exactly equal to the
amount of force need to keep it in the circular path of the cage (centripetal force FC). Since the weight is exactly what is
needed, the cage does not need to apply a normal force on the cycle. Theoretically
it would be possible to cut the very top of the sphere off and the cycle would still
follow the circular path. The rider can live with FC = w although it is risky. |
What happens if the cycle is too fast?
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If the cycle is going too fast, then the weight (w)
is not enough to keep it in the circular path at the top of the arc. The cage
must make up the difference by applying a normal force (FN).
The weight and the normal force create the needed centripetal force (FC). The only risk with going too
fast is that cage may not be physically capable of applying enough normal force...since
the sphere is made out of metal rather than cardboard this usually is not a big concern The rider can live with FC > w |
The Horizontal Loop
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In the case of the cycle and rider riding around in horizontally inside
the sphere we must again look at all the forces that are acting on the cycle/rider
combination. There are three forces, the weight of the cycle/rider combination (w), the force of the cage on the tires of the
cycle (FN), and the force of
static friction against the sides of the tires (fs).
We know that the force of friction must be static friction because if the tires
were sliding the cycle would be sliding down the wall of the sphere. In this horizontal loop the normal force (FN) is always directed toward the center of the cage, the the normal force is the centripetal force (FC). It's not that these forces are equal, they are actually the same force! Since the normal force and the centripetal force are actually the same force in this case, according to the formula, higher speeds (or smaller radii) will create greater normal forces. |
What happens if...
| ...the cycle is too slow? | ...the cycle is the perfect speed? | ...the cycle is too fast? |
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| If the cycle is going too slow, then the normal force (FN) will not be great enough to create
enough static friction (fsmax)
to counteract the weight (w) of the cycle.
The bike will begin to slide down the side of the wall...game over! The rider can not live with fsmax < w |
If the cycle is going just the right speed, then the normal force (FN) is large enough to create a force
of static friction (fsmax)
that just cancels out the weight (w).
With no net force in the vertical direction the cycle will not move up or down. The rider can live with fsmax = w |
If the cycle is going too fast, then the normal force (FN) will be large enough to create more
static friction (fsmax)
than is needed. As a result, static friction (fs)
will equally oppose the weight (w) of the
cycle. With no net force in the vertical direction the cycle will not move up or down. The rider can live with fsmax > w |
If the rider of the cycle is skilled enough to only create situations that can be lived with, he or she will have a long and healthy career as a Sphere of Fear Rider.
