Diavolo!

This guy is Allo Diavolo:

He was a circus daredevil. At the dawn of the 20th century he worked on a number of stunts dressed in his ominous horned outfit. These days a lot of people, including me, have heard of him as an example in the pages of physics textbooks. In my case it was Halliday and Resnick, a standard (and good) freshman physics text. Diavolo did a trick where he looped the loop riding a bicycle. It's pretty impressive:

The breathless circus ad copy claims that this stunt is more or less certain death. It wasn't, of course. I wouldn't want to try it, but it's certainly a physical possibility. How?

As it happens, it's a basic fact of classical mechanics at an object in instantaneous uniform circular motion will undergo an acceleration. After all, an acceleration is just change in velocity, and velocity is not just a speed. It's a speed in a particular direction. If the direction is changing, the velocity is changing. If the velocity is changing, there's an acceleration. Newton was the guy who figured out acceleration hundreds of years ago. One of his famous laws of motion is that force equals mass times acceleration. Therefore if we know something about the forces and accelerations acting on Diavolo, we can say something about the requirements to do this trick without going splat.

An object in uniform circular motion is undergoing an acceleration equal to:

The velocity is v, the radius of the circle is r. The bicycle's motion isn't quite uniform; the speed is changing along with the direction. But this is ok, our equation remains valid for circular motion as long as we're interested in the component of the acceleration that's perpendicular to the surface of the track. And that's what we're after. We want to see whether he stays on it or not. To do so, he needs that acceleration we wrote above.

There's two forces acting on him. One is the force of gravity. It's equal to mg, where m is his mass and g is the acceleration due to gravity at the earth's surface. The other force is the so-called normal force, which is just the force the track exerts on him as it prevents him from ghosting through the surface. If his speed is just barely enough to prevent a fall, the normal force will be zero. Therefore the only force acting is the mg gravity, which will as Newton said be equal to the mass times acceleration:

Do a little algebra jazz and find v:

Halliday and Resnick estimate the radius of the loop at 2.7 meters, which plugged into the above equation give a minimum speed of about 5 m/s, or around 11.2 miles per hour at the top of the loop.

What makes it especially tough to do in practice is that this translates to a considerably higher speed at the bottom of the loop. There the normal force is going to be quite high, and it's the normal force that we think of and feel as the "g-force". Keeping balanced and steering while experiencing these powerful and rapidly changing forces is quite the trick.

How about we make this a quick little Monday exercise? Using the equations for kinetic energy and gravitational potential energy, estimate his speed at the bottom of the loop. From there, repeat the procedure we used above to find the g-force. (Hint: g-force is N/m). Good luck!

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