The school year has come to an end and summer vacation has begun… time to stop learning for two months, right?
WRONG! So please, sharpen your pencils and put new batteries in your calculator (both graphing and scientific calculators are acceptable), because it’s time for another installment of Circus Science.
I worked at a circus camp for two summers. In addition to teaching juggling, slapstick, and trampoline, I also helped put flying trapeze safety belts on the campers. After spending hours watching the campers swing back and forth, flipping and flying in the air, I realized that a flying trapeze is just a giant pendulum, and can be broken down and explained with a few simple formulas and phenomena. Let’s take a closer look, shall we?
Note: In order to make calculations simpler, we will assume that the acrobat stays in line with the trapeze, keeps their body in a straight line, and doesn’t swing their legs, keeping the acrobat-trapeze system a simple pendulum.
For starters, what determines the amount of time it takes for the trapeze to swing back and forth? Contrary to common belief, the size of weight of the acrobat on the trapeze has no influence on swing time. The amount of time for one complete swing (the time from when the acrobat leaves the platform to the time they return), also known as the period, is solely dependent on the length of the trapeze’s cables. Longer cables, longer period.
Don’t believe me? Go look at a g randfather clock. The longer the pendulum, the greater amount of time it will take to swing back and forth. The formula T=2π expresses this relationship between period and length of the trapeze’s cables. T, the period, is equal to two times pi, times the square root of the length of cables divided by the acceleration due to gravity (which is 9.81 meters per second per second on Earth, but that’s for another article). When a flier wants to be caught by a catcher, the difficulty is in determining when each will begin their swing, because they both have different periods.
We can also determine the amount of energy the acrobat has and their maximum speed while they are swinging. There are two types of energy we are concerned about: potential energy and kinetic energy. Potential energy is stored energy due to position, and kinetic energy is energy due to motion. When the acrobat is standing on the platform, they have no kinetic energy-they are not moving. They do, however, have potential energy because of how high up off the ground they are. The formula for potential energy is PE=mgh, when PE is potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height about the ground. Once the acrobat leaves the board and starts to swing they begin to lose potential energy because their h value decreases. This lost potential energy changes into kinetic energy (energy is neither created nor destroyed, it just changes form), and the acrobat begins move faster. The formula for kinetic energy is KE=, where KE is kinetic energy, m is the object’s mass, and v is velocity.
Potential energy continues to decrease and kinetic energy increases until the acrobat reaches the lowest point of the swing. At this point, all of the potential energy has been converted into kinetic energy and the acrobat is moving at the fastest they will move. Then as the begin the swing upwards towards the peak of the swing, they slow down, kinetic energy decreases, and potential energy increases as the h value grows. This cycle of potential energy decreasing then increasing, and kinetic energy increasing and decreasing continues as the acrobat swing back and forth.
We have just scratched the surface of the physics involved in the flying trapeze. From centripetal force and momentum and how they make it easy to perform tricks at the highest point of a swing, to the forces endured by the catcher when they lock arms with the flier, there’s still plenty more to discuss. But it’s summer vacation, so I guess I’ll give you a little break. Until next time!
Matthew “Phineas” Lish, 17, is an award-winning clown and juggler, and has been trained by members of the Big Apple Circus Clown Care Units, as well as Ringling Bros. and Barnum & Bailey Clown College graduates. Notable performances include off-Broadway, the Ronald McDonald House, the Century Club with Dick Cavett, and guest ringmaster at the Big Apple Circus. He currently holds the world record for juggling clubs while bouncing on a pogo stick.
This article was originally written for White Tops magazine, and is published here with permission of the author.