Before Alison Sheets was an assistant professor at Ohio State University, she was a competitive gymnast who knew her way around a trampoline. Over dinner one day, she began explaining the dynamics of trampoline bouncing games to her colleague Manoj Srinivasan, an assistant professor in the mechanical and aerospace engineering department. Srinivasan had never (and still hasn’t) been on a trampoline, so he had never heard of a “seat drop war,” in which two players alternately bounce on their feet and their butt, vying to be the last player bouncing as they lose energy and it becomes harder and harder to bounce high enough to stand up from the sitting phase.
Now, Srinivasan knows a whole lot more about trampoline game theory than most people who have actually been on a trampoline. He, Sheets and their colleague Yang Wang decided to write a paper on the mechanics of the seat drop war, exploring the physics of stealing an opponent’s energy and the complex dynamics of the zero-sum game.
When two people bounce such that for a period of time, they’re both in contact with the trampoline, a dramatic transfer of energy occurs, allowing the second person to steal some (or most) of the first’s energy.
This is what it looks like in a more simplified view. To figure out the pure mechanics of trampoline bouncing, Srinivasan bounced balls on a mini-trampoline. Later, they took into account a little bit of game theory, since the whole process becomes more complicated once human strategy comes into play.
According to the paper, a player should aim to hit the trampoline halfway through an opponent’s bounce. The researchers write (emphasis in the original) “if mass-2 makes contact when mass-1 is approximately half-way through its bounce, the energy transfer is essentially 100% in a single bounce.” The transfer of energy between players is greater when you’re closer together, so to most effectively steal all of someone’s energy, sit close. And it wouldn’t hurt to start with a little more energy—so if you’re not the heavier player, jump high!
Go forth, and win ridiculous trampoline competitions. Although the researchers do note that “while the energy transfers may make multiple people bouncing on a trampoline more fun, they also make such bouncing more dangerous and unpredictable.”
Physics nerds, make sure to read the whole paper in PLOS ONE.