In the mid 19th century, a Frenchman by the name of Jules Leótard developed the art of trapeze, whilst wearing some skin-tight clothing that would later be named after him. Given that he was constantly experimenting to see what was possible, he fell frequently and violently, and it’s a wonder that he didn’t die given that his safety provision was a swimming pool, as opposed to say, netting or giant crash mats. Quite how trapeze-diving hasn’t become an Olympic sport yet baffles me, but I went trapezing last month and even without the water it was a pretty awesome time.
Flying on a trapeze is simply a combination of timing and physics and, given that I’m constantly working on the first and enamoured of the latter, it was always going to be fun. A trapeze is, essentially, a pendulum: a surprisingly heavy metal bar suspended by two ropes from the ceilings. One climbs a ladder, leans thrillingly far out on a rather precarious platform whilst being held back by a helper, grabs the bar and on a given signal, jumps into the air and lets gravity do the rest.
The potential energy of a trapeze artist is at its maximum when the artist is about to jump, a value roughly equivalent to mgh (mass * gravity * height of the pendulum above its lowest point). The maximum speed is therefore simply (2gh)/2, which comes out to about 5.8m/s (a mere 13mph) in the space where I was practising. Note that mass is omitted in this second formula: the bigger you are, the exact same rate at which you fall. Jumping forwards to get a speed boost also does nothing, the only variable is ‘h’, the height at which one starts. Pendula are quite amazing in many other ways too: no matter how high you start their swing, they will ‘always’ (physicists beware) take the same amount of time to return to where they started (their period). If you ever need to make a measurement but only have a stopwatch and some string, a pendulum with a period of one second is one metre long. I learned most of what I know about penulda from Walter Lewin and if you haven’t yet seen his lectures…enjoy.
Simply flying on a trapeze, whilst fun, will soon take a toll on the arms and air-resistance will kill the fun before too long. So, instead, we move on to tricks. One fun trick which I’m not yet skilled enough to perform is to move between standing on top of the trapeze, to hanging underneath it by one’s feet. Other than the thrill of rapid inversion, this brings a second adrenaline rush in that it extends the length of the pendulum quite significantly, and therefore brings with it a very significant sudden acceleration (h is extended by the artist’s height, upping the maximum speed).
Most tricks, however, go the other way, and involve the artist pulling themself up onto, over and around the bar in various positions. This requires very little in the way of upper-body strength. A pull-up on a static bar requires overcoming gravity (F=gm), or simply lifting one’s body weight. On a trapeze there is an additional centripetal force of mv^2/r (where r, radians, is helping us calculate the angular acceleration) at the nadir of a downswing on a trapeze, in my case 5.8m/s as calculated above, this force is around 2/3 that of gravity. Despite this fact, most male first-timers on trapeze will always try to pull-up during their initial downswing – I don’t know why, muscle reflex maybe from pull-up bars maybe – which is the equivalent of trying to lift their own body weight plus two-thirds. They invariably fail to do so.
At the zenith of a swing, however, this centripetal force nears 0 and, furthermore, the artist has significant upwards momentum in their favour. Lifting one’s legs or body at this point requires far less effort than it would on a static bar, and there’s a feeling of approaching weightlessness if the timing is precise. Physics and timing, all you need in trapeze and all you need in life.
Here’s a video of my first time.
Not the most graceful, but it got better, and I even jumped off my trapeze onto a catcher the last couple of times.