We Eats Trapeze Beats As Breakfast Treats!

I was recently asked to do an analysis of static trapeze beat technique by a friend, which requires some light, conceptual math. Before we start doing any adding or multiplying or whatever, we have to start by taking the same first step that we take in every kind of math problem: We need to wrap our heads around what question we really want to answer, preferably with bad drawings and snark. Now, truth be told, I might go off the rails right from the git go here, by assuming that what Megan wanted was a mathematical justification of using one beat technique over anther (something about making an ass out of u and me). If that’s the case, please clarify and I’ll course correct. Until then, we’re going to think about math and we’re going to have FUN!

Step 1: Snarky Drawings

Here are 4 different snapshots of a good, old fashioned full beat in its most archetypical form.

From left to right in the photo above they are: the back beat at it’s maximum height, the bottom of the swing when the spine is vertical, half way through the front beat, and the front beat at it’s maximum height. I’ve drawn all four by using stick figures, because, as we said earlier, the drawings should be Bad. I told you that doing math was fun! What we want to know is why the arms bend at the back of the beat, press the bar down to the pelvis at the front of the beat, and bend the spine during some parts of the beat and not others.

Step 2: Glamour Shots

Beats involve swinging, and swinging involves following a curved path around a central axis. Quiz time! What does your body rotate around when you perform a full beat: the rigging, the bar, or your shoulders? Answer now, then we’ll figure out the answer for sure by looking at the path traced by the body’s center of mass during a beat. Your body’s center of mass is about where your belly button is when your arms are above your head, and about 10cm or 4in below that when your arms are down by your sides. Let’s take a look at the four snapshots from above, this time using real photos of a real beat!

In all four snapshots, I’ve marked the performer’s center of mass with an orange circle, the shoulder with a pink circle and one end of the bar with a green circle. Now, let’s superimpose them on top of each other.

I’ve aligned all four snapshots at the end of the bar in the first photo, and at the shoulder in the second. Now, here’s the trick: The center of mass of a rotating object will trace a circle around its axis of rotation. The orange circles in both of the photos above show us four points along the center of mass’s circular path. It should be pretty clear just from this that the center of mass rotates around the shoulder and not around the bar, but let’s make sure we’re absolutely convinced.

I’ve added a green circular path around the bar in the first image and a pink circular path around the shoulder in the second image. The center of mass in all four snapshots is very very close to the pink circular path, so we can confidently proclaim that the body is indeed rotating around the shoulder: yay!

If you’re cranky right now because I straight up just ignored the rigging as a rotational axis option, that’s fair. You can repeat the analysis we just did to convince yourself that the center of mass is not rotating around the rigging. I’m being lazy and skipping it, because the axis is clear already and I want to talk about swinging trapeze for a second.

Step 3: Irritating Technicalities

I just told you that your body rotates around your shoulders and not the rigging, but you probably know from experience that the trapeze bar also moves back and forth some during a beat. If the trapeze bar moves back and forth, then that’s a swing, and a swing means that there’s some rotation around the rigging. That’s not fair, Charlie. The thing is, even though the bar is swinging around an axis located at the rigging, you are not. Your center of mass stays directly beneath the rigging the entire time, which is the reason the bar has to move in the first place. Let’s look at more pictures!

In the photos above, I’ve used the snapshot of the bottom of the beat as the base image and superimposed each of the other three snapshots on top of it, aligning the centers of mass vertically. In the first image, we can see that when the performer performs the back beat, the bar moves forward. The forward movement of the bar compensates for the backward movement of the performer’s center of mass, keeping their center of mass directly under the rigging. The second and third images show the performer during the front beat. Here, the center of mass moves forward and the bar moves backward to compensate, keeping the center of mass under the rigging in a similar way.

Why do we care about swinging, anyway? What’s wrong with swinging on static trapeze? In theory, nothing, however there are two reasons not to.

1). Swinging on anything changes the direction and magnitude of forces applied to the rigging, so the rigging must be changed to accommodate those forces. You could rig a static trapeze in a way that allows for swinging, but then you’d basically have a swinging trapeze which has its own beat technique designed to maximize swing.

2). A swing small enough for standard static trapeze rigging to accommodate is difficult to time and typically makes the skills that follow it look and feel messier, and that’s likely not something any of us want.

Step 4: Fidgety Details

Okay, so now you’re hopefully on board with where your center of mass should be and why, but what’s the deal with that little hiccuppy pull up at the top of the back beat and the front planchie thing at the top of the front beat? What about arching/hollow body/piking? Is there a such a thing as a Perfect Beat Technique? No, but also yes. Technique choice depends on what you’re trying to do, so for the rest of today we’ll have to pick one specific goal. Let’s choose the archetypical full beat, in which the spine rotates a full 180 degrees and is horizontal to the floor at the top of both the front and back beat.

Step 5: Wacky Waving Inflatable Tube Acrobats!

The role of arm position and body shape in beats is two fold: first, to keep the body’s center of mass aligned under the rigging to eliminate unintentional swinging as we discussed previously, and second, to orient the body to adjust how much torque is created by the gravitational force, and thereby control the speed of the swing. I talked about torque created by gravity pretty extensively in Dat Torque, so if this next part gets a little thick, pop back over there for a refresher!

Remember that torque is what causes a thing to rotate and that torque is created by forces that push on the thing perpendicular to the radius of the circular path it traces. A force is a push in a straight line, and you can think of torque as kind of a circular push. The important thing to know is that you can’t have torque without a force, and the more torque there is the faster you’ll rotate, or in our case, swing. The formula for torque is totally simple:

This shows us that we can get more torque by either increasing the force or the distance the thing is from the rotational axis. When there’s only one point of contact between the thing (your body) and its axis of rotation (your shoulders), the only force available to create torque from is the gravitational force. We can’t change the gravitational force unless we go to Mars or something and rad space vacations are taking forever, Elon. That means that the only option we have to change the torque and by extension, our swing speed, is to change the distance between our body parts and the rotational axis. To make this part not require the Weird Math S, we’ll assume that all of our body’s mass is located at our center of mass. Let’s start at the top of the front beat.

We know that to maximize torque, we need as much of our body as possible to be as far away from our rotational axis as possible. While also being as perpendicular to gravity as we can manage. And while keeping our center of mass directly under the rigging. The body position that most effectively achieves both of these goals is a front planche. If you keep your arms extended over your head, your center of mass will move out from under the rigging, you’ll generate a significant swing, and that’s not static trapeze anymore.

By the way, in the above photo I have overshot the ideal, horizontal position. Overshooting and undershooting is easy to do, because the torque that drives the forward motion of the beat needs to balance the torque that drives the backward motion of the beat, and that’s really hard to do when body position is our only means of control and our bodies are not symmetrical from front to back. In other words, whoopsiedoodles!

Let’s check out the back beat.

Here’s the thing about the back beat: in order to get the spine parallel to the floor, your arms need to rotate from straight overhead to extended behind your back at a ninety degree angle. While remaining shoulder width apart. And not pulling up through a dislocate. That is not something that my anatomy will do, and most of you have anatomy that won’t do it either. That means we’re left to make the best approximation of a parallel spine that we can by compensating wildly with a cornucopia of less than ideal body shapes.

The first is by bending the back as high on the spine as possible while keeping the hip pits fully open. The goal is to bend the back only as much as necessary to bring the majority of the body (legs and pelvis, minimum) to horizontal. Arching to your maximum extension will bring your body closer to its rotational axis and reduce your torque in the following forward swing. There are lo-ho-hovely full beat variations that involve this, but we agreed to just talk about the archetypical form for today.

The second is bending the arms in that little hiccup, which increases the speed of the swing. Understanding why and how has to do with conservation of momentum and is a little cray. I’m going to give that discussion its own post since this one is already like a thousand pages. In that post I’ll also talk about the effect that body shape has in the middle of the beat. Until then, comment away with your observations as you train, tell me other things you’d like me to say words about, and if you’d like to know when I publish new blog posts and other goodies, drop your email below (I will never share your email or send you garbage, scout’s honor).

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