I’ve thought a fair amount on how linear momentum is built when skating on one foot. But angular momentum is important too, and there are three axes to consider. Here are some initial thoughts.
Vertical Axis
At its core, figure skating takes place in a rotating reference frame in which the rate of rotation around the vertical axis equals the rate of orbit around the circle (like a tidally locked planetary orbit). Therefore, angular momentum is built-in at all times.
Let’s watch this video by Gary Beacom and think about Axel takeoff:
Gary Beacom starts with the angular momentum of a good edge, but adds more by swinging his leg through (we think of this in terms of its linear momentum effects, but it also adds more or less angular momentum, depending on how wide the swing of the leg is). Most of the increase in angular rotation in the air happens by decreasing the body’s rotational inertia, same as in a spin.
To land the Axel, you want to ideally end up with the same amount of angular momentum you started with. That is the challenge of the Braxel Special Figure.
As Gary Beacom states, adding extra angular momentum is clearly a bad idea — most likely because you will have trouble “removing” that angular momentum at the end, while staying on one foot. One “solution”, which should work if you don’t add too much angular momentum on takeoff, is to accept a tighter circle on landing than you took off from. This is likely quite common.
But what if you want to land on the same circle you started on? Mrs. Kelly shows how controlling that angular momentum on exit can be challenging, even with a waltz jump. So how is that done? Note that twisting your spine (“checking”) does NOT change your body’s overall angular momentum. I see two possibilities here:
- Maybe there is some way to work the one-foot edge to change angular momentum, or allow it to “burn off” slowly through friction.
- (More likely): You need to arch the spine up and outward upon landing the waltz jump, to decrease the overall lean of the body. Similar to how BI8 figure is checked. This by itself does not change angular momentum, of course. But there may be some kind of interaction with the ice that changes the angular momentum. More to follow in a later post…
Left-to-Right Axis
Rotation around the axis running left-to-right through your hips should NOT happen: if it does for very long, you will fall forward or backwards. But what about transient rotation around this axis? That is where counter-balance of the free foot comes in.
Consider a basic swing roll, with the free leg moving from back to front. Why don’t you fall backwards? One reason could be bracing against your heel. But more interestingly, the swing role involves push-pull against the ice, which gains power by launching your upper body forward, creating a nose-dive rotation. The swing of the free leg exactly counter-balance this rotation. The beauty of the swing roll is its slow smoothness, in contrast to the faster center balance movement of, for example, loops. Our bodies should be able to do perfect counter-balance at any speed, to prevent pitching forward or backward.
More to follow, with an in-depth consideration of counter balance.