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# Dynamical Model of a Quad Axel

by George S. Rossano

 The following is a simple dynamical model of a quad Axel that illustrates the performance a skater needs to complete this jump.  This is one of many such models that could be created for this jump. The parameters of this model are: Air time:  0.78 sec Takeoff rotation rate:  2.47 rotations per second Pre-rotation at takeoff:  0.249 rotation Moment of inertia in-flight:  as shown in graph Although the ISU tolerates any amount of pre-rotation on jumps, we have limited the model to a pre-rotation less than the one-quarter rotation that, by a strict application of the rules, should result in an under-rotation call. Normalized Moment of Inertia This is an adjustable parameter of the model. For this hypothetical moment of inertia sequence the skater spends about 200 msec pulling in, and 100 msec opening up to land.  Nearly 1/2 second is spent mid-flight near the minimum moment of inertia.  The time modeled pulling in is shorter than occurs in actual competition for Axel type jumps. The results of the model are shown in the following graphs. Flight of the Jump Rotation Rate In-Flight Rotations Completed This model achieves a peak rotation rate of 6.0 rotations per second and a landing rotation speed of 3.0 rotations per second. The parameters for this model, other than the in-flight moment of inertia, are at the limits of demonstrated performance for elite skaters.  The challenge for this model is for the skater to get over the right side and pulled in within 200 msec, faster than the current demonstrated performance for elite skaters.  A secondary challenge is holding the landing, for a landing rotation rate of 3 rotations per second. One possible variation of this model would be for the skater to achieve a peak speed of 6.25 rotations per second (perhaps within the reach of current elite skaters), which would allow a lower rotation rate at the landing, that would be easier to control.  The higher peak rotation rate would not, however, alleviate the challenge of approaching the minimum moment of inertia within 200 msec for an Axel takeoff. In summary, to land a true quad Axel, skaters will have to figure out how to get over the right leg and pulled in faster than they currently do, or figure out how to achieve a significantly higher peak rotation rate than they currently do. Copyright 2020 by George S. Rossano