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by George S. Rossano

The following is a simple dynamical model of a quad Lutz that illustrates the inflight characteristics of a jump with 0.75 seconds of air time. The parameters of this model are:
Although the ISU tolerates any amount of prerotation on jumps, we have limited the model to a prerotation less than the onequarter rotation that, by a strict application of the rules, should result in an underrotation call. Even the best executed quads have at least this prerotation. Normalized Moment of Inertia
This model is derived from an aggregate of several competition quad Lutz examples, and illustrates the main features of a true quad Lutz jump  as opposed to pseudo quads that are often prerotated by onehalf rotation on the takeoff and may also be missing rotation on the landing. For this jump the skater spends about 200 msec pulling in and 75 msec opening up to land. About 475 msec is spent midflight near the minimum moment of inertia. Note that during midflight the skater typically makes small adjustments to their position and the minimum moment of inertia is generally not reached until late in midflight. We specify times for pulling in and opening up using the initial and final air times when the moment of inertia is onehalf the initial moment of inertia. The above moment of inertia sequence is an "ideal" example for a jump with 0.75 seconds of air time. Individual jump attempts with the same air time show variations in the time to pull in and check out, and show variations in the consistency with which the near minimum air position (and rotation rate) is held. In our model for true quads we include a small prerotation at takeoff, and full rotation at the landing. This small prerotation seems to be necessary to develop the initial angular momentum needed to complete a quad, and is smaller than what would trigger an underrotation call under a strict interpretation of ISU rules. Jumps that are missing more than this onequarter prerotations we consider pseudo quads, from a dynamical point of view. The inflight characteristics of this jump are shown in the following graphs. Flight of the Jump
Rotation Rate InFlight
Rotations Completed
This model has a peak rotation rate of 5.8 rotations per second and a landing rotation speed of 2.8 rotations per second. One could construct a family of models with slightly varying air times and initial rotation rates. All of such examples would qualitatively look similar to the graphs presented here. Copyright 2020 by George S. Rossano 