Optimum takeoff angles for triple jump

An approximate single-rigid-body (SRB) model for triple jump (Okubo and Hubbard, 2025) is used numerically to investigate total distance in terms of run-up speed and hop, step and jump takeoff angles. At each speed a single optimal combination of takeoff angles produces maximum total distance. Using the model with previously measured realistic elite takeoff angles confirms roughly linear correlation between loss of horizontal velocity and gain in vertical velocity during support. It is striking that the simple assumptions in the SRB model (regarding body orientation and lack of pitching angular velocity in flight) are able to account, even loosely, for the velocity conversion process, Yu and Hay, (1996). As total distance increases, the likelihood of a jump-dominated optimal strategy also increases with these features: horizontal speed is maintained in hop and step; jump and step takeoff angles are the largest and smallest, respectively, of the three; step distance is shortest. In the speed range 10.0-10.5 m/s the optimum jump-dominated technique is always best, but only marginally (almost too marginally to notice). The model evaluates importance of run-up speed which mostly affects takeoff speeds, but has almost no effect on optimal takeoff angles. Although the model is deterministic, it can be used with random initial conditions to understand uncertainty effects in jumper execution. Use of the model shows that phase ratios are not controllable parameters but only results.