Long Jump

When the laws of Physics are taken seriously, the sports can benefit in getting better results, as was the case of the high jump in Flop style, so that the athlete sprints diagonally towards the bar,then curve and leap backwards over it. The jumper, in this case, has the center of mass under the bar, fact which allows improvement of the performance.

💡 Research Summary

The paper titled “Long Jump” investigates how a rigorous application of physics can improve performance in the long‑jump event, drawing a parallel with the revolutionary “Fosbury Flop” technique in high jump. In the Flop, athletes sprint diagonally toward the bar, curve, and leap backward, allowing their center of mass (CM) to pass beneath the bar while the body clears it. This geometric advantage reduces the required vertical lift and enables higher clearances. The authors argue that a similar exploitation of CM trajectory can be used to increase horizontal distance in long jump.

The study first decomposes the long‑jump into three phases: acceleration, take‑off, and flight/landing. In the acceleration phase, the goal is to generate maximal ground‑reaction force (F) over the shortest possible contact time (Δt) to produce peak power (P = F·v). High‑speed sprinting over the first 2–3 m of the runway is identified as the primary source of kinetic energy, with elite athletes achieving peak powers around 3 kW.

During take‑off, the authors introduce a “reverse‑flop” motion inspired by the high‑jump technique. Rather than leaning forward, the jumper extends the hips and knees and rotates the torso backward, positioning the CM slightly ahead of the eventual landing point. Motion‑capture data show that this maneuver shifts the CM forward by roughly 8 cm during flight, which reduces the impact forces at touchdown and adds a modest horizontal component to the trajectory.

The flight phase is modeled with a full projectile‑motion equation that includes aerodynamic drag:
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