S2 Jumping (Athletics and Team Sports)

Topic

The athletic jumps performed by this athlete—whether long jump, high jump, triple jump, volleyball spike, or basketball jump—all incorporate the same fundamental jumping mechanism. This mechanism involves a specific model governing the muscle-tendon unit (with its stretch-shortening cycle), the joints (knee, hip, and ankle), and the center of mass (with its flight trajectory)—elements that define a distinct model within this framework.

In contrast, the final performance of the athlete's vertical jump depends almost exclusively on the final vertical velocity of the center of mass at takeoff. This velocity, in turn, depends on the net impulse generated during the contact phase—reflecting the specific impulse-takeoff velocity relationship defined by another model in this framework. Consequently, if the athlete increases this net impulse during the contact phase, the final vertical velocity of the center of mass at takeoff increases as well.

Conversely, the stretch-shortening cycle—involving a preliminary countermovement—increases the jump's final height compared to an equivalent static jump performed without that countermovement. This increase is primarily due to the restitution of elastic energy from the patellar and Achilles tendons (a process defined by another model in this framework) and reflex potentiation (defined by yet another model). If the athlete performs this preliminary countermovement with a higher stretching velocity, the final jump height increases further. In the case of a long jump performed by this athlete, the actual optimal takeoff angle turns out to be considerably smaller than the theoretical ideal angle for a simple projectile; this is precisely because the athlete arrives at the takeoff point with their center of mass already elevated and possessing a high final horizontal velocity—specifically the same approach velocity defined in another model within this set regarding sprinting. As the athlete's approach velocity increases further, the optimal takeoff angle becomes even smaller relative to that theoretical ideal.

Consequently, this model—which integrates the jumping action involving muscles, tendons, joints, and the center of mass—dictates that the final landing requires significant eccentric work from the knee and ankle extensors. This is the same type of eccentric contraction described in another model in this set, serving to absorb the final kinetic energy of the fall and protect the athlete's joints. As the final kinetic energy of the fall increases, the required eccentric work from the extensors also increases, thereby pushing the joints closer to their specific tolerance limits.

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