Jumping - Physics of Jumping

Physics of Jumping

All jumping involves the application of force against a substrate, which in turn generates a reactive force that propels the jumper away from the substrate. Any solid or liquid capable of producing an opposing force can serve as a substrate, including ground or water. Examples of the latter include dolphins performing traveling jumps, and Indian skitter frogs executing standing jumps from water.

Jumping organisms are rarely subject to significant aerodynamic forces and, as a result, their jumps are governed by the basic physical laws of ballistic trajectories. Consequently, while a bird may jump into the air to initiate flight, no movement it performs once airborne is considered jumping, as the initial jump conditions no longer dictate its flight path.

Following the moment of launch (i.e., initial loss of contact with the substrate), a jumper will traverse a parabolic path. The launch angle and initial launch velocity determine the travel distance, duration, and height of the jump. The maximum possible horizontal travel distance occurs at a launch angle of 45 degrees, but any launch angle between 35 and 55 degrees will result in ninety percent of the maximum possible distance.

Muscles (or other actuators in non-living systems) do physical work, adding kinetic energy to the jumper's body over the course of a jump's propulsive phase. This results in a kinetic energy at launch that is proportional to the square of the jumper's velocity. The more work the muscles do, the greater the launch velocity and thus the greater the acceleration and the shorter the time interval of the jump's propulsive phase.

Mechanical power (work per unit time) and the distance over which that power is applied (e.g., leg length) are the key determinants of jump distance and height. As a result, many jumping animals have long legs and muscles that are optimized for maximal power according to the force-velocity relationship of muscles. The maximum power output of muscles is limited, however. To circumvent this limitation, many jumping species slowly pre-stretch elastic elements, such as tendons or apodemes, to store work as strain energy. Such elastic elements can release energy at a much higher rate (higher power) than equivalent muscle mass, thus increasing launch energy to levels beyond what muscle alone is capable of.

A jumper may be either stationary or moving when initiating a jump. In a jump from stationary (i.e., a standing jump), all of the work required to accelerate the body through launch is done in a single movement. In a moving jump or running jump, the jumper introduces additional vertical velocity at launch while conserving as much horizontal momentum as possible. Unlike stationary jumps, in which the jumper's kinetic energy at launch is solely due to the jump movement, moving jumps have a higher energy that results from the inclusion of the horizontal velocity preceding the jump. Consequently, jumpers are able to jump greater distances when starting from a run.