Jumping

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Jumping or leaping is a form of locomotion or movement in which an organism or non-living (e.g., robotic) mechanical system propels itself through the air along a ballistic trajectory. Jumping can be distinguished from running, galloping, and other gaits where the entire body is temporarily airborne by the relatively long duration of the aerial phase and high angle of initial launch.

Some animals, such as the kangaroo, employ jumping (commonly called hopping in this instance) as their primary form of locomotion, while others, such as frogs, use it only as a means to escape predators. Jumping is also a key feature of various activities and sports, including the long jump, high jump, and show jumping.

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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. They can release this enenrgy at a much higher rate (higher power) than thus increasing launch energy to levels beyond what muscle alone is capable of.

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