Terminal velocity

From Wikipedia, the free encyclopedia

For other uses, see Terminal velocity (disambiguation).

The terminal velocity of an object falling towards the earth, in non-vacuum, is the speed at which the gravitational force pulling it downwards is equal and opposite to the atmospheric drag (also called air resistance) pushing it upwards. At this speed, the object ceases to accelerate downwards and falls at constant speed. An object moving downwards at greater than terminal velocity (for example because it previously used power to descend, it fell from a thinner part of the atmosphere or it changed shape) will slow until it reaches terminal velocity.

For example, the terminal velocity of a skydiver in a normal free-fall position with a closed parachute is about 195 km/h (120 mph or 54 m/s). This velocity is the asymptotic limiting value of the acceleration process, since the effective forces on the body more and more closely balance each other as it is approached. In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on.

Higher speeds can be attained if the skydiver pulls in his limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 89 m/s), which is also the maximum speed of the Peregrine Falcon diving down on its prey.

The reason an object reaches a terminal velocity is that the drag force resisting motion is directly proportional to the square of its speed. At low speeds the drag is much less than the gravitational force and so the object accelerates. As it speeds up the drag increases, until eventually it equals the weight. Drag also depends on the cross sectional area. This is why things with a large surface area such as parachutes have a lower terminal velocity than small objects like cannon balls.

Mathematically, terminal velocity is described by the equation

where

V_t is the terminal velocity,

m is the mass of the falling object,

g is gravitational acceleration,

C_d is the drag coefficient,

ρ is the density of the fluid the object is falling through, and

A is the object's cross-sectional area.

This equation is derived from the drag equation by setting drag equal to mg, the gravitational force on the object.

Note that the density increases with decreasing altitude, ca. 1% per 80 m (see barometric formula). Therefore, for every 160 m of falling, the "terminal" velocity decreases 1%. After reaching the local terminal velocity, while continuing the fall, speed decreases to change with the local terminal velocity.