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An object reaches terminal velocity when the downward force of gravity (F_g) equals the upward force of drag (F_d). The net force on the body is then zero, and the result is that the velocity of the object remains constant.

In physics, terminal velocity is the velocity at which the air resistance force of a falling object equals the weight of the object minus the acting force due to air, which halts acceleration and causes speed to remain constant.

As an object accelerates (usually downward due to gravity), the air resistance produced by the passing through a fluid medium, increases. At a particular speed, the drag force produced will be equal to the downward force, mostly the weight (mg), of the object. Eventually, it plummets at a constant speed called terminal velocity. Terminal velocity varies directly with the ratio of drag to weight. More drag means a lower terminal velocity, while increased weight means a higher terminal velocity. An object moving downwards at greater than terminal velocity (for example because it was affected by a force downward or 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 free-fall position with a semi-closed parachute is about 195 km/h (120 mph or 54 m/s).^[1] 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),^[1] which is also the maximum speed of the peregrine falcon diving down on its prey.^[2] Competition speed skydivers fly in the head down position reaching even higher speeds. The current world record is 614 mph or 988 km/h by Joseph Kittinger, set at high altitude where the lesser density of the atmosphere decreased drag.^[1]

An object falling on Earth will fall 9.8 meters per second faster every second (9.8 m/s²). 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 given by

   ^{see derivation}

where

V_t is the terminal velocity,

m is the mass of the falling object,

g is gravitational acceleration at the Earth's surface,

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.

So it can be said that, on Earth, the terminal velocity of an object changes due to the properties of the fluid, mass and the cross sectional area of the object.

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.

• Terminal Velocity - NASA site