Terminal velocity
From Free net encyclopedia
- For other uses, see Terminal velocity (disambiguation).
The terminal velocity of an object falling towards the ground, 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 without power at greater than the 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 down 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). This speed increases to about 320 km/h (200 Mph) if the skydiver pulls in his limbs—see also freeflying. This is also the terminal velocity of the Peregrine Falcon diving down on its prey, and of a typical bullet according to a 1920 U.S. Army Ordnance study [1].
The reason an object reaches a terminal velocity is because 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 and feathers have a lower terminal velocity than small objects like bricks and cannon balls.
Mathematically, terminal velocity is described by the equation
- <math>V_t= \sqrt{2mg \over C_d \rho A}</math>
where
- Vt is the terminal velocity,
- m is the mass of the falling object,
- g is gravitational acceleration,
- Cd 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.
Approximation
Approximating terminal velocity is much more easily done than calculating the terminal velocity because of the difficulty in finding the value of Cd. One simple small scale method is to hang an object out a car window by a thin string. The terminal velocity of the object is the speed of the car when the object hangs at a 45° angle. This can be easily proven mathematically because it is when the atmospheric drag (in the horizontal direction) is equal to the force of gravity. It is when air resistance and gravity is the same.