Examples
Based on wind resistance, for example, the terminal velocity of a skydiver in a belly-to-earth (i.e. face down) free-fall position is about 195 km/h (122 mph or 54 m/s). This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity 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 or her limbs (see also freeflying). In this case, the terminal velocity increases to about 320 km/h (200 mph or 90 m/s), which is almost the terminal velocity of the Peregrine Falcon diving down on its prey. The same terminal velocity is reached for a typical .30-06 bullet dropping downwards—when it is returning to earth having been fired upwards, or dropped from a tower—according to a 1920 U.S. Army Ordnance study.
Competition speed skydivers fly in the head down position and reach even higher speeds. The current world record is 1342.8 km/h (833.9 mph, equivalent of Mach 1.24) by Felix Baumgartner who skydived from 24 miles above earth on 14 October 2012. The record was set due to the high altitude where the lesser density of the atmosphere decreased drag.
An object falling toward the surface of the Earth will fall 9.80655 meters (or 32.18 feet) per second faster every second (an acceleration of 9.80655 m/s² or 32.18 ft/s²). The reason an object reaches a terminal velocity is that the drag force resisting motion is approximately 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 accelerates, the drag increases, until it equals the weight. Drag also depends on the projected area. This is why objects with a large projected area relative to mass, such as parachutes, have a lower terminal velocity than objects with a small projected area relative to mass, such as bullets.
Mathematically, terminal velocity—without considering buoyancy effects—is given by
where
- = terminal velocity,
- = mass of the falling object,
- = acceleration due to gravity,
- = drag coefficient,
- = density of the fluid through which the object is falling, and
- = projected area of the object.
Mathematically, an object approaches its terminal velocity asymptotically.
Buoyancy effects, due to the upward force on the object by the surrounding fluid, can be taken into account using Archimedes' principle: the mass has to be reduced by the displaced fluid mass, with the volume of the object. So instead of use the reduced mass in this and subsequent formulas.
On Earth, the terminal velocity of an object changes due to the properties of the fluid, the mass of the object and its projected cross-sectional surface area.
Air density increases with decreasing altitude, ca. 1% per 80 metres (262 ft) (see barometric formula). For objects falling through the atmosphere, for every 160 metres (525 ft) 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.
Read more about this topic: Terminal Velocity
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