Terminal velocity
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Terminal velocity is the speed reached by an object falling in an atmosphere when atmospheric drag equals the object's weight, which halts acceleration and causes speed to remain constant.
As the object keeps on accelerating downwards, the drag produced is increased. 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 mass. More drag means slower terminal velocity. Increased mass means 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 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.
On August 16th, 1960 U.S. Air Force Captain Joe Kittinger came close to breaking the sound barrier during a free-fall from the high altitude balloon Excelsior III, at an altitude of 102,800 feet (approximately 20 miles), hitting a speed of 614 mph (274 m/s) as reported by National Geographic. This made Captain Kittinger the fastest human on the planet.
An object falling 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
where
- Vt is the terminal velocity,
- m is the mass of the falling object,
- g is gravitational acceleration at the Earth's surface,
- 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.
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.
