Terminal velocity is the maximum speed attainable by an object as it falls through a fluid (air is the most common example). It is reached when the sum of the drag force (Fd) and the buoyancy is equal to the downward force of gravity (FG) acting on the object. Since the net force on the object is zero, the object has zero acceleration. For objects falling through air at normal pressure, the buoyant force is usually dismissed and not taken into account, as its effects are negligible. As the speed of an object increases, so does the drag force acting on it, which also depends on the substance it is passing through (for example air or water). At some speed, the drag or force of resistance will be equal to the gravitational pull on the object. At this point the object stops accelerating and continues falling at a constant speed called the terminal velocity (also called settling velocity). An object moving downward faster than the terminal velocity (for example because it was thrown downwards, it fell from a thinner part of the atmosphere, or it changed shape) will slow down until it reaches the terminal velocity. Drag depends on the projected area, here represented by the object's cross-section or silhouette in a horizontal plane. An object with a large projected area relative to its mass, such as a parachute, has a lower terminal velocity than one with a small projected area relative to its mass, such as a dart. In general, for the same shape and material, the terminal velocity of an object increases with size. This is because the downward force (weight) is proportional to the cube of the linear dimension, but the air resistance is approximately proportional to the cross-section area which increases only as the square of the linear dimension. For very small objects such as dust and mist, the terminal velocity is easily overcome by convection currents which can prevent them from reaching the ground at all, and hence they can stay suspended in the air for indefinite periods. Air pollution and fog are examples.
Examples
Based on air resistance, for example, the terminal speed of a skydiver in a belly-to-earth (i.e., face down) free fall position is about 55 m/s (180 ft/s). This speed is the asymptotic, limiting value of the speed, and the forces acting on the body balance each other more and more closely as the terminal speed is approached. In this example, a speed of 50.0% of terminal speed 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 their limbs (see also freeflying). In this case, the terminal speed increases to about 90 m/s (300 ft/s), which is almost the terminal speed of the peregrine falcon diving down on its prey. The same terminal speed is reached for a typical .30-06 bullet dropping downwards—when it is returning to the ground having been fired upwards or dropped from a tower—according to a 1920 U.S. Army Ordnance study. Competition speed skydivers fly in a head-down position and can reach speeds of 150 m/s (490 ft/s). The current record is held by Felix Baumgartner who jumped from an altitude of 38,887 m (127,582 ft) and reached 380 m/s (1,200 ft/s), though he achieved this speed at high altitude where the density of the air is much lower than at the Earth's surface, producing a correspondingly lower drag force.
The biologist J. B. S. Haldane wrote, To the mouse and any smaller animal [gravity] presents practically no dangers. You can drop a mouse down a thousand-yard mine shaft; and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes. For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal's length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force.
Physics For terminal velocity in falling through air, where viscosity is negligible compared to the drag force, and without considering buoyancy effects, terminal velocity is given by
V t = 2 m g ρ A C d {\displaystyle V_{t}={\sqrt {\frac {2mg}{\rho AC_{d}}}}}
where
V t {\displaystyle V_{t}} represents terminal velocity,
m {\displaystyle m} is the mass of the falling object,
g {\displaystyle g} is the acceleration due to gravity,
C d {\displaystyle C_{d}} is the drag coefficient,
ρ {\displaystyle \rho } is the density of the fluid through which the object is falling, and
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