Terminal velocity is the term for the speed an object reaches when the force of drag, or air resistance, pushing against it is equal to the force of gravity pulling it down. An object dropped from a height will initially accelerate because of gravity. The atmosphere, however, exerts an opposing force, or drag, which increases as the object moves faster. After a time, a point is reached where the two opposing forces are equal, and after this, the object’s speed remains constant unless another force acts on it: this speed is known as its terminal velocity. The final speed depends on the object’s weight, its shape, and the density of the atmosphere.
Weight and atmospheric density can vary from place to place. While an object’s mass, which can be defined as the amount of matter it contains, is the same wherever it is located, its weight depends on the strength of the local gravitational field. This does not vary on the Earth on a scale that is directly noticeable to humans, but in other places such as the Moon or Mars it will be very different. The density of the atmosphere decreases with altitude, so air resistance is greater near the ground than at great heights.
Weight and Drag
The amount of drag that acts on a falling object depends on the density of the atmosphere and the shape of the object. The greater the density of the atmosphere, the more resistance there is to movement. Over short vertical distances, the difference in density will be small, and insignificant for most purposes, but for something falling from the upper atmosphere there is a big difference, which complicates terminal velocity calculations.
Drag is also very dependent on the shape of the falling body. If a piece of heavy material, such as lead, is made into a bullet-like shape and dropped, point downwards, from a great height, it will experience relatively little drag, and will reach a high terminal velocity. If the same piece of lead is made into a thin disk, and dropped so that it is flat relative to the Earth’s surface, it will experience much greater air resistance, and will reach a much lower terminal velocity in less time.
The amount of downward force on a falling object depends on its weight, which is the interaction of the object’s mass with the force of gravity. The greater the mass, the greater the force will be, and, therefore, the greater the terminal velocity. If the above experiment is conducted using a light material, such as aluminum, the final speeds for both shapes would be less than for the lead shapes. It is important to understand, however, that acceleration due to gravity is the same for all objects; it is the drag factor that causes the variations with weight and shape. If the experiment with different lead and aluminum shapes is carried out in a vacuum, all the objects will accelerate at the same rate, irrespective of weight or shape, because the drag factor due to air has been eliminated.
Calculation
Determining the terminal velocity for an object dropped from a given height can be complicated. Some of the factors, such as mass and acceleration due to gravity, are straightforward, but it is also necessary to know the drag coefficient, a value that depends crucially on the shape of the object. For many objects, the drag coefficient is determined by experiment, as the calculations would be very difficult for complex shapes. Since the density of the atmosphere varies with altitude, this variation also needs to be taken into account, unless the distance to fall is quite short.
Examples
A raindrop has a terminal velocity of around 17 mph (27 kph). In contrast, a large hailstone could achieve 42 mph (68km/h), which is enough to cause injury. A lead bullet shot straight into the air would, on falling back toward the ground, reach around 152 mph (245 kph).
A skydiver, facing the ground with limbs spread to maximize air resistance, will typically have a terminal velocity of about 124 mph (200 km/h). Diving head first, with arms and legs tucked in, the same skydiver could reach about 200 mph (320 km/h) or more. The precise speeds depend on the initial altitude, and much higher speeds can be reached by diving from extreme altitudes, where the atmosphere is much thinner. For objects falling toward the Earth from outside the atmosphere, for example meteorites, the terminal velocity may be less than the initial speed relative to the Earth. In these cases, the object slows down toward the final speed.
