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What Is Terminal Velocity?

Skydivers increase air resistance by spreading out their bodies.
Aerial bombs are given a bullet-like shape to raise their speed and accuracy.
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  • Originally Written By: Brendan McGuigan
  • Revised By: Phil Riddel
  • Edited By: Bronwyn Harris
  • Images By: Joggie Botma, Greg Goebel
  • Last Modified Date: 25 August 2014
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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.

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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.

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Discuss this Article

anon347524
Post 16

Thanks for that explanation. Concerning the safety concerns of firing small arms directly in the air question if a 9 mm caliber pistol was angled upward and fired as opposed to directly upwards or straight up. could that potentially inflict serious harm to a bystander? If it is elliptical, as opposed to up, then down? In short, how much of a factor does the angle the bullet is fired at play into this equation? It's an honest question. Loved your explanation, by the way. Very informative.

anon290719
Post 13

I don't understand which will have a larger terminal velocity, a small object or a large object. Same for an object with a larger mass or a smaller mass.

I'm in tenth grade chemistry/physics, and I just don't get it.

anon207185
Post 9

I am still confused about terminal velocity! Some schematic images may have helped!

anon158233
Post 8

Raindrops are not "very aerodynamic" as the article states, although they would be if they actually had the classic "raindrop" shape with a pointed tail. Small raindrops are spheres while large raindrops are flatter and have high drag.

anon135403
Post 7

newton's second law is right because if you take the example of a bouncy ball and a feather and drop it at the same time, the ball falls first, yet it says that all objects fall at the same rate of 9.8m/s2.

the reason the feather takes longer to fall is because of air resistance, which makes it take longer, but if you had no air in a clear container and turned it upside down they would fall at the same rate.

anon108126
Post 5

Why when I was taught about gravity did I learn Newton's law that two objects of similar shapes but different weights would fall at the same rate? Was Newton's Law wrong?

anon71842
Post 4

what about a parachuter?

anon25850
Post 1

The question has been raised of how dangerous shooting firearms in the air is to persons downrange. News reports of Middle Easterners celebrations commonly mention the revelers' shooting into the air.

Shooting perfectly vertically, the projectile (thing projected = bullet) will rise until it comes to a stop. It will then have dispersed all of its energy originally provided by the propellant. The bullet will then free fall just as if it had been dropped from a stationary balloon or helicopter. Its terminal velocity will depend on a range of factors: shape, size, weight, density, and to a very small degree the temperature, barometric pressure and humidity (atmospheric density, which affect viscosity of the atmosphere), and the altitude (atmosphere is "thinner" thus of less viscosity at high altitude).

A 2,000 pound bullet fired from a 16" naval gun will (assuming it possible to fire the gun straight up) free fall at a very high velocity due to its great weight (mass) relative to its cross-sectional area. A "BB" (iron core ball 0.177" dia.) will fall at a relatively low velocity, probably not enough to do any injury to other than the eye. Lead shot of small diameter (dust, #12, #8, #7 1/2, #6, #4, 4 buckshot, 3 BS, 2 BS, 1 BS, 0 buckshot, 00 buck, 000 buck) will not fall fast enough to kill, though the large sizes (00, 000) could do some injury.

Skeet and trap clubs are located in densely populated areas. The small diameter shot used in the shells will not "carry" very far and will fall within the club's land area. It is dangerous at range only to the eye.

In a vacuum, a feather will fall at the same rate as a lead cannonball if they are dropped from the same height. Dust kicked up by the astronauts on the moon fell to the moon surface at the same rate as much larger dense objects due to the near-vacuum conditions on the moon.

Adult humans fall at approximately 125-150 miles per hour when skydiving with arms and legs held out and falling "flat." If the same skydiver rolls up into a ball (s)he will fall considerably faster. A large person will fall faster than a small person due to the greater weight of the large person in relation to the cross-sectional area as compared to the small person.

Mice can fall from any height without any injury, while an animal of similar design, a rat, will be killed. Small fluffy cats may survive a fall from a great height while large short haired cats will be killed.

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