What is Terminal Velocity?

science engineering

Terminal velocity is the term for the state an object reaches when the force of drag acting on it is equal to the force of gravity acting on it. When an object reaches its terminal velocity, it no longer accelerates, remaining at whatever velocity it was already traveling or else slowing down.

As an object accelerates, the amount of drag exerted on it increases. This means that more force is necessary to sustain the same level of acceleration. If that external force is increasing, as in a car or plane, then the object can be accelerated well past its terminal velocity. If, however, the only force being exerted on it is the force of gravity, then eventually the drag will become as great as the static force of gravity, and the object will cease to accelerate.

An object may also decelerate towards terminal velocity, if it was initially moving faster than terminal velocity. This may be because it entered from somewhere with less drag, such as the thinner upper atmosphere, or because it was initially launched with some external force other than gravity at a greater velocity. In this way, terminal velocity can be viewed as a sort of equilibrium point that objects in freefall naturally gravitate towards.

Strictly speaking, an object never actually reaches its terminal velocity, it simply reaches a state which approximates it. Instead, in a manner similar to Zeno’s paradox of motion, the object comes closer and closer to its terminal velocity, reducing its acceleration to miniscule amounts, until the acceleration is no longer even measurable or functional, and terminal velocity is said to have been achieved.

Different objects will have drastically different terminal velocities. A person in freefall, for example, has a terminal velocity of approximately 184 ft./s (56m/s) or roughly 124mph (200kph). A raindrop, in contrast, although very aerodynamic, is also not very dense, and so has a terminal velocity of around 25 ft./s (82m/s) or roughly 17mph (27kph). A lead bullet shot up straight in the air, on the other hand, has a terminal velocity of around 223 ft./s (68m/s) or 152mph (245kph).

Calculating the terminal velocity of an object means calculating the drag exerted on the object, and then comparing that to the weight of the object to determine the net force. To do this, you need to know the frontal area of the object, the gas density it is falling through, and a drag coefficient. It’s not a particularly easy calculation to make, although there are online calculators which can help you make rough estimates as to an object’s terminal velocity. The basic rules of thumb, though, are that objects will have a higher terminal velocity when: there is more of it, making a heavier weight; the density of the gas it’s falling through is lower, as in upper atmosphere; the object has a lower drag coefficient, meaning it has been built to be more streamlined, like a raindrop; or there is less area to drag, usually meaning the object is more dense.

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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.

- anon25850

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