# What is terminal velocity?

What is terminal velocity? I've heard the term especially when the Discovery Channel is covering something about sky diving. Also, it is commonly known that HALO (Hi-Altitude, Lo-Opening) infantry reach terminal velocity before their chutes open.

Can the terminal velocity be different for one individual weighing 180 pounds versus an individual weighing 250 pounds?

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– mbq♦ Dec 16 '10 at 14:34

## 3 Answers

Terminal velocity is the maximum velocity that you can reach during free-fall. If you imagine yourself falling in gravity, and ignore air resistance, you would fall with acceleration $g$, and your velocity would grow unbounded (well, until special relativity takes over). This effect is independent of your mass, since

$F = ma = mg \Rightarrow a = g$

Where terminal velocity arises is that air resistance is a velocity dependent force acting against your free fall. If we had, for example, a drag force of $F_D=KAv^2$ ($K$ is just a constant to make all the units work out, and depends on the properties of the fluid you're falling through, and $A$ is your surface area along the direction of motion) then the terminal velocity is the velocity at which the forces cancel (i.e., no more acceleration, so the velocity becomes constant):

$F = 0 = mg - KAv_t^2 \Rightarrow v_t=\sqrt{mg/KA}$

So we see that a more massive object can in fact have a larger terminal velocity.

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I will note that terminal velocity is not necessarily the maximum velocity you reach, since you can start out faster than $v_t$. – David Zaslavsky♦ Dec 16 '10 at 21:43
And one example of what David is talking about is rolling a ball: it will eventually stop with terminal velocity of $v_t = 0$ :-) In any case, it's worth pointing out that the concept of terminal velocity is just a special case of systems trying to reach stable equilibrium using the second law of thermodynamics (that is, friction). – Marek Dec 16 '10 at 22:45
Ah! Extremely good point. I was supposing a system falling from rest, but now I'm supposing I wasn't explicit on that. – wsc Dec 16 '10 at 23:09

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Actually, the real terminal velocity on Earth is $0$. Smack!... – Raskolnikov Dec 17 '10 at 10:57

You can find a good article here: http://en.wikipedia.org/wiki/Terminal_velocity

In the context you provide, terminal velocity is the maximum speed that an object in free fall reaches in the atmosphere.

When an object is falling, or in free fall, there are two forces that determine whether it will accelerate downwards or not:

• gravity (trying to accelerate the body downwards)
• air friction (trying to push the body upwards)

Initially, as the body is not moving, there is no air drag, and the object starts falling due to gravity. Now, as the object speeds up, the gravity contribution remains constant, whereas the drag increases with the speed of the object. Finally a point is reached where the drag is so much that the object does not accelerate anymore. Velocity stays constant and it is called terminal velocity.

The value for it is proportional to $\sqrt{m}$ so clearly objects of different weights have, in general different terminal velocities (heavier objects having higher values), but there are also other factors to account for, like how aerodynamic the object is. A sphere has higher terminal velocity than a sheet of metal of the same mass.

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If the falling body is non-spherical, then the drag will be dependent upon the bodies orientation. Skydivers exploit this to fly(fall) in formation, assume a higher drag configuration to slow down, or a lower drag configuation to speed up.

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