4
$\begingroup$

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 reaches terminal velocity before their chutes open.

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

Improve this question
$\endgroup$
2
8
$\begingroup$

Terminal velocity is the (asymptotic) 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 cross-sectional area perpendicular to 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.

Improve this answer
$\endgroup$
7
  • 1
    $\begingroup$ I will note that terminal velocity is not necessarily the maximum velocity you reach, since you can start out faster than $v_t$. $\endgroup$ – David Z Dec 16 '10 at 21:43
  • 1
    $\begingroup$ 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). $\endgroup$ – Marek Dec 16 '10 at 22:45
  • 1
    $\begingroup$ Ah! Extremely good point. I was supposing a system falling from rest, but now I'm supposing I wasn't explicit on that. $\endgroup$ – wsc Dec 16 '10 at 23:09
  • 3
    $\begingroup$ Actually, the real terminal velocity on Earth is $0$. Smack!... $\endgroup$ – Raskolnikov Dec 17 '10 at 10:57
  • $\begingroup$ @Raskolnikov Only because K is representing quite a density when considering the ground... $\endgroup$ – ib11 Apr 25 '19 at 1:41
4
$\begingroup$

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.

Improve this answer
$\endgroup$
2
$\begingroup$

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.

Improve this answer
$\endgroup$
1
  • $\begingroup$ It's useful but I think it doesn't answer the question. Maybe you had to put it in a comment. $\endgroup$ – Deschele Schilder Jan 6 '20 at 4:08
0
$\begingroup$

Yes. (by the way, don't watch to much discovery channel! It provides you with scientifically fake news, most of the time)

Look at this picture:

It contains all the info you need. Can you discover that info? Let's assume the body has the form of a ball. In the picture, one can read that the terminal velocity is the (in theory asymptotic) velocity when the drag becomes equal to the weight. So...?

Here you can read the full article.

Don't you have a gut feeling (I know these don't count in the sciences, but it IS where they start) what the answer will be? It seems clear to me that a heavyweight will have a higher terminal disease that a lightweight!

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.