# terminal velocity

Tomorrow I’m making a 10,000 foot tandem skydive. We’re supposed to do 6,000 free fall.

So:

(i) How fast will I be falling when I reach my terminal velocity?
(ii) How long will it take me to get there?
(iii) How long will a 6,000 foot free-fall take?

I’m 180 lbs of bone, muscle and guts.

I) 100 - 120 mph depending on the position that you assume during the jump. Since you will be strapped to an instructor spread eagle face down, I would figure you will be going just over 100 mph.

III) If you are traveling at 105 mph, then your free-fall should last about 45 seconds according to my calculations.

Hmm… Can’t say for sure. Best guess is that your terminal velocity will be about 120 - 130 mph, assuming I didn’t screw anything up, but it depends on all sort of things like how you fall. Still, that’s the general range I’ve heard for a skydiver, so hopefully it’s right.

Assuming that it is, you’ll take something like 20 seconds or so to reach terminal velocity, and 36 or so to fall 6000 feet (which may seem a bit low, but consider that without air resistance, it’d only take about 20 seconds for the 6000 foot fall, and you’d be going at about 450 mph when you hit the 4000 foot level).

So there’s my thoughts. Having never skydived, I could of course be wrong, but hey, it’s something.

One does not accelerate steadily to terminal velocity. Terminal velocity is simply the speed where the force of drag exactly cancels out the weight of the person.

the equation for finding drag is:

F = (rho) * U[sup]2[/sup] * S * C[sub]d[/sub]

Where F is the force of drag (your weight), rho is the density of air, S is the surface area and C[sub]d[/sub] is the coefficient of drag.

Rather than trying to estimate these for you, I’ll say that I understand terminal velocity to generally be around 120-140 mph for a human.

If you want to try your hand at it, I’ll estimate that F = 180 lbs., S = 15 square ft., rho = 0.002377 slugs/ft.[sup]3[/sup], and [sub]d[/sub] = .75. Using those numbers, you can find U in ft./sec. The units work out (1 pound = 1 slug foot per second squared). I’d do it, but my calculator’s in the other room.