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Surface area drag? Answered

Anyone know how to calculate how fast you will fall if you weigh 170 pounds and you have surface area a feet squared (if you wan't to calculate it I am thinking about 14 square feet


Jack A Lopez

7 years ago

Based on your numbers, I get an answer for a terminal velocity of about 40 m/s, or about 90 miles/hour, and the time to accelerate from 0 to that speed is about 8 seconds. This was done assuming a constant downward force of m*g, and an upward drag force proportional to velocity squared.  I did not solve the diffe eq myself.  The math is just done using the formulas I found here:

I picked a drag coefficient of C=1.0, and of course that's just a wild guess. 
Actual results with your Wile E. Coyote styled, Acme(r) Batman(r) suit may vary.  Some  additional details are included in the comments in the attached Octave(r) script.

jj.incJack A Lopez

Answer 7 years ago

lol, thanks, you know exactly what I was thinking.


7 years ago

G = 32 ft per second squared. That is the acceleration of a falling object. It will accelerate until it hits terminal velocity which is the air resistance against the object. In a vacuum there is no terminal velocity as there is no wind resistance.
According to Wikipedia this is the formula:

Derivation for terminal velocity

Mathematically, defining down to be positive, the net force acting on an object falling near the surface of Earth is (according to the drag equation):

F_{net} = m a = m g - {1 \over 2} \rho v^2 A C_\mathrm{d} \ .

At equilibrium, the net force is zero (F = 0);

m g - {1 \over 2} \rho v^2 A C_\mathrm{d} = 0 \ .

Solving for v yields

\sqrt\frac{2mg}{\rho A C_\mathrm{d}} \ .

That actually doesn't show everything because of the limits of copy and paste, so to see the entire article and formula's , its here:


NOW, there are a lot of other factors involved such as the relative humidity, the air pressure and temperature, and the elevation and wind speed. Those are the environmental factors. Then there are the object factors including what kind of clothes you are wearing (if any) and what fabric its made from. Weather you have wings or trailing capes. All that stuff. But in general, without getting to specific and caught in the minute detail,
Terminal velocity of a human is 117-125mph in random posture (tumbling) . If the human uses the bullet shaped position, (sometimes used by experienced sky divers or seen in movies), then their terminal velocity can reach speeds up to 210mph. Then you go splat.


7 years ago