# Q & A: Parachute Surface Area

Q:
what is the effect of surface area on the rate at which a parachute falls?
- Jenna (age 13)
Collegeville, Pa, US
A:
Jenna -

The answer to your question is a bit more complex than you were probably expecting, but here goes...

Part 1
The force of air resistance on a parachute (figuring the parachute is basically spread out flat against the air) is directly proportional to the parachute's surface area, so long as the parachute is moving fairly quickly through the air. That means that if you double the surface area you double the force of air resistance:

Fair resistance = SurfaceArea x OtherStuff

Part 2
Now's where we've gotta do a little math... The net downward force on the parachuter is the force of gravity minus the force of air resistance. So:

Fnet = (9.81 m/s^2 x Mass) - (SurfaceArea x OtherStuff)

The net force on the parachuter determines their acceleration (the rate at which they speed up or slow down): F=ma, so...

(Mass x Acceleration) = (9.81m/s^2 x Mass) - (SurfaceArea x OtherStuff)

Do a little rearranging and you get this:

Acceleration = 9.81 m/s^2 - (SurfaceArea)(OtherStuff)/(Mass)

Part 3
Getting from knowing the Acceleration to knowing the actual Speed is tricky, because that "OtherStuff" actually includes the parachuter's velocity. I'm not going to go into the details of solving that for you here, but i think the basic gist should be clear:

The Moral of This Story
More Surface Area = Falling More Slowly

-Tamara

(published on 10/22/2007)

## Follow-Up #1: effect of parachute area on time of the fall

Q:
Is the time taken for a parachute to fall proportionally related to the surface area of the parachute? That is, if the surface area is doubled does the time taken to fall double? Why/why not?
- Anonymous
A:

The short answer to your question is that, after a certain point, doubling the size of a parachute does not affect the time of fall (or your velocity).

A really amazing experimental explanation of this is here: