Dropping items from an airplane.

[PFarmer]

Dropping items from an airplane.

This is real world, so think air density, terminal velocity, and nonlinear acceleration? etc…
Check out the DropSim on NASA GRC. This is exactly what I’m trying to calculate.


I have a firm grasp on D drag, Cd coefficient of drag, r air density, V velocity, A area of object.
D = Cd .5 r V^2 A

The air density equation is a little complex, involving air pressure, temperature, altitude, etc…, but I’m fairly confident in all of this because when I plug in the terminal velocity of 115 fps from the DropSim, then drag = weight. Thus acceleration is 0, and the object is at terminal velocity.

I’m dropping a 5 pound object from 1000 feet. Cd = 1.14. A = 40 in^2. r = 0.002304103.

I thought all of the above would be the hard part, but it is really just a bunch of constants and a few simple equations.

Where I’m stuck is a acceleration & d distance & maybe v velocity.
I have a lot of equations I’m working with, but I don’t want to muddy the waters. I would like fresh opinions, and/or answers. I know this is not constant acceleration. I know I’m looking for acceleration as it approaches 0; terminal velocity; drag = weight. I don’t know how to find the acceleration, and therefore, I can’t find the velocity…or the distance.
Any help is appreciated.

Thanks

-Paul

 

[SteamKing]

If you want to find acceleration, then you have to find the forces acting on your object. After all F = ma even for stuff dropped out of an airplane.

You know gravity is always acting, and drag is also a force. The drag is acting to retard motion, so it is changing with the trajectory of the falling object. This is where things get tricky.