Calculating a Parachute Descent

1. Jun 4, 2010

Lunar_Lander

Hello,

I'm still working on my balloning project and now I have arrived at the problem of getting a accurate idea of a descent velocity/time. I am sure that the formula to get the velocity is:

$$\sqrt{m*g/0.5*\rho*A}$$

Now density changes with altitude, causing a higher velocity at high altitude and a decreasing velocity while closing in on Earth. In the formula, m is the mass of the payload and A is the cross-sectional area of the parachute.

Question: How can I implement $$\rho(h)$$, that is the density as a function of altitude, into the formula above? Integration over $$\rho$$?

My previous approach was to get myself the atmospheric densities for 4000 m-levels out of the 1976 U.S. Standard Atmosphere, to calculate the velocity by putting in each of the densities in turn, and finally to average the velocities. I don't know if this is also OK, but I can imagine that it is less accurate than a analytical solution I am looking for here.