# How much is the ideal rocket equation affected by air drag?

by vjk2
Tags: affected, drag, equation, ideal, rocket
 P: 127 $\textbf F = \textbf F_{gravity} + \textbf F_{thrust} + \textbf F_{drag}$ Depends how complicated you want to get. For a full simulation, you have to start with the rotation of the Earth at the launch site, and use this as the rocket's initial motion. Gravity drops off slowly (${1\over r^{2}}$), thrust increases slightly as the atmospheric pressure is no longer "bottling it up", and drag peaks and falls off as the rocket reaches the speed of sound, which varies with air temperature. You can simplify a lot of that - flat, non-rotating Earth, constant thrust, drag as some simple, approximate function - but there is still no simple equation to say, "after 30 seconds, the rocket has velocity v at altitude h." Rocket science...