# Calculating drag

by LastOneStanding
Tags: drag
 P: 708 Hi all, For the past few years, building model rockets has been a hobby of mine. I've designed a few of my own, and I'd like to be able to do stability, height, etc. calculations before actually building the rocket. My question: If you know the mass of the rocket, the magnitude of the force being applied it, and the force of drag as a function of velocity, how do you calculate the rocket's velocity at any time. There's a similar question here: http://www.physicsforums.com/showthread.php?t=48326 but that problem simplifies things by making drag a constant times v, instead the actual physical case of a constant times v squared. I seem to recall that you aren't allowed to apply a non-linear function to the dependent variable in a differential equation, so you can't just change the v in the formula given in that thread to a v^2. Even if I'm wrong here, I'm still not entirely sure how to continue from where the thread left off as my integration skills are a little rusty. Could someone please help? Thanks, LastOneStanding
 Mentor P: 21,663 THIS is the equation you are looking for. Its pretty easy to apply if you know the values to plug in... Going from that to speed/altitude, I'm pretty lazy when it comes to equation solving, so using f=ma (and a decreasing mass with time) and the drag equation, and throw it into an Excel spreadsheet using a numerical solving method. If you need help doing that, I can probably help you tonight.
Mentor
P: 21,663
Ok, I was bored, so I did the spreadsheet/graph. Its attached. I didn't check it thoroughly, but the graph looks right. I had to clip the data to make it small enough to upload - stretch it down to about 500 and you'll get a flight profile for just about the entire ascent (even after engine shutoff).
Attached Files
 profile.zip (38.3 KB, 34 views)

P: 708

## Calculating drag

Hey, thanks so much russ! This is a huge help, I really appreciate this! I knew that was the equation for calculating the force of drag, it was just using that to calculate the velocity at any time that I couldn't figure out.

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