Calculating Drag for Model Rockets

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Calculating the velocity of a model rocket involves understanding the mass, applied force, and drag force, which is dependent on velocity. The drag force is typically modeled as a function of velocity squared, complicating the integration process for velocity over time. Using Newton's second law (F=ma) and accounting for decreasing mass during flight can simplify calculations. One effective method is to use a numerical solving approach in Excel, which can graph the rocket's speed and altitude throughout its ascent. This approach provides a practical solution for hobbyists looking to predict rocket performance before construction.
VantagePoint72
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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: https://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
 
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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.
 
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).
 

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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.
 

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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