Calculating Drag for Model Rockets

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Discussion Overview

The discussion revolves around calculating the velocity of model rockets over time, considering factors such as mass, applied force, and drag as a function of velocity. Participants explore the complexities of integrating these variables into a cohesive model for predicting rocket performance.

Discussion Character

  • Technical explanation
  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant seeks guidance on calculating rocket velocity using mass, applied force, and a drag force that varies with the square of velocity, expressing uncertainty about the application of non-linear functions in differential equations.
  • Another participant suggests using the force equation (f=ma) along with the drag equation, proposing a numerical method via Excel for solving the equations, indicating a preference for practical application over theoretical derivation.
  • A third participant shares a spreadsheet and graph that models the rocket's ascent, although they note that the data was not thoroughly checked, implying potential limitations in accuracy.
  • A later reply expresses gratitude for the shared resources, indicating that the initial participant found the provided equation helpful but still struggles with the integration process to determine velocity over time.

Areas of Agreement / Disagreement

Participants generally agree on the importance of the drag equation and numerical methods for solving the problem, but there remains uncertainty regarding the integration of non-linear functions in the context of the differential equations involved.

Contextual Notes

Limitations include the potential inaccuracies in the shared spreadsheet, the participant's uncertainty about applying non-linear functions in differential equations, and the lack of detailed verification of the results presented.

Who May Find This Useful

Individuals interested in model rocketry, physics students working on related calculations, and hobbyists looking for practical methods to analyze rocket performance may find this discussion beneficial.

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).
 

Attachments

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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