Calculating Drag for Model Rockets

  • Thread starter Thread starter VantagePoint72
  • Start date Start date
  • Tags Tags
    Drag
Click For Summary
SUMMARY

This discussion focuses on calculating the velocity of model rockets by incorporating drag as a function of velocity. The key equation involves using Newton's second law (F=ma) alongside the drag equation, which is proportional to the square of the velocity (v^2). The user, LastOneStanding, seeks assistance in applying these concepts to derive the rocket's velocity over time, especially after engine shutoff. A practical solution involves using Excel for numerical solving methods to simulate the rocket's ascent profile.

PREREQUISITES
  • Understanding of Newton's second law (F=ma)
  • Familiarity with drag equations, specifically drag proportional to v^2
  • Basic knowledge of differential equations
  • Proficiency in using Excel for numerical analysis
NEXT STEPS
  • Research numerical methods for solving differential equations
  • Learn how to implement drag equations in Excel
  • Explore advanced modeling techniques for rocket flight dynamics
  • Study the effects of varying mass on rocket ascent profiles
USEFUL FOR

Model rocket enthusiasts, aerospace engineers, and anyone interested in the physics of rocket flight and performance optimization.

VantagePoint72
Messages
820
Reaction score
34
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
 
Physics news on Phys.org
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.
 

Similar threads

Undergrad Drag Coefficient of a 'flexible' object (e.g. a piece of paper)
  • · Replies 4 ·
Replies
4
Views
2K
Rocket equations of motion w/ drag and gravity
  • · Replies 7 ·
Replies
7
Views
6K
Coefficient of Drag on a model rocket
  • · Replies 8 ·
Replies
8
Views
5K
Is there a way to calculate the Drag coefficient from any given object?
  • · Replies 3 ·
Replies
3
Views
2K
Help with drag coefficient calculated from ballistic coefficient
  • · Replies 3 ·
Replies
3
Views
8K
Coefficient of drag and surface smoothness
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Modeling a Bottle Rocket: Analyzing the Maximum Altitude
  • · Replies 4 ·
Replies
4
Views
5K
Model Rocket- What does the 'v' in drag=kv^2 really mean?
  • · Replies 5 ·
Replies
5
Views
2K
High School Calculating Heat from Drag force on a Rocket Airframe
  • · Replies 24 ·
Replies
24
Views
2K
Undergrad Drag equation - relative flow velocity
  • · Replies 11 ·
Replies
11
Views
4K