Solving Rocket Launch Equations in matlab

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SUMMARY

The discussion focuses on solving the apogee of a Super Loki rocket using MATLAB, specifically through numerical and analytic techniques. The key parameters include a payload mass of 6 kg, a thrust of 18 kNt, and a burn time of 2.1 seconds. The user encountered issues with the MATLAB function ode45 while attempting to solve the differential equation dv/dt = -F/M, indicating a need for proper time step selection. The discussion emphasizes the importance of showing detailed work in problem-solving rather than vague descriptions of attempts.

PREREQUISITES
  • Understanding of differential equations and their applications in physics
  • Familiarity with MATLAB, specifically the ode45 function
  • Knowledge of rocket propulsion principles, including thrust and specific impulse
  • Basic concepts of numerical methods for solving equations
NEXT STEPS
  • Research the implementation of MATLAB's ode45 for solving differential equations
  • Study the derivation and application of the rocket motion equations from NASA's educational resources
  • Explore techniques for selecting appropriate time steps in numerical simulations
  • Learn about the effects of atmospheric resistance on rocket trajectories
USEFUL FOR

Students and engineers involved in aerospace engineering, particularly those working on rocket design and simulation, as well as anyone interested in applying MATLAB for solving complex physics problems.

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Homework Statement


A Super Loki rocket (http://en.wikipedia.org/wiki/Loki_(rocket )) is used to launch a small
payload to above 100 km altitude in a sub orbital flight. Ignoring atmospheric resistance, find the
apogee using both numerical and analytic techniques (solve the differential equations given in
the lecture notes). Use the specifications given below.
Payload mass (unpowered 2ndstage)
6 kg
Thrust (constant until burnout–kilo-Newtons)
18 kNt
Launch (take-off) mass
29 kg
Burntime
2.1 sec
HTBP solid fuel specific impulse
238 sec
At the end of the 2.1 sec burn, the payload is explosive bolt“ launched” to coast to apogee. This
does NOT effect the calculations.




Homework Equations


Basically my question is what differential equation am I to use to solve this? I'm using the equations give here
http://exploration.grc.nasa.gov/education/rocket/rktpow.html
I solved the problem analytically already so I have a general idea what the answer should look like.



The Attempt at a Solution


I attempted to use ode45 to solve the equation dvdt = -F/M but the ode solver gets an error with the time step I'm using.
 
Last edited by a moderator:
Physics news on Phys.org
Are we supposed to guess what you did? You still must show specific work, rather than say, "I did this. It didn't work. What went wrong?"
 

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