# Solving Rocket Launch Equations in matlab

1. Apr 18, 2013

### mysticboon

1. The problem statement, all variables and given/known data
A Super Loki rocket (http://en.wikipedia.org/wiki/Loki_(rocket [Broken])) 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.

2. Relevant 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.

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 6, 2017
2. Apr 18, 2013

### SteamKing

Staff Emeritus
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?"