This document contains figures and simulations related to modeling a rocket launch and dart separation using MATLAB. It includes: 1) Figures showing the rocket model, equations of motion, simulation scripts and functions, thrust curve, and comparison to Rocksim simulation results. 2) Simulations with the main rocket only and with dart separation of 25%, 50%, 75%, and 90% of the total mass. 3) Analysis of the shear pin used for dart separation, including determining the internal pressure and radial pressure required to shear the pin. 4) Results of the shear pin simulation and radial pressure calculations for two cases.

1. Appendix A:
Figure 1A: Setting up of a background to build MATLAB code

2. 1
Figure 2A: FBD of rocket using three DOF (+) angles of attack and (-) angles of attack

3. 2
Figure 3A: Transforming 2nd
order ODE non-linear IVPs into a series
of 1st
order ODE non-linear IVPS

4. 3
Figure 4A: Part I of the Script File for
rocket simulation
Figure 5A: Part II of the Script File for rocket simulation

5. 4
Figure 6A: Part I of the Function File for rocket simulation

6. 5
Figure 7A: Part II of the Function File for rocket simulation

7. 6
Figure 7A: Thrust curve used in simulation
Figure 8A: Main rocket built in Rocksim (simulation is based off)
Figure 9A: Dart section of rocket built in Rocksim (simulation is based off)

8. 7
Figure 10A: Rocksim simulation (used as a comparison to MATLAB simulation)
Position graph on top and velocity graph on bottom

9. 8
Simulation 1: Main Rocket flight – no dart (can compare these graphs to Rocksim simulation)
Figure 11A: Matlab Simulation results using ODE45 – no dart separation

10. 9
Simulation 2: Dart simulation - 25% of mass in the dart section
Figure 12A: Matlab Simulation results using ODE45 – dart separation with 25% of total mass

11. 10
Simulation 3: dart simulation - 50% of mass in the dart section
Figure 13A: Matlab Simulation results using ODE45 – dart separation with 50% of total mass

12. 11
Simulation 4: dart simulation - 75% of mass in the dart section
Figure 14A: Matlab Simulation results using ODE45 – dart separation with 75% of total mass

13. 12
Simulation 5: dart 90% of mass in dart section
Figure 15A: Matlab Simulation results using ODE45 – dart separation with 90% of total mass

14. 13
Appendix B:
Figure 1B: Shear pin analysis

15. 14
𝜎 =Pi =
𝜎 =Pi =
Figure 2B: Determining internal pressure to achieve shear force of 314N

16. 15
Figure 3B: Determining radial pressure on airframe walls

17. 16
Figure 4B: Simplification tree for shearing a shear pin
Case II Section
Case I Section

18. 17
Case I:
Figure 5B: Shear pin results
Figure 6B: Case I radial pressure results

19. 18
Case II
Figure 7B: Case II radial pressure results
Ignore section – out of
bounds of actual pressure