Elizabeth Harkness Trajectory Design Group Contact Preliminary Trajectory Model: Vertical Launch

1. Elizabeth HarknessTrajectory Design Group ContactPreliminary Trajectory Model:Vertical Launch AAE 450 Spring 2008

2. Comparison of Launch System Performance Comparison of altitudes using vertical launch trajectory. -Plot generated by: Elizabeth Harkness -From code generated by: Junichi Kanehara and Amanda Briden -with assistance from: Elizabeth Harkness AAE 450 Spring 2008 Trajectory Optimization

3. Comparison of Launch System Performance 1. Initial conditions for Balloon and Aircraft Launches found in cited articles. AAE 450 Spring 2008 Trajectory Optimization

4. Model Assumptions • Values input into code are from Vanguard data Table 20. Payload of 100 lbs, orbit at 180 statute miles. • All stages are modelled vertically. • Poor assumption • Does not take into account the lengthy portion of trajectory through the atmosphere. • Preliminary test of trajectory code and comparison of three of the launch methods AAE 450 Spring 2008

5. References Heister, S., “AAE 539 atmosphere4” [https://engineering.purdue.edu/AAE/Academics/Courses/aae539/2008/std.%20atmosphere%20matlab%20code%20for%20HW1%20Prob2.] Howell, K., “AAE 340 Dynamics and Vibrations," Numerical Integration and Spherical Coordinates, Purdue University, West Lafayette, IN, 2006. Klauans, B., and Raughards, J., “The Vanguard Satellite Launching Vehicle An Engineering Summary," The Martin Company, Engineering Report No. 11022, Baltimore, MD, April 1960. (pp.170) Kloster, K., and Longuski, J., Personal Conversation, January 15-16, 2008. Longuski, J., “AAE 508 Optimization in Aerospace Engineering Lectures," Lecture #10, Purdue University, West Lafayette, IN, 2008, pp. 62. Wade, M., “Cape Canaveral," Encyclopedia Astronautica.  [http://www.astronautix.com/sites/capveral.htm.  Accessed 1/16/08.] AAE 450 Spring 2008 Trajectory Optimization

6. Elizabeth HarknessTrajectory Design Group ContactParametric Study of Steering Law and Drag Effects AAE 450 Spring 2008

7. 63.4° Effects of changing the initial launch angle. • Trial #1 (mPL = 5 kg) • Assumptions: • No wind model • Linear tangent steering law Plot generated by E. Harkness from code written by A. Briden, E. Harkness and K. Donahue AAE 450 Spring 2008 Trajectory Design

8. Trends • ΔVDrag decreases with steering angle • ΔVTotal increases with steering angle ΔVTotal versus end-of-first-stage launch angle ΔVDrag versus end-of-first-stage launch angle Plots generated by E. Harkness from code written by A. Briden and E. Harkness AAE 450 Spring 2008

9. AAE 450 Spring 2008 Trajectory Design

10. References Howell, K., “AAE 340 Dynamics and Vibrations," Numerical Integration and Spherical Coordinates, Purdue University, West Lafayette, IN, 2006. Kloster, K., and Longuski, J., Personal Conversation, January 15-16, 2008. Longuski, J., “AAE 508 Optimization in Aerospace Engineering Lectures," Lecture #10, Purdue University, West Lafayette, IN, 2008, pp. 62. AAE 450 Spring 2008 Trajectory Design

11. Elizabeth HarknessTrajectory Design Group Contact, MAT Trajectory Contact14 February 2008Trajectory Input/ Output Interfacingwith the MAT Codes AAE 450 Spring 2008

12. Interfacing with MAT • MAT Outputs to Trajectory Inputs • ID, Trajectory Output Array • MAT Output Array includes: type of launch, number of stages, thrusts, burn times, mass flow rates, exit areas, exit pressures for all stages. • Trajectory Inputs (from Trajectory) • Steering Angles and other steering law parameters (for manual run version) • Initial Conditions defined by type of launch AAE 450 Spring 2008

13. Procedure • Call MAT Code main_loop.m >>[ID,Trajectory_Input]= main_loop • Produce Trajectory Input File >>AAE450_Trajectory_run(ID,Trajectory_Input) • Run Trajectory Main Code >>AAE450_Trajectory_Main Output • Δv (all components and total), orbital characteristics, maximum acceleration (G’s), plots of trajectory. AAE 450 Spring 2008

14. Input Variable Definitions (MAT) AAE 450 Spring 2008

15. Input Variable Definitions (User) • Ground and Balloon Launch • Aircraft Launch AAE 450 Spring 2008

16. Initial Conditions • Ground: • Aircraft: • Balloon: AAE 450 Spring 2008

17. Elizabeth HarknessTrajectory Design Group ContactMAT Trajectory Contact28 February 2008Trajectory Optimisationwith Model Analysis AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Design 17 17

18. Effect of ΔV on GLOW and Cost Plots Created by Elizabeth Harkness, from numbers generated with the MAT code AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Design 18 18 Eye Candy

19. With a moderate decrease in ΔV (15 – 30%): • Gross lift-off weight decreases significantly (50 – 85%) • Large cost decreases (20 – 50%) Final Analysis: First Round Final Analysis: AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Design Numbers generated by MAT and Traj codes, compiled by E. Harkness. 19 19

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