Elizabeth Harkness Trajectory Design Group Contact Preliminary Trajectory

Elizabeth Harkness Trajectory Design Group Contact Preliminary Trajectory Model: Vertical Launch AAE 450 Spring 2008

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

Comparison of Launch System Performance Launch System I. C. s 1 thmax % Improvement from Ground hi = 0 km vi = 0 m/s 1707 s 4372 km NA Balloon hi = 30. 5 km vi = 0 m/s 1791 s 4686 km 7. 2 % Aircraft hi = 16. 8 km 1821 s vi = 56. 58 m/s 4786 km 9. 5 % 1. Initial conditions for Balloon and Aircraft Launches found in cited articles. AAE 450 Spring 2008 Trajectory Optimization

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

References Heister, S. , “AAE 539 atmosphere 4” [https: //engineering. purdue. edu/AAE/Academics/Courses/aae 539/2008/std. %20 atmo sphere%20 matlab%20 code%20 for%20 HW 1%20 Prob 2. ] 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

Elizabeth Harkness Trajectory Design Group Contact Parametric Study of Steering Law and Drag Effects AAE 450 Spring 2008

Effects of changing the initial launch angle. Trial #1 (m. PL = 5 kg) Assumptions: -No wind model -Linear tangent steering law 63. 4° AAE 450 Spring 2008 Trajectory Design Plot generated by E. Harkness from code written by A. Briden, E. Harkness and K. Donahue

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

AAE 450 Spring 2008 Trajectory Design

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

Elizabeth Harkness Trajectory Design Group Contact, MAT Trajectory Contact 14 February 2008 Trajectory Input/ Output Interfacing with the MAT Codes AAE 450 Spring 2008

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

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

Input Variable Definitions (MAT) AAE 450 Spring 2008

Input Variable Definitions (User) § Ground and Balloon Launch § Aircraft Launch AAE 450 Spring 2008

Initial Conditions § Ground: § Balloon: § Aircraft: AAE 450 Spring 2008

Elizabeth Harkness Trajectory Design Group Contact MAT Trajectory Contact 28 February 2008 Trajectory Optimisation with Model Analysis AAE 450 Spring 2008 Trajectory Design 17

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

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

AAE 450 Spring 2008 20

AAE 450 Spring 2008 21