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

AAE 450 Spring 2008 Comparison of Launch System Performance Trajectory Optimization 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 Comparison of Launch System Performance Trajectory Optimization Launch System I.C.s 1 t hmax h max % Improvement from Ground Ground h i = 0 km v i = 0 m/s 1707 s4372 kmNA Balloon h i = 30.5 km v i = 0 m/s 1791 s4686 km7.2 % Aircraft h i = 16.8 km v i = m/s 1821 s4786 km9.5 % 1. Initial conditions for Balloon and Aircraft Launches found in cited articles.

AAE 450 Spring 2008 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 atmosphere4” [ sphere%20matlab%20code%20for%20HW1%20Prob2.] Howell, K., “AAE 340 Dynamics and Vibrations," Numerical Integration and Spherical Coordinates, Purdue University, West Lafayette, IN, Klauans, B., and Raughards, J., “The Vanguard Satellite Launching Vehicle An Engineering Summary," The Martin Company, Engineering Report No , Baltimore, MD, April (pp.170) Kloster, K., and Longuski, J., Personal Conversation, January 15-16, 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. [ Accessed 1/16/08.] Trajectory Optimization

AAE 450 Spring 2008 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. Trajectory Design 63.4° Trial #1 (m PL = 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 Plots generated by E. Harkness from code written by A. Briden and E. Harkness ΔV Drag versus end-of-first-stage launch angle ΔV Total versus end-of-first-stage launch angle Trends ΔV Drag decreases with steering angle ΔV Total increases with steering angle

AAE 450 Spring 2008 Trajectory Design

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

AAE 450 Spring 2008 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 >>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 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:  Aircraft:  Balloon:

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

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

AAE 450 Spring AAE 450 Spring 2008 Trajectory Design 19 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: Final Analysis: Numbers generated by MAT and Traj codes, compiled by E. Harkness.

AAE 450 Spring

AAE 450 Spring