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Allen Guzik Trajectory

This presentation discusses trajectory optimization for vehicle launches, including initial assessments, wind data analysis, drag comparisons, and the effects of atmosphere on ascent. It also explores the effect of changing steering angles on the resulting trajectory and orbit angle, as well as the sensitivity of the orbit to errors in steering angles.

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Allen Guzik Trajectory

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  1. Allen GuzikTrajectory AAE 450 Spring 2008 Trajectory Optimization 1/25

  2. Delta V at Each Latitude • Initial Assessment • Only looks at Velocity gained from the rotation of the Earth • Assume Launched Vertically and directly East AAE 450 Spring 2008 Trajectory Optimization 2/25

  3. Location and Wind • Average Wind Velocities • 4 m/s • 5 m/s • 7 m/s • Launch Locations • Federal • Commercial (Already Approved) • Proposed Map Provided From www.googgle.com, Edited by Allen Guzik AAE 450 Spring 2008 Trajectory Optimization 3/25

  4. Backup Slides • Wind Data Source: Brian Budzinski found the data. (http://www.windstuffnow.com/main/wind_charts.htm) AAE 450 Spring 2008 Trajectory Optimization 4/25

  5. Backup Slides • FAA Launch Locations Source: Kyle Donohue gathered the data (www. faa.gov) AAE 450 Spring 2008 Trajectory Optimization 5/25

  6. Backup Slides • Earth Help Basic Calculation AAE 450 Spring 2008 Trajectory Optimization 6/25

  7. Sample Airplane Launch Trajectory Code Can Now Predict Orbits From an Aircraft Launch Ascent Trajectory Launch Site Initial Height of 12,200 m AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 7/25

  8. ΔV Drag Comparison Purpose Attempt to validate how the trajectory code estimates drag Compare vehicle mass to Δv drag Compare drag from different launching configurations • Assumptions • Same initial steering law conditions • Orbit obtained is not considered • Same dimensions • Conclusions • Lighter Vehicle Increases Δv drag • Airplane and Balloon Launches decrease Δv drag • Trajectory Code handles drag appropriately, however the magnitude of the results need to be verified. AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 8/25

  9. Backup Slides Sample Affect of Atmosphere on Ascent Both Cases are for a GROUND LAUNCH With Atmosphere No Atmosphere AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 9/25

  10. Backup Slides Sample Balloon Ascent 30,500 m AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 10/25

  11. Ψ3 Effect on Trajectory • Purpose • Attempt to understand how changing steering angles affects the resulting trajectory. • Feasibility of spin stabilization of third stage • Will be used to know how to get into orbit for different vehicles. • Help write code for a better trajectory model prediction. • Aid in understanding other launch systems (i.e. plane and balloon) • Assumptions • Only Change Ψ3 • Hold Ψ1 and Ψ2 constant (-15˚, -30˚). • 3 Stage Vehicle (Juno I Inputs) • Ground launch • Payload (5 kg) AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 11/25

  12. Other Plots • Conclusions • Best Results occur at the previous steering angle • Spin stabilized third stage is feasible. AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 12/25

  13. Backup Slides AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 13/25

  14. Backup Slides AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 14/25

  15. Backup Slides AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 15/25

  16. Airplane Trajectory Results Bradley Ferris Junichi Kanehara Example Orbit Too Aggressive for D&C Conclusions - Good airplane launch trajectories are possible - Airplane launches can be cheaper than balloon launches - Unfortunately D&C cannot control trajectory’s prescribed path AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 16/25

  17. Ψ3 Error Sensitivity • Purpose • Find how sensitive the orbit is from an error in Ψ3 • D&C needs this for their controller • Model Used for Analysis • LB-SA-DA-DA • Conclusions • - Perigee is greatly effected by Ψ3 error (1˚ ~= 10% error) • - If there is error, best case is for the error to be more negative AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 17/25

  18. Backup Slides AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 18/25

  19. Backup Slides AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 19/25

  20. Presentation Slides: Ψ3 Effect on Trajectory and Resulting Orbit Angle of Ψ2 • Purpose • Attempt to understand how changing steering angles affects the resulting trajectory. • Feasibility of spin stabilization of third stage • Will be used to know how to get into orbit for different vehicles. • Help write code for a better trajectory model prediction. • Aid in understanding other launch systems (i.e. plane and balloon) • Assumptions • Only Change Ψ3 • Hold Ψ1 and Ψ2 constant (-15˚, -30˚). • 3 Stage Vehicle (Juno I Inputs) • Ground launch • Payload (5 kg) • Conclusions • Best Results occur at the previous steering angle • Spin stabilized third stage is feasible. AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 20/25

  21. Presentation Slides: Ψ3 Error Sensitivity • Purpose • Find how sensitive the orbit is from an error in Ψ3 • D&C needs this for their controller • Model Used for Analysis • LB-SA-DA-DA • Conclusions • - Perigee is greatly effected by Ψ3 error (1˚ ~= 10% error) • - If there is error, best case is for the error to be more negative AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 21/25

  22. Backup Slides (If needed) AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 22/25

  23. Backup Slides (If Needed) AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 23/25

  24. Backup Slides (If Needed) AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 24/25

  25. Backup Slides (If Needed) AAE 450 Spring 2008 AAE 450 Spring 2008 Trajectory Optimization 25/25

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