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

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1 Allen Guzik Trajectory 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 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 Edited by Allen Guzik Trajectory Optimization 3/25

4 Backup Slides Wind Data Source: Brian Budzinski found the data. ( Trajectory Optimization 4/25

5 Backup Slides FAA Launch Locations Source: Kyle Donohue gathered the data (www. faa.gov) Commercially Approved Locations Name of Facility Loacation Kodiak Launch Complex Kodiak Island, Alaska California Spaceport Lompoc, California Virgina Space Flight Center Wallops Island, Virgina Florida Space Authority Cape Canaveral, Florida Sea Launch Platform Equatorial Pacific Ocean Mojave Civilian Test Flight Center Mojave, California Southwest Regional Spaceport Upham, New Mexico Federal Locations Name of Facility Loacation Vandenburg AFB Southern California Edwards AFB Southern California White Sands Missile Range New Mexico Wallops Flight Facility Wallops Island, Virgina Cape Canaveral Spaceport Cape Canaveral, Florida Proposed Locations Name of Facility Loacation Spaceport Washington Moses Lake, Washington Nevada Test Site Nye County, Nevada Utah Spaceport Wah Wah Valley, Utah Great Falls Spaceport Montana South Dakota Spaceport South Dakota Oklahoma Spaceport Burns Flat, Oklahoma Gulf Coast Regional Brezoria County, Texas Wisconsin Spaceport Sheboygan, Wisconsin Spaceport Alabama Baldwin county, Alabama South Texas Spaceport Willacay County, Texas West Texas Spaceport Pecos County, Texas Trajectory Optimization 5/25

6 Backup Slides Earth Help Basic Calculation 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 Trajectory Optimization 7/25

8 V Drag Comparison Purpose Attempt to validate how the trajectory code estimates drag Compare vehicle mass to v drag Compare drag from different launching configurations Conclusions Launch Type GLOW [kg] Lighter Vehicle Increases v drag Airplane, Balloon, Ground, Drag V Comparison V Drag With Atmosphere Model V Total Assumptions % V Drag of Total Same initial steering law conditions Orbit obtained is not considered Same dimensions No Atmosphere Model V Drag V Total Airplane 29, , % 0 9,876 Airplane 5, , % 0 10,447 Balloon 5, , % 0 2,895 Ground 29, , % 0 10,677 Ground 5, , % 0 9,982 Airplane and Balloon Launches decrease v drag Trajectory Code handles drag appropriately, however the magnitude of the results need to be verified. Trajectory Optimization 8/25

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

10 Backup Slides Sample Balloon Ascent 30,500 m Trajectory Optimization 10/25

11 Ψ 3 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 Ψ 3 Hold Ψ 1 and Ψ 2 constant (-15, -30 ). 3 Stage Vehicle (Juno I Inputs) Ground launch Payload (5 kg) Trajectory Optimization 11/25

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

13 Backup Slides Trajectory Optimization 13/25

14 Backup Slides Trajectory Optimization 14/25

15 Backup Slides Trajectory Optimization 15/25

16 Airplane Trajectory Results Bradley Ferris Junichi Kanehara Model Name SA-SA-DT-DT MA-SA-DA-DA LA-SA-DA-DT Cost $2,107,448 $2,247,287 $2,487,533 Airplane Trajectory Results Comparable Balloon Cost $2,157,403 $2,524,942 $2,752,318 Delta V [m/s] 8,988 8,765 8,987 Perigee [km] Apogee [km] 1, , ,742.8 Eccentricity 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 Trajectory Optimization 16/25

17 Purpose Find how sensitive the orbit is from an error in Ψ 3 D&C needs this for their controller Ψ 3 Error Sensitivity Model Used for Analysis LB-SA-DA-DA Sensitivity of Perigee to Psi3 Perigee Nominal Value Requested Orbit 110% 100% 90% Perigee Percent Error Perigee [km] Psi3 Angle Change from the Nominal [degree] Conclusions - Perigee is greatly effected by Ψ 3 error (1 ~= 10% error) - If there is error, best case is for the error to be more negative Percent Error 80% 70% 60% 50% 40% 30% 20% 10% 0% Psi3 Angle Change from the Nominal [degree] Trajectory Optimization 17/25

18 Backup Slides Percent Error Eccentricity Percent Error 20% 15% 10% 5% 0% Psi3 Angle Change from the Nominal [degree] Eccentricity Sensitivity of Eccentricity to Psi Psi3 Angle Change from the Nominal [degree] Eccentricity Nominal Value Trajectory Optimization 18/25

19 Backup Slides Percent Error 20% 15% 10% 5% Apogee Percent Error Apogee [km] 9,000 8,500 8,000 7,500 7,000 6,500 Sensitivity of Apogee to Psi3 Apogee Nominal Value 0% Psi3 Angle Change from the Nominal [degree] 6, Psi3 Angle Change from the Nominal [degree] Trajectory Optimization 19/25

20 Presentation Slides: Ψ 3 Effect on Trajectory and Resulting Orbit 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 Ψ 3 Hold Ψ 1 and Ψ 2 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. Angle of Ψ 2 Trajectory Optimization 20/25

21 Presentation Slides: Ψ 3 Error Sensitivity Purpose Find how sensitive the orbit is from an error in Ψ 3 D&C needs this for their controller Model Used for Analysis LB-SA-DA-DA Sensitivity of Perigee to Psi3 Perigee Nominal Value Requested Orbit 110% 100% 90% Perigee Percent Error Perigee [km] Conclusions Psi3 Angle Change from the Nominal [degree] - Perigee is greatly effected by Ψ 3 error (1 ~= 10% error) - If there is error, best case is for the error to be more negative Percent Error 80% 70% 60% 50% 40% 30% 20% 10% 0% Psi3 Angle Change from the Nominal [degree] Trajectory Optimization 21/25

22 Backup Slides (If needed) Percent Error Eccentricity Percent Error 20% 15% 10% 5% 0% Psi3 Angle Change from the Nominal [degree] Eccentricity Sensitivity of Eccentricity to Psi Psi3 Angle Change from the Nominal [degree] Eccentricity Nominal Value Trajectory Optimization 22/25

23 Backup Slides (If Needed) Percent Error 20% 15% 10% 5% Apogee Percent Error Apogee [km] 9,000 8,500 8,000 7,500 7,000 6,500 Sensitivity of Apogee to Psi3 Apogee Nominal Value 0% Psi3 Angle Change from the Nominal [degree] 6, Psi3 Angle Change from the Nominal [degree] Trajectory Optimization 23/25

24 Backup Slides (If Needed) Trajectory Optimization 24/25

25 Backup Slides (If Needed) Trajectory Optimization 25/25