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

AAE 450 Spring 2008 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

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

AAE 450 Spring 2008 Backup Slides  Wind Data Source: Brian Budzinski found the data. ( Trajectory Optimization 4/25

AAE 450 Spring 2008 Backup Slides  FAA Launch Locations Source: Kyle Donohue gathered the data (www. faa.gov) Trajectory Optimization Federal Locations Name of FacilityLoacation Vandenburg AFBSouthern California Edwards AFBSouthern California White Sands Missile RangeNew Mexico Wallops Flight FacilityWallops Island, Virgina Cape Canaveral SpaceportCape Canaveral, Florida Commercially Approved Locations Name of FacilityLoacation Kodiak Launch ComplexKodiak Island, Alaska California SpaceportLompoc, California Virgina Space Flight CenterWallops Island, Virgina Florida Space AuthorityCape Canaveral, Florida Sea Launch PlatformEquatorial Pacific Ocean Mojave Civilian Test Flight CenterMojave, California Southwest Regional SpaceportUpham, New Mexico Proposed Locations Name of FacilityLoacation Spaceport WashingtonMoses Lake, Washington Nevada Test SiteNye County, Nevada Utah SpaceportWah Wah Valley, Utah Great Falls SpaceportMontana South Dakota SpaceportSouth Dakota Oklahoma SpaceportBurns Flat, Oklahoma Gulf Coast RegionalBrezoria County, Texas Wisconsin SpaceportSheboygan, Wisconsin Spaceport AlabamaBaldwin county, Alabama South Texas SpaceportWillacay County, Texas West Texas SpaceportPecos County, Texas 5/25

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

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

AAE 450 Spring 2008 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 Trajectory Optimization Airplane, Balloon, Ground, Drag ΔV Comparison Launch Type GLOW [kg] With Atmosphere ModelNo Atmosphere Model ΔV DragΔV Total % ΔV Drag of Total ΔV DragΔV Total Airplane29,023759, %09,876 Airplane5, , %010,447 Balloon5,593142, %02,895 Ground29, , %010,677 Ground5, , %09,982  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. 8/25

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

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

AAE 450 Spring 2008 Ψ 3 Effect on Trajectory Trajectory Optimization 11/25  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)

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

AAE 450 Spring 2008 Backup Slides Trajectory Optimization 13/25

AAE 450 Spring 2008 Backup Slides Trajectory Optimization 14/25

AAE 450 Spring 2008 Backup Slides Trajectory Optimization 15/25

AAE 450 Spring 2008 Airplane Trajectory Results Trajectory Optimization 16/25 Conclusions - Good airplane launch trajectories are possible - Airplane launches can be cheaper than balloon launches - Unfortunately D&C cannot control trajectory’s prescribed path Airplane Trajectory Results Model NameCost Comparable Balloon Cost Delta V [m/s] Perigee [km] Apogee [km] Eccentricity SA-SA-DT-DT$2,107,448$2,157,4038, , MA-SA-DA-DA$2,247,287$2,524,9428, , LA-SA-DA-DT$2,487,533$2,752,3188, , Too Aggressive for D&C Example Orbit Bradley Ferris Junichi Kanehara

AAE 450 Spring 2008 Ψ 3 Error Sensitivity Trajectory Optimization  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 17/25  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

AAE 450 Spring 2008 Backup Slides Trajectory Optimization 18/25

AAE 450 Spring 2008 Backup Slides Trajectory Optimization 19/25

AAE 450 Spring 2008 Presentation Slides: Ψ 3 Effect on Trajectory and Resulting Orbit Trajectory Optimization 20/25  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) Angle of Ψ 2  Conclusions –Best Results occur at the previous steering angle –Spin stabilized third stage is feasible.

AAE 450 Spring 2008 Presentation Slides: Ψ 3 Error Sensitivity Trajectory Optimization  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 21/25  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

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

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

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

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