1. AAE 450 Spring 2008 Trajectory Code Validation Slides 04/12/08

2. AAE 450 Spring 2008 Trajectory Simulation – Drag Loss  Results:  Compare to Shuttle (2029633 kg GLOM): 107 m/s Titan IV/Centaur (886420 kg GLOM): 156 m/s (from SMAD) Trajectory Optimization Chua – 01/31

3. AAE 450 Spring 2008 Scott Breitengross Feb 7, 2008 Trajectory group, Delta V Delta V determination, Saturn V comparison

4. AAE 450 Spring 2008 Changes and Assumptions  All stages masses modified to Saturn V  Engine thrust and exit area modified  Burn Time and mass flow rate modified  Stage diameters modified  Assume ΔV_Leo is same Trajectory *All Saturn V specs provided by http://www.nasm.si.edu/collections/imagery/apollo/saturnV.htm

5. AAE 450 Spring 2008 ΔV Calculations Trajectory Future Work  Continue on Trajectory Model Launch TypeΔV_GravΔV_DragΔV_Total Default Inputs1310 m/s293 m/s~15000 m/s Saturn V Inputs 2362 m/s 36 m/s ~11000 m/s

6. AAE 450 Spring 20086 Brad Ferris 02/21/08 Trajectory Analyst Modeling Drag Assistance provided by Jayme Zott, Kyle Donohue

7. AAE 450 Spring 20087 Modeling  Assumptions: –Atmosphere molecular weight is constant –Angle of Attack is zero  Speed of Sound: a = [γRT] 1/2  Use Mach Number to get C D  Apply Equation for Drag D = C D * q * S Trajectory Optimization

8. AAE 450 Spring 20088 Validation Trajectory Optimization  With function, notice drag behavior  Over most Mach numbers, drag without function is higher Figure by Brad Ferris

9. AAE 450 Spring 20089 Orbit parameters  Without Function –762 / 232710 km (periapsis / apoapsis) –Eccentricity: 0.942 –Delta V Drag: 461 m/s –Delta V Total: 10760 m/s –Steering Angles: 6,-28,-28 deg. Trajectory Optimization  With Function –807 / 232477 km (periapsis / apoapsis) –Eccentricity: 0.942 –Delta V Drag: 384 m/s –Delta V Total: 10672 m/s –Steering Angles: 6,-28,-28 deg.

10. AAE 450 Spring 200810 Drag and Time Trajectory Optimization Figure by Brad Ferris

11. AAE 450 Spring 200811 Junichi (Jun) Kanehara 02/21/2008 Trajectory Validation of Thrust in the Trajectory Codes

12. AAE 450 Spring 200812 Test #1 Trajectory Procedure Set Drag = 0>> Assume No Atmosphere Calculate for each stage, using the data from Ariane 4, Saturn V and Pegasus 3.Compare with the historical data. Results The calculated values matched with the historical data!! (3-5 or more significant figures) Special Thanks to Kevin & Mr. Tsohas for helping us

13. AAE 450 Spring 200813 Test #2 Trajectory Full Atmosphere Exit Pressure and Exit Area were calculated. Thrust in Vacuum Condition Thrust in Sea Level Condition

14. AAE 450 Spring 200814 Trajectory Backup Slides # of engines: 41st Stage2nd Stage3rd Stage ThrustSea Level676.9 [kN] Vacuum758.578562.7[kN] IspSea Level248.5 [s] Vacuum278.4293.5445.1[s] Pressurechamber5.85 3.50[MPa] Nozzle Expansion Ratio(epsilon)10.4830.862.5 Ariane 4 Special Thanks to Mr. Tsohas for providing the data

15. AAE 450 Spring 200815 Trajectory Backup Slides Saturn V, First Stage ThrustSea Level6,747.50[kN] Vacuum7,740.50[kN] IspSea Level265[s] Vacuum304[s] Pressurechamber7.0[MPa] Nozzle Expansion Ratio(epsilon)16

16. AAE 450 Spring 200816 Solve for and get Trajectory Backup Slides Solve for and get Special Thanks to D.Lattibeaudiere for co-working on prop_test.m

17. AAE 450 Spring 200817 Test #1: Delta_V_Thrust_Total  Ariane 4:10,120[m/s]  Saturn V:13,470 [m/s]  Pegasus: 8,360 [m/s] Backup Slides

18. 18 Amanda Briden 2/28/08 APM, Trajectory Group Ballistic Coefficient Analysis ‘measure of its ability to overcome air resistance in flight’ 1 AAE 450 Spring 2008

19. 19 AAE 450 Spring 2008 Trajectory Ballistic Coefficient Definition where m - total mass C D - drag coefficient f(M) - calculated by Aerothermal solve_cd.m S – reference area; stage diameter BC: Large Launch Vehicles transonic regime M = 1.19 @ t = 70s out of atmosphere 10s vertical flight Expect: - Larger BC for more massive launch vehicles our region

20. 20 Thank you to Jun Kanehara, Elizabeth Harkness, Alan Schwing, and Kevin Kloster for all of their help this week! BC: Sample MATs Launch Vehicles end of 1 st stage S changes Conclusions: - Trends are as expected - Our vehicle cannot easily overcome air resistance AAE 450 Spring 2008 Trajectory

21. 21AAE 450 Spring 2008 Trajectory Future Work  Optimize final design cases  Write report References: 1."Ballistic coefficient." Wikipedia January 18, 2008 February 27, 2008. 2.Longuski, Prof. J. "AAE 450 Spacecraft Design Lecture #6." Purdue University, West Lafayette, IN. 3.Longuski, Prof. J. Ballistic Coefficient interview. February 20, 2008. 4. Kloster, Kevin. Ballistic Coefficient interview. February 20-27, 2008. Backup Slides

22. 22 Steering Angles Used In Analysis VehicleAlt @ end of stage 1 (km)mdot1 (kg/s)tburn1 (s)psi1e (deg)psi2e (deg)Psi3e (deg) Pegasus94.43206.1367387-25-30 Saturn V109.7513,360.2416187400 Ariane 4571,112.1920587400 SB-HA-DA-DA (8700 km/s) Traj Ver 5.3 194.096.847196.5-14-20 SG-SA-DT-DT (9051 km/s) Traj Ver 5.3 71.4414.208182.40-10 LG-SA-DT-DT (10,000 km/s) Traj Ver 5.3 56.4418.391171.234-26 AAE 450 Spring 2008 Trajectory