Trajectory Code Validation Slides

Transcription

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

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

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

4 Changes and Assumptions All stages masses modified d to Saturn V Engine thrust and exit area modified Burn Time and mass flow rate modified Stage diameters modified Assume ΔV_Leo is same *All Saturn V specs provided by AAE 450 Spring 2008

5 ΔV Calculations l Launch Type ΔV_Grav ΔV_Drag ΔV_Total Default Inputs 1310 m/s 293 m/s ~15000 m/s Saturn V Inputs 2362 m/s 36 m/s ~11000 m/s Future Work Continue on Model AAE 450 Spring 2008

6 Brad Ferris 02/21/08 Analyst Modeling Drag Assistance provided by Jayme Zott, Kyle Donohue AAE 450 Spring <#>

7 Assumptions: Modeling 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 AAE 450 Spring <#> Optimization

8 Validation With function, notice drag behavior Over most Mach numbers, drag without function is higher rag (N) D Drag Force v. Mach Number W/O Function Cd Function Mach Number Figure by Brad Ferris AAE 450 Spring <#> Optimization

9 Orbit parameters Without Function 762 / km (periapsis p / apoapsis) p Eccentricity: Delta V Drag: 461 m/s Delta V Total: m/s Steering Angles: 6,-28,-28 deg. With Function 807 / km (periapsis / apoapsis) Eccentricity: Delta V Drag: 384 m/s Delta V Total: m/s Steering Angles: 6,-28,-28 deg. AAE 450 Spring <#> Optimization

10 Drag and Time Drag v. Time Dr rag (N) W/O Function Cd Function Time (s) Figure by Brad Ferris AAE 450 Spring <#> Optimization

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

12 T dt m Test #1 Procedure Set Drag = 0 >> Assume No Atmosphere T Δ V t = g, thrust dt m 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 AAE 450 Spring

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

14 Backup Slides Ariane 4 # of engines: 4 1st Stage 2nd Stage 3rd Stage Thrust Sea Level [kn] Vacuum [kn] Isp Sea Level [s] Vacuum [s] Pressure chamber [MPa] Nozzle Expansion Ratio (epsilon) Special Thanks to Mr. Tsohas for providing the data AAE 450 Spring

15 Backup Slides Saturn V, First Stage Thrust Sea Level 6, [kn] Vacuum 7, [kn] Isp Sea Level 265 [s] Vacuum 304 [s] Pressure chamber 7.0 [MPa] Nozzle Expansion Ratio (epsilon) 16 AAE 450 Spring

16 Backup Slides 1 γ 1 1 * γ γ 1 1 A 1 γ γ + p 1 e γ + p 1 e ε = = Ae 2 p0 γ 1 p 0 Solve for p e p 0 and get p e 1 γ 1 γ * 2 2 γ γ p e * SL = 0γ 1 + ( e a) ε γ 1 γ + 1 p 0 T A p p p A Solve for * A and get Ae Special Thanks to D.Lattibeaudiere for co-working on prop_test.m t AAE 450 Spring

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

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

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

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

21 Backup Slides 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 i interview. i February 20, Kloster, Kevin. Ballistic Coefficient interview. February 20-27, AAE 450 Spring

22 Steering Angles Used In Analysis Vehicle end of stage 1 (km) mdot1 (kg/s) tburn1 (s) psi1e (deg) psi2e (deg) Psi3e (deg) Pegasus Saturn V , Ariane , SB-HA-DA-DA (8700 km/s) Traj Ver 5.3 SG-SA-DT-DT (9051 km/s) Traj Ver 5.3 LG-SA-DT-DT (10, km/s) Traj Ver AAE 450 Spring