Trajectory Code Validation j y Slides 04/12/08 04/12/08 AAE 450 Spring 2008
Trajectory Simulation – Drag Loss � Results: � Results: � Compare to Shuttle (2029633 kg GLOM): 107 m/s Titan IV/Centaur (886420 kg GLOM): 156 m/s (from SMAD) Chua – 01/31 AAE 450 Spring 2008 Trajectory Optimization
Scott Breitengross Feb 7, 2008 Trajectory group, Delta V Delta V determination, Saturn V comparison AAE 450 Spring 2008
Changes and Assumptions � All stages masses modified to Saturn V All t difi d t S t V � Engine thrust and exit area modified � Burn Time and mass flow rate modified � Stage diameters modified Stage diameters modified � Assume Δ V_Leo is same *All Saturn V specs provided by http://www.nasm.si.edu/collections/imagery/apollo/saturnV.htm AAE 450 Spring 2008 Trajectory
Δ V C l Δ V Calculations l ti Launch Type Δ V_Grav Δ V_Drag Δ V_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 Trajectory Model � Continue on Trajectory Model AAE 450 Spring 2008 Trajectory
Brad Ferris 02/21/08 02/21/08 Trajectory Analyst Modeling Drag Modeling Drag Assistance provided by Jayme Zott, Kyle Donohue AAE 450 Spring 2008 6<#>
Modeling � Assumptions: A ti – Atmosphere molecular weight is constant – Angle of Attack is zero � Speed of Sound: a = [ γ RT] 1/2 � Use Mach Number to get C D � Apply Equation for Drag Apply Equation for Drag D = C D * q * S AAE 450 Spring 2008 7<#> Trajectory Optimization
V lid ti Validation � With Drag Force v. Mach Number function, 25000 notice drag 20000 behavior W/O F W/O Function ti Cd Function 15000 � Over most rag (N) M Mach h D 10000 numbers, 5000 drag drag without 0 0 1 2 3 4 5 function is Mach Number higher Figure by Brad Ferris AAE 450 Spring 2008 8<#> Trajectory Optimization
Orbit parameters � Without Function � Without Function � With Function With F ti – 762 / 232710 km – 807 / 232477 km (periapsis / apoapsis) (p p p p ) (periapsis / apoapsis) (periapsis / apoapsis) – Eccentricity: 0.942 – Eccentricity: 0.942 – Delta V Drag: 461 m/s – Delta V Drag: 384 m/s g – Delta V Total: 10760 – Delta V Total: 10672 m/s m/s – Steering Angles: Steering Angles: – Steering Angles: St i A l 6,-28,-28 deg. 6,-28,-28 deg. AAE 450 Spring 2008 9<#> Trajectory Optimization
D Drag and Time d Ti Drag v. Time 25000 20000 W/O Function Cd Function 15000 rag (N) Dr 10000 5000 0 0 50 100 150 200 250 Time (s) Figure by Brad Ferris AAE 450 Spring 2008 10<#> Trajectory Optimization
Junichi (Jun) Kanehara 02/21/2008 02/21/2008 Trajectory Validation of Thrust in the Trajectory Codes AAE 450 Spring 2008 11
T dt ∫ m T Test #1 t #1 P Procedure d • Set Drag = 0 >> Assume No Atmosphere = ∫ T ∫ Δ Δ • Calculate for each stage, g , V V dt dt th thrust t m using the data from Ariane 4, Saturn V and Pegasus 3 3. Compare with the historical data. 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 2008 12 Trajectory
T Test #2 t #2 •Full Thrust in Vacuum Condition Thrust in Vacuum Condition Atmosphere •Exit Pressure and Pressure and Exit Area were Thrust in Sea Level Condition calculated. AAE 450 Spring 2008 13 Trajectory
Backup Backup Slides Ariane 4 # of engines: 4 1st Stage 2nd Stage 3rd Stage Thrust Thrust Sea Level Sea Level 676.9 676.9 [kN] [kN] Vacuum 758.5 785 62.7 [kN] Isp Isp Sea Level Sea Level 248 5 248.5 [s] [s] Vacuum 278.4 293.5 445.1 [s] Pressure chamber h b 5.85 5.85 3.50 [MPa] Nozzle Expansion Ratio (epsilon) 10.48 30.8 62.5 Special Thanks to Mr. Tsohas for providing the data AAE 450 Spring 2008 14 Trajectory
Backup Backup Slides Saturn V, First Stage Thrust Sea Level 6,747.50 [kN] Vacuum Vacuum 7 740 50 7,740.50 [kN] [kN] Isp Sea Level 265 [s] Vacuum 304 [s] Pressure chamber 7.0 [MPa] Nozzle Expansion Ratio (epsilon) 16 AAE 450 Spring 2008 15 Trajectory
Backup Backup Slides ⎡ γ − ⎤ 1 1 1 ⎛ ⎛ ⎞ ⎞ ⎛ ⎛ ⎞ ⎞ γ γ + + γ γ + + ⎛ ⎛ ⎞ ⎞ γ γ γ γ * ⎢ ⎢ ⎥ ⎥ γ γ − A A 1 1 p p 1 1 1 p p 1 1 − ε = = ⋅ ⋅ − 1 1 ⎜ e ⎟ ⎜ e ⎟ ⎜ ⎟ ⎢ ⎥ γ − ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ A 2 p 1 p ⎢ ⎥ e 0 0 ⎣ ⎦ p e p Solve for and get e p 0 1 ⎧ ⎫ γ − γ + 1 1 2 ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎪ γ ⎪ γ − 2 2 p 1 ( ) = γ − + − ε * ⎨ ⎢ ⎥ ⎬ * ⎜ ⎟ e ⎜ ⎟ T A p 1 p p A γ γ − γ γ + SL 0 e a ⎝ ⎝ ⎠ ⎠ ⎝ ⎝ ⎠ ⎠ 1 1 p p ⎪ ⎪ ⎣ ⎣ ⎦ ⎦ ⎪ ⎪ 0 0 ⎩ ⎩ ⎭ ⎭ * Solve for A and get A Special Thanks to D.Lattibeaudiere e f for co-working on prop_test.m ki t t AAE 450 Spring 2008 16 Trajectory
Backup Backup Slides Test #1: 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 2008 17
Amanda Briden 2/28/08 2/28/08 APM, Trajectory Group Ballistic Coefficient Analysis Ballistic Coefficient Analysis ‘measure of its ability to overcome air resistance in flight’ 1 AAE 450 Spring 2008 18
Ballistic Coefficient Definition BC: Large Launch Vehicles m = BC BC C S transonic regime D M = 1.19 @ t = 70s where m - total mass C D - drag coefficient f(M) out of atmosphere - calculated by Aerothermal solve_cd.m S – reference area; stage diameter g 10s vertical flight Expect: p - Larger BC for more massive launch vehicles our region AAE 450 Spring 2008 19 Trajectory
BC: Sample MATs Launch Vehicles Conclusions: - Trends are as expected Trends are as expected end of 1 st stage - Our vehicle cannot easily S changes 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 2008 20 Trajectory
Backup Slides Future Work � Optimize final design cases � Write report References: 1. "Ballistic coefficient." Wikipedia January 18, 2008 February 27, 2008 <http://en.wikipedia.org/wiki/Ballistic_coefficient>. 2. Longuski, Prof. J. "AAE 450 Spacecraft Design Lecture #6." Purdue University, West Lafayette, IN. 3. 3 Longuski, Prof. J. Ballistic Coefficient interview. February 20, 2008. L ki P f J B lli ti C ffi i t i t i F b 20 2008 4. Kloster, Kevin. Ballistic Coefficient interview. February 20-27, 2008. AAE 450 Spring 2008 21 Trajectory
Steering Angles Used In Analysis Vehicle Alt @ end of stage 1 (km) mdot1 (kg/s) tburn1 (s) psi1e (deg) psi2e (deg) Psi3e (deg) Pegasus g 94.43 206.136 73 87 -25 -30 Saturn V 109.75 13,360.24 161 87 40 0 Ariane 4 57 1,112.19 205 87 40 0 SB-HA-DA-DA 194.09 6.847 196.5 -14 -20 -20 (8700 km/s) Traj Ver 5 3 Traj Ver 5.3 SG-SA-DT-DT 71.44 14.208 182.4 0 -10 -10 (9051 km/s) Traj Ver 5.3 LG-SA-DT-DT 56.44 18.391 171.2 34 -26 -26 (10 000 k / ) (10,000 km/s) Traj Ver 5.3 AAE 450 Spring 2008 22 Trajectory
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