trajjyectory code validation slides...slides saturn v, first stage thrust sea level 6,747.50 [kn]...

Trajectory Code Validation j ySlides04/12/0804/12/08

AAE 450 Spring 2008

Trajectory Simulation – Drag LossResults:Results:

Compare to Shuttle (2029633 kg GLOM): 107 m/sTitan IV/Centaur (886420 kg GLOM): 156 m/s

AAE 450 Spring 2008

(from SMAD)

Trajectory OptimizationChua – 01/31

Scott BreitengrossFeb 7, 2008

Trajectory group, Delta V Delta V determination, Saturn V comparison

AAE 450 Spring 2008

Changes and AssumptionsAll t difi d t S t VAll stages masses modified to Saturn VEngine thrust and exit area modifiedBurn Time and mass flow rate modifiedStage diameters modifiedStage diameters modifiedAssume ΔV_Leo is same

*All Saturn V specs provided by http://www.nasm.si.edu/collections/imagery/apollo/saturnV.htm

AAE 450 Spring 2008Trajectory

ΔV C l l tiΔV CalculationsLaunch 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 WorkContinue on Trajectory ModelContinue on Trajectory Model


Brad Ferris02/21/0802/21/08

Trajectory AnalystModeling DragModeling Drag

Assistance provided by Jayme Zott, Kyle Donohue

AAE 450 Spring 2008 6<#>

ModelingA tiAssumptions:– Atmosphere molecular weight is constant– Angle of Attack is zero

Speed of Sound: a = [γRT]1/2

Use Mach Number to get CD

Apply Equation for DragApply Equation for DragD = CD * q * S

AAE 450 Spring 2008 7<#>Trajectory Optimization

V lid tiValidationDrag Force v. Mach NumberWith

20000

25000

W/O F ti

function, notice drag

15000ra

g (N

)W/O FunctionCd Function

behaviorOver most M h

5000

10000DMach numbers, drag

00 1 2 3 4 5

Mach Number

drag without function is


higher Figure by Brad Ferris

Orbit parametersWithout Function With F tiWithout Function– 762 / 232710 km

(periapsis / apoapsis)

With Function– 807 / 232477 km

(periapsis / apoapsis)(p p p p )– Eccentricity: 0.942– Delta V Drag: 461 m/s

(periapsis / apoapsis)– Eccentricity: 0.942– Delta V Drag: 384 m/s

– Delta V Total: 10760 m/sSteering Angles:

g– Delta V Total: 10672

m/sSt i A l– Steering Angles:

6,-28,-28 deg.– Steering Angles:

6,-28,-28 deg.


D d TiDrag and TimeDrag v. Time

20000

25000

15000

rag

(N)

W/O FunctionCd Function

5000

10000Dr

00 50 100 150 200 250

Time (s)


Figure by Brad Ferris

Junichi (Jun) Kanehara02/21/200802/21/2008Trajectory

Validation of Thrust in the Trajectory Codes

AAE 450 Spring 2008 11

T t #1 P d

T dtm∫

Test #1 Procedure• Set Drag = 0 >> Assume No Atmosphere

• Calculate for each stage,th tTV dtΔ = ∫ g ,

using the data from Ariane 4, Saturn V and Pegasus

3 Compare with the historical data

thrustV dtm

Δ ∫

3. Compare with the historical data.

ResultsThe calculated values matched with the historical data!!(3-5 or more significant figures)

AAE 450 Spring 2008 12Trajectory

Special Thanks to Kevin & Mr. Tsohas for helping us

T t #2Test #2•Full Thrust in Vacuum ConditionAtmosphere

•Exit Pressure and

Thrust in Vacuum Condition

Pressure and Exit Area were calculated. Thrust in Sea Level Condition


BackupBackup Slides Ariane 4

# of engines: 4 1st Stage 2nd Stage 3rd Stage

Thrust Sea Level 676.9 [kN]Thrust Sea Level 676.9 [kN]

Vacuum 758.5 785 62.7 [kN]

Isp Sea Level 248 5 [s]Isp Sea Level 248.5 [s]

Vacuum 278.4 293.5 445.1 [s]

h bPressure chamber 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

BackupBackup Slides Saturn V, First Stage

Thrust Sea Level 6,747.50 [kN]

Vacuum 7 740 50 [kN]Vacuum 7,740.50 [kN]

Isp Sea Level 265 [s]

Vacuum 304 [s]

Pressure chamber 7.0 [MPa]

Nozzle Expansion Ratio (epsilon) 16


BackupBackup Slides 1 11

* 11 1 1p pAγ

γ γγγ γ−

−⎡ ⎤

⎛ ⎞ ⎛ ⎞+ +⎛ ⎞ ⎢ ⎥11

0 0

1 1 12 1

e e

e

p pAA p p

γ γγγ γεγ

− ⎛ ⎞ ⎛ ⎞+ +⎛ ⎞ ⎢ ⎥= = ⋅ ⋅ −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎢ ⎥−⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦

1

Solve for and get 0

epp ep

( )11 2

1* *

00

2 2 11 1

eSL e a

pT A p p p Ap

γγγγ

γ εγ γ

−+−

⎧ ⎫⎡ ⎤⎛ ⎞⎛ ⎞⎪ ⎪= − + −⎨ ⎬⎢ ⎥⎜ ⎟⎜ ⎟− +⎝ ⎠ ⎝ ⎠⎣ ⎦⎪ ⎪

⎩ ⎭

Solve for and get

0pγ γ⎝ ⎠ ⎝ ⎠⎣ ⎦⎪ ⎪⎩ ⎭*A eA Special Thanks to D.Lattibeaudiere

f ki t t


for co-working on prop_test.m

Backup

Test #1:

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 2008 17

Amanda Briden2/28/082/28/08

APM, Trajectory GroupBallistic Coefficient AnalysisBallistic Coefficient Analysis‘measure of its ability to overcome air resistance in flight’1

18AAE 450 Spring 2008

Ballistic Coefficient Definition

mBC

BC: Large Launch Vehicles

SCBC

D

=transonic regimeM = 1.19 @ t = 70s

wherem - total massCD- drag coefficient f(M)

- calculated by Aerothermal solve_cd.mS – reference area; stage diameter

out of atmosphere

g

10s vertical flight

Expect:p- Larger BC for more massive launch vehicles

19AAE 450 Spring 2008Trajectory

our region

BC: Sample MATs Launch Vehicles

Conclusions:

Trends are as expectedend of 1st stageS changes

- Trends are as expected- Our vehicle cannot easily overcome air resistance

20

Thank you to Jun Kanehara, Elizabeth Harkness, Alan Schwing, and Kevin Kloster for all of their help this week!


Future Work

Backup Slides

Optimize final design casesWrite 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 L ki P f J B lli ti C ffi i t i t i F b 20 20083. Longuski, Prof. J. Ballistic Coefficient interview. February 20, 2008.4. Kloster, Kevin. Ballistic Coefficient interview. February 20-27, 2008.


Steering Angles Used In Analysis

Vehicle Alt @ end of stage 1 (km) mdot1 (kg/s) tburn1 (s) psi1e (deg) psi2e (deg) Psi3e (deg)

Pegasus 94.43 206.136 73 87 -25 -30g

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 (8700 km/s)Traj Ver 5 3

194.09 6.847 196.5 -14 -20 -20

Traj Ver 5.3

SG-SA-DT-DT (9051 km/s)Traj Ver 5.3

71.44 14.208 182.4 0 -10 -10

LG-SA-DT-DT (10 000 k / )

56.44 18.391 171.2 34 -26 -26(10,000 km/s)Traj Ver 5.3


trajjyectory code validation slides...slides saturn v, first stage thrust sea level 6,747.50 [kn]...

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