AAE 450 Spring 2008

Trajectory Code Validation Slides04/12/08

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 OptimizationChua – 01/31

AAE 450 Spring 2008

Scott BreitengrossFeb 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 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

AAE 450 Spring 2008

ΔV Calculations

Trajectory

Future Work Continue on Trajectory Model

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

AAE 450 Spring 2008 6<#>

Brad Ferris02/21/08

Trajectory AnalystModeling Drag

Assistance provided by Jayme Zott, Kyle Donohue

AAE 450 Spring 2008 7<#>

Modeling Assumptions:

– 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 DragD = CD * q * S

Trajectory Optimization

AAE 450 Spring 2008 8<#>

Validation

Trajectory Optimization

Drag Force v. Mach Number

0

5000

10000

15000

20000

25000

0 1 2 3 4 5

Mach Number

Dra

g (

N)

W/O Function

Cd Function

With function, notice drag behavior

Over most Mach numbers, drag without function is higher

Figure by Brad Ferris

AAE 450 Spring 2008 9<#>

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.

AAE 450 Spring 2008 10<#>

Drag and Time

Trajectory Optimization

Drag v. Time

0

5000

10000

15000

20000

25000

0 50 100 150 200 250

Time (s)

Dra

g (

N)

W/O Function

Cd Function

Figure by Brad Ferris

AAE 450 Spring 2008 11

Junichi (Jun) Kanehara02/21/2008Trajectory

Validation of Thrust in the Trajectory Codes

AAE 450 Spring 2008 12

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.

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

Tdt

m

thrust

TV dt

m

Special Thanks to Kevin & Mr. Tsohas for helping us

AAE 450 Spring 2008 13

Test #2

Trajectory

•Full Atmosphere

•Exit Pressure and Exit Area were calculated.

Thrust in Vacuum Condition

Thrust in Sea Level Condition

AAE 450 Spring 2008 14Trajectory

Backup Slides

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

Thrust Sea Level 676.9     [kN]

  Vacuum 758.5 785 62.7 [kN]

Isp Sea Level 248.5     [s]

  Vacuum 278.4 293.5 445.1 [s]

Pressure chamber 5.85 5.85 3.50 [MPa]

Nozzle Expansion Ratio (epsilon) 10.48 30.8 62.5  

Ariane 4

Special Thanks to Mr. Tsohas for providing the data

AAE 450 Spring 2008 15Trajectory

Backup Slides Saturn V, First Stage

Thrust Sea Level 6,747.50 [kN]

  Vacuum 7,740.50 [kN]

Isp Sea Level 265 [s]

  Vacuum 304 [s]

Pressure chamber 7.0 [MPa]

Nozzle Expansion Ratio (epsilon) 16  

AAE 450 Spring 2008 16

Solve for and get

111 2

1* *

00

2 21

1 1e

SL e a

pT A p p p A

p

Trajectory

Backup Slides 1 11

* 11

0 0

1 11

2 1e e

e

p pA

A p p

Solve for and get 0

ep

p

*A eA Special Thanks to D.Lattibeaudierefor co-working on prop_test.m

ep

AAE 450 Spring 2008 17

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

Amanda Briden2/28/08

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

AAE 450 Spring 2008

19AAE 450 Spring 2008Trajectory

Ballistic Coefficient Definition

SC

mBC

D

wherem - total massCD- drag coefficient f(M) - calculated by Aerothermal solve_cd.mS – reference area; stage diameter

BC: Large Launch Vehicles

transonic regimeM = 1.19 @ t = 70s

out of atmosphere

10s vertical flight

Expect:- Larger BC for more massive launch vehicles

our region

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 1st stageS changes

Conclusions:

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

AAE 450 Spring 2008Trajectory

21AAE 450 Spring 2008Trajectory

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. Longuski, Prof. J. Ballistic Coefficient interview. February 20, 2008.

4. Kloster, Kevin. Ballistic Coefficient interview. February 20-27, 2008.

Backup Slides

22

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 -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 (8700 km/s)Traj Ver 5.3

194.09 6.847 196.5 -14 -20 -20

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 km/s)Traj Ver 5.3

56.44 18.391 171.2 34 -26 -26

AAE 450 Spring 2008Trajectory