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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

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SLIDE 1

Trajectory Code Validation j y Slides

04/12/08 04/12/08

AAE 450 Spring 2008

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SLIDE 2

Trajectory Simulation – Drag Loss

Results: Results:

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

AAE 450 Spring 2008

(from SMAD)

Trajectory Optimization

Chua – 01/31

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SLIDE 3

Scott Breitengross

Feb 7, 2008 Trajectory group, Delta V Delta V determination, Saturn V comparison

AAE 450 Spring 2008

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SLIDE 4

Changes and Assumptions

All t difi d t S t V All stages masses modified to Saturn V Engine thrust and exit area modified Burn Time and mass flow rate modified Stage diameters modified Stage diameters modified Assume ΔV_Leo is same

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

AAE 450 Spring 2008

Trajectory

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SLIDE 5

ΔV C l l ti ΔV Calculations

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 Trajectory Model Continue on Trajectory Model

AAE 450 Spring 2008

Trajectory

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SLIDE 6

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<#>

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SLIDE 7

Modeling

A ti 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 Drag Apply Equation for Drag D = CD * q * S

AAE 450 Spring 2008 7<#>

Trajectory Optimization

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SLIDE 8

V lid ti Validation

Drag Force v. Mach Number

With

20000 25000

W/O F ti

function, notice drag

15000 rag (N)

W/O Function Cd Function

behavior Over most M h

5000 10000 D

Mach numbers, drag

1 2 3 4 5 Mach Number

drag without function is

AAE 450 Spring 2008 8<#>

Trajectory Optimization

higher

Figure by Brad Ferris

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SLIDE 9

Orbit parameters

Without Function With F ti Without 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/s Steering Angles: g – Delta V Total: 10672 m/s St i A l – Steering Angles: 6,-28,-28 deg. – Steering Angles: 6,-28,-28 deg.

AAE 450 Spring 2008 9<#>

Trajectory Optimization

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SLIDE 10

D d Ti Drag and Time

Drag v. Time

20000 25000 15000 rag (N)

W/O Function Cd Function

5000 10000 Dr 50 100 150 200 250 Time (s)

AAE 450 Spring 2008 10<#>

Trajectory Optimization

Figure by Brad Ferris

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SLIDE 11

Junichi (Jun) Kanehara

02/21/2008 02/21/2008 Trajectory Validation of Thrust in the Trajectory Codes

AAE 450 Spring 2008 11

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SLIDE 12

T t #1

P d

T dt m

∫

Test #1

Procedure

  • Set Drag = 0

>> Assume No Atmosphere

  • Calculate

for each stage,

th t

T V dt Δ = ∫

g , using the data from Ariane 4, Saturn V and Pegasus 3 Compare with the historical data

thrust

V dt m Δ

∫

  • 3. Compare with the historical data.

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

AAE 450 Spring 2008 12

Trajectory

Special Thanks to Kevin & Mr. Tsohas for helping us

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SLIDE 13

T t #2 Test #2

  • Full

Thrust in Vacuum Condition Atmosphere

  • Exit

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

AAE 450 Spring 2008 13

Trajectory

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SLIDE 14

Backup Backup 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 b Pressure chamber 5.85 5.85 3.50 [MPa] Nozzle Expansion Ratio (epsilon) 10.48 30.8 62.5

AAE 450 Spring 2008 14

Trajectory

Special Thanks to Mr. Tsohas for providing the data

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SLIDE 15

Backup Backup 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

AAE 450 Spring 2008 15

Trajectory

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SLIDE 16

Backup Backup Slides

1 1 1 * 1 1

1 1 p p A

γ γ γ γ

γ γ

− −

⎡ ⎤ ⎛ ⎞ ⎛ ⎞ + + ⎛ ⎞ ⎢ ⎥

1 1

1 1 1 2 1

e e e

p p A A p p

γ γ γ

γ γ ε γ

−

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

1

Solve for and get

e

p p

e

p

( )

1 1 2 1 * *

2 2 1 1 1

e SL e a

p T A p p p A p

γ γ γ γ

γ ε γ γ

− + −

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

Solve for and get

p γ γ ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ ⎪ ⎪ ⎩ ⎭

*

A

e

A

Special Thanks to D.Lattibeaudiere f ki t t AAE 450 Spring 2008 16

Trajectory

for co-working on prop_test.m

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SLIDE 17

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

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SLIDE 18

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

18 AAE 450 Spring 2008

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SLIDE 19

Ballistic Coefficient Definition

m BC

BC: Large Launch Vehicles

S C BC

D

=

transonic regime M = 1.19 @ t = 70s where m - total mass CD- drag coefficient f(M)

  • calculated by Aerothermal solve_cd.m

S – reference area; stage diameter

  • ut of atmosphere

g 10s vertical flight

Expect: p

  • Larger BC for more

massive launch vehicles

19 AAE 450 Spring 2008

Trajectory

  • ur region
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SLIDE 20

BC: Sample MATs Launch Vehicles Conclusions: Trends are as expected

end of 1st stage S changes

  • Trends are as expected
  • Our vehicle cannot easily
  • vercome air resistance

20

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

AAE 450 Spring 2008

Trajectory

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SLIDE 21

Future Work

Backup Slides

  • 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 L ki P f J B lli ti C ffi i t i t i F b 20 2008 3. Longuski, Prof. J. Ballistic Coefficient interview. February 20, 2008. 4. Kloster, Kevin. Ballistic Coefficient interview. February 20-27, 2008.

21 AAE 450 Spring 2008

Trajectory

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SLIDE 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

g Saturn V 109.75 13,360.24 161 87 40 Ariane 4 57 1,112.19 205 87 40 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

  • 10
  • 10

LG-SA-DT-DT (10 000 k / ) 56.44 18.391 171.2 34

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(10,000 km/s) Traj Ver 5.3

22 AAE 450 Spring 2008

Trajectory