AAE 450 Spring 2008 1<#>

Brandon White3/20/2008

Structures Group Contact

Inert Mass Standard Deviation JustificationOther Work

AAE 450 Spring 2008 2<#>

Standard Deviation Justification

“Happiness is the absence of striving for happiness.” – Chuang-Tzu

Value input into Monte Carlo: 2.255%– 5 times the Vanguard 1st

Stage Std. Dev.– Accounts for small

manufacturing tolerances.– High Tech Companies +

Small Tolerances High Costs

Final launch vehicles designed under the assumption of Space grade Aluminum– Cutting tolerances at .01”

Using Non-Space grade Aluminum shows opportunity for 200g and 1kg launch vehicles– Cutting tolerances at 0.125”

Standard Deviations

  SB-HA-DA-DA MB-HA-DA-DA LB-HA-DA-DA

Monte Carlo 2.255% 2.255% 2.255%

Non-Space Grade 2.28% 2.32% 8.94%

Space-Grade 3.13% 2.88% 4.42%

AAE 450 Spring 2008 3<#>

Inertia Model

“The person who writes for fools is always sure of a large audience.” – Arthur Shopenhauer

Geometry assumptions made due to unknown characteristics– Payload, Avionics in the 3rd

Stage all assumed to be a point mass located at the base of the Nose Cone

– LITVC assumed to be a point mass at the base of the 1st stage Nozzle

– Avionics in the 1st and 2nd Stage assumed to be wall mounted to the inter-stage skirts

• Constant thickness of 10cm

Masses of each are minor in comparison to entire rocket, but this causes small inaccuracies in calculations

SOLID

SOLID

S

Skirt

Skirt

Pressurant Tank

Oxidizer Tank

Payload, Avionics

Avionics

Avionics

LITVC

AAE 450 Spring 2008 4<#>

Backup Slides – References Krando Metal Products, http://www.krando.com/

Luminum, http://www.luminum.org/data/dtolaero.html

“Art, like morality, consists in drawing the line somewhere.” –G.K. Chesterton

AAE 450 Spring 2008 5<#>

Backup Slides – Thickness Tolerances for Aluminum

“The beautiful thing about learning is nobody can take it away from you.” – B.B. King

Thickness (meters)

 Tolerance +/-Greater Than Less Than

0.00014986 0.000254 0.0000254

0.000254 0.0004064 0.0000381

0.0004064 0.000635 0.0000381

0.000635 0.0008128 0.0000381

0.0008128 0.0009906 0.0000381

0.0009906 0.0011938 0.0000508

0.0011938 0.0016002 0.0000508

0.0016002 0.0020066 0.0000508

0.0020066 0.0024892 0.0000635

0.0024892 0.0032004 0.0000889

0.0032004 0.0040132 0.0001016

0.0040132 0.0050038 0.0001524

0.0050038 0.0062992 0.0002286

0.0062992 0.008001 0.0003048

0.008001 0.0100076 0.0004318

0.0100076 0.016002 0.0005842

0.016002 0.0249936 0.0007874

0.0249936 0.040005 0.0009906

0.040005 0.0599948 0.001397

0.0599948 0.08001 0.001905

0.08001 0.0999998 0.00254

0.0999998 0.1599946 0.003302

Space Grade

Non-Space GradeCredit: Molly Kane

AAE 450 Spring 2008 6<#>

Inertia Matrix Math Model

“If I’m not back in 5 minutes, wait longer.” – Ace Ventura

Calculates Ixx, Iyy, Izz at the center of mass of the launch vehicle

Assumes ALL products of inertia (ex. Ixy) equal to zero (vehicle is symmetric in radial directions)

Outputs values at different time steps.– First Stage: Full Propellant,

Empty Propellant– Second Stage: Full Propellant,

Empty Propellant– Third Stage: Full Propellant,

Empty Propellant

xx xy xz

xy yy yz

xz yz zz

I I I

I I I

I I I

AAE 450 Spring 2008 7<#>

Evolution of Inertia Code

PROP

PROP

PROP

SOLID

SOLID

S

Skirt

Skirt

Pressurant Tank

Oxidizer Tank

Payload

O

O

O

F

F

FSOLID

SOLID

S

Skirt

Skirt

Pressurant Tank

Oxidizer Tank

Payload, Avionics

Avionics

Avionics

LITVC

SOLID

SOLID

S

“That’s it man, game over man, game over!” – Bill Paxton in Aliens