AAE 450 Spring 2008

Jerald A. Balta3/27/2008

Propulsion Team/CADFinal Slides

AAE 450 Spring 2008

Balloon Cost Modifier Balloon Cost Items

– Balloon – Price quote from Aerostar International

– Helium – Priced at $4.87 per cubic meter– Gondola- Constant Price of $13205.30

200g case 1 kg case 5 kg caseBalloon 82,007.00 60,848.00 157,070.00Helium 14,813.00 10,644.00 32,979.00Gondola 13,205.30 13,205.30 13,205.30Total 110,025.30 84,697.30 203,254.30

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Balloon Cost

AAE 450 Spring 2008

Payload Mass(lbm

Payload Mass(kg Cost

500 226.8 $10,0002000 907.18 $30,0008000 3628.7 $100,000

0

20000

40000

60000

80000

100000

120000

0 1000 2000 3000 4000

Payload Mass (kg)

Cos

t (do

llar)

Cost Trend Equation y = -0.0011x2 + 30.62x +

3111.1 y= Cost x=Balloon Payload

Balloon Model

Free Body Diagram Two forces acting on

Spherical Balloon– Buoyancy Force

• Defined by difference between masses of lifting gas and air multiplied by gravitational constant

– Weight

Buoyancy

Weight

Derivation of Balloon Dimensions

Lifting Coefficient– Ρg is density of lifting

gas

– Ρa is density of air

Boyle’s and Guy Sac laws– Rho is density– P is pressure– T is Temperature

l a gC

l a gC l a gC

0

0 0

TP

P T

Derivation of Balloon Dimensions Continued Combine Equations to

determine lifting coefficient for different heights

Take into account 95% Gas purity and standard excess of 15% lifting gas

Final Equation for Volume of Gas in relation to Mass– V is Volume of lifting gas– M is total Mass

,00

*l lC C

,00

*l lC C

, ,00.85*0.95*l F lC C

, * * *l F TotalC V g M g

Gondola Costs•Structures Cost of $1205.30

•Material•Welding•Riveting

•Avionics Cost of $12000•One Battery•Sensors

Total Gondola Cost of $13,205.30

Provided by Sarah Shoemaker, Structures Group, and Avionics Group

Ground Support and Handling Cost Modifier Handling – Personnel required for handling

of fuels, toxic materials, etc Ground Support – Based on estimation of

salaries of necessary personnel– Assumed $100/hour salary– 6 engineers from all teams and one manager

Cost ModifierStage 1 200g case 1 kg case 5 kg caseHandling 2000 2000 2000Ground Support 14000 14000 14000Total 16000 16000 16000Stage 2Handling 8000 8000 8000Ground Support 14000 14000 14000Total 22000 22000 22000Stage 3Handling 8000 8000 8000Ground Support 14000 14000 14000Total 22000 22000 22000

References Defense Energy Support Center, “MISSILE FUELS STANDARD

PRICES EFFECTIVE 1 OCT 2007,” Aerospace Energy Reference, November 2007

Larson, W.J., Wertz, J.R., "Space Cost Modeling," Space Mission Analysis and Design, 2nd ed., Microcosm, Inc., California and Kluwer Academic Publishers, London, 1992, pp. 715-731.

Smith, Mike, Phone Conversation, Aerostar International, February 15, 2008

Tangren, C.D., "Air Calculating Payload for a Tethered Balloon System," Forest Service Research Note SE-298, U.S. Department of Agriculture - Southeastern Forest Experiment Station, Asheville, North Carolina, August 1980.