AAE 450 Spring 2008

Propulsion Back-Up Slides

Propulsion

AAE 450 Spring 2008

Engine Performance Characteristics

604.11480.01.06.0292.1309.3Stages 2,3

604.41752.06.02.1337.6352.3Stage 1

Ae/AtExit

Mach #C*

(m/s)O/F

Ratio

ChamberPressure

(Mpa)Isp(s)

Isp,vac

(s)

Propulsion

AAE 450 Spring 2008

Propellant and Pressurant Cost� Propellant

– Stage 1 -Hydrogen Peroxide and HTPB

– Stage 2,3 -AP/HTPB/Al

� Pressurant– Nitrogen– 12 MPa– 1st Stage Only

Propulsion

$83.15166.3$46,5605169.8Total

--$19238.43

--$5,0461009.22

$83.15166.3$41,3204122.21

5 kg

$19.1038.2$11,4101330.0Total

--$22645.13

--$1,685336.92

$19.1038.2$9,500947.91

1 kg

$29.5059.0$17,6702065.9Total

--$18737.33

--$2,833566.62

$29.5059.0$14,6501462.01

200 g

PressurantCost ($)

PressurantMass (kg)

PropellantCost ($)

PropellantMass (kg)StageVehicle

Mixture Ratio OptimizationO/FHybrid ~ 6 Hybrid – H2O2/HTPB

Pressure vs. Pump

Table A.9.2.3.1 Cost of Turbopumps 3

Number of Turbopumps Purchased

Minimum Cost per Pump

Maximum Cost per Pump

3-15 $300,000 $500,000 15-20 $100,000 $150,000

Table A.9.2.3.1 Pressurant Mass and Cost per Launch Vehicle

Payload Pressurant Mass (kg)

Pressurant Cost ($)

200 g 59.0 $29.50 1 kg 38.2 $19.10 5 kg 166.3 $83.15

Top Twelve PropellantsTable A.4.2.2.4.1 Propellant Specific Impulses

Propellant Specific Impulse (Isp) Units Liquid Oxygen / Liquid Hydrogen (cryo) 380 1 Seconds Liquid Oxygen / RP – 1 (cryo) 291 1 Seconds Liquid Oxygen / Hydrazine (cryo) 300 1 Seconds Hydrogen Peroxide / Hydrazine (storable) 282 1 Seconds Hydrogen Peroxide / RP – 1 (storable) 267 1 Seconds Nitrogen Tetroxide / RP – 1 (storable) 267 1 Seconds Hydrogen Peroxide / HTPB (hybrid, storable) 268 2 Seconds Nitrogen Tetroxide / HTPB (hybrid, storable) 270 2 Seconds Hydrogen Peroxide / GAP (hybrid, storable) 256 2 Seconds DB/AP-HMX/Al (solid) 265 3 Seconds HTPB/AP/Al (solid) 260 3 Seconds DB/AP/Al (solid) 260 3 Seconds

Footnotes: All specific impulses are at sea level conditions, these are not Isps used, these were used to aid in propellant selection (see thermo chemistry A.4.2.2.5 for more information)

Change in Performance� Min Alt. for no separation – 21,900 m� Separation Ae/At = 3.25� Isp,v = 283.1� Isp, sl = 245.3� % Diff Isp From Launch Alt = 16 %

23.19%57670750705 kg

23.33%16440214401 kg

23.36%2610034050200 g

% Diff ThrustThrust,sl (N)Thrust,vac (N)

Prop Mass and Fraction Per Stage

88.40%4338Stage 3

91.75%11001009Stage 2

91.01%45304123Stage 1

5 kg

88.50%5145Stage 3

91.66%368337Stage 2

90.71%1045948Stage 1

1 kg

71.57%5237Stage 3

78.69%720567Stage 2

80.71%18111462Stage 1

200 g

Prop Mass Fraction Per StageMass Stage (kg)Mass Prop (kg)

Payload Mass and Fractions

0.09%567411.52%43.415

0.07%14631.96%50.951

0.01%25840.38%52.060.2

Payload Mass Fraction TotalTotal Mass (kg)

Payload MassFraction

Stage 3 (kg)Third StageMass (kg)

MassPayload

Stage Mass and Allocation

0.77%43Stage 3

19.39%1100Stage 2

79.85%4530Stage 1

5 kg

3.48%51Stage 3

25.12%368Stage 2

71.40%1045Stage 1

1 kg

2.02%52Stage 3

27.87%720Stage 2

70.11%1811Stage 1

200 g

Mass Allocation Per StageMass Stage (kg)

Percent Delta V Breakdown

25.00%Stage 3

35.00%Stage 2

40.00%Stage 1

5 kg

35.00%Stage 3

30.00%Stage 2

35.00%Stage 1

1 kg

30.00%Stage 3

35.00%Stage 2

35.00%Stage 1

200 g

Delta V PercentageStage

12<#>

Engine Sizing� The amount of propellant required for each

rocket/stage was determined in Model Analysis

� Inert mass fraction, finert, was optimized between the structures and propulsion groups for final design

)1(

)1)(1)((

MRf

fMRmmm

inert

inertavionicspayp −

−−+=

13<#>

Engine Cost� Cost of Engines calculated from equations

based on mass flow, thrust, and dry weight� Cost equations are extrapolated from

historical valuesPayload 1st Stage

Engine Cost2nd Stage

Engine Cost3rd Stage

Engine CostTotal Engine

Cost

200g $679,720 $263,690 $79,930 $1,023,340

1kg $634,090 $209,930 $86,860 $930,880

5kg $1,138,700 $339,700 $80,900 $1,559,300

14<#>

Historical Failure Probability� U.S. Solid Rocket Systems (Failures/Attempts)

– 6 / 412 (1.4%) Failures between 1980-20041

– 19 / 3382 (0.56%) Failures between 1964-19982

� Solid Propulsion Failure Rates (Failures/Attempts)

– Upper Stage 0.0161 161/10000

– Monolithic 0.0025 25/10000

– Segmented 0.0077 77/10000

– Total 0.0056 56/10000

AAE 450 Spring 2008

Propulsion – Propellants

Engine Performance Characteristics

AAE 450 Spring 2008

200g Launch Vehicle Stage 1 Stage 2 Stage 3

Vacuum Thrust [N] 34,045 8,783 625.0Mass Flow [kg/s] 10.69 2.738 0.1942Burn time [s] 136.8 207.7 191.9Propellant Mass [kg] 1,462 566.6 37.26Exit Area [m^2] 0.5430 0.0400 0.0030

Exit Pressure [Pa] 2,821 11,454 11,454Nozzle Length [m] 1.704 0.4645 0.1239Engine mass [kg] 96.94 51.53 8.40Pressure of ox, fuel tanks [MPa] 2.07 6.00 6.00

Engine Performance Characteristics

AAE 450 Spring 2008

1 kg Launch Vehicle Stage 1 Stage 2 Stage 3

Vacuum Thrust [N] 21,436 6,052 743.4

Mass Flow [kg/s] 6.730 1.880 0.2310

Burn time [s] 140.8 179.2 195.3

Propellant Mass [kg] 947.9 336.9 45.09

Exit Area [m^2] 0.3422 0.0278 0.00340

Exit Pressure [Pa] 2,821 11,454 11,454

Nozzle Length [m] 1.352 0.3856 0.1352

Engine mass [kg] 72.62 36.44 9.534

Pressure of ox, fuel tanks [MPa] 2.07 6.00 6.00

Engine Performance Characteristics

AAE 450 Spring 2008

5 kg Launch Vehicle Stage 1 Stage 2 Stage 3

Vacuum Thrust [N] 75,073 15,257 692.4

Mass Flow [kg/s] 23.57 4.74 0.22

Burn time [s] 174.9 213.0 178.4

Propellant Mass [kg] 4,123 1,009 38.37

Exit Area [m^2] 1.198 0.0700 0.0030

Exit Pressure [Pa] 2,821 11,454 11,454

Nozzle Length [m] 2.530 0.6122 0.1304

Engine mass [kg] 193.5 75.72 8.560

Pressure of ox, fuel tanks [MPa] 2.07 6.00 6.00

AAE 450 Spring 2008

Propulsion

Hybrid and Solid Standard DeviationsHybrid Propellant

Solid Propellant Liquid Propellant Hybrid Propellant

Mass of Propellant

0.12 % 0.734 % 0.854 %

Mass flow rate 1.0 % 0.4923 % 1.4923 %

For hybrid propellants, we cannot find historical standard deviations. The two percent deviations for liquid and solid propellant are added together to calculate a hybrid propellant percent standard deviation.

Percent Deviations for Each Propellant Type

AAE 450 Spring 2008

LITVC� 1st and 2nd stage control

� 4 valves per stage for perpendicular to centerline injection of H2O2

� 1st stage tap-off of main H2O2 tank

� 2nd stage bring own H2O2 pressurized tank

� Considered main part of engine for weight/cost due to low complexity

� Costs include:

– 4 valves per stage @ $100/valve

– Extra propellant

– Extra tank on 2nd stage

Propulsion

AAE 450 Spring 2008

LITVC Calculations

0.8*side mainF F=

� Input– Thrust (vac)– Mass Flow rate– Stage Burn Time

� Calculations

Propulsion

Image courtesy E. Glenn Case IV1

0.8*side mainF F=

0.9*side mainm m=ɺ ɺ

1

3injection burnt t=

*prop side injectionm m t= ɺ

AAE 450 Spring 2008

Ideal Mass Ratios

Propulsion Team

1.186----4

2.1711.8051.9453

2.6852.6362.7492

2.8173.4903.4671

PegasusSaturn VBellerophon (1 kg)Stage #

Mass Ratio Comparison (1 kg case)

3.2161.9453

3.1552.7492

2.3433.4671

ActualIdealStage #

ii

ii

bo

i

c

c

m

m

iβλλµ +== 10

( )∑=

=∆3

1

lni

iicV µ

props

si mm

m

+=βgIc spi ⋅=

AAE 450 Spring 2008

References� Heister, Stephen D.� Humble, R. W., Henry, G. N., Larson, W. J., Space Propulsion Analysis and

Design, McGraw-Hill, New York, NY, 1995.� Javorsek, D., and Longuski, J.M., “Velocity Pointing Errors Associated with

Spinning Thrusting Spacecraft,”Journal of Spacecraft and Rockets, Vol. 37, No. 3, 2000, pp. 359-360.

� Klaurans, B. “The Vanguard Satellite Launching Vehicle,” The Martin Company. No. 11022, April 1964.

� Knauber, R.N., “Thrust Misalignments of Fixed-Nozzle Solid Rocket Motors,”Journal of Spacecraft and Rockets, Vol. 33, No. 6, 1996, pp. 794-799.

� Sutton, George P., Biblarz, Oscar “Solid Propellants,” Rocket Propulsion Elements, 7th ed., Wiley, New York, 2001.

� Ventura, M., “The Lowest Cost Rocket Propulsion System,” General Kinetics Inc, Huntington Beach, CA, Jul. 2006.

� Tsohas, John.

Propulsion

AAE 450 Spring 2008

Balloon Design

Helium – Priced at $4.87 per cubic meter of gas

Balloon – Price quote from Aerostar International

Gondola- Constant Price of $13,200

200g case 1 kg case 5 kg caseBalloon $82,000 $60,800 $157,000Helium $14,800 $10,600 $33,000Gondola $13,200 $13,200 $13,200Total $110,000 $84,600 $203,200

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 Gay Lussac’s laws– Rho is density– P is pressure– T is Temperature

l a gC ρ ρ= −

l a gC ρ ρ= −l a gC ρ ρ= −

0

0 0

TP

P T

ρρ

=

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– Mtotal is total mass

,00

*l lC Cρρ

=

, ,00.85*0.95*l F lC C=

, * * *l F TotalC V g M g=

Balloon Cost

AAE 450 Spring 2008

Payload Mass(lbm)

Payload Mass(kg) Cost

500 230 $10,0002000 910 $30,0008000 3600 $100,000

0

20000

40000

60000

80000

100000

120000

0 1000 2000 3000 4000

Payload Mass (kg)

Co

st (

do

llar)

Cost Trend Equation� Y = -0.0011X2 + 30.62X +

3111.1� Y = Cost� X = Balloon Payload

Gondola Costs

•Structures Cost of $1,200•Material•Welding

•Riveting

•Avionics Cost of $12,000•One Battery•Sensors

�Total Gondola Cost of $13,200

Provided by Sarah Shoemaker, Structures Group, and Avionics Group

AAE 450 Spring 2008

Propulsion

Lift

Weight

DVertical0 1000 2000 3000 4000 5000 6000

4.5

5

5.5

6

6.5

7

Change in Reynolds Number over time

Time (s)

log

10

(Re

)

0 1000 2000 3000 4000 5000 60000

1000

2000

3000

4000

Change in balloon drag over time

Time (s)

Dra

g (

N)

0 1000 2000 3000 4000 5000 60000

0.01

0.02

0.03

0.04

0.05

Change in balloon acceleration over time

Time (s)

Acc

ele

rati

on

(m

/s2)

Determination of rise time

Assumptions• Constant sphere• Constant CD = 0.2• Barometric formula• Kinematic viscosity variation with temperature• Constant acceleration over time steps of 1 second

DHorizontal

0 0.5 1 1.5 2 2.5 3

x 104

2.95

3

3.05

3.1

3.15

3.2

3.25

3.3

3.35x 10

4

Altitude (meter)

Lift

ing

Fo

rce

(N

ew

ton

s)Lifting Force of the Balloon

Thanks to Jerald Balta for modifying the balloon code to output this.

0 0.5 1 1.5 2 2.5 3

x 104

10

20

30

40

50

60

70

80

90

Altitude (meter)

Dia

me

ter

of

Ba

llo

on

(m

)Change in diameter with altitude

Thanks to Jerald Balta for modifying the balloon code to output this.

0 1000 2000 3000 4000 5000 60000

2

4

6

8

10

12

14

16

18

20Change in balloon velocity over time

Time (s)

Ve

loci

ty (

m/s

)

X: 5741Y: 19.7

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

– Six engineers and one project manager

Cost ModifierStage 1 200g case 1 kg case 5 kg caseHandling $2,000 $2,000 $2,000Ground Support $14,000 $14,000 $14,000Total $16,000 $16,000 $16,000Stage 2Handling $8,000 $8,000 $8,000Ground Support $14,000 $14,000 $14,000Total $22,000 $22,000 $22,000Stage 3Handling $8,000 $8,000 $8,000Ground Support $14,000 $14,000 $14,000Total $22,000 $22,000 $22,000Overall $60,000 $60,000 $60,000

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.

Nozzle (specs and CAD)

� Conical Nozzle – 12°Conical Nozzle– Conical because of solid and

hybrid propellants.– All stages have same nozzle

� Sizing– Nozzle Dimensions based off of

the exit area from MAT output– ε = 60; Throat Area and Throat

Diameter are determined.

Case Dthroat

(m)

Dexit

(m)

Athroat(m^2)

Aexit

(m^2)

Dstage

(m)

5 kg

Stage 1 0.159 1.235 0.0200 1.198 1.839

Stage 2 0.0039 0.299 0.0017 0.070 0.817

Stage 3 0.008 0.0618 0.00005 0.003 0.275

1 kg

Stage 1 0.085 0.660 0.0057 0.342 1.126

Stage 2 0.024 0.189 0.00047 0.028 0.567

Stage 3 0.008 0.062 0.00005 0.003 0.290

200 g

Stage 1 0.107 0.831 0.00905 0.543 1.302

Stage 2 0.029 0.226 0.00067 0.04 0.674

Stage 3 0.008 0.062 0.00005 0.003 0.272

Nozzle Dimensions per stage (Metric & English units)

Test Facilities

• Purdue (Zucrow High Pressure Laboratories)� Propellants/ Oxidizers currently tested: H2O2, Liquid Hydrocarbon, LOX� For Hybrid test we need H2O2, and (excluding 5 kg Stage1) all other engines

can be tested at Purdue.� Table below shows Zucrow’s HPL capabilities.

� Kelly Space and Technology � Up to 20,000 lbf (88,960 N) thrust stand capabilities.� Propellant tanks and data acquisition systems already at test site.� Located in San Bernardino, CA.� Can test our 5 kg: stage 1 engine at 75,073 Newtons of thrust.

Maximum Capability

Value Units

Thrust 44,480 N

Chamber Pressure 4.137 MPa

Mass Flow Rate 6.803 kg/s

References

� 1 Scott Meyer, private meeting at Zucrow Test Laboratories. February 8th, 2008. Test facility overview and private tour of the large rocket test stand.

� 2 Kelly Space and Technology. Jet and Rocket Engine Test Site (JRETS) URL: http://www.kellyspace.com/ [last updated Jan. 31st 2008].

� 3 MAT Output file from AAE 450 course website. 5kg, 1kg, and 200 g caseshttps://engineering.purdue.edu/AAE/Academics/Courses/aae450/2008/spring/large/3_5kg/v125/5kg_MAT_out_v125.txt

AAE 450 Spring 2008