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AAE 450 Spring 2008
Propulsion Back-Up Slides
Propulsion
AAE 450 Spring 2008
Engine Performance Characteristics
Isp,vac
(s)Isp(s)
ChamberPressure
(Mpa)O/F
RatioC*
(m/s)Exit
Mach # Ae/At
Stage 1 352.3 337.6 2.1 6.0 1752.0 4.4 60
Stages 2,3 309.3 292.1 6.0 1.0 1480.0 4.1 60
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
Vehicle StagePropellantMass (kg)
PropellantCost ($)
PressurantMass (kg)
PressurantCost ($)
200 g
1 1462.0 $14,650 59.0 $29.50
2 566.6 $2,833 - -
3 37.3 $187 - -
Total 2065.9 $17,670 59.0 $29.50
1 kg
1 947.9 $9,500 38.2 $19.10
2 336.9 $1,685 - -
3 45.1 $226 - -
Total 1330.0 $11,410 38.2 $19.10
5 kg
1 4122.2 $41,320 166.3 $83.15
2 1009.2 $5,046 - -
3 38.4 $192 - -
Total 5169.8 $46,560 166.3 $83.15
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 %
Thrust,vac (N) Thrust,sl (N) % Diff Thrust
200 g 34050 26100 23.36%
1 kg 21440 16440 23.33%
5 kg 75070 57670 23.19%
Prop Mass and Fraction Per Stage
Mass Prop (kg) Mass Stage (kg) Prop Mass Fraction Per Stage
200 g
Stage 1 1462 1811 80.71%
Stage 2 567 720 78.69%
Stage 3 37 52 71.57%
1 kg
Stage 1 948 1045 90.71%
Stage 2 337 368 91.66%
Stage 3 45 51 88.50%
5 kg
Stage 1 4123 4530 91.01%
Stage 2 1009 1100 91.75%
Stage 3 38 43 88.40%
Payload Mass and Fractions
MassPayload
Third StageMass (kg)
Payload MassFraction
Stage 3 (kg) Total Mass (kg)Payload Mass Fraction Total
0.2 52.06 0.38% 2584 0.01%
1 50.95 1.96% 1463 0.07%
5 43.41 11.52% 5674 0.09%
Stage Mass and Allocation Mass Stage (kg) Mass Allocation Per Stage
200 g
Stage 1 1811 70.11%
Stage 2 720 27.87%
Stage 3 52 2.02%
1 kg
Stage 1 1045 71.40%
Stage 2 368 25.12%
Stage 3 51 3.48%
5 kg
Stage 1 4530 79.85%
Stage 2 1100 19.39%
Stage 3 43 0.77%
Percent Delta V BreakdownStage Delta V Percentage
200 g
Stage 1 35.00%
Stage 2 35.00%
Stage 3 30.00%
1 kg
Stage 1 35.00%
Stage 2 30.00%
Stage 3 35.00%
5 kg
Stage 1 40.00%
Stage 2 35.00%
Stage 3 25.00%
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 2008Propulsion – 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 0.0030Exit 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
1
3injection burnt t
*prop side injectionm m t
AAE 450 Spring 2008
Ideal Mass Ratios
Propulsion Team
Stage # Bellerophon (1 kg) Saturn V Pegasus
1 3.467 3.490 2.817
2 2.749 2.636 2.685
3 1.945 1.805 2.171
4 -- -- 1.186
Mass Ratio Comparison (1 kg case)Stage # Ideal Actual
1 3.467 2.343
2 2.749 3.155
3 1.945 3.216
ii
ii
bo
i
c
c
m
m
i
10
3
1
lni
iicV
props
si mm
m
gIc 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 DesignHelium – Priced at $4.87 per cubic meter of gasBalloon – Price quote from Aerostar InternationalGondola- 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
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
– Mtotal is total mass
,00
*l lC C
, ,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 2008Propulsion
Lift
Weight
DVertical 0 1000 2000 3000 4000 5000 60004.5
5
5.5
6
6.5
7Change in Reynolds Number over time
Time (s)
log1
0(Re
)
0 1000 2000 3000 4000 5000 60000
1000
2000
3000
4000Change in balloon drag over time
Time (s)
Drag
(N)
0 1000 2000 3000 4000 5000 60000
0.01
0.02
0.03
0.04
0.05Change in balloon acceleration over time
Time (s)
Acce
lera
tion
(m/s
2 )
Determination of rise timeAssumptions• 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
Forc
e (N
ewto
ns)
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)
Diam
eter
of B
allo
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)
Velo
city
(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 cases https://engineering.purdue.edu/AAE/Academics/Courses/aae450/2008/spring/large/3_5kg/v125/5kg_MAT_out_v125.txt
AAE 450 Spring 2008