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Project Bellerophon 1

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Trajectory - Steering Law

• Function of time • Defines the orientation of the launch

vehicle

b

br

2e

3e

1e


Model Analysis

5,616 possible combinations for each payload

… …

Launch Vehicle

Stage 1 Stage 2 Stage 3 Launch Method

Material Propellant

Ground

Aircraft

BalloonCryogenic

Storable

Hybrid

Solid

Aluminum

Steel

Titanium


Historical Catastrophic Risk

Number ofLaunches

Success of Previous10 Launches

10 60.00 %20 80.00 %30 100.00 % s

Number of Launches Success RateLess than 12 60.00 %Less than 24 80.00 %24 or greater 93.84 %

Pegasus

Our Vehicles


Aircraft Steering Law – Parameter Optimization

tb2

25% tb2

25% tb2

Ψmid1=5 deg

Ψmid2=0 deg

Ψe2

To be optimized

tclimb

1st Stage: tangent law

2nd Stage: 3 linear sections


Definition of Eccentricity

• e = c/a

a: Semi-Major Axis

b:

Sem

i-M

inor

Axis

c: center to focus


Risk Assessment - Non-Catastrophic FailureMonte Carlo Histograms - 200g Payload

200g Periapsis Altitude Histogram; std = 21.803 km, mean = 437.44 km

200g Eccentricity Histogram; std = 0.0467, mean = 0.438


Risk Assessment - Non-Catastrophic FailureMonte Carlo Histograms - 1kg Payload

1kg Periapsis Altitude Histogram; std = 15.774 km, mean = 367.727 km

1kg Eccentricity Histogram; std = 0.041094, mean = 0.173289


Risk Assessment - Non-Catastrophic FailureMonte Carlo Histograms - 5kg Payload

5kg Periapsis Altitude Histogram; std = 20.215 km, mean = 516.546 km

5kg Eccentricity Histogram; std = 0.050, mean = 0.445


Performance Characteristics - 200 g Payload

BALLOON STRUCTURE GONDOLA STRUCTUREFeatures FeaturesMinimum volume: 3237.7 m3 Dimensions: 0.876[3] x 0.876[3] x 3.346[4] m3

Maximum volume: 279,950 m3 Material: Aluminum Minimum diameter: 18.3547 m Thickness: 0.04 mMaximum diameter: 81.1635 m Weight: 177.188 kg

Material: Polyethylene plastic film PROPULSIONGas used: Helium FeaturesShape: Spherical Propellant type:

STRUCTURES Stage 1 H2O2 & HTPBFeatures Stage 2 HTPB/AP/Al & H2O2

[5]

Length: Stage 3 HTPB/AP/AL Stage 1 4.9929 m Propellant amount: Stage 2 1.7678 m Stage 1 1462.00 kg Stage 3 0.9874 m Stage 2 566.64 kgDiameter: Stage 3 37.26 kg Stage 1 1.3015 m Engine type: Stage 2 0.6741 m Stage 1 Hybrid Stage 3 0.2721 m Stage 2 SolidInert mass: [1] Stage 3 Solid Stage 1 349.477 kg Thrust: Stage 2 153.4559 kg Stage 1 34045.3 N Stage 3 14.8011 kg Stage 2 8782.6 NMaterial: Stage 3 625 N Stage 1 Al ISP: Stage 2 Al Stage 1 352.3 seconds Stage 3 Al Stage 2 309.3 secondsThickness: [2] Stage 3 309.3 seconds Stage 1 0.0037 m Expansion ratio: Stage 2 0.0055 m Stage 1 60 Stage 3 0.0022 m Stage 2 60

AVIONICS Stage 3 60

Features NOTESMass: 1. Inert masses include tank, skirt, and nose cone masses. Stage 1 6.024 kg 2. Thickness values pertain to the fuel tanks. Stage 2 30.2664 kg 3. Gondola square base width and length. Stage 3 1.2 kg 4. Gondola height.Total system power: 200 Watts 5. Used for LITVC.


Performance Characteristics - 1 kg Payload

BALLOON STRUCTURE GONDOLA STRUCTUREFeatures FeaturesMinimum volume: 2,197.9 m3 Dimensions: 1[3]x1[3]x3.849[4] m3

Maximum volume: 190,040 m3 Material: AluminumMinimum diameter: 16.1312 m Thickness: 0.04 mMaximum diameter: 71.3312 m Weight: 227.114 kg

Material: Polyethylene plastic film PROPULSIONGas used: Helium FeaturesShape: Spherical Propellant type:

STRUCTURES Stage 1 H2O2 & HTPBFeatures Stage 2 HTPB/AP/Al & H2O2

[5]

Length: Stage 3 HTPB/AP/Al Stage 1 4.1555 m Propellant amount: Stage 2 1.4816 m Stage 1 947.9 kg Stage 3 1.0554 m Stage 2 336.92 kgDiameter: Stage 3 45.09 kg Stage 1 1.1264 m Engine type: Stage 2 0.5669 m Stage 1 Hybrid Stage 3 0.2900 m Stage 2 SolidInert Mass: [1] Stage 3 Solid Stage 1 97.0893 kg Thrust: Stage 2 30.6403 kg Stage 1 21435.5 N Stage 3 5.8567 kg Stage 2 6052.4 NMaterial: Stage 3 743.4 N Stage 1 Al ISP: Stage 2 Al Stage 1 352.3 seconds Stage 3 Al Stage 2 309.3 secondsThickness: [2] Stage 3 309.3 seconds Stage 1 0.0032 m Expansion ratio: Stage 2 0.0046 m Stage 1 60 Stage 3 0.0024 m Stage 2 60

AVIONICS Stage 3 60

Features NOTESMass: 1. Inert masses include tank, skirt, and nose cone masses. Stage 1 6.024 kg 2. Thickness values pertain to the fuel tanks. Stage 2 30.2664 kg 3. Gondola square base width and length. Stage 3 1.2 kg 4. Gondola height.Total system power: 200 Watts 5. Used for LITVC.


Performance Characteristics - 5 kg Payload


200 g Failure


1 kg Failure


John Tsohas’ Table200 g Payload

Stage mprop/(mi+mprop) V/stage mstage/GLOM Isp

1 80.7% 3,808 m/s (32%) 70.11% 352.2s

2 78.69% 4,358 m/s (37%) 27.87% 309.3s

3 71.57% 3,740 m/s (31%) 2.02% 309.3s

1 kg Payload

1 77.11% 3,818 m/s (39%) 70.48% 352.2s

2 74.3% 3,211 m/s (32%) 25.97% 309.3s

3 72.7% 2,864 m/s (29%) 3.55% 309.3s

5 kg Payload

1 83% 3,211 m/s (32%) 78.95% 352.2s

2 79.44% 3,963 m/s (39%) 20.2% 309.3s

3 71.76% 2,978 m/s (29%) 0.85% 309.3s

Saturn V

Stage mprop/(mi+mprop) V/stage mstage/GLOM Isp

1 94.09% 75.83% 265-310s

2 92.04% 16.28% 421s

3 44.81% 7.89% 421s

Ariane 5 ECA

1 86.28% 71.81% 250-275s

2 93.17% 24.00% 434s

3 44.31% 4.19% 446s


John Tsohas’ Table II

PayloadProp mass fraction – 3rd stage Payload mass fraction Payload mass fraction (3rd

Stage)

200 g 0.0038 0.0077% 0.38%

1 kg 0.016 0.05733% 1.64%

5 kg 0.0935 0.07949% 9.35%

VehicleProp mass fraction – 3rd stage Payload mass fraction Payload mass fraction (3rd

Stage)

Saturn V 0.0354 3.91% 49.6%

Ariane 4 0.0186 2.06% 1.64%

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