Mission Design Requirements

First priority is to deliver takeoff mass to aircraft team.

Deliver 5kg item to ISS

24 hour launch lead time

Vehicle must be launched from below or inside carrier aircraft

Propellants cannot be toxic.

Upper stage must have good orbital insertion accuracy

Vehicle must use off-the-shelf rocket motors

Desirable Booster Characteristics

Minimum takeoff mass

Restart-capable upper stage motor

Simple and reliable upper-stage motor

High Isp upper stage motor

Minimum number of stages

One rocket motor per stage

Minimize G-Forces seen by payload

Preliminary Booster Calculations

•Created Excel Spreadsheet•Database of rocket motors from trade studies•Losses neglected:

•Gravity•Drag

•Calculates:• V produced by each stage• upper stage structural mass• booster takeoff mass• Max G-Force during launch

•Input Variables:• Stage Specifications• Payload Mass

Booster Calculatormp1 me1 mp2 me2 mp3 me3 mpl T1 T2 T3 Isp1 Isp2 Isp3

3923 416 1286 98 310 80.20679 40 170000 80000 33300 260 293 330

1st Stage: ATK Orion 50XLmb01 2230.207 R1 2.816297 2nd Stage: ATK Star 31m01 6153.207 R2 4.495047 3rd Stage: SpaceX Kestrel 2 (Would like lighter, slightly smaller engine with similar ISP, but suffi cient)mb02 528.2068 R3 7.890381 (Pump fed would reduce weight of upper stage structure, but add compexity)m02 1814.207 Need very light structure for 2nd stage (85kg including 52kg engine)mb03 120.2068 Stage 3 G-Forces reduced by throttlingm03 430.2068 G-Force at Stage Burnout Total system mass at launch: 6153.207 kgdv1 2011.145 1 7.770246dv2 3093.411 2 15.43892dv3 3832.083 3 28.2388

delta v 8936.64 Adding more liquid fuel reduces max g-forces SpaceX tanks: 3385kg of propellant Propellant mass fraction of 3nd stageIncreasing payload mass reduces max g-forces Empty stage 2: 360kg 0.794451Stage 1 burnout g-force closer to 5.5g Our estimated stage 2 mass: 28.20679 kg (not ideal because motor slightly oversized, pressure fed tanks heavy)

Not including engine (SpaceX gets 0.91 with same engine on Falcon 1)

Biggest problem for second stage is lack of small liquid motors of high Isp in production)Upcoming LOX-Methane motors hold biggest potential by boosing Isp to 350Given current limitations, desired change would be to get increased payload requirements, to allow bigger 1st stage)

Propellant Density (kg/m3) We get lower launch mass with solid upper stage, but need liquid for ISS maneuver due to restart requirements.

Kerosene 806LOX 1140 Tank pressure: 1.17 Mpa

Oxidizer to fuel ratio for 2nd stage: 2.35 Volume of tanks: Total Tank Mass: 4.875 kgHelium m3 Helium 1 kg composite

Mass of liquid oxygen: 217.4627 kg LOX 0.190757 m3 LOX 2.718284 kg alloy/compositeMass of Kerosene: 92.53731 kg Kerosene 0.114811 m3 Kerosene 1.156716 kg composite

Must study anti-slosh baffl es for LOX tank, as SpaceX had issue with propellant sloshing with 2nd Falcon I launch. Remaining 3rd stage mass budget23.33179 kg

Assumes 1 spherical tankTank RadiusHelium m

Tank material for LOX-Kerosene: Aluminum-Lithium Al 2135 LOX 0.357109 mKerosene 0.30151 m

Solid Rocket Motorstrade study

Star 26B Thiokol 261 23 272 0.66 64,731 34.6 0.91Star 26C Thiokol 264 32 272 0.66 63,389 35Star 30E Thiokol 667 45 291 182,216 35.4 0.88Star 37FM Thiokol 1147 81 290 0.93 311,041 47.9 0.932Star 48B Thiokol 2137 126 286 1.25 591,142 66 0.929Star 48Bs Thiokol 2134 124 286 1.24 578,401 77.109 0.939Star 48A s Thiokol 2574 144 283 1.24 693,030 77.109 0.942Star 31 Thiokol 1384 98 294 0.76 380,883 80 0.929Star 63D Thiokol 3499 248 283 1.6 921,828 84.7 0.929Star 63F Thiokol 4590 326 297 1.6 1,277,319 104.6 0.929Perigee Orbit Transfer MotorFourth Academy4635 496 280 1.4 222.8 0.929Star 75 Thiokol 8068 565 288 1.91 2,174,539 242.8 0.93MIHT Russian 6000 1000 220 1.5 245.2SR-19 Aerojet 7032 795 288 1.33 267.7Zefiro 9 Fiat-Avio 11100 1000 294 1.9 313Castor 4BXLThiokol 11482 1513 267 1.02 429Algol 3A United Technologies14732 2030 259 1.14 464.7 0.868MIHT-2 Russian 13000 1500 280 1.55 490.3RSA 3-2 South Africa 10971 1771 284 1.3 519Castor 4AXLThiokol 14851 1723 269 1.02 599.8LK 1 IAI 13990 1240 272 1.35 774Pegasus Orion 50XLATK 4350 420 289 1.28 196.4 0.904

Liquid Rocket Motors• 2 separated tanks• Can be stopped or restarted• High specific impulse• 3 types• RP-1 widely used for first stages such as Saturn V and Atlas V

- Temperature of Combustion: 3,670 deg K. - Isp (sl): 300. - Fuel Density: 0.806 g/cc. - Fuel Freezing Point: -73 deg C. - Fuel Boiling Point: 147 deg C - Oxidiser Density: 1.140 g/cc. - Oxidiser Freezing Point: -219 deg C. - Oxidiser Boiling Point: -183 deg C.

7

Upper Stage Motors• Desired variable thrust, engine restart capability• Compared hybrid and liquid rocket motors

– Hybrids quickly eliminated due to lower Isp, high structural mass, and poor commercial availability

• For system simplicity/reliability, pressure-fed liquid motor deemed desirable.

• Results of liquid motor trade study led to:– SpaceX Kestrel 2 upper stage rocket motor– Currently used as upper stage for SpaceX Falcon I booster– Pressure-fed LOX-RP1 rocket motor– 52kg motor and nozzle– Isp of 330s– Flight-proven design– Currently in serial production

Rocket Motor DatabaseUpper Stage liquid motors (3rd stage)Motor Fuel Country Thrust Isp Engine Mass Pressure source Propellant Mass FractionHM10 Lox-LH2 France 61.8kN 443 145kg pump Very cryogenicRD-161P H202-Kerosene Russia 24.5kN 319 105kg pump Non-cryogenicLR101-11 Lox-Kerosene USA 5.3kN 246 22kg pump Cryogenic oxidizerKestrel 2 Lox-Kerosene USA 33.3kN 330 52kg Pressure Cryogenic oxidizer 1.67m nozzle diameter, Oxidizer/fuel ratio 2.35, Chamber pressure 930kpaLunar ATK Lox-Methane USA 16.7kN 355 30kg Pump Cryogenic propellant and oxidizer In Development for lunar ascent vehicleXR-5M15 Lox-Methane USA 35.7kN 355 50kg Pump Cryogenic propellant and oxidizer In Development for lunar ascent vehicleS5.92 N204-UDMH Russia 19.6kN 327 75kg Pump Hypergolic--toxic propellantsS5.98M N204-UDMH Russia 19.6kN 326 95kg Pump Hypergolic--toxic propellantsRD-680 N204-UDMH Ukraine 5.6kN 320 30kg Pump Hypergolic--toxic propellants

XLR-132 N204-MMH USA 16.7kN 328 54kg Pump Hypergolic--toxic propellants Out of production

Upper Stage solid motors (2nd Stage) Empty PropellantStar 17 solid USA 19.6kN 286 7 72 0.881M-V-4 solid Japan 52.0kN 298 118 1312 0.917483Star 37FM solid USA 47.9kN 290 81 1066 0.929 Diameter: 0.933m, 1.676m long, 63s burnStar 30E solid USA 35.4kN 291 45 622 0.932Star 30BP solid USA 27.0kN 292 38 505 0.931Orion 38 solid USA 36.0kN 287 108 770 0.876993Orion 50 solid USA 118.2kN 290 345 3370 0.907133Star 37 solid USA 43.5kN 260 63 558 0.898551 Diameter 0.66m, 0.84m longStar 37XFPsolid USA 31.5kN 290 71 884 0.925654 Diameter 0.93m, 1.52m long

1st stage solid motorsATK Orion 50XL USA 170kN 260 416 3923 0.904125 Diameter: 1.28m, 3.11m long, 69.8s burn, +- 5 degree vector control, 33.86 expansion ratio, 121kg nozzle, 0.8465m diameter nozzle, non-constant thrust profile, max thrust 195kN, average is 170kNFiat-Avio Zefiro 9 Italy 300kN 260 1000 10100 0.90991Nissan M-3B-J Japan 132kN 260 300 3300 0.916667 In development--not yet in productionMIHT-3 Russia 245.2kN 255 1000 5000 0.833333ATK Star 48B USA 66.0kN 255 126 2011 0.941039 Diameter: 1.245m, TE-M-711, 84s burnNissan M-129A Japan 77.5kN 260 360 1840 0.836364ATK Star 31 USA 80kN 262 98 1286 0.929191 Diameter: 0.762m, TE-M-762, Antares III, 2.9m long, including nozzle, 46s burn, flown 1979-1994, isp=293 if used as second stage, max thrust 105kN, average 80kN, almost flat thrust profile, 58 expansion ratio, 0.71675m nozzle diamaterTX-354-3 USA/Japan 258.9kN 262 695 3729 0.842902Nissan M34 Japan 294.2kN 264 1000 11000 0.916667Nissan M33-20-4 USA 268.6kN 247 535 3317 0.861111ATK Castor 1 USA 237.2kN 260 664 3692 0.847567X-259 USA 74.0kN 250 300 1100 0.785714Aerotek M56A-1 USA 228.5kN 260 466 4704 0.909865 Out of production

Booster Design• 3 stage Booster

– 1st stage: ATK Orion 50XL (Solid)– 2nd stage: ATK Star 31 (Solid)– 3rd stage: SpaceX Kestrel 2 (LOX-RP1 liquid)

Booster Design

Interstages

2nd StageATK

Star31

1st StageATK

Orion50XL

3rd StageSpaceX Kestrel 2

Fairing

Stage SpecificationsStage 1 Stage 2 Stage 3

Rocket Motor ATK Orion 50XL ATK Star 31 SpaceX Kestrel 2

Propellant Solid Solid LOX-RP1 Liquid

Empty Mass 416kg 98kg 84kg

Propellant Mass 3923kg 1286kg 350kg

Specific Impulse 260s 293s 330s

Thrust 170kN 80kN 33.3kN

Burn Time 69.8s 46s 34s

Comparison to PegasusAirLaunch PegasusXL

1 stage maneuver Zero-velocity gravity Winged pull-up

Takeoff Mass 6,298kg 23,130kg

Carrier Aircraft C-17 Lockheed L-1011

Aircraft Mounting Internal Cargo Bay External Wing Pylon

Payload to LEO 150kg (1) 443kg

Diameter 1.7m 1.27m

Length 12.5m 17.6m

Upper Stage Pressure-fed liquid Solid+HAPS System (2)

(1) Payload for AirLaunch mission is 120kg fuel and 30kg satellite(2) Monopropellant hydrazine thruster for upper stage trajectory error correction

Comparison to Pegasus

Pegasus

AirLaunch

Gravity Turn Simulations:• Used Joe Mueller’s Matlab code to simulate

gravity turn• Parameters that can be varied in code:

– Flight Path Angle (FPA)– Height at which ignition 3 starts– Mass of Stage 3 Propellant

Launch Flight Path Angle: 87.97 Deg.

Trials System mass Eccentricity Perigee Altitude

Apogee Altitude

1 6278 kg 0.00918 240.42 km 363.12 km

2 6293 kg 0.00183 322.42 km 346.96 km

3 6298 kg 0.00093 330.46 km 342.84 km

Targeted ISS Orbital elements

0.00053 334 km 341 km

C-17 carrier aircraft

LV initial launch conditions:

t = 0 seconds

V ≈ 0 m/s

H ≈ 12 km

FPA ≈ 88°

Launch Vehicle (LV)

Launch Vehicle (LV) initial launch conditions:

FPA

Launch trajectory:• Simulations produced the following direct launch trajectory

to reach ISS:Targeted ISS perigee

altitude of 334 km

3D Orbit of Payload:• Matlab simulation produced the following orbit:

Payload’s Low Earth Orbit

Inclination: 51°

Detailed orbit simulations:Satellite Tool Kit (STK) orbit simulations:

STK simulation:• Used STK to simulate orbit of

payload relative to ISS• Apoapsis and Periapsis visible• Enjoy the excellent video