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 Calculator

Solid Rocket Motors trade study

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): Fuel Density: g/cc. - Fuel Freezing Point: -73 deg C. - Fuel Boiling Point: 147 deg C - Oxidiser Density: 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 Database

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

Booster Design Interstages 2 nd Stage ATK Star31 1 st Stage ATK Orion50XL 3 rd Stage SpaceX Kestrel 2 Fairing

Stage Specifications Stage 1Stage 2Stage 3 Rocket MotorATK Orion 50XLATK Star 31SpaceX Kestrel 2 PropellantSolid LOX-RP1 Liquid Empty Mass416kg98kg84kg Propellant Mass3923kg1286kg350kg Specific Impulse260s293s330s Thrust170kN80kN33.3kN Burn Time69.8s46s34s

Comparison to Pegasus AirLaunchPegasusXL 1 stage maneuverZero-velocity gravityWinged pull-up Takeoff Mass6,298kg23,130kg Carrier AircraftC-17Lockheed L-1011 Aircraft MountingInternal Cargo BayExternal Wing Pylon Payload to LEO150kg (1) 443kg Diameter1.7m1.27m Length12.5m17.6m Upper StagePressure-fed liquidSolid+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: Deg. TrialsSystem massEccentricityPerigee Altitude Apogee Altitude kg km km kg km km kg km km Targeted ISS Orbital elements km341 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