Arbitrary Payload Cost Optimization to LLO

1. Arbitrary Payload Cost Optimization to LLO Tasks: Payload Cost / Mass Optimization (Launch to LLO) Disprove Momentum Transfer Alternative Disprove Spinning Mass Tether Alternative 3/5/09 Kris Ezra Attitude Group Translunar Phase 1

2. Engine Selection • Mission Parameters • Required Thrust: 1.850 N • Time of Flight : 351 days • Launch Vehicle: Falcon 9 • Payload Mass: 9953 kg • Engine Options • BHT-1500 Hall Thruster (Tmax = 250 mN) • BHT-8000 (Tmax = 512 mN) • TM-50 (Tmax = 996 mN) Based on price per kilogram of payload to LLO: Recommend BHT-8000 Kris Ezra Attitude Group Translunar Phase

3. BHT-8000 Hall Thruster • Characteristics: • Mass Flow Range = 4-44 mg/s • Max Thrust = 0.512 mN • Thruster Mass = 20 kg • Result: • Cost: ~$26,400 / kg payload • Mass Flow: 2.03x10-5 kg/s • Power: 8.436 kW / Engine • Optimal Engine Number = 4 Kris Ezra Attitude Group Translunar Phase

4. Empirical Curves BHT-8000 Hall Thruster Kris Ezra Attitude Group Translunar Phase

5. Empirical Curves TM-50 Hall Thruster Kris Ezra Attitude Group Translunar Phase

6. BHT-1500 Hall Thruster • Characteristics: • Mass Flow Range = 3-10 mg/s • Max Thrust = 250 mN • Thruster Mass = 6 kg • Result: • Cost: ~$26,800 / kg • Mass Flow: 6.9x10-6 kg/s • Power: 6.381 kW / Engine • Engine Count: 11 Credit Brad Appel for empirical thruster behavior Kris Ezra Attitude Group Translunar Phase

7. BHT-8000 Hall Thruster • Characteristics: • Mass Flow Range = 4-44 mg/s • Max Thrust = 0.512 mN • Thruster Mass = 20 kg • Result: • Cost: ~$26,400 / kg payload • Mass Flow: 2.03x10-5 kg/s • Power: 8.436 kW / Engine • Engine Count: 4 Kris Ezra Attitude Group Translunar Phase

8. TM-50 Hall Thruster • Characteristics: • Mass Flow Range = 12-30 mg/s • Max Thrust = 0.0.966 mN • Thruster Mass = 30.5 kg • Result: • Cost: ~$38,296 / kg payload • Mass Flow: 3x10-5 kg/s • Power: 61.198 kW / Engine • Engine Number: 2 Kris Ezra Attitude Group Translunar Phase

9. Rationale for Discarding Momentum Transfer Concept: The momentum transfer concept was analyzed just using work/energy relationships subject to the conditions that the Lander could not experience an acceleration greater than 10g and that the Lander would initially be traveling at an orbital speed of 1.7 km/s. Because the constraint on the system is an acceleration and the frame of the moving Lander is not inertial, the system was analyzed using work/energy but in an inertial frame. This approach has obvious limitations; however, it also should provide a more conservative analysis meaning that, if the results are unfeasible for this simplified model, the addition of a gravitational component by the moon will only make exacerbate the outcome. Shown below is a plot of the acceleration felt by the Lander versus collision/spring distance through which some force must act to slow the Lander to zero. A reasonable distance for this “collision” would be between 1 and 2 meters since a spring of this relaxed length must be carried on the OTV with a mass less than that of the Lander descent propellant. From the graph, it can be seen that, at this distance, the accelerations are on the order of 1x105 Earth g’s. This is four orders of magnitude higher than that sustainable by the communications equipment (10g) and is probably higher than what is able to be withstood by the molecular bonds in the vehicular structure. Additionally, to maintain an acceleration less than 10g during a deceleration from 1.7 km/s it would be necessary to have a collision distance of approximately 150 km. For these reasons among others, the momentum transfer concept is infeasible. Momentum Transfer Alternative Acceleration sustainable by Communication Equipment: 10g Most Conservative Reasonable Collision Distance: 1-2 m Earth g’s Sustained at this Distance: 1x105 Collision distance required at 1.7 km/s = ~150 km Because the sustained acceleration in a reasonable spring collision would be four orders of magnitude higher than the communication equipment capability (and maybe higher than the molecular collusion of the structure) this alternative is entirely infeasible. Kris Ezra Attitude Group Translunar Phase

10. Rationale for Discarding Momentum Transfer Concept: The momentum transfer concept was analyzed just using work/energy relationships subject to the conditions that the Lander could not experience an acceleration greater than 10g and that the Lander would initially be traveling at an orbital speed of 1.7 km/s. Because the constraint on the system is an acceleration and the frame of the moving Lander is not inertial, the system was analyzed using work/energy but in an inertial frame. This approach has obvious limitations; however, it also should provide a more conservative analysis meaning that, if the results are unfeasible for this simplified model, the addition of a gravitational component by the moon will only make exacerbate the outcome. Shown below is a plot of the acceleration felt by the Lander versus collision/spring distance through which some force must act to slow the Lander to zero. A reasonable distance for this “collision” would be between 1 and 2 meters since a spring of this relaxed length must be carried on the OTV with a mass less than that of the Lander descent propellant. From the graph, it can be seen that, at this distance, the accelerations are on the order of 1x105 Earth g’s. This is four orders of magnitude higher than that sustainable by the communications equipment (10g) and is probably higher than what is able to be withstood by the molecular bonds in the vehicular structure. Additionally, to maintain an acceleration less than 10g during a deceleration from 1.7 km/s it would be necessary to have a collision distance of approximately 150 km. For these reasons among others, the momentum transfer concept is infeasible. Spinning Mass Tether Alternative Acceleration sustainable by Communication Equipment: 10g Required Tether Length to Match Orbital Velocity: ~50 km Propellant Mass minus Mass of Tether at this Length: -325 kg Orbital Height: ~100 km Result: Weight of tether exceeds propellant mass and tether length is nearly half the orbital height. Completely infeasible. Kris Ezra Attitude Group Translunar Phase

11. References Jacobson, D.T., and Janokovsky, R.S., “Performance Evaluation of a 50 kW Hall Thruster”, AIAA 99 0457, NASA/TM, Accessed 2 Mar. 2009. URL: http://gltrs.grc.nasa.gov/reports/1999/TM-1999-209447.pdf Pote, B., Hruby, V., and Monheiser J. “Performance of an 8 kW Hall Thruster” IEPC 99 080. Accessed 2 Mar 2009. URL: http://sgc.engin.umich.edu/erps/IEPC_1999/9080.pdf Busek Co. “Hall Effect Thruster Systems” busek.com. Accessed 28 Feb. 2009. URL: http://www.busek.com/halleffect.html Appel, B. “Cost Optimization Code Draft I” 2 Mar. 2009. Kris Ezra Attitude