Extraterrestrial Warehouse Design to Facilitate a Hub-Spoke Reverse-Logistic Supply-Chain Distribution Model Navin Chari Dalhousie University, Canada

OBJECTIVE •Warehouse design to transfer goods from a terrestrial launch site to: • International Space Station (ISS), hotels, and a lunar-base •Minimize the net distribution cost (ΔV) by finding the optimal location and mass flow (weighting factors), for each link in the supply-chain •Comparison of different fuel types and propulsion technologies such as: •Ion propulsion, VASMR, electrical, nuclear, and solar thermal •Utilization of Environmental control and life-support systems (ECLSS) •Procurement of Helium-3 from the Moon •Facility design based on required oxygen, water, food, fuel, and waste

FACILITY LOCATIONS •Getting into orbit and the effects of gravity and air drag [2]:

•2 opposite located docking areas to enable a unidirectional flow •1 for shuttle between the different facilities •1 for spacecraft commuting with spaceport

•Return-trip for the ISS and hotels: ΔVISS = 2(ΔVWH-ISS,tp + ΔVWH-ISS,ta)

•150 000 passengers/year would stay in a hotel at a price of $72 000, [1] •Model takes 10% of that number each with a 5 day stay

•Helium-3 will be transferred directly from the lunar-craft to the Earthbound vehicle, so it will not require warehouse space.

ΔVLaunch = ΔVOrbit + ΔVGravity + ΔVDrag

ΔVHTL = 2(ΔVWH-HTL,tp + ΔVWH-HTL,ta)

•Sphere of Influence point (rSI) is the point between the Earth and the Moon where the gravitational forces are equal. •Spacecraft needs to do a transfer to rSI using Earth’s gravity and then another to the lunar base, using a method known as patched conics [3]:

•70% average passenger load capacity, with the remainder to rotate hotel staff, consumables, cargo, construction items [1] •Streamlining the 30% to attain a 100% passenger load, the revenues would increase and the cost of the ticket would also decrease [1]

•Exploitation of Helium-3 and other resources from the Moon: •Scarcity, fusion energy research and future energy security concerns

•Return-trip for the Lunar-Base: ΔVLB = ΔVWH-SI + ΔVSI + ΔVSI-LB + ΔVLB-SI + ΔVSI + ΔVSI-WH •Total ΔV Expenditure: ΔVTotal = ΔVLaunch + ΔVISS + ΔVHTL + ΔVLB + ΔVEarthReturn

FACILITY LOCATIONS •Biak Spaceport (LAPAN / RKA) as the location to have the launch facility •ISS has a perigee (hISS,p) = 361 km and apogee (hISS,a) = 437 km •Altitude of the ISS (hISS) will vary according to the following rules: hWH ≤ hISS,p  hISS = hISS,p hWH ≥ hISS,a  hISS = hISS,a hISS = hWH

Resource

Mass/Pers. (kg) LOX 0.50 Water 0.50 Food 1.00 Waste 0.30 Hydrazine 0.25 TOTAL 2.55

PROBLEM STATEMENT • DVGravity = 1 080 m/s, DVDrag = 220 m/s (Ariane 1st stage burn) [2] • DVEarthReturn ≈ 0 due to aerobraking in the Earth's atmosphere • rSI ≈ rL1,

SUBJECT TO: hLEO- ≤ hWH ≤ rSI hLEO- ≤ hHTL ≤ hGSO 0 ≤ hLB ≤ hLLO φISS + φHTL + φLB = 1

•Solution for hWH in 4 regions (hLEO-, hISS,p, hISS,a, rSI) based on weights:

1 875

Resource LOX Water Food Waste Hydrazine Argon TOTAL

Mass (kg) 3 216 3 216 6 433 1 930 2 108 5 027

Density (kg/m3) 1 141 1 000 933 1 650 880 9 000

Volume (m3) 2.819 3.216 6.892 1.170 2.396 0.559 17.051

•Resource are modelled as departments with the following constraints •All of the resources should span both ends of the facility •Grouped together by target destinations (Argon and Hydrazine) •Separate food away from fuel and waste, but keep it close to water

   DV    mi 1  exp   g I    0 sp 

•Available mpay = mi - mveh – mfuel ≈ 28 000 kg for the cargo Total Requirements Summary for the Lunar-Base: Resource Hydrazine Argon Helium-3 TOTAL

MassIn (kg) 500 5 027

MassOut (kg)

27 928 27 928

5 527

Density Volume (kg/m3) (m3) 880 0.568 9 000 [10] 0.559 82.3 [11] 339.346 340.473

Total Mass Requirements for the Warehouse:

Hotel ISS Lunar-Base TOTAL

MassIn (kg) 14 063 411 5 527 20 000

MassOut (kg) 1 875 55 27 928 29 858

Total (kg) 15 938 465 33 455 49 858

φ (%) 31.97 0.93 67.10

CONCLUSION •Required mass to supply the ISS is very small in comparison •VASIMR greatly reduces the mass of fuel and cost to travel/transport •However travel time is expected to take a round-trip of 180 days [8] •6 vehicles would be required to keep the supply chain in equilibrium •Single hydrazine powered craft to supply both the ISS and hotel •Energy required to go to these locations are minimal •Vehicle is envisioned as being small, making frequent excursions •As the consumption by the hotel tourists increases it may be advisable to procure Argon from the Moon to mitigate the storage of that fuel •ΔV to go the Moon’s surface from the lunar-base (LLO) is very small

THERMAL PASSIVITY •Energy balance is based on is the conduction (Cij) and radiation (Rij) exchange factors, their respective parameters ΩC and ΩR, and the net heat transfer rate qi N

•Applied to the segments from the warehouse to the ISS

1 563 14 063

Volume (m3) 2.739 3.125 6.697 1.136 1.776 15.473

Total Resource Requirements for the Warehouse:

•Using a successfully tested Argon propelled VASIMR engine [9] •Argon ≈ 1/20th cost of Xenon and is very abundant [8] •mfuel ≈ 4 500 kg for the inbound journey, total mass (mi) ≈ 34 400 kg

Facility

•Using a constrained Nelder-Mead Simplex algorithm

•Use Hohmann Transfer orbital changes via the vis-viva equation:

1 875

Density (kg/m3) 1 141 1 000 933 [6] 1 650 [6] 880

•Ariane 5 rocket can carry 20 000 kg into LEO [7] •Hotel & ISS accounts for ≈ 14 500 kg, leaving ≈ 5 500 kg for the Moon •500 kg of hydrazine to accommodate the extra incoming mass for its return back to Earth, leaves 5 000 kg for the lunar-base •mveh ≈ 2 000 kg, based on NASA's planned 5% vehicle mass [8],

Ψ(hWH, hHTL, hLB) = ΔVLaunch + φ ΔVT

•Solving using an SQP algorithm, leads to local solutions

CHANGING ORBITS

MassOut (kg)

•Drop-off and loading onto the other craft in a FIFO discipline

Warehouse Layout and the Resource Specific Space Allocation

ASSUMPTIONS:

•where φ = [φISS φHTL φLB], and ΔV = [ΔVISS ΔVHTL ΔVLB]

General Layout of the Lagrangian Points in a 2-Body System

MassIn (kg) 3 125 3 125 6 250

m fuel

OBJECTIVE FUNCTION: •Altitudes of the warehouse (hWH), hotels (hHTL) and lunar-base (hLB) will be determined concurrently with the following bounds: •Hotels: Low Earth Orbit (LEO) to Geosynchronous Orbit (GSO) •Lunar-Base: Surface of the Moon to Low Lunar Orbit (LLO) •Warehouse : LEO to the Earth-Moon L1 Lagrangian point rL1,

Hotel Requirements Summarized over a 1 Month Horizon:

•Warehouse’s primary function for the lunar-base will be to store fuel: •ECLSS performed insitu, or fully automated Helium-3 extraction

•75% of the ticket price collected as revenue [1]

•Expanding to the multiple structures, further efficiencies are attained

LAYOUT DESIGN

•Environmental control and life-support systems (ECLSS) •Water and oxygen can be recovered using a closed-loop system [4] •Ability to recycle/reuse food and waste [4] •Average daily requirement ≈ 1 kg of oxygen, 5 L of drinking water [5]

MOTIVATION

•Decreased price would also encourage a greater number of passengers, roughly each time the fare is reduced 20%, the traffic doubles [1]

REQUIREMENTS

C j 1

ij

N

(C )(T j  Ti )  Rij ( R )(T j4  Ti 4 )  qi

i  1,, N

j 1

•Inverse solution yields the radiation parameters of absorptivity and emissivity, which can be used to attain the desired surface realization [12] N

 ( R )    i (Ti  Td ,i ) 2 i 1

SOLUTION PARAMETERS: •Shape: 2.574 m cube •Thickness: 10 mm •Material: Aluminum •Altitude: 437 km •Rotation: [90°; 23.43°; 90°] •Td,i = 300 K •ζi = 1 •Solved via SQP algorithm

•Transfer mechanism of the Helium-3 to the Earth-bound craft has not been identified, and may prove to be an interesting source of future research dealing with inflatable flexible structures

REFERENCES [1] J. P. Penn and C. A. Lindley, “Requirements and Approach for a Space Tourism Launch System,” Acta Astronautica, vol. 52, pp. 49-75, 1 2003. [2] P. W. Fortescue and J. P. W. Stark, Spacecraft Systems Engineering. Chichester; New York: Wiley, 1995. [3] V. A. Chobotov, Orbital Mechanics. Reston, Va.: American Institute of Aeronautics and Astronautics, 2002. [4] W. E. Hammond, Design Methodologies For Space Transportation Systems. Reston, Va.: American Institute of Aeronautics and Astronautics, 2001. [5] P. H. Gleick, “Basic Water Requirements For Human Activities: Meeting Basic Needs,” Water International., vol. 21, no. 2, p. 83, 1996. [6] L. Stander and L. Theodore, Environmental Regulatory Calculations Handbook. Hoboken, N.J.: WileyInterscience, 2008. [7] Arianespace, “Ariane 5: Users manual,” 2008. [8] T. W. Glover, F. R. C. Daz, A. V. Ilin, and R. Vondra, “Projected Lunar Cargo Capabilities Of High-power VASIMR Propulsion,” in The 30th International Electric Propulsion Conference, September 17-20, 2007. [9] L. D. Cassady, W. J. Chancery, B. W. Longmier, C. Olsen, G. McCaskill, M. Carter, T. W. Gloverk, J. P. Squire, F. R. C. Diaz, and E. A. I. Bering, “VASIMR Technological Advances And First Stage Performance Results,” in 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, American Institute of Aeronautics and Astronautics, 2-5 August 2009. [10] V. Arinin, O. Mikhailova, M. Mochalov, and V. Urlin, “Quasi-isentropic Compression Of Liquid Argon At Pressure≈1000 GPa," Journal of Experimental and Theoretical Physics Letters, vol. 87, no. 4, pp. 209-212, 2008. [11] W. E. Keller, Helium-3 and Helium-4,. New York: Plenum Press, 1969. [12] N. Chari, “Spacecraft Thermal Design Optimization,” 2009.