Overall Study Results: Propellant From Moon

Just the overall results are given here.  The details supporting this are much more voluminous.  The basic notion,  Figure 1,  is to manufacture propellants on the moon,  probably using potentially-recoverable ice deposits near the south pole.  I initially looked at elongated halo orbits about the moon as a means to more easily access the south polar region off the moon from orbit.  Delivery is to low Earth orbit,  at low inclination eastward.  The idea is to base a lander on the moon,  flying loaded to a station in halo orbit,  and returning to the lunar surface with tank empties plus a bit of cargo.  The orbit-to-orbit transport vehicle to LEO,  is based at the station in the halo orbit about the moon.  It flies fully laden from there to LEO,  and returns to the halo station with empties plus that same little bit of cargo.  

Figure 1 – Basic Notion of Lunar Propellant Manufacture for Use in LEO

There are actually two halo orbit cases to consider,  although overall,  they are more-or-less a wash.  One is the proposed halo orbit for NASA’s “Gateway” station about the moon.  This one has an apoapsis radius that lies beyond the Hill sphere for orbit stability about the moon.  It also has a periapsis altitude much higher than that used during Apollo,  which acts to increase the delta-vee (dV) required of any lander operating from that halo station.  Long-term,  anything in this halo will eventually leave the moon and go into orbit about the Earth.  That is the direct result of having an apoapsis distance outside the Hill sphere.  Thus the halo station requires periodic correction burns,  just to stay in this orbit.

Using LOX-LCH4 propulsion that does not push the state-of-the-art as hard as SpaceX does with its Raptor engines,  it takes almost 48 metric tons of propellant manufacture on the lunar surface to deliver 1 metric ton of propellant to LEO via the NASA halo station,  and have the two vehicles return to their bases.  This does not include the propellant necessary for orbital correction burns to stabilize the station in this NASA halo orbit!    The transport vehicle is the smaller for this case,  while the lander is the larger,  as indicated in Figure 2.  This unstable halo orbit choice may actually be driven by the dV capability of SLS/Orion block 1 configuration,  which cannot reprise the Apollo 8 mission.

The “recommended halo” eliminates entirely the need to ship propellant to the halo station for periodic correction burns,  precisely because it is stable.  It has an apoapsis right at the Hill sphere limit,  and a periapsis at a distance comparable to the old Apollo missions,  to reduce lander dV requirements.  It takes about 51 metric tons of propellant manufacture on the moon to deliver 1 metric ton of propellant to LEO,  as also indicated in Figure 2.  For this case the transport is larger,  and the lander is smaller.  

Neither of these halo-based options is more “economical” than the projections for shipping propellant up to LEO from Earth’s surface,  for SpaceX’s Starship/Superheavy vehicle,  as indicated in the Figure.  That vehicle also uses LOX-LCH4 propellants,  so that comparison truly is “fair” in that sense.  

Figure 2 – Results for the Halo Orbit Cases

The alternative would be to manufacture propellant on the lunar surface,  and send it directly from there to LEO,  without utilizing any sort of halo orbit station as a waypoint.  This does require entry from the lunar transfer orbit directly into a low lunar circular orbit that is polar,  so that the south pole can be reached directly.  The reverse is the return.  Landings and takeoffs would be from-and-to this low polar lunar orbit. 

The dV requirements for the direct trip are higher than even the halo transport dV’s.  It was not possible to get “reasonable” results with LOX-LCH4 propulsion for this mission,  the Isp levels are simply too low.  I had to resort to the higher Isp of LOX-LH2 propulsion to get something “reasonable” in size.  However,  since there may well be recoverable ice,  but no free carbon,  on the moon,  it is far more likely that it will be LOX-LH2 propellants that actually get manufactured there,  anyway.  The corresponding results are given in Figure 3.

Figure 3 – Results For Direct Delivery of Lunar Propellant to LEO,  Using LOX-LH2 Propulsion

This is the only outcome that is better than trying to ship propellant up from Earth’s surface to LEO,  even using a vehicle as capable as SpaceX’s Starship/Superheavy.   It takes 14 metric tons of lunar propellant manufacture to support the delivery of 1 metric ton of propellant from the moon to LEO.  This includes the vehicle returning all the way to a landing near the moon’s south pole,  with empties and some cargo. 

Outcomes

In summary,  direct shipment from the moon to LEO is the best option,  but it will require the higher Isp of LOX-LH2 propulsion!  Using LOX-LCH4 is not feasible in any “reasonable” vehicle sizes,  primarily limited by achievable mass ratio as you increase propellant.  This requires manufacture on the moon of 25.1 metric tons of LOX-LH2 to deliver 1 ton of LOX-LH2 as payload to LEO. (corrected)

Failing that,  shipping propellant up from Earth’s surface to LEO is the next best option,  using the SpaceX Starship/Superheavy vehicle,  which is powered by LOX-LCH4 propulsion.  This is projected to require the manufacture of some 32 to 47 metric tons of LOX-LCH4 propellant on Earth to deliver 1 metric ton of it (or instead a ton of LOX-LH2) to LEO. This depends upon deliverable payload being 100-150 tons.

The halo station options turned out to be the least attractive.  Doing it with two vehicles instead of one reduces payload delivered for the propellant used,  by two vehicle payload fractions compounded (because there are two vehicles),  instead of just one.   The two halo options are not much different at about 48 (NASA) and about 51 (recommended) metric tons propellant to be manufactured on the moon to deliver 1 ton of propellant to LEO.  The NASA halo requires still more propellant manufacture on the moon than that about-48 figure,  because its halo station requires correction burns just to stay in its orbit long term!  The “recommended halo” avoids that requirement,  and gets a smaller lander design,  at the expense of a larger transport vehicle to LEO.

Conclusion

The final result says go with the higher-Isp LOX-LH2 propulsion,  and operate direct from the lunar surface to LEO fully laden,   and back to the lunar surface very lightly laden.  Return trips return the empty tanks for the next propellant shipment,  plus in this study,  a couple of tons of payload that could be base operating supplies.

Be Aware

The dV requirements used in this study include 8% of midpoint speed as dV budgets for course correction,  and 0.2 km/s budgets for rendezvous and docking,  once close (within at most 10 km).  Lunar takeoff ideal dV values were factored-up by 1.0083 for gravity losses,  and lunar landing ideal dV values were factored-up by 1.50 for losses plus the dominant hover and divert budget requirements.  Everything else was presumed loss-free “impulsive”,  for factor 1.00 applied to ideal values from basic 2-body orbital mechanics.  The 3-body approach and departure problems were approximated by the “far V” versus “near V” energy approximation. 

Explanations

There are some fundamental trends of mass ratio capability and the dV it can produce,  vs added propellant and Isp,  which help explain these results.  These are depicted generically in Figure 4.  

Figure 4 – Trends That Explain Results

The “knees” in these curves are not so apparent in the MR vs added Wp plot,  but they are very apparent in the dV vs added Wp plots parametric on Isp.  Where the slope is steep,  you will get a better (lower) propellant burned vs payload delivered ratio.  Where the slope is shallow,  that ratio will be large and unfavorable. 

Basically,  there is a favorable range of deliverable dV at each Isp level.  For the 450 s Isp level typical of LOX-LH2 propulsion,  this is up to 8 km/s dV for really nice results,  and up to about 11 km/s at the very most.  Beyond that,  it is a very serious diminishing-returns problem:  adding a lot of propellant for almost no improvement. 

For the 350-400 s Isp level typical of LOX-LCH4 propulsion,  the most favorable range is up to about 7 km/s dV.  At the most,  it is about 9 km/s.  Beyond that,  this is pretty much pointless.

By switching the halo station based lander and transport designs to LOX-LH2 (instead of LOX-LCH4),  the propellant to payload ratios could be significantly reduced,  perhaps looking more like those of Earth launch with Starship/Superheavy,  or maybe even slightly better. 

Regardless,  the lunar surface based and launched single direct transfer design approach is still the best,  despite it being only marginally favorable on the dV vs Wp curve. That is because it is a single vehicle,  and not two vehicles,  as in the other scenarios.  This scenario would look even better if its propulsion were nuclear thermal at 700+ s of Isp. 

As it is with LOX-LH2 propulsion,  the total vehicle dV requirement could be reduced a little,  making the propellant used/propellant delivered ratio even better,  if an LEO tug were used to retrieve the vehicle from an elliptical capture orbit about the Earth.  The same tug could put the vehicle back into the elliptical orbit for departure.  That reduces the arrival and departure dV’s significantly,  and it eliminates the rendezvous and docking dV requirement.  This gain is largely offset by the need for propellant deliveries to power the tug,  though.

Caveat

Ullage solutions for multiple burns with cryogenic liquid propulsion were NOT determined for any of these design rough-outs.  But they will have to be,  to flesh out all the design requirements!  Attitude control was also not addressed,  although given adequate acceleration levels,  some of those thrusters could supply the ullage function.  That is determined by the settling time constants that are acceptable. 

Corrections 12-10-2023:

I had not followed through fully on the spreadsheet for the direct vehicle.  The 14:1 delivery ratio figure goes with an otherwise-converged design that had far-insufficient thrust to takeoff and land,  resulting in too low an inert mass.    When I corrected that,  the vehicle proved to be enormous at 3000 tons,  with a really bad-looking delivery ratio.  I reconverged multiple times with multiple candidate engine numbers and thrusts,  until all the gees looked good,  including landing with hover capability,  but with takeoff reduced to 0.5 gees over lunar surface gravity.  That got me to the corrected figure.