An Ex Rocket Man's Take On It: Initial Study for Tug Missions LEO to LLO

Previous studies (References 1 and 2) explored the use of reusable space tug-assist for interplanetary departures and arrivals. For this purpose, an extended elliptic orbit was used for its high perigee speed very near escape speed. The tug provides the big speed increase to just below escape, staying in the ellipse for recovery back to low orbit. The interplanetary craft only has to supply that smaller speed increase from just below escape to above, for hyperbolic departure.

Lunar trajectories are different, there being no hyperbolic-escape departure (or arrival). An extended ellipse will take a craft to the moon’s vicinity, where the 3-body effects of Earth, moon and craft, will warp the trajectory into a figure-8 low-altitude flyby of the moon, and automatic return to Earth’s vicinity. This was the lunar transfer trajectory used for the Apollo moon missions.

There is only a modest speed change required, behind the moon (as viewed from Earth), to enter a retrograde low lunar orbit, or to leave it for return to Earth. Something representative of the velocity requirements analysis, for such a lunar mission, is given in Figure 1 below. (All figures are located at the end of this article.) Values were obtained using the 2-body analysis of my “orbit basics.xlsx” spreadsheet tool, which simply automates the standard textbook equations in a convenient way.

The question explored in this article is whether a reusable space tug with chemical propulsion could transport dead-head “payload” items from low circular Earth orbit (LEO) to low circular lunar orbit (LLO), and then return unladen to LEO, without refueling. This question was explored with modest-technology storable propellants, modest-technology oxygen-methane (LOX-LCH4), and modest-technology oxygen-hydrogen (LOX-LH2), plus some crude but representative assumptions for inert fractions. The storables examined were specifically nitrogen tetroxide (NTO) and monomethyl hydrazine (MMH).

A Tug Using Storables is Probably Feasible, But Not Very Attractive

We would like to use storables to avoid the evaporation losses and evaporation mitigations that are inherent with cryogenics. Only a thin insulation with a reflective foil outer layer is required to avoid solar heating, plus small in-tank heaters to prevent freezing, when shaded in space.

The engine needs to be turbopumped, to achieve significant final chamber pressure without needing high-pressure tankage. This would be more like the old liquid-propellant Titan missiles than any modern pressure-fed thruster systems. I picked a nominal chamber pressure of 2000 psia (136.1 std atm, 137.9 bar), with a nozzle expansion sized to an arbitrary 50:1 mild vacuum area ratio, on a nominal 18-8 degree curved bell shape. The nozzle kinetic energy efficiency and throat discharge coefficients that I used are pretty standard. Engine thrust/(Earth) weight ratio was simply presumed to be about 70.

The turbopump drive cycle is unspecified, but is presumed to involve a dumped massflow fraction of 5% of the propellants drawn from tankage. Nominal as-sized vacuum thrust for the reference engine was 22,050 lb (10 metric tons-force) on an exit area of 293.4 square inches (0.1893 square meters), which can be rescaled to a more appropriate thrust level, as needed. Vacuum specific impulse at full thrust was near 322 sec, as indicated in Figure 2 below. Values were computed from standard compressible flow analysis, and models for characteristic velocity (c*) and oxidizer/fuel mass ratio (r), using my “liquid rockets.xlsx” spreadsheet worksheet “r noz alt”, that automates the standard textbook equations in a very convenient way. The propellant data I used for c* and r came from Reference 3.

A tug vehicle was rough-sized using the estimated engine performance, these velocity requirements, and a presumed as-built-and-loaded inert mass fraction of 5%, typical of many upper stages today. The calculation was a rough size-out followed by two linked rocket equation analyses: all the laden burns combined in the first one, followed by all the unladen burns combined in the second one. The user sets the as-built propellant mass fraction iteratively, until he can just barely accomplish the mission, with a positive value of “propellant remaining” that is close to zero. This was done in a convenient spreadsheet file “space tug stuff.xlsx”, specifically the worksheet “scrtch size”.

These rocket equation calculations lead to start and stop vehicle masses for each set of burns, to which input min and max vehicle acceleration limits can be applied to determine min and max limits on thrust values. The user has to look at those, and decide how many engines of what actual design thrust level are needed, and how many engines to actively burn laden, and unladen. That sets the actual applied thrusts, and the actual resulting vehicle gees. The worksheet rescales from the input value of reference thrust to this design thrust per engine that is needed.

There are inputs for the masses of the guidance and control unit, and the electric power source for it, as part of an inert mass buildup calculation (the tug is unmanned). The final propellant mass determines a mass estimate of the empty tank inert mass, using an R-ratio input representing propellant mass divided by filled tank mass. The final design thrust level per engine, and number of engines, determines the total engine inert mass by means of the thrust/weight ratio input. The sum of these inert masses is an estimate of the vehicle inert mass, to be compared with the inert mass figured from the 5% assumption in the rocket equation calculations. Inert mass is not automatically converged, however! Even so, if the two estimates are close, that is “good enough”.

The results obtained for the storable-propellant tug sizing are given in Figure 3 below. While such a design is possible, the payload mass fraction is quite low, at somewhere near only 2%. That means a very large tug vehicle, to be kept supplied on-orbit with very large quantities of the NTO-MMH propellants, must be used to transport even modest payloads to LLO this way. The full-load propellant/payload mass ratio is over 42:1!

That outcome is quite unattractive, because of the bad logistics the propellant/payload ratio implies. Anything we could do to push the state of the art of the engines would help, but not by all that much, because we are inherently playing in the wrong ballpark: our effective exhaust velocity relative to the magnitude of the velocity requirements, is simply far too low.

A Tug Using LOX-LCH4 is Quite Feasible, But Still Less Than Attractive

A similar engine-sizing analysis was performed with the same engine sizing spreadsheet, just using propellant data for LOX-LCH4. This was also for a modest-technology design, not one pushing the state-of-the-art so hard as the SpaceX Raptor engines do! This is a 3000 psia (204.1 std atm, 206.8 bar) chamber pressure, with a presumed 5% bleed fraction representing its cycle. Its nozzle expansion was sized to permit test-firing in the open air at sea level, operating at full thrust, but on the verge of separating in the nozzle. That produced an area ratio of about 65 in its 18-8 degree curved bell. The re-scalable reference engine sized vacuum thrust was 22,050 lb (10 metric tons-force), at an exit area of 252.0 square inches (0.1626 square meters), operating at a vacuum specific impulse of about 349 sec. This is illustrated in Figure 4 below.

I should have revised the tank R ratio downward a little, to reflect the need for extra insulation and header tank construction approaches because of the cryogenics, but I did not. As-sized at an as-built 5% inert, the LOX-LCH4 tug vehicle sized with a substantially-higher payload fraction of about 7%, as shown in Figure 5 below. This is a marked improvement over the storables tug, but is still only a single-digit payload percentage. This is definitely technically feasible to do, but the logistics of propellant supply are still rather unattractive, when considering any significant payload mass. The propellant/payload mass ratio is still rather high at just over 12:1!

A Tug Using LOX-LH2 is Quite Feasible, But Also Becoming Much More Attractive

I did not do an arbitrary spreadsheet engine sizing for the LOX-LH2 case. Instead I used the actual data for the RL-10C-1-1 engine as “representative” of a modest-technology design, as this basic engine series has a history going back over 60 years now. It is an expander cycle with no dumped bleed, and a 57:1 thrust/weight ratio. Vacuum Isp is 453 sec. I got this data from Reference 4.

I took this data and went straight to the tug vehicle sizing spreadsheet, shown in Figure 6 below. Instead of the arbitrary 1-ton payload resize, I resized the payload to 12 metric tons, so that the listed vacuum thrust of the RL-10 engines, at 3 engines total, 3 active laden, 1 active unladen, would provide the desired gees within the kinematic limits for both sets of burns.

The results proved to be very-significantly better, with a payload fraction of over 21%, and a propellant/payload mass ratio of only about 3.4! With numbers in this range, the on-orbit propellant supply logistics for the tug vehicle become much more attractive. There are more high-technology engines available (such as the RS-25 series), which would improve things somewhat further still.

For massive improvement, there might be nuclear thermal, using hydrogen only, but also with the risks involved in routinely using reactors in LEO and near-Earth space. The inherently higher inert fractions associated with low engine thrust/weight, will offset some of the higher Isp advantage of nuclear thermal, though.

Discussion of Results and Conclusions

Despite the crudity of this study, the clear winner (by far) is LOX-LH2. See Figure 7 below.

But with those cryogenics, there are some severe design constraints not modeled in this study! Those include thicker insulation on the tank exteriors, and a header-tank design approach. With LOX-LCH4, SpaceX has shown that a simple single-membrane inter-tank bulkhead can be used between the main hydrogen and oxygen tanks. This is because the LOX and LCH4 temperatures are just not that far apart.

However, the experiences with the Centaur stage and LOX-LH2 show that only hours of stage life can be obtained, even with a common bulkhead composed of a double membrane with insulation between them. The “hotter” LOX just bleeds too much heat into the very much colder LH2! The tug missions are multiple days long, not hours, so a common bulkhead is just not very feasible.

The external insulation can still be fairly modest, if internal header-tank construction is used, enabled by the fact that the first set of burns occurs laden, and uses the largest propellant mass. If the header is inside the main tank, it can use the empty main tank as part of its insulation scheme! That is the way to get the mission-required days of stage life, without resorting to active cooling!

References:

#1. G. W. Johnson, “Tug-Assisted Arrivals and Departures”, posted 12-1-2024, to the “exrocketman” blog site http://exrocketman.blogspot.com.

#2. G. W. Johnson, “Elliptic Capture”, posted 10-1-2024, to the “exrocketman” blog site http://exrocketman.blogspot.com.

#3. Pratt & Whitney Aircraft, “Aeronautical Vest-Pocket Handbook, 12^th Edition, 21^st printing, December 1969.

#4. Wikipedia article “RL10”, last updated 24 November 2024, article retrieved 4 December 2024.

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