Starship On-orbit refueling - Options and Discussion

[TomH]

If the idea is a quite low LEO, well below Starlink or ISS (like 200-250 km) is there much debris there?

About zero. At this low altitude air resistance removes any debris within about 6 months.

One thing to remember is that things in VLEO are affected by solar storms, especially the very big ones. I am sure that most people participating in the thread already know this, but for those who do not, solar storms heat the upper atmosphere, causing it to expand. For things in the lowest of orbits, atmospheric density can increase multiple times (at those specific altitudes), greatly accelerating natural orbital decay.

[StraumliBlight]

Specifically, while the Kevlar straps tend to do just fine, the "bladder" layer that actually holds pressure turns to glass at cryogenic temperatures.

NASA have investigated inflatable cryogenic tanks, there was a 2022 Titan Sample Return mission concept using it.

Currently, materials are being evaluated for cryogenic applications, including polyimide films, annealed metal films, and fluorinated ethylene propylene (FEP) which is LOx compatible. Various joint configurations are also under evaluation, with adhesive lap joints of barrier materials exhibiting high strength even at cryogenic temperatures, which was also shown in testing at NASA Lewis in the 1960s (Ref. 54). Additional design features are also being developed, including equatorial skirt mounting systems, integral slosh baffles and propellant management devices (PMDs), and tanks with cylindrical form factors.

ESA: Flexible Storage Solutions for Human Spaceflight Activities [Feb 17, 2023]

The bladder was manufactured from several pieces of Fluorinated Ethylene Propylene (FEP) monolith sheet, formed under vacuum, and induction welded together to form a cylindrical body between the two domes. The upper part of the bladder dome has a fluid interface that is already mated before finally welding the bladder together. Structural restraints are provided by a net of high-strength ribbons, manufactured from Poly-Benzyl-Oxylate (PBO) trade name ‘Zylon’. Zylon is one of the strongest types of fiber available and is coated with a VITON elastomer to protect the fiber against UV degradation. The restraint ribbons are wrapped around the tank and are sewn together at specific locations, where the meridian and hoop ribbons overlap. This provides the desired assembly joint strength and maintain tank shape in a repeatable way after many cycles of stowing and deployment.

[Chatskiy]

Right, I just have to share it!

"ISS Astronauts Matthew Dominick and Don Pettit demonstrate how spacecraft can transfer rocket fuel, or propellant, in microgravity using water bottles, water, and a fizzy tablet."

[TheRadicalModerate]

This got discussed briefly way up thread somewhere, but it bears being revived:  Will the depot and HLS store subcooled prop, or boiling prop?

I think the use of subcooled prop is unlikely, for the following reasons:

1) Tanker prop will arrive at the depot boiling.  It will have been launched through the atmosphere with high heating through the tanker skin.  It will have received extremely hot gas via autogenous pressurization, which will transfer heat to the remaining prop, and it will spend some time in orbit, being heated by the sun and earth emissions, before it reaches the depot.

2) The depot would need a lot of power to subcool the prop.  Note that this is done rapidly enough on the pad by using LN2 as a heat sink.  You can't do that on-orbit; the cryocooling needs to do it--if there is any.  If you're gonna subcool boiling tanker prop as it's received, that likely severely limits the transfer rate between the tanker and the depot.

3) Even if the depot were to subcool just before the HLS came in to RPOD, the HLS tanks are going to be hot, and it's unlikely that you can do just-in-time prop transfer so that the HLS finishes refueling and disconnects only a few minutes before its departure burn.  Think about how little hold time Starship has right now; that's likelyl the limit on-orbit, too--at least if you want to get subcooled advantage.

If boiling prop is used everywhere in space, then a v3 tank holding 1600t of subcooled prop becomes a tank holding ~1490t of boiling prop.  A 2300t v4 tank will become a ~2150t tank with boiling prop.


While we're on the subject of tank capacity:  Is the 1600t number for v3 just the prop in the mains, or does it include prop in the headers as well?  If it includes the headers, then HLS, which doesn't have headers, will lose another 10-20t of prop on-orbit.

[Twark_Main]

This got discussed briefly way up thread somewhere, but it bears being revived:  Will the depot and HLS store subcooled prop, or boiling prop?

I think the use of subcooled prop is unlikely, for the following reasons:

1) Tanker prop will arrive at the depot boiling.  It will have been launched through the atmosphere with high heating through the tanker skin.  It will have received extremely hot gas via autogenous pressurization, which will transfer heat to the remaining prop, and it will spend some time in orbit, being heated by the sun and earth emissions, before it reaches the depot.

2) The depot would need a lot of power to subcool the prop.  Note that this is done rapidly enough on the pad by using LN2 as a heat sink.  You can't do that on-orbit; the cryocooling needs to do it--if there is any.  If you're gonna subcool boiling tanker prop as it's received, that likely severely limits the transfer rate between the tanker and the depot.

3) Even if the depot were to subcool just before the HLS came in to RPOD, the HLS tanks are going to be hot, and it's unlikely that you can do just-in-time prop transfer so that the HLS finishes refueling and disconnects only a few minutes before its departure burn.  Think about how little hold time Starship has right now; that's likelyl the limit on-orbit, too--at least if you want to get subcooled advantage.

If boiling prop is used everywhere in space, then a v3 tank holding 1600t of subcooled prop becomes a tank holding ~1490t of boiling prop.  A 2300t v4 tank will become a ~2150t tank with boiling prop.


While we're on the subject of tank capacity:  Is the 1600t number for v3 just the prop in the mains, or does it include prop in the headers as well?  If it includes the headers, then HLS, which doesn't have headers, will lose another 10-20t of prop on-orbit.

Yes.

Starship will use boiling propellant. But also, the depot will have a ZBO chiller that can (optionally) be run continuously for days to achieve some measure of subcooling if you want to store a few percent of extra propellant.

The propellant will heat up before the burn so you still need a larger tank on the HLS side, but it still saves some tankage on the depot side.

Note that if you want this option it requires a heat exchanger cryocooler, not just a system which re-liquifies the boil-off.

[TheRadicalModerate]

Yes.

Starship will use boiling propellant. But also, the depot will have a ZBO chiller that can (optionally) be run continuously for days to achieve some measure of subcooling if you want to store a few percent of extra propellant.

The propellant will heat up before the burn so you still need a larger tank on the HLS side, but it still saves some tankage on the depot side.

Note that if you want this option it requires a heat exchanger cryocooler, not just a system which re-liquifies the boil-off.

I'm assuming that depots have the forward and common domes pushed forward, so it's possible that, if the depot can hold 1600t of boiling prop in its extended tanks, it could potentially subcool that to be 1600t of subcooled prop before fueling the HLS.¹

The problem is the heating on the HLS side, which almost certainly has tankage with less volume than the depot.  So the subcooling is worthless unless the HLS has its own cryocooling (unlikely), or if you can do just-in-time refueling before the burn (also unlikely).

This is a big deal, because that missing 110t of prop in the HLS (i.e., 1490t instead of 1600t) is the thing that makes the VLEO-refuel-BLT-NRHO-LS-NRHO cycle non-viable (well, that and boiloff, sump losses, ullage losses, FPR, and maybe the lack of headers).  That's what forces the double refueling in both VLEO and HEEO, which is definitely not a simplification.

So it's worth thinking about whether there's any practical way to take advantage of subcooling.  I still think it adds just as much if not more complexity to the conops than the final tanking orbit, but it's a near thing.

Of course, the thing that really simplifies things is skipping NRHO and using LLO as a staging orbit.  Then the margins are pretty robust.

____________
¹If the HLS is refueling in VLEO first, then the fueling that occurs in the FTO is pretty modest, since there's plenty of prop already in the HLS, and they might not need to re-jigger the depot domes.  But if the goal is to skip the VLEO refueling and go straight to the minimum FTO, the depot has to boost up and refuel a nearly-empty HLS, with enough prop to get back to VLEO.  That requires tanks that are considerably larger than the HLS, for obvious reasons.

[rsdavis9]

Repeating here.

You miss the point that subcooled propellant is boiling at a pressure below 1 bar. So just keep the pressure at this lower point.

For example LOX at 20kPa or about .2 bar the temp is 78K

So if you let the pressure drop in the tank it gets to whatever temp(and density) that you want at the expense of boiling off some of the propellant. If the tanker delivers the prop before it warms that much then the normal boiloff will keep it subcooled. We have zero knowledge as to what the delivery temp will be. I will take the bet that it will still be a temp below 1 atm boiling.(ie subcooled)

[Twark_Main]

Repeating here.

You miss the point that subcooled propellant is boiling at a pressure below 1 bar. So just keep the pressure at this lower point.

For example LOX at 20kPa or about .2 bar the temp is 78K

So if you let the pressure drop in the tank it gets to whatever temp(and density) that you want at the expense of boiling off some of the propellant. If the tanker delivers the prop before it warms that much then the normal boiloff will keep it subcooled. We have zero knowledge as to what the delivery temp will be. I will take the bet that it will still be a temp below 1 atm boiling.(ie subcooled)

Yep, I thought "what about below 1 bar?" about a minute after posting, but it was late and I remembered Cunningham's law so I figured I'd let someone else spill that ink.  Thanks.

[TheRadicalModerate]

Repeating here.

You miss the point that subcooled propellant is boiling at a pressure below 1 bar. So just keep the pressure at this lower point.

For example LOX at 20kPa or about .2 bar the temp is 78K

So if you let the pressure drop in the tank it gets to whatever temp(and density) that you want at the expense of boiling off some of the propellant. If the tanker delivers the prop before it warms that much then the normal boiloff will keep it subcooled. We have zero knowledge as to what the delivery temp will be. I will take the bet that it will still be a temp below 1 atm boiling.(ie subcooled)

OK, let's dig down on this.

We have two ultimate constraints in the system:

1) We want the density of the prop as high as possible on the  target ship.  As a practical matter for right now, that target is the HLS, and we are very close to the margins for completing the mission.  So getting the maximum amount of prop (by mass) into the tanks is important.

2) We must have a fluid state that prevents prop at the inlets to the engines' turbopumps from cavitating.  That's some region on an enthalpy-temperature chart that's safe.  I suspect that this will really--ahem--boil down to a region of <pressure, density, temperature> tuples that are safe.  I would expect to see <4bar, 1140kg/m³, 106K>, which is boiling LOX in microgravity, and <6bar, 1230kg/m³, 71K>, which should be close to what launch conditions with subcooling and hydrostatic pressure are, to be included near the extremes of that region.  A similar exercise for LCH4 has to be done.

So here are two questions:

a) Is there an advantage to storing prop at low pressure, applying more cooling power, even if near-flight conditions require higher pressures?

b) What does this mean for the target, in terms of getting the prop in a state that's burn-ready?

I assume that the target won't have cryocooling, so it's likely that the prop will warm up, become less dense, and self-pressurize.  However, it might be possible to flow the prop in under low-pressure, low-temperature conditions, then use some kind of stored gas (either inert or supercritical O2 or CH4) to bring the system up to flight pressure just before the burn.  That could conceivably leave the prop in a subcooled state for a short while. 

However, the trade for that is that the boiloff rate will be very high if there's no active cooling.  Whether the complexity of non-equilibrium pressurization and the high boiloff rates are worth it may depend on how long the target (likely HLS) has to wait between undocking from the depot and when the burn starts.

The reason I'm diving down this rabbit hole is I need a semi-reliable number for the total prop mass for a v3 or v4 HLS.  Rule of thumb is that subcooled prop consumes allows about 8% more prop (by mass) than boiling prop.  That's what I'm using unless somebody can convince me otherwise.

[eriblo]

Repeating here.

You miss the point that subcooled propellant is boiling at a pressure below 1 bar. So just keep the pressure at this lower point.

For example LOX at 20kPa or about .2 bar the temp is 78K

So if you let the pressure drop in the tank it gets to whatever temp(and density) that you want at the expense of boiling off some of the propellant. If the tanker delivers the prop before it warms that much then the normal boiloff will keep it subcooled. We have zero knowledge as to what the delivery temp will be. I will take the bet that it will still be a temp below 1 atm boiling.(ie subcooled)

OK, let's dig down on this.

We have two ultimate constraints in the system:

1) We want the density of the prop as high as possible on the  target ship.  As a practical matter for right now, that target is the HLS, and we are very close to the margins for completing the mission.  So getting the maximum amount of prop (by mass) into the tanks is important.

2) We must have a fluid state that prevents prop at the inlets to the engines' turbopumps from cavitating.  That's some region on an enthalpy-temperature chart that's safe.  I suspect that this will really--ahem--boil down to a region of <pressure, density, temperature> tuples that are safe.  I would expect to see <4bar, 1140kg/m³, 106K>, which is boiling LOX in microgravity, and <6bar, 1230kg/m³, 71K>, which should be close to what launch conditions with subcooling and hydrostatic pressure are, to be included near the extremes of that region.  A similar exercise for LCH4 has to be done.

So here are two questions:

a) Is there an advantage to storing prop at low pressure, applying more cooling power, even if near-flight conditions require higher pressures?

b) What does this mean for the target, in terms of getting the prop in a state that's burn-ready?

I assume that the target won't have cryocooling, so it's likely that the prop will warm up, become less dense, and self-pressurize.  However, it might be possible to flow the prop in under low-pressure, low-temperature conditions, then use some kind of stored gas (either inert or supercritical O2 or CH4) to bring the system up to flight pressure just before the burn.  That could conceivably leave the prop in a subcooled state for a short while. 

However, the trade for that is that the boiloff rate will be very high if there's no active cooling.  Whether the complexity of non-equilibrium pressurization and the high boiloff rates are worth it may depend on how long the target (likely HLS) has to wait between undocking from the depot and when the burn starts.

The reason I'm diving down this rabbit hole is I need a semi-reliable number for the total prop mass for a v3 or v4 HLS.  Rule of thumb is that subcooled prop consumes allows about 8% more prop (by mass) than boiling prop.  That's what I'm using unless somebody can convince me otherwise.

You do it just like you do it when you launch: You store the propellants at whatever temperatures you want to use them (or even colder if you need to maximize storage density and have time to accumulate some heat before usage) - in this case by maintaining the corresponding equilibrium tank pressure points since you are not concerned about ambient atmospheric pressure. Then you temporarily pressurize the tanks to whatever pressure you need for transfers/burns (which is not an equilibrium but maintainable for that duration).

When done you revert back to whatever pressure/temperature point you want to store the propellants at now - for the simplest implementation this just requires venting any excess ullage gas. In many cases it might not be needed because of RCS requirements and the fact that any substantial liquid volume will collapse even hot gas with a minimal temperature increase.

The difference in boil-off due to the slightly higher heat accumulation between different cryogenic temperatures will likely not be a significant consideration.

[OTV Booster]

Repeating here.

You miss the point that subcooled propellant is boiling at a pressure below 1 bar. So just keep the pressure at this lower point.

For example LOX at 20kPa or about .2 bar the temp is 78K

So if you let the pressure drop in the tank it gets to whatever temp(and density) that you want at the expense of boiling off some of the propellant. If the tanker delivers the prop before it warms that much then the normal boiloff will keep it subcooled. We have zero knowledge as to what the delivery temp will be. I will take the bet that it will still be a temp below 1 atm boiling.(ie subcooled)

OK, let's dig down on this.

We have two ultimate constraints in the system:

1) We want the density of the prop as high as possible on the  target ship.  As a practical matter for right now, that target is the HLS, and we are very close to the margins for completing the mission.  So getting the maximum amount of prop (by mass) into the tanks is important.

2) We must have a fluid state that prevents prop at the inlets to the engines' turbopumps from cavitating.  That's some region on an enthalpy-temperature chart that's safe.  I suspect that this will really--ahem--boil down to a region of <pressure, density, temperature> tuples that are safe.  I would expect to see <4bar, 1140kg/m³, 106K>, which is boiling LOX in microgravity, and <6bar, 1230kg/m³, 71K>, which should be close to what launch conditions with subcooling and hydrostatic pressure are, to be included near the extremes of that region.  A similar exercise for LCH4 has to be done.

So here are two questions:

a) Is there an advantage to storing prop at low pressure, applying more cooling power, even if near-flight conditions require higher pressures?

b) What does this mean for the target, in terms of getting the prop in a state that's burn-ready?

I assume that the target won't have cryocooling, so it's likely that the prop will warm up, become less dense, and self-pressurize.  However, it might be possible to flow the prop in under low-pressure, low-temperature conditions, then use some kind of stored gas (either inert or supercritical O2 or CH4) to bring the system up to flight pressure just before the burn.  That could conceivably leave the prop in a subcooled state for a short while. 

However, the trade for that is that the boiloff rate will be very high if there's no active cooling.  Whether the complexity of non-equilibrium pressurization and the high boiloff rates are worth it may depend on how long the target (likely HLS) has to wait between undocking from the depot and when the burn starts.

The reason I'm diving down this rabbit hole is I need a semi-reliable number for the total prop mass for a v3 or v4 HLS.  Rule of thumb is that subcooled prop consumes allows about 8% more prop (by mass) than boiling prop.  That's what I'm using unless somebody can convince me otherwise.

Is there any reason that the empty depot w/cryo cooler can't stay connected to the topped off HLS to maintain prop conditioning? It'll have to disconnect eventually but why not wait until it has to?

[TheRadicalModerate]

Is there any reason that the empty depot w/cryo cooler can't stay connected to the topped off HLS to maintain prop conditioning? It'll have to disconnect eventually but why not wait until it has to?

Yeah, I thought about that after posting.  It obviously adds some complexity to the QD, because it now needs to recover vent gases from the target to return them as liquid.

But there's some irreducible minimum interval from undock to burn.  During that period, the target has to leave the keep-out zone, possibly do minor orbital corrections, do checkouts, and then do the burn.  Whether that's just a handful of minutes or as much as an orbit or two, I have no idea. 

It'd be nice to get a handle on this, because if we're dealing with boiling prop at flight pressure, that could be ~8% less (a number I've seen bandied about with no decent provenance) than the subcooled number.  For a 1600t v3 prop load, that would reduce it to 1493t, a 107t reduction.  If the HLS inert mass (dry mass, crew module, returning samples, unusable prop in the sumps and ullage gas) is 135t, that's 230m/s of extra delta-v, which is non-trivial.

[Twark_Main]

Is there any reason that the empty depot w/cryo cooler can't stay connected to the topped off HLS to maintain prop conditioning? It'll have to disconnect eventually but why not wait until it has to?

Yeah, I thought about that after posting.  It obviously adds some complexity to the QD, because it now needs to recover vent gases from the target to return them as liquid.

There are already vent connections on the QD, correct?

The plumbing is a bit more complex (it adds one new valve config, and it means you want to locate the cryocooler to minimize the length of an additional plumbing config), but I believe the QD connector is the same.

Note that adding constraints doesn't necessarily add mass, eg if the existing hardware already satisfies those constraints.


Do we know where the cryocooler would (notionally) be plumbed in to the existing pipes? Can this be done as just a "software upgrade?"   

[Twark_Main]

~8% less (a number I've seen bandied about with no decent provenance)

Comparing row 27 with row 36, I get 7.6%.

Or alternately you can use the equation to calculate the average density assuming different densities or mix ratios. Hint: WolframAlpha will look up density values using empirically-derived standard NIST curves.

[OTV Booster]

Is there any reason that the empty depot w/cryo cooler can't stay connected to the topped off HLS to maintain prop conditioning? It'll have to disconnect eventually but why not wait until it has to?

Yeah, I thought about that after posting.  It obviously adds some complexity to the QD, because it now needs to recover vent gases from the target to return them as liquid.

But there's some irreducible minimum interval from undock to burn.  During that period, the target has to leave the keep-out zone, possibly do minor orbital corrections, do checkouts, and then do the burn.  Whether that's just a handful of minutes or as much as an orbit or two, I have no idea. 

It'd be nice to get a handle on this, because if we're dealing with boiling prop at flight pressure, that could be ~8% less (a number I've seen bandied about with no decent provenance) than the subcooled number.  For a 1600t v3 prop load, that would reduce it to 1493t, a 107t reduction.  If the HLS inert mass (dry mass, crew module, returning samples, unusable prop in the sumps and ullage gas) is 135t, that's 230m/s of extra delta-v, which is non-trivial.

Alternatively, pull in near boiling props and return subchilled props. Boiloff minimized. Hopefully it also reduces target boiloff between disconnect and start of burn. Would the QD need more inlets/outlets to do this?


Yeah, we really need a handle on transfer details. I bet SX and NASA feel the same way.

[TheRadicalModerate]

~8% less (a number I've seen bandied about with no decent provenance)

Comparing row 27 with row 36, I get 7.6%.

Or alternately you can use the equation to calculate the average density assuming different densities or mix ratios. Hint: WolframAlpha will look up density values using empirically-derived standard NIST curves.

I don't understand what Proponent was using for tank pressures.  We're not that interested in chamber pressure in this case.  I suspect that all of the densities are at 1bar, but I'm not sure.  Since we're mostly discussing what happens when we drop the pressure to depress the boiling point (and therefore raise the boiling density), that's fairly important omission for our purposes.

[rsdavis9]

Is there any reason that the empty depot w/cryo cooler can't stay connected to the topped off HLS to maintain prop conditioning? It'll have to disconnect eventually but why not wait until it has to?

Yeah, I thought about that after posting.  It obviously adds some complexity to the QD, because it now needs to recover vent gases from the target to return them as liquid.

But there's some irreducible minimum interval from undock to burn.  During that period, the target has to leave the keep-out zone, possibly do minor orbital corrections, do checkouts, and then do the burn.  Whether that's just a handful of minutes or as much as an orbit or two, I have no idea. 

It'd be nice to get a handle on this, because if we're dealing with boiling prop at flight pressure, that could be ~8% less (a number I've seen bandied about with no decent provenance) than the subcooled number.  For a 1600t v3 prop load, that would reduce it to 1493t, a 107t reduction.  If the HLS inert mass (dry mass, crew module, returning samples, unusable prop in the sumps and ullage gas) is 135t, that's 230m/s of extra delta-v, which is non-trivial.

Alternatively, pull in near boiling props and return subchilled props. Boiloff minimized. Hopefully it also reduces target boiloff between disconnect and start of burn. Would the QD need more inlets/outlets to do this?


Yeah, we really need a handle on transfer details. I bet SX and NASA feel the same way.

Once again for space, boiling at what pressure? Subcooled at what pressure. It's meaningless unless the pressure is specified.
I'm betting take in gas output liquid for the cryocooler.

When they first started subcooling for f9 there was always 2 ways they were doing it. LN2 bath or pull a vacuum and boil off until correct temp. Cryocooling on earth works by compressing gas and allowing it to expand and thereby cool off until some percent is liquified.

[Twark_Main]

pressure

...

pushing down on me

Best you can do is the triple point, where LOX is 1306.1 kg/m³ and CH4 is 452.5 kg/m³.

Actually operating at the triple point would be impractical (because the range of temperatures where the propellant is liquid is 0 degrees wide), but those densities are the best you can do with low pressure subcooling. That is, unless you plan to use slush propellants...   


https://efs.idsse.ac.cn/module1/pure/o2/TP.html

https://efs.idsse.ac.cn/module1/pure/ch4/TP.html

[OTV Booster]

Is there any reason that the empty depot w/cryo cooler can't stay connected to the topped off HLS to maintain prop conditioning? It'll have to disconnect eventually but why not wait until it has to?

Yeah, I thought about that after posting.  It obviously adds some complexity to the QD, because it now needs to recover vent gases from the target to return them as liquid.

But there's some irreducible minimum interval from undock to burn.  During that period, the target has to leave the keep-out zone, possibly do minor orbital corrections, do checkouts, and then do the burn.  Whether that's just a handful of minutes or as much as an orbit or two, I have no idea. 

It'd be nice to get a handle on this, because if we're dealing with boiling prop at flight pressure, that could be ~8% less (a number I've seen bandied about with no decent provenance) than the subcooled number.  For a 1600t v3 prop load, that would reduce it to 1493t, a 107t reduction.  If the HLS inert mass (dry mass, crew module, returning samples, unusable prop in the sumps and ullage gas) is 135t, that's 230m/s of extra delta-v, which is non-trivial.

Alternatively, pull in near boiling props and return subchilled props. Boiloff minimized. Hopefully it also reduces target boiloff between disconnect and start of burn. Would the QD need more inlets/outlets to do this?


Yeah, we really need a handle on transfer details. I bet SX and NASA feel the same way.

Once again for space, boiling at what pressure? Subcooled at what pressure. It's meaningless unless the pressure is specified.
I'm betting take in gas output liquid for the cryocooler.

When they first started subcooling for f9 there was always 2 ways they were doing it. LN2 bath or pull a vacuum and boil off until correct temp. Cryocooling on earth works by compressing gas and allowing it to expand and thereby cool off until some percent is liquified.

What pressure? That very point is being debated on this and the previous page.
Hey, I'm easy. Whatever works.

[TheRadicalModerate]

Still trying to get a handle on this.

The advantage of dropping the pressure in the depot tanks is not that the liquid is colder, but rather that the vapor is colder, because it boiled off at a lower temperature.  That makes it much easier for the cryocooler to liquefy it back to a temperature that would be heavily subcooled if the system suddenly went up to flight pressure.

Note that liquid density is (almost) solely a function of temperature, so if the boiling point of LOX is 78K @ 0.25bar, and you suddenly raise the pressure to 6bar, it'll still have almost the same 1200kg/m³ density.  (It's really 1kg/m³ denser at the higher pressure, but it's close enough for government work.)

If all prop arrived at the depot in a subcooled state (say, 65K @ 6bar), then a single-stage cryocooler would work fine.  You could transfer the prop to the depot, lower the pressure to 0.25bar, and the depot's cooler would only need to provide effective power to remove the heat leaking into the tanks from the outside.  Irrespective of the pressure, the boiling rate will always be the same after the system reaches equilibrium.

However, that's not what we're gonna get.  Instead, the prop will have heated up during the time it took the tanker to launch and do the RPOD, and will likely be at the boiling point for 6bar (or whatever on-orbit flight pressure is).  So the largest, quickest transfer of heat power into the depot is probably the prop transfer itself, not the leakage from the outside.

I don't know how you deal with that.  I suspect, if you're going to deal with subcooling at all, you then need a multi-stage cooler, which runs until all that heat accumulated during flight has been removed.  Then the last stage (optimized solely for returning low-pressure vapor at low temperature to the liquid state) can run, and the other stages can shut down.  But this doesn't help in terms of the power requirements to deal with the pulse of transferred heat that arrives with new prop.


I'm somewhat more bullish on subcooling on-orbit now, for two reasons:

1) However much power can be dedicated to the cooler, we can pick a pressure where it can have a gas as the input, and it can cool with a very small temperature drop, simply by removing the heat of vaporization.

2) I really like OTV Booster's idea of keeping the target Starship attached until just before its departure burn, with the depot re-liquefying its boiloff.  That way, the depot's cryocooler can do double duty and continue to keep the prop subcooled as long as possible.  Note that this works especially well if the cryocooler is designed to accept gas only, so the boiloff from the target can be circulated back to the depot, then returned as subcooled prop.


I did some cutting and pasting with the NIST isobaric data to make a table of all the densities for LOX and LCH4.  I also computed the average density.  For LCH4 = (111K, 6bar), and LOX = (90K, 6bar) which is boiling temperature at flight pressure, the average density is 835kg/m³.  For LCH4 = (101K, 0.5bar) and LOX = (90K, 0.5bar), which uses the melting points + 10ºC for both fluids, density is 894.3kg/m³. 

That's a 7.1% advantage from subcooling.  That would make v3 tankage at flight pressure and boiling temperature 1486t.  So, if we get some subcooling out of the orbital system, we could wind up with any prop mass between 1486t and 1600t.

So we still don't have a definitive number, but at least we have a range that's plausible.

Again, I expect that power is the limiting factor for how much subcooling is possible.  I wonder if batteries can make a significant dent in getting new prop down to the target temperature.  That'd save the depot having to deploy huge amounts of solar cells.