Starship On-orbit refueling - Options and Discussion

[Redclaws]

This is really, really, really off topic.  Spectacularly so.

[TheRadicalModerate]

Does anybody have an estimate for how much solar wing and radiator area it would take just to have a depot with bare metal tanks and a brute-force cryocooler that could keep up with VLEO levels of boiloff?

[OTV Booster]

Does anybody have an estimate for how much solar wing and radiator area it would take just to have a depot with bare metal tanks and a brute-force cryocooler that could keep up with VLEO levels of boiloff?

Somebody (I thought it was you) said the power to run a cryo cooler would be 2-3 times the power needed to evaporate the propellant. Figure the sun is putting out 1400 W/m^2 at a 55-60% duty cycle. Worst case it's broiling the stainless half the ship. Are we talking about a ship with a heat shield? More options but still nothing worse than stainless flat on to the sun. Stainless has sucko reflectance (I'm not even sure of the term so I can't even look it up) and sucko thermal transmission for a metal.


To add only a minor inconvenience to this indeterminant mess the earth will throw back heat that varies from day to night and between landmass and water, plus's a few other variables like snow and cloud cover, rock vs forest etc. Maybe NOAA or NASA has numbers somewhere. If I remember, I'll look for it tomorrow. Bedtime now.


Oh, one other thing. ZBO or something less?

[TheRadicalModerate]

Does anybody have an estimate for how much solar wing and radiator area it would take just to have a depot with bare metal tanks and a brute-force cryocooler that could keep up with VLEO levels of boiloff?

Somebody (I thought it was you) said the power to run a cryo cooler would be 2-3 times the power needed to evaporate the propellant. Figure the sun is putting out 1400 W/m^2 at a 55-60% duty cycle. Worst case it's broiling the stainless half the ship. Are we talking about a ship with a heat shield? More options but still nothing worse than stainless flat on to the sun. Stainless has sucko reflectance (I'm not even sure of the term so I can't even look it up) and sucko thermal transmission for a metal.


To add only a minor inconvenience to this indeterminant mess the earth will throw back heat that varies from day to night and between landmass and water, plus's a few other variables like snow and cloud cover, rock vs forest etc. Maybe NOAA or NASA has numbers somewhere. If I remember, I'll look for it tomorrow. Bedtime now.


Oh, one other thing. ZBO or something less?

Let's assume ZBO.

First, even in earth orbit, you can point the nose of the tanker/depot at the sun, which effectively puts the main tanks out of reach of direct heating.  There will obviously be some re-radiation from the nose onto the top of the LCH4 tank, but it's going to be dramatically reduced.  This will require some small amount of propellant, because tidal forces want the nose to point toward the center of the Earth, but I'd guess that the amount needed over a refueling campaign would be tiny.

That leaves you with albedo heating from the Earth, which is non-trivial but nothing like direct insolation.

I'm not sure what you're driving at comparing the cryocooler power to the evaporation.  If you're saying that evaporative cooling is more efficient, that may be true--but since we're assuming near-ZBO, it's probably irrelevant.

TPS tiles should have better-than-average emissivity and of course ridiculously low thermal conductivity, but I doubt that helps very much in steady state.  It'll help a bit if you can arrange to have the tiles pointed at Earth on the daylit side and pointed at space on the night side, allowing the heat that piled up on the daylit side (and didn't get conducted towards the bare metal very much, raising the tile surface temperature) to partially radiate away before the next orbit.  But I'd think that this effect would be fairly modest.

[Paul451]

but still nothing worse than stainless flat on to the sun. Stainless has sucko reflectance (I'm not even sure of the term so I can't even look it up) and sucko thermal transmission for a metal.

Reflectance is the term. Stainless is typically around 50%, not great, but there's plenty of worse materials. However, not-very-special white paint might be between 75-85%, compared to polished silver at around 90%. There are special whites that exceed 90%. And various "whitest whites" that the internet loves vying for the momentary record, but they are notoriously fragile. Nonetheless, you should be able to find a suitable white coating that gets 85% reflectance.

Of course, highly reflective materials tend to have awful emissivity, so hold onto their heat once they have it. But there'll be an optimal paint with the right balance of high reflectance and high emissivity.

I assume the trade tilts wildly towards preferring reflectance over emissivity for any sun-facing side.

So, if a depot doesn't need to re-enter, you should expect at least a white coating. And ideally, IMO, a good white coating over a material with low thermal conductivity. Painting the regular heat tiles might be a quick'n'dirty way to get both. But since you don't need a material that can survive the temperatures of re-entry, there's probably vastly better options for thermal tiles that are robust enough to survive launch. Low conductivity lets you keep the heat on the surface material and let it radiate away on the Earth's night-side before it penetrates to the tank.

To add only a minor inconvenience to this indeterminant mess the earth will throw back heat that varies from day to night and between landmass and water, plus's a few other variables like snow and cloud cover, rock vs forest etc. Maybe NOAA or NASA has numbers somewhere. If I remember, I'll look for it tomorrow. Bedtime now.

Earth's albedo is around 0.3 (30%) and the depot will be in an orbit where it's roughly 50% of the sky. There's no reason to try to get any more precise than that, we lack the necessary details about Starship's thermal properties to calculate anything useful, anyway.

Oh, one other thing. ZBO or something less?

That's a decision you make after you've worked out the thermal properties of Starship.

Similarly, you need to know how much heat you are getting rid of in order to work out radiator area, to know whether you can rely on flat-panel radiator on (or built into) the body, or will need to deploy "wings". And hence where you would put the radiators.

First, even in earth orbit, you can point the nose of the tanker/depot at the sun, which effectively puts the main tanks out of reach of direct heating.

Reduces exposed area from roughly 450mē (50x9m, ignoring the nose taper) down to roughly 65mē (ignoring the sun's half-degree "width".) A 7-fold reduction while also keeping that direct heat away from the tank walls.

It also means you can tune each of the three surfaces (nose, dorsal, ventral) for three separate tasks. Make the nose highly reflective, pointed to the sun. Angle the ventral, heat-shield side to Earth and give it a reflective coating, while the low thermal conductivity of the tiles (or a substitute) provide insulation. Point the dorsal side away from both the sun and Earth, with a highly transmissive and highly emissive coating, to help naturally radiate away heat from the tanks to the deep-space background.

And you get all of that before you need to worry about any multi-layered thermal shielding, cryo-cooling, etc. Reducing the amount of energy they have to deal with.

[OTV Booster]

Does anybody have an estimate for how much solar wing and radiator area it would take just to have a depot with bare metal tanks and a brute-force cryocooler that could keep up with VLEO levels of boiloff?

Somebody (I thought it was you) said the power to run a cryo cooler would be 2-3 times the power needed to evaporate the propellant. Figure the sun is putting out 1400 W/m^2 at a 55-60% duty cycle. Worst case it's broiling the stainless half the ship. Are we talking about a ship with a heat shield? More options but still nothing worse than stainless flat on to the sun. Stainless has sucko reflectance (I'm not even sure of the term so I can't even look it up) and sucko thermal transmission for a metal.


To add only a minor inconvenience to this indeterminant mess the earth will throw back heat that varies from day to night and between landmass and water, plus's a few other variables like snow and cloud cover, rock vs forest etc. Maybe NOAA or NASA has numbers somewhere. If I remember, I'll look for it tomorrow. Bedtime now.


Oh, one other thing. ZBO or something less?

Let's assume ZBO.

First, even in earth orbit, you can point the nose of the tanker/depot at the sun, which effectively puts the main tanks out of reach of direct heating.  There will obviously be some re-radiation from the nose onto the top of the LCH4 tank, but it's going to be dramatically reduced.  This will require some small amount of propellant, because tidal forces want the nose to point toward the center of the Earth, but I'd guess that the amount needed over a refueling campaign would be tiny.

That leaves you with albedo heating from the Earth, which is non-trivial but nothing like direct insolation.

I'm not sure what you're driving at comparing the cryocooler power to the evaporation.  If you're saying that evaporative cooling is more efficient, that may be true--but since we're assuming near-ZBO, it's probably irrelevant.

TPS tiles should have better-than-average emissivity and of course ridiculously low thermal conductivity, but I doubt that helps very much in steady state.  It'll help a bit if you can arrange to have the tiles pointed at Earth on the daylit side and pointed at space on the night side, allowing the heat that piled up on the daylit side (and didn't get conducted towards the bare metal very much, raising the tile surface temperature) to partially radiate away before the next orbit.  But I'd think that this effect would be fairly modest.

I was looking for upper bounds, worst case, which would be tank wall to the sun. Nose on would be the way to go in the real world. I wonder if some multilayer insulation on the tank top would be of benefit. Much of the nose has tiles so there's some help there. More on this below.


That 2-3x number is something I read in these forums. AIUI, if the propellant gets 1kW of heating it will take 2-3kW of power to remove that heat and IIRC, it was presented as a rule of thumb and included real world inefficiencies. I lack the personal tools needed to verify this but would very much like to know it's validity.


The orientation of the tiles in relation to the earth is not straightforward. Picture earth at the origin,  the ship at the 12 o'clock position and the sun also at 12 but much further out. The nose is pointed towards the sun, the tail towards earth. The tiles can point anywhere because they're not in play. At the 3 and 9 o'clock position the nose is still pointed at the sun, the tail is pointed off into space and the ship orients on its roll axis to point the tiles towards earth. At the six o'clock the nose is still pointing towards the sun but the earth is in the way, the tail is pointing into space and again, the tiles are free to radiate in whatever direction they want. I fantasize a tile glaze with the properties of thermal white paint.


Earth's thermal input is nowhere near that of the sun but it is not insignificant. There's that specular reflection from the oceans. Then there is good reflection from snow and clouds. Emissivity varies widely. The bare red soil of Arizona reemits much more than the Amazon. Throw in general greenhouse and local greenhouse caused by humidity and it's a very complex model. Especially for VLEO where the ground view is highly localized.


A complete refueling campaign for one client ship could conceivably be done in a few days. Two launch sites each launching every 12 hours. Hookup, transfer, unhooking then clearing the area every six hours. Boiloff probably wouldn't be much of a problem. Realistically, two weeks sounds optimistic for first efforts.


With the tankers broiling in the sun during approach and severe attitude restrictions during transfer, I can't imagine boiloff not being a problem.


IIUC correctly, tidal forces will not only draw one end of the ship towards the earth but because of gravitational irregularities, the ship will end up tumbling. If a depot is a one campaign accumulator intended to return to earth for reuse, using thrust to counter this would be the way to go. If it's a long term facility, CMG's or reaction wheels would make more sense.

[OTV Booster]

but still nothing worse than stainless flat on to the sun. Stainless has sucko reflectance (I'm not even sure of the term so I can't even look it up) and sucko thermal transmission for a metal.

Reflectance is the term. Stainless is typically around 50%, not great, but there's plenty of worse materials. However, not-very-special white paint might be between 75-85%, compared to polished silver at around 90%. There are special whites that exceed 90%. And various "whitest whites" that the internet loves vying for the momentary record, but they are notoriously fragile. Nonetheless, you should be able to find a suitable white coating that gets 85% reflectance.

Of course, highly reflective materials tend to have awful emissivity, so hold onto their heat once they have it. But there'll be an optimal paint with the right balance of high reflectance and high emissivity.

I assume the trade tilts wildly towards preferring reflectance over emissivity for any sun-facing side.

So, if a depot doesn't need to re-enter, you should expect at least a white coating. And ideally, IMO, a good white coating over a material with low thermal conductivity. Painting the regular heat tiles might be a quick'n'dirty way to get both. But since you don't need a material that can survive the temperatures of re-entry, there's probably vastly better options for thermal tiles that are robust enough to survive launch. Low conductivity lets you keep the heat on the surface material and let it radiate away on the Earth's night-side before it penetrates to the tank.

To add only a minor inconvenience to this indeterminant mess the earth will throw back heat that varies from day to night and between landmass and water, plus's a few other variables like snow and cloud cover, rock vs forest etc. Maybe NOAA or NASA has numbers somewhere. If I remember, I'll look for it tomorrow. Bedtime now.

Earth's albedo is around 0.3 (30%) and the depot will be in an orbit where it's roughly 50% of the sky. There's no reason to try to get any more precise than that, we lack the necessary details about Starship's thermal properties to calculate anything useful, anyway.

Oh, one other thing. ZBO or something less?

That's a decision you make after you've worked out the thermal properties of Starship.

Similarly, you need to know how much heat you are getting rid of in order to work out radiator area, to know whether you can rely on flat-panel radiator on (or built into) the body, or will need to deploy "wings". And hence where you would put the radiators.

First, even in earth orbit, you can point the nose of the tanker/depot at the sun, which effectively puts the main tanks out of reach of direct heating.

Reduces exposed area from roughly 450mē (50x9m, ignoring the nose taper) down to roughly 65mē (ignoring the sun's half-degree "width".) A 7-fold reduction while also keeping that direct heat away from the tank walls.

It also means you can tune each of the three surfaces (nose, dorsal, ventral) for three separate tasks. Make the nose highly reflective, pointed to the sun. Angle the ventral, heat-shield side to Earth and give it a reflective coating, while the low thermal conductivity of the tiles (or a substitute) provide insulation. Point the dorsal side away from both the sun and Earth, with a highly transmissive and highly emissive coating, to help naturally radiate away heat from the tanks to the deep-space background.

And you get all of that before you need to worry about any multi-layered thermal shielding, cryo-cooling, etc. Reducing the amount of energy they have to deal with.

Found an interesting paper from 2020. [size=78%]https://tfaws.nasa.gov/wp-content/uploads/TFAWS2020-CT-103-Wilhite-Paper.pdf[/size]


It's about a newer high thermal rejection coating. Among the interesting points is a theoretical 99.9% rejection and a treated sphere at 1 AU could theoretically reach equilibrium at <50K. It postulates a 10mm thickness which I doubt would survive EDL, which would rule out return and relaunch. This paper may have been quoted earlier in this thread or another on NSF.


You make an excellent point in that the ships thermal properties need to be known before focusing on how good is good enough. We sometimes get ahead of ourselves here.


The average albedo OTOH, is not so helpful. VLEO gives such a restricted view of the surface that worst case needs to be explored. It's not impossible that some areas will be so far from the average that mitigation aimed at the average will still allow significant boil off. This may not be, but it should be looked at.


The question of a tanker/accumulator vs depot heavy is one I've sunk my teeth into. The accumulator would work well at VLEO. Depot Heavy would need to be higher. The higher up, the less the earth fills the sky and the more the average of the albedo dominates local extremes. Soooo many moving parts.

[edzieba]

Remember that as well as active cryocoolers and/or added passive heat rejection mechanisms (deployable sunshields, non-reenterable coatings and MLI, etc), both also need to trade against the no-part option of launch more propellant and let any boil-off boil off. Depending on loiter time and final prop load required (which will not always be a full load), that will not necessarily even require an additional launch, and instead mean greater prop loads for any tanker flight(s) topping up the accumulation tanker/depot.

At some point down the road you may end up with enough propellant in orbit over a long enough period of time that the cost of boiloff trades poorly against the cost of developing and operating a low boiloff system. But I suspect that trade point is far further off than the first few years of operation.

[Greg Hullender]

Remember that as well as active cryocoolers and/or added passive heat rejection mechanisms (deployable sunshields, non-reenterable coatings and MLI, etc), both also need to trade against the no-part option of launch more propellant and let any boil-off boil off. Depending on loiter time and final prop load required (which will not always be a full load), that will not necessarily even require an additional launch, and instead mean greater prop loads for any tanker flight(s) topping up the accumulation tanker/depot.

At some point down the road, you may end up with enough propellant in orbit over a long enough period of time that the cost of boiloff trades poorly against the cost of developing and operating a low boiloff system. But I suspect that trade point is far further off than the first few years of operation.

I agree that it's worth at least knowing how bad the boiloff problem is if you do nothing at all, but, as a practical matter, it would seem reasonable to at least do the cheap things to minimize boiloff in the vehicle that accumulates the propellants. That is, keep the nose pointed at the sun, rotate it so the heat shield faces the Earth, cover the nose with Solar White (the paint version, not the tile version), etc. Then see how far it falls short.

[DanClemmensen]

Remember that as well as active cryocoolers and/or added passive heat rejection mechanisms (deployable sunshields, non-reenterable coatings and MLI, etc), both also need to trade against the no-part option of launch more propellant and let any boil-off boil off. Depending on loiter time and final prop load required (which will not always be a full load), that will not necessarily even require an additional launch, and instead mean greater prop loads for any tanker flight(s) topping up the accumulation tanker/depot.

At some point down the road, you may end up with enough propellant in orbit over a long enough period of time that the cost of boiloff trades poorly against the cost of developing and operating a low boiloff system. But I suspect that trade point is far further off than the first few years of operation.

I agree that it's worth at least knowing how bad the boiloff problem is if you do nothing at all, but, as a practical matter, it would seem reasonable to at least do the cheap things to minimize boiloff in the vehicle that accumulates the propellants. That is, keep the nose pointed at the sun, rotate it so the heat shield faces the Earth, cover the nose with Solar White (the paint version, not the tile version), etc. Then see how far it falls short.

Why would Depot have a TPS tiles at all rather than a specialized shield? It will never EDL. IF you are using a Tanker as a Depot, then you don't have a long-term storage problem.

[edzieba]

Remember that as well as active cryocoolers and/or added passive heat rejection mechanisms (deployable sunshields, non-reenterable coatings and MLI, etc), both also need to trade against the no-part option of launch more propellant and let any boil-off boil off. Depending on loiter time and final prop load required (which will not always be a full load), that will not necessarily even require an additional launch, and instead mean greater prop loads for any tanker flight(s) topping up the accumulation tanker/depot.

At some point down the road, you may end up with enough propellant in orbit over a long enough period of time that the cost of boiloff trades poorly against the cost of developing and operating a low boiloff system. But I suspect that trade point is far further off than the first few years of operation.

I agree that it's worth at least knowing how bad the boiloff problem is if you do nothing at all, but, as a practical matter, it would seem reasonable to at least do the cheap things to minimize boiloff in the vehicle that accumulates the propellants. That is, keep the nose pointed at the sun, rotate it so the heat shield faces the Earth, cover the nose with Solar White (the paint version, not the tile version), etc. Then see how far it falls short.

Why would Depot have a TPS tiles at all rather than a specialized shield? It will never EDL. IF you are using a Tanker as a Depot, then you don't have a long-term storage problem.

A non-returning depot is a premature optimisation, and an unnecessary expenditure of a Starship. There is currently only one mission profile (HLS) that might require more propellant than could be carried by a standard Starship, it would be flying at most once per year if that, and could also be serviced with two regular sized Starships. Returning the Starship used as a depot means you get to use it again for something else rather than it floating in orbit doing nothing for a year or more (assuming it even has sufficient in-orbit endurance to do so).

[Barley]

The average albedo OTOH, is not so helpful. VLEO gives such a restricted view of the surface that worst case needs to be explored. It's not impossible that some areas will be so far from the average that mitigation aimed at the average will still allow significant boil off. This may not be, but it should be looked at.

The thermal time constants will matter here. 

If they are several days, or hours, an average should be reasonably good.  The correct average to use might not be the arithmetic average, and it might not be over the entire Earth, but there should be a single number rather than having to model the ground in detail.

OTOH if the time constants are seconds then a pass over the worst case spot could be significant.

[Barley]

IIUC correctly, tidal forces will not only draw one end of the ship towards the earth but because of gravitational irregularities, the ship will end up tumbling. If a depot is a one campaign accumulator intended to return to earth for reuse, using thrust to counter this would be the way to go. If it's a long term facility, CMG's or reaction wheels would make more sense.

When working the dynamics remember that a tank full of fluid is not a rigid body.  A tank half full of liquid is even less rigid.  For a tanker some effects will be orders of magnitude greater than for a rigid body.

I'm not sure exactly which effects will dominate, but I have a difficult time envisioning the nose pointing to the sun while it slowly rotates around the long axis to keep one side towards Earth.  It really wants to enter an end over end tumble. It's going to take work to stop that.

(Also all the attitude control work ends up heating the fluid -- probably not significant but somebody should probably calculate that to confirm it).

[OTV Booster]

Remember that as well as active cryocoolers and/or added passive heat rejection mechanisms (deployable sunshields, non-reenterable coatings and MLI, etc), both also need to trade against the no-part option of launch more propellant and let any boil-off boil off. Depending on loiter time and final prop load required (which will not always be a full load), that will not necessarily even require an additional launch, and instead mean greater prop loads for any tanker flight(s) topping up the accumulation tanker/depot.

At some point down the road you may end up with enough propellant in orbit over a long enough period of time that the cost of boiloff trades poorly against the cost of developing and operating a low boiloff system. But I suspect that trade point is far further off than the first few years of operation.

I suspect you're right on the timeline, but it will happen.


Once refueling is shown to work I expect it to take off, so to speak. Give it 3-5 years and infrastructure, not all of it SX, will start popping up. I'd expect it to be commercial sat servicing for the most part. Probably hypergolics to start with. 3-5 years is long enough to get refueling built into new sat launches.

[TheRadicalModerate]

Remember that as well as active cryocoolers and/or added passive heat rejection mechanisms (deployable sunshields, non-reenterable coatings and MLI, etc), both also need to trade against the no-part option of launch more propellant and let any boil-off boil off. Depending on loiter time and final prop load required (which will not always be a full load), that will not necessarily even require an additional launch, and instead mean greater prop loads for any tanker flight(s) topping up the accumulation tanker/depot.

At some point down the road you may end up with enough propellant in orbit over a long enough period of time that the cost of boiloff trades poorly against the cost of developing and operating a low boiloff system. But I suspect that trade point is far further off than the first few years of operation.

If you're only interested in a depot in LEO, the slop with the last lift tanker launch may easily cover the boiloff.  However, you also need to deal with cislunar refueling, where the way the delta-v budget works out gives you extremely slim margins, even with a full 1500t tanker taking prop to NRHO for an LSS.

Given that you want to recover that tanker (otherwise, you expend one for every lunar mission), you're probably restricted to bare metal tanks and TPS.  But then that makes it essential minimize transit boiloff without solar white coatings, sunshields, etc.  If you only have passive cooling, then you're in a race as to whether you lose more prop doing a 40-90 day BLT and saving 350m/s of delta-v but allowing a longer time for boiloff to occur, or doing the fast transit to NRHO and spending that delta-v.  Even a fairly modest amount of cryocooling solves a lot of problems here.

Also, don't forget that the LSS itself has to store prop for 60-90 days in NRHO, as well as enduring the daylight surface temperatures near the poles.  I'm sure that passive cooling will play some role in the LSS propellant management, but will it be enough to hold boiloff to a reasonable number to meet the requirements?  I wouldn't be surprised to see some kind of cryocooling built into even the Option A LSS.  And if that tech's available for the LSS, then it's likely available for tankers/depots.

[TheRadicalModerate]

IIUC correctly, tidal forces will not only draw one end of the ship towards the earth but because of gravitational irregularities, the ship will end up tumbling. If a depot is a one campaign accumulator intended to return to earth for reuse, using thrust to counter this would be the way to go. If it's a long term facility, CMG's or reaction wheels would make more sense.

When working the dynamics remember that a tank full of fluid is not a rigid body.  A tank half full of liquid is even less rigid.  For a tanker some effects will be orders of magnitude greater than for a rigid body.

I'm not sure exactly which effects will dominate, but I have a difficult time envisioning the nose pointing to the sun while it slowly rotates around the long axis to keep one side towards Earth.  It really wants to enter an end over end tumble. It's going to take work to stop that.

(Also all the attitude control work ends up heating the fluid -- probably not significant but somebody should probably calculate that to confirm it).

A fair point.  But I think the x-axis rotation (to keep TPS pointed at daylit Earth and space on the night side) could be omitted if the dynamics get too hairy.  The first-order requirement is to keep direct sun off of the tanks as much as possible, by pointing the nose at the sun.

It'd be interesting to look at the tidal effects on the propellant if the nose is pointed in some direction other than radially wrt the Earth.  Are they strong enough to force prop into two blobs, or are they small enough that they can't overcome surface tension in half an orbit?  What does that do to the dynamics of the tanker/depot itself?  How does that change based on the amount of prop in the depot?

[TheRadicalModerate]

The question of a tanker/accumulator vs depot heavy is one I've sunk my teeth into. The accumulator would work well at VLEO. Depot Heavy would need to be higher. The higher up, the less the earth fills the sky and the more the average of the albedo dominates local extremes. Soooo many moving parts.

Two big reasons to stay in VLEO:

1) It's more prop-efficient as an overall refueling architecture.

2) The chance of a depot/tanker accident has to be at least an order of magnitude higher than other spacecraft, and it can generate an awful lot of debris.  Even if it just failed passively and couldn't deorbit, it's a pretty big hazard.  Getting it to passively deorbit in a few months is probably pretty high on the requirements list.

This is yet another reason why I like plain ol' tankers with a depot kit, as opposed to non-EDL depots, and why I think it's better to bring down the accumulator when its mission is done.

[TheRadicalModerate]

The thermal time constants will matter here. 

If they are several days, or hours, an average should be reasonably good.  The correct average to use might not be the arithmetic average, and it might not be over the entire Earth, but there should be a single number rather than having to model the ground in detail.

OTOH if the time constants are seconds then a pass over the worst case spot could be significant.

Since you're trying to minimize the flux into hundreds or even thousands of tonnes of propellant, I'd guess that an average will be just fine.

[Greg Hullender]

Given that you want to recover that tanker (otherwise, you expend one for every lunar mission), you're probably restricted to bare metal tanks and TPS.  But then that makes it essential minimize transit boiloff without solar white coatings, sunshields, etc. 

Table 1 in the article I linked to above said that applying 5 mils (about 1/8 mm) of Solar White paint on top of stainless steel reduced absorption of solar energy from 53% to 8.5%. That seems like a very fine improvement for very little cost. Especially if you only need to paint the nose.

[TheRadicalModerate]

Given that you want to recover that tanker (otherwise, you expend one for every lunar mission), you're probably restricted to bare metal tanks and TPS.  But then that makes it essential minimize transit boiloff without solar white coatings, sunshields, etc. 

Table 1 in the article I linked to above said that applying 5 mils (about 1/8 mm) of Solar White paint on top of stainless steel reduced absorption of solar energy from 53% to 8.5%. That seems like a very fine improvement for very little cost. Especially if you only need to paint the nose.

Well, more than half the nose of any EDL-capable Starship is TPS, which you almost certainly can't paint.  The question would be whether to clean off the solar white after EDL would be worth it, vs. just soaking up the rays.  Remember, the nose for a tanker is kinda like the outside of a dewar.  Only a fraction of the heat that's radiated inward, into the payload bay, will warm the top of the LCH4 tank. 

I'll bet a hunk of MLI in the payload bay to cover the dome would be vastly easier to engineer than figuring out how to paint the nose.  The paint won't survive entry.  I have no clue what scorching it would do to the heat distribution during EDL.  Probably nothing good.