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23 minutes ago, Codraroll said:

Two questions immediately spring to mind here.

The first is, how?   ....

And if you go down to the molecular scale, what could possibly be going on to cause excessive boil-off?  ....

I think it comes down to heating of the craft by the Sun (and possibly the reflected radiation from the lite side of the Earth).  The time in the Earth's shadow doesn't radiate much of that heating, so it's a net heating.  It's why the ISS has heat radiators.  Heating cryogenic propellants will increase the vapour pressure inside until the vessel ruptures.  However, by venting some of the boiloff, the specific heat of vapourization goes with the released vapour and helps keep the cryogenic propellants cool and vapour pressure down.

There are potentially some design tweaks that could reduce this.  But as far as I know, it's something that still needs research to find what is worth the increase in mass.

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2 hours ago, Jacke said:

Well, let's see if someone can establish an equivalent atmosphere floating base on Earth; I suspect they're a lot more complicated that it seems.  Especially as if it starts falling it's doomed and everyone has to fly off it pronto.  Then there's the whole problem of establishing them from orbit and taking and sending back rockets from orbit.  And as you mentioned, it would need to get near everything that isn't available in Venus's atmosphere hauled from Earth or elsewhere in the Solar System.

It's not really comparable because Venus is just such a better place to use airships.

From this nice blog post https://spaceflighthistory.blogspot.com/2020/08/venus-is-best-place-in-solar-system-to.html

Quote

Venus settlers would float where Vega 1 and Vega 2 floated, but Landis rejected helium balloons. He noted that, on Venus, a human-breathable nitrogen/oxygen air mix is a lifting gas. A balloon containing a cubic meter of breathable air would be capable of hoisting about half a kilogram, or about half as much weight as a balloon containing a cubic meter of helium. A kilometer-wide spherical balloon filled only with breathable air could in the Venusian atmosphere lift 700,000 tons, or roughly the weight of 230 fully-fueled Saturn V rockets. Settlers could build and live inside the air envelope. 

The air envelope supporting a settlement would not necessarily maintain a spherical form. Lack of any pressure differential would allow the gas envelope to change shape fluidly over time. It would also limit the danger should the envelope tear. The internal and external atmospheres would mix slowly, so the settlement atmosphere would not suddenly turn poisonous, nor would the settlement rapidly lose altitude.  [Emphasis added]

A repair crew would not require pressure suits, Landis explained. They would, of course, need air-tight face masks to provide them with oxygen and keep out carbon dioxide; adding goggles and unpressurized protective garments would keep them safe from acid droplets.

And here's a fun article looking at how it is possible that empty rocket stages might be capable of floating in Venus' atmosphere https://selenianboondocks.com/2013/11/venusian-rocket-floaties/

"Atmospheric recovery" of rockets is an idea he also floats (pun intended).

It's a crazy idea, and I think the idea of any colony being self-sustaining is pretty poor (space is just a terrible place for lifeboating, Earthly fallout shelters make more sense), but an Earth-dependent/space-dependent floating Venus colony could be a project for completion in a time frame of maybe a millennia. Especially if it turns out humans can't be born and properly grow in Mars gravity or lunar gravity, it's worth a shot.

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Envelope math time.

Let's go worst case scenario here. Starship radiates no heat, reflects no heat, and has 500 square meters of area exposed to the sun. 1380W/m2 hits Starship from the sun, for a total of 690000W. The latent heat of vaporization of oxygen is 214,000J/kg, and Methane is 510,000J/kg. Oxidizer to fuel ratio is roughly 3.5, so average latent heat of vaporization is ~280,000J/kg.

In this scenario where zero mitigation is taken and all of the heat hitting Starship goes towards boiling off the propellants, Starship loses about 2.5 kilograms per second. It will spend ~60% of its time in sunlight (probably a bit high, but again, worst case scenario), so a whole 129.6 tons of propellant is lost from Starship per day. Starship would have to launch nearly one refueling flight per day just to keep up with the losses, in the optimistic 150 tons to orbit reusable config (about the higher end of what has been estimated for reusable mode).

This is obviously not a realistic scenario, but it highlights how conservative assumptions can lead to large estimates.

Stainless steel has something like an albedo of 0.6 (60 percent reflected, 40 percent absorbed), and with the nose facing the sun at all times, the exposed surface area is about 64 square meters. This decreases the incoming power to around 36000W.

Starship will also naturally radiate some heat away.

LOX is about 54K, CH4 is around 90K, some of the ship isn't up against cryogens at all, but I will assume the ship's skin is at an average of 60K, conservatively low. Stainless steel's emissivity, I'm finding a large range, let's go for something conservatively low at 0.55 (values up to 0.85 are reported). Starship's surface area is about 1500m^2, it should be higher probably, but again, conservatively low. Plugging those into the Stefan-Boltzmann equation gives a radiative flux of, uh, about 600W. Not great.

Radiative flux scales with temperature to the fourth power, but we still won't get nearly enough flux even raising the entire skin temperature to 110K, the upper end of methane boiling temperatures.

One thing that could be done is to have a double hull for the nose cone, which is pointing towards the sun here, which is moderately well insulated from the rest of the tanks. This could even be done by just having the nose cone empty as with a normal non depot starship. The interior would be coated to reduce interior radiation transfer.

This would allow the, worst case scenario, 64 square meter circle to get much hotter than the rest of the ship and radiate more effectively. The nose is conical, but I'm not sure how to do the math on that, so I'm going to take the volume of an equivalent sphere (should be roughly equal to that of a half sphere stretched by a factor of 2, but not exact). This gives a surface area of about 250 square meters.

To offset the rest of the flux from solar heating, the nose would have to rise to about 260-270K.

Conduction to the rear of the ship over the surface area of the very thin tank walls (let's be extremely generous and assume 5 centimeters thick taking into account internal radiation bypassing the nose shield and stringers and such) (surface area ~1.4 square meters) (90K CH4 tank immediately behind 270K nose cone) will be calculated also. The section between the tank and the nose is, what, 10 meters long on an unmodified non depot starship? The depot one may be different but the extra length helps us here. Heat getting to the fuel is now 369W, and as we found earlier, Starship radiates about 600W by itself. Even assuming it doesn't, we have reduced the boiloff, in theory, to 114kg/day. Even if I'm off by a factor of 10, just by pointing Starship in the right direction, with not that much modification, that's like a ton of fuel per day, which is well manageable.

Unfortunately, it isn't that simple because the Earth is reflecting and radiating heat as well. This ends up totaling roughly 345W/m2 averaged over night and day at the surface, as the Earth is (mostly) in equilibrium, and has four times as much surface area as it does cross sectional area. If Starship is 400km up, this decreases slightly to about 305W/m2, although the atmosphere is further out than the surface so it will be a bit higher than that.

Now we get into the wonderful world of materials having different reflectivities and emissivities for different wavelengths, and I'm going to handwave this and say everything is the same as it is coming from the sun.

Starship is pointing at the sun, so can't really control its Earthwise orientation. Averaged over the orbit, I'm going to assume an average Earth facing cross sectional area of 300 square meters (450 is the max, 64 is the minimum, approximately at least, this whole post is filled with approximations). With the same albedo of 0.6, Starship will receive an average of 36,600W from the Earth.

Due to our solar mitigations, assuming they actually work, the Earth radiation now dominates and is much more difficult to protect against. It is possible the heat shield has better radiative characteristics and could be oriented towards Earth for maximum effect, but the depot probably won't have a heat shield... It could have some other thermal protection in its place, though. This is beyond the scope of my analysis.

Total power reaching the fuel is roughly 36,600-600+370 = 36,370W. This is about 0.13kg/s, or 11.2 tons per day. Not great.

If we conservatively estimate 100 tons of propellant per trip, and a full load of 1300 tons required, that is 13 trips for the principal, and then 1 more trip for every 9 days it takes.

If we assume two ships per week, or one ship every two weeks from each of the four pads, that is a total of 22 refueling launches over the course of 77 days if I did the math right.

 

Keep in mind that this is all an extremely rough approximation, but it shows how upper teens could be a realistic number. High ones could also be realistic if the assumptions on capacity, flight rate, load needed, and thermal protection were changed. We simply don't know enough.

If my calculations are correct, and Earth heating is the driving force, deep space boiloff should be incredibly minor. Unfortunately this means pointing the crew compartment at the sun, which is explicitly what they talk about not doing for Mars.

Edited by Ultimate Steve
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Another thought, subcooling the propellants (I forget if starship does this or not) could provide a buffer against boiloff. Propellant seems to have an average of about 2kJ/kg K of heat capacity. At 100 tons per mission, that's 200MJ of free ish cooling per Kelvin. If everything is subcooled by 5K, that's a gigajoule. At the 36300ish watts of heating I calculated above, that is about seven to eight hours of boiloff buffer. Not much given that we were talking about days between flights, but enough to be significant.

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57 minutes ago, Ultimate Steve said:

Conduction to the rear of the ship over the surface area of the very thin tank walls (let's be extremely generous and assume 5 centimeters thick taking into account internal radiation bypassing the nose shield and stringers and such) (surface area ~1.4 square meters) (90K CH4 tank immediately behind 270K nose cone) will be calculated also. The section between the tank and the nose is, what, 10 meters long on an unmodified non depot starship? The depot one may be different but the extra length helps us here. Heat getting to the fuel is now 369W, and as we found earlier, Starship radiates about 600W by itself. Even assuming it doesn't, we have reduced the boiloff, in theory, to 114kg/day. Even if I'm off by a factor of 10, just by pointing Starship in the right direction, with not that much modification, that's like a ton of fuel per day, which is well manageable.

Now you've got me wondering whether the emissivity of the heat shield tiles comes into play, assuming we are using a reusable tanker Starship. Obviously they are not good at conducting heat, which makes them less useful...but they have VERY good emissivity, so that's something to consider.

Also wondering if pointing Starship engines-first at the sun makes any difference.

I could see a stretched depot Starship with a disposable fairing that covers a deployable heat shade, too; that's a possibility.

Methane is not a super great coolant by any means but it's better than some things. They could go in a direction similar to ACES and use gaseous boiloff from both tanks to operate a small internal combustion engine that pumps methane gas into a radiator, compresses it, and then recycles it back in to make a Carnot heat engine. It's been a while since I took thermodynamics so I am not sure about the physics of using a larger mass of coolant to make up for poorer coolant properties and lower power.

19 minutes ago, Royalswissarmyknife said:

The hype is at the max!

Here we go!

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1 hour ago, Ultimate Steve said:

Unfortunately this means pointing the crew compartment at the sun, which is explicitly what they talk about not doing for Mars.

They can also point the engine section at the sun with much the same effect. But for Mars some sort of active cooling will be needed.

There was a comment somewhere about earlier Mars probes having no boiloff problems, but I'm pretty sure those used storable hypergolic propellants, not cryogenics

2 minutes ago, Ultimate Steve said:

Confirmation that hot staging is all 6 engines, not what I expected. Spicy!

No, I was expecting just the Vacs, to be nearer the vents. Hmm, did they ever test how well the engines start confined in a vented interstage, vs open air?

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3 minutes ago, Minmus Taster said:

Alright, cast your bets folks! How far is this thing getting, I think they'll make it pretty far into the boosters burn before losing control or breaking up.

I'm going to bet safe and say scrub. That'd at least leave me with the small satisfaction of being right, amidst all the other disappointment.

If not scrub, then I guess it will make it up real high, but perhaps not to the intended orbit. Engine-outs are still a major risk.

Edited by Codraroll
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