This has been a great discussion about absorbance, emissions, and insulation for depots. Thank you everyone for sharing your insights.
Am surprised by these numbers, They indicate that a shield only cuts the heat flux by about half.That astonishes me, because the Skylab astronauts reported an immediate dramatic reduction in temperature once their sun shield was deployed.Am also surprised by the initial calculation that the sun facing side has a temperature of only 320*K. I'd always thought that the sun facing sides baked, rather than be at 320*K, which is room temperature.
So the heat shield is only dropping the heat flux from the sun by 44%. Very sad.
However, the other side of the Starship is facing deep space in our simplified scenario. So we get to solve the equation again, but this time in the other direction:outer temp: 88Kinner temp: 90Kheat flux: -3 W/m2So the net heat flux is 723W/m2 into the Starship.
Now this is the worst case scenario - deep space, or a highly elliptical orbit. In VLEO the sun is occluded 1/2 the time, and so now we have to start calculating rates. The system will heat up for half an orbit, and cool down for half an orbit. The tiles themselves absorb heat, which we would have to take into account. Will leave that for another post.
Quote from: TheRadicalModerate on 01/16/2025 04:32 amQuote from: Twark_Main on 01/16/2025 01:12 amQuote from: TheRadicalModerate on 01/15/2025 10:43 pm3) Once you've committed to moving the domes forward, you might as well move them as far forward as possible for both the tanker and depotI can't see why that would be true. Unnecessary dry mass is unnecessary.Moving the domes doesn't increase dry mass. Same number of ring segments, just arranged differently.Wait, I take it back: you have to add another meter or two to the LCH4 downcomer. That's... what? another 400kg? Same thing for hot-gas piping to the LCH4 ullage space, but that's very light.This assumes the total vehicle length must be the same, but of course that's not necessarily true. On a dedicated tanker the payload bay is entirely vestigial. As Musk has said, the mass-optimized tanker would look "weird."
Quote from: Twark_Main on 01/16/2025 01:12 amQuote from: TheRadicalModerate on 01/15/2025 10:43 pm3) Once you've committed to moving the domes forward, you might as well move them as far forward as possible for both the tanker and depotI can't see why that would be true. Unnecessary dry mass is unnecessary.Moving the domes doesn't increase dry mass. Same number of ring segments, just arranged differently.Wait, I take it back: you have to add another meter or two to the LCH4 downcomer. That's... what? another 400kg? Same thing for hot-gas piping to the LCH4 ullage space, but that's very light.
Quote from: TheRadicalModerate on 01/15/2025 10:43 pm3) Once you've committed to moving the domes forward, you might as well move them as far forward as possible for both the tanker and depotI can't see why that would be true. Unnecessary dry mass is unnecessary.
3) Once you've committed to moving the domes forward, you might as well move them as far forward as possible for both the tanker and depot
Yep, that's what I'm saying tends to get over-weighted.Currently everything is bespoke, and honestly it will be that way for a long time. The paper labels read "SN33 common dome," not "Type 1 common dome."
Quote from: TheRadicalModerate on 01/16/2025 04:32 amAs for insulation thickness: once the heat is past the emitting layer(s), it doesn't matter how thick the insulation is, because the heat will eventually conduct into the tank. The time scale we're dealing with is multiple months, so everything will be in equilibrium one way or another.Sorry, but this is not right. In practice you run the calculation iteratively, homing in on the correct exterior temperature.You're seeking to make sure the R-value equation and the net radiant flux (absorption minus emission, as calculated above) give the same heat flux, because at equilibrium they must.The result is that at equilibrium the outer surface will be hotter (and therefore outgoing emission greater, and therefore net heat flux lower) the thicker you make the insulation. In other words, thicker is better.
As for insulation thickness: once the heat is past the emitting layer(s), it doesn't matter how thick the insulation is, because the heat will eventually conduct into the tank. The time scale we're dealing with is multiple months, so everything will be in equilibrium one way or another.
Starship is a cylinder and not a pancake. This only increases the back-side radiation by a factor of pi/2 (ie negligible), but on the illuminated side you probably want to numerically integrate over the curvature, accounting for cosine loss.
Am surprised by these numbers, They indicate that a shield only cuts the heat flux by about half.That astonishes me, because the Skylab astronauts reported an immediate dramatic reduction in temperature once their sun shield was deployed.
Quote from: Twark_Main on 01/16/2025 09:54 pmStarship is a cylinder and not a pancake. This only increases the back-side radiation by a factor of pi/2 (ie negligible), but on the illuminated side you probably want to numerically integrate over the curvature, accounting for cosine loss.When you integrate along the curve with the cosine losses to the irradiance, you find that the net incident radiation is proportional to the cross-section. So a pancake works fine.
Emissivity is a different story, but to tell it you need to know a whole bunch of stuff about the orbit. Even the night side of Earth is pretty hot in IR, and the angular width of the Earth from VLEO is large enough that considerably less than πrL will be radiating into cold space.
Quote from: Twark_Main on 01/16/2025 05:59 amQuote from: TheRadicalModerate on 01/16/2025 04:32 amQuote from: Twark_Main on 01/16/2025 01:12 amQuote from: TheRadicalModerate on 01/15/2025 10:43 pm3) Once you've committed to moving the domes forward, you might as well move them as far forward as possible for both the tanker and depotI can't see why that would be true. Unnecessary dry mass is unnecessary.Moving the domes doesn't increase dry mass. Same number of ring segments, just arranged differently.Wait, I take it back: you have to add another meter or two to the LCH4 downcomer. That's... what? another 400kg? Same thing for hot-gas piping to the LCH4 ullage space, but that's very light.This assumes the total vehicle length must be the same, but of course that's not necessarily true. On a dedicated tanker the payload bay is entirely vestigial. As Musk has said, the mass-optimized tanker would look "weird."Fair enough--to a point. If you don't need more propellant in a depot than you do in a tanker, then don't move the domes more forward than you need to do to optimize prop delivered to LEO. But that's going to depend on your boiloff rates. There's likely to be some lag between the final fill to a depot and when the target Starship pulls the prop out. If more tankage ensures that you can do a full fill in the FTO, then an extra ring segment is well worth it.
Quote from: Twark_Main on 01/16/2025 05:59 amYep, that's what I'm saying tends to get over-weighted.Currently everything is bespoke, and honestly it will be that way for a long time. The paper labels read "SN33 common dome," not "Type 1 common dome."They already have jigs and tooling for making ring segments, and common and forward domes are the same (with both of them moving to EDomes). To the limited extent that things are bespoke, it's because they're changing too fast to make it worth investing in tooling. That's not going to be true for much longer, and it's certainly not going to be true at the level of the stackable subassemblies made out of ring segments, domes, and stringers.Those suckers are big. Maintaining separate stations and holding areas for lots of variants is expensive. It also eats space that could be better devoted to production. They need production, because they need to get cadence up. And to the extent that reusability comes online, they'd much rather devote space to inspection and refurbishment than to squirrelly one-offs.
Quote from: Twark_Main on 01/16/2025 05:59 amQuote from: TheRadicalModerate on 01/16/2025 04:32 amAs for insulation thickness: once the heat is past the emitting layer(s), it doesn't matter how thick the insulation is, because the heat will eventually conduct into the tank. The time scale we're dealing with is multiple months, so everything will be in equilibrium one way or another.Sorry, but this is not right. In practice you run the calculation iteratively, homing in on the correct exterior temperature.You're seeking to make sure the R-value equation and the net radiant flux (absorption minus emission, as calculated above) give the same heat flux, because at equilibrium they must.The result is that at equilibrium the outer surface will be hotter (and therefore outgoing emission greater, and therefore net heat flux lower) the thicker you make the insulation. In other words, thicker is better.That's all true, but you're assuming that the SOFI has good emissivity. The coatings I've seen described are optically reflective particles in an optically transparent matrix, backed by an aluminized layer that's IR-reflective.[snip]
Since it isn't orange, we can presume they are already specc'ing SOFI covered in some sort of space-rated high-emissivity high-albedo paint.These coatings are already widely available, even going back to the first Dragon launch:https://phys.org/news/2013-03-white-coating-spacex-dragon-trunk.htmlhttps://www.aztechnology.com/product/1/az-93
I'm betting on a tile that's a Whipple shield, with an advanced coating on the outside. The tile form factor allows the coating to have a fairly exotic but scalable application method. It'd be lovely if the Whipple shield could do double duty as MLI, but I suspect that making it waterproof will also make it hard to evacuate in space.
My apologies if this has been asked before, or whether it should be on a different thread. Does on-orbit refueling have any precedent outside of SpaceX? I know Stoke Space is planning to use it for their upcoming Nova rocket, but are there any historical examples of this being used, or even just historical plans? Something akin to the myriad of alternate shuttle designs they made in the '60s and '70s?
Quote from: Overtone on 01/16/2025 11:39 amThis has been a great discussion about absorbance, emissions, and insulation for depots. Thank you everyone for sharing your insights.Good discussion, but I haven't seen the math.Let's take a Starship with heat shield of 6cm thick (including the tiles, the blankets, and the backup ablative), give it an R value of 30 in Imperial units (5.28 in MKS), for an Reffective of 0.32 m2K/W. We'll give the heat shield and absorption of 1.0 (probably pessimistic) and emissivity of 0.98.Now for the simplest scenario: The heat shield is facing the Sun, 1300 W/m2. What will be the equilibrium temperature and heat flux into the Starship at the boiling point of LOX, 90K?Now we have two simultaneous equations to solve:emitted heat = 5.67e-8 * 0.98 * Texternal4heat flux through insulation = ΔT/R = (Texternal - 90)/0.32That's a 4th order equation, but fortunately spreadsheets are really good at this kind of thing, and the equilibrium answer is:outer temp: 320Kinner temp: 90Kheat flux through insulation: 726W/m2So the heat shield is only dropping the heat flux from the sun by 44%. Very sad.However, the other side of the Starship is facing deep space in our simplified scenario. So we get to solve the equation again, but this time in the other direction:outer temp: 88Kinner temp: 90Kheat flux: -3 W/m2So the net heat flux is 723W/m2 into the Starship. Still very sad.How much LOX will that heat flux boil?Q=m⋅LQ = heat into the system = 723 J/sL = latent heat of vaporization for LOX = 213kJ/kg. m = mass of the LOX being boiledsolving for m, we get 0.00339 kg/secNow the fuel tank for LOX is about 20mx9m = 180m2 (this is a square cow, the real one is cylindrical), so every second we are boiling .6kg of LOX. That's 2.2t per hour.Is that right? Someone check my math please.Now this is the worst case scenario - deep space, or a highly elliptical orbit. In VLEO the sun is occluded 1/2 the time, and so now we have to start calculating rates. The system will heat up for half an orbit, and cool down for half an orbit. The tiles themselves absorb heat, which we would have to take into account. Will leave that for another post.https://docs.google.com/spreadsheets/d/1esN27mUh7s2gFvXzmvM6x1aU_AnVjfvRYwnGs5U2plw/edit?usp=sharing
Just checked out the spreadsheet.Absorption shouldn't change with exterior temperature.Net should be equal to absorption minus emission, not absorption plus emission.The "rows of temperature" is an interesting approach. I would have used the goal seek feature, selecting the temperature and seeking the error term to zero.
This is further pessimistic because it assumes you don't point the nose at the Sun, which is something you probably want to do. You can stuff a bunch of MLI under the nose cone (where won't freeze up on the pad, unlike trying to surround the tanks).I think this is the minimal implementation of etudiant's "shade." You still need the foam, however, in order to manage thermal heating and reflected sunlight from the Earth.
Quote from: InterestedEngineer on 01/16/2025 08:02 pmhttps://docs.google.com/spreadsheets/d/1esN27mUh7s2gFvXzmvM6x1aU_AnVjfvRYwnGs5U2plw/edit?usp=sharingJust checked out the spreadsheet.Absorption shouldn't change with exterior temperature.Net should be equal to absorption minus emission, not absorption plus emission.The "rows of temperature" is an interesting approach. I would have used the goal seek feature, selecting the temperature and seeking the error term to zero.
https://docs.google.com/spreadsheets/d/1esN27mUh7s2gFvXzmvM6x1aU_AnVjfvRYwnGs5U2plw/edit?usp=sharing