Author Topic: Starship On-orbit refueling - Options and Discussion  (Read 337028 times)

Offline Greg Hullender

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1320 on: 08/14/2022 11:09 pm »
The tiles mentioned were not really intended or explored for EDL. I wonder if anybody's been looking at different fillers. If the heat shield tiles had a Y2O3 glaze they might be able to thin them for lower mass.


Edit to add: Y2O3 is hydrophobic. That's a big thing for the tiles. Not a total solution but a step in the right direction.
I think the trouble is that the heat-shield tiles need to be emissive in the range from about 1 to 8 microns. That rules out coating them with anything like Y2O3. Or anything else that reflects most solar energy, for that matter.
Maybe I'm misunderstanding. See pg3, bottom chart showing a piece of the Y2O3 transmission spectrum. I'd cut n paste but it's not cooperating. [size=78%]https://iopscience.iop.org/article/10.1088/1757-899X/1240/1/012001/pdf[/size]


The chart shows low transmission from about 2 to 10 microns. I've assumed this to mean it readily adsorbs these wavelengths which should also mean it readily emits at these wavelengths. Wrong?


I've tried looking up an emission spectra and hit paywalls and yttria mixed with other things. Also, why 2-10 microns? Isn't this a bit past the far UV? I thought the ideal emission range was in the near IR.
Ah. In this case, low transmission means it reflects those wavelengths, which means it is almost completely non-emissive in that range. Otherwise it wouldn't look white in the visible.

The problem is that the heat tiles get up to 1650 Kelvin, which means their emission curve (see the chart I posted two pages back) has a lot of overlap with the solar one. That chart shows that over 90% of the IR spectrum at 1650 is between 1 and 8 microns. That has way too much overlap with the solar spectrum. Solar white, in particular, is super reflective from 1/4 micron to 8 microns.

That means you can't make a single kind of tile that serves both purposes.

« Last Edit: 08/14/2022 11:09 pm by Greg Hullender »

Offline OTV Booster

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1321 on: 08/15/2022 04:12 pm »
The tiles mentioned were not really intended or explored for EDL. I wonder if anybody's been looking at different fillers. If the heat shield tiles had a Y2O3 glaze they might be able to thin them for lower mass.


Edit to add: Y2O3 is hydrophobic. That's a big thing for the tiles. Not a total solution but a step in the right direction.
I think the trouble is that the heat-shield tiles need to be emissive in the range from about 1 to 8 microns. That rules out coating them with anything like Y2O3. Or anything else that reflects most solar energy, for that matter.
Maybe I'm misunderstanding. See pg3, bottom chart showing a piece of the Y2O3 transmission spectrum. I'd cut n paste but it's not cooperating. [size=78%]https://iopscience.iop.org/article/10.1088/1757-899X/1240/1/012001/pdf[/size]


The chart shows low transmission from about 2 to 10 microns. I've assumed this to mean it readily adsorbs these wavelengths which should also mean it readily emits at these wavelengths. Wrong?


I've tried looking up an emission spectra and hit paywalls and yttria mixed with other things. Also, why 2-10 microns? Isn't this a bit past the far UV? I thought the ideal emission range was in the near IR.
Ah. In this case, low transmission means it reflects those wavelengths, which means it is almost completely non-emissive in that range. Otherwise it wouldn't look white in the visible.

The problem is that the heat tiles get up to 1650 Kelvin, which means their emission curve (see the chart I posted two pages back) has a lot of overlap with the solar one. That chart shows that over 90% of the IR spectrum at 1650 is between 1 and 8 microns. That has way too much overlap with the solar spectrum. Solar white, in particular, is super reflective from 1/4 micron to 8 microns.

That means you can't make a single kind of tile that serves both purposes.
Thank you. Between some slippery decimals, antique eyes and a bad assumption, I was off track.


I was going to leave my response at that but started thinking and came to a conclusion that will make me sound like a whiney 'it's my idea and I'm in love with it' type of guy. I'll risk it.


There's one assumption. From 10-100 microns, except for a couple of notches, the chart shows high transmission. The assumption is that, as in the visible range, this equates to emissivity.


Here's my thinking. Tiles with solar white characteristics in pre-EDL sunlight should run cooler than black tiles. In the early stages of EDL the thermal input is first friction, then compression heating. The solar white would most probably have about the same rejection characteristics as the black tiles. Starting from a lower temp would probably not have a significant impact but it might be worth a BOE for somebody that knew how to do it.


Where there would be a difference is when the plasma starts to build up and radiative input becomes dominant. The solar white will reject more of this than the black, dropping the peak temperature and shifting the black body emissions away from the visible and deeper into the IR. How much? I have not a clue.


If the black body peak moves far enough it's a strong Planck in my argument for solar white tiles.  :D
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Offline Jim

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1322 on: 08/15/2022 04:52 pm »

An idea I've put out is for a constant rpm constant load two stroke. Liquid propellant used for cooling and combustion.  Inexpensive, stone simple to maintain. When run off of liquid propellant the compression stroke has, in effect, already been done. Should be crazy efficient at small scale.


For those with minimal experience with piston ICE's, with constant rpm and load the complexity of 'breathing' and mixing are simplified and efficiency can approach the theoretical Carnot limits. Get rid of the compression stroke, add in the perfectly characterized cooling requirements, and it's better yet.


The major trade to look at is tapping unvaporized propellant vs increased efficiency. I noodled feeding it with boiloff but the cooling gets tricky and the compression stroke shows up again. Maybe gas fed can work, maybe not.

Being a simple easily maintained system, it's good for Mars use too.


some related info

https://www.ulalaunch.com/docs/default-source/extended-duration/development-status-of-an-integrated-propulsion-and-power-system-for-long-duration-cryogenic-spaceflight-2012.pdf

Offline Greg Hullender

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1323 on: 08/15/2022 04:52 pm »
Where there would be a difference is when the plasma starts to build up and radiative input becomes dominant. The solar white will reject more of this than the black, dropping the peak temperature and shifting the black body emissions away from the visible and deeper into the IR. How much? I have not a clue.
I really liked that idea too, but what I could find wasn't encouraging.

"Convection is the primary means of heat transfer to a vehicle entering Earthís atmosphere at speeds under about 15,000 m/s." (Advanced Aerospace Medicine On-line--Tutorial, Section III Space Operations, Chapter 4 Basic Concepts of Manned Spacecraft Design, 4.1.7 Returning from Space, p 322, Federal Aviation Administration, Retrieved 15 Aug 2022).

15 kps is well above Earth escape velocity (about 11 kps), and very-low-earth-orbit velocity is under 8 kps. So the heat transfer will mostly be convective, not radiative, and, hence, I don't think Solar White is going to help.

Offline Greg Hullender

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1324 on: 08/15/2022 05:47 pm »

An idea I've put out is for a constant rpm constant load two stroke. Liquid propellant used for cooling and combustion.  Inexpensive, stone simple to maintain. When run off of liquid propellant the compression stroke has, in effect, already been done. Should be crazy efficient at small scale.

For those with minimal experience with piston ICE's, with constant rpm and load the complexity of 'breathing' and mixing are simplified and efficiency can approach the theoretical Carnot limits. Get rid of the compression stroke, add in the perfectly characterized cooling requirements, and it's better yet.


The major trade to look at is tapping unvaporized propellant vs increased efficiency. I noodled feeding it with boiloff but the cooling gets tricky and the compression stroke shows up again. Maybe gas fed can work, maybe not.

Being a simple easily maintained system, it's good for Mars use too.


some related info

https://www.ulalaunch.com/docs/default-source/extended-duration/development-status-of-an-integrated-propulsion-and-power-system-for-long-duration-cryogenic-spaceflight-2012.pdf
Very interesting. I like the idea of eliminating hydrazine, helium, most of the batteries, etc. That document seems to be from about 2011, so I wondered whatever happened to the idea. Looking further, I also found "ACES Stage Concept: Higher Performance, New Capabilities, at a Lower Recurring Cost," Section IV: Integrated Vehicle Fluids (IVF), Jonathan Barr, ULA, 2015, which was a little easier read, albeit less detailed.

ULA abandoned ACES in 2020 in favor of the Centaur V, but I can't find any indication whether Centaur V uses the internal-combustion-engine approach of IVF or not. It certainly offers long-duration missions with multiple relights though.

If you put something like this on Starship, I'm wondering where the exhaust would go. Some of the documentation for ACES makes it sound like it used the main engine bell. Does that make sense?

Offline JayWee

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1325 on: 08/15/2022 06:08 pm »
https://www.ulalaunch.com/docs/default-source/extended-duration/development-status-of-an-integrated-propulsion-and-power-system-for-long-duration-cryogenic-spaceflight-2012.pdf
Very interesting. I like the idea of eliminating hydrazine, helium, most of the batteries, etc. That document seems to be from about 2011, so I wondered whatever happened to the idea.
ULA's parents (and Shelby) put a stop to it. Would jeopardize SLS.

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1326 on: 08/15/2022 06:16 pm »
Where there would be a difference is when the plasma starts to build up and radiative input becomes dominant. The solar white will reject more of this than the black, dropping the peak temperature and shifting the black body emissions away from the visible and deeper into the IR. How much? I have not a clue.
I really liked that idea too, but what I could find wasn't encouraging.

"Convection is the primary means of heat transfer to a vehicle entering Earthís atmosphere at speeds under about 15,000 m/s." (Advanced Aerospace Medicine On-line--Tutorial, Section III Space Operations, Chapter 4 Basic Concepts of Manned Spacecraft Design, 4.1.7 Returning from Space, p 322, Federal Aviation Administration, Retrieved 15 Aug 2022).

15 kps is well above Earth escape velocity (about 11 kps), and very-low-earth-orbit velocity is under 8 kps. So the heat transfer will mostly be convective, not radiative, and, hence, I don't think Solar White is going to help.
Grumble, grumble. Thought radiative dominated at 8km/s reentry. Sniff, sniff. I guess I did love that idea just a little.
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Offline OTV Booster

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1327 on: 08/15/2022 06:19 pm »
https://www.ulalaunch.com/docs/default-source/extended-duration/development-status-of-an-integrated-propulsion-and-power-system-for-long-duration-cryogenic-spaceflight-2012.pdf
Very interesting. I like the idea of eliminating hydrazine, helium, most of the batteries, etc. That document seems to be from about 2011, so I wondered whatever happened to the idea.
ULA's parents (and Shelby) put a stop to it. Would jeopardize SLS.
Shelby's day is past. Can't patent an idea. It's too good an idea for somebody to not go there.
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Offline Jim

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1328 on: 08/15/2022 06:28 pm »


If you put something like this on Starship, I'm wondering where the exhaust would go. Some of the documentation for ACES makes it sound like it used the main engine bell. Does that make sense?

In separate nozzles for settling.

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1329 on: 08/15/2022 06:35 pm »

An idea I've put out is for a constant rpm constant load two stroke. Liquid propellant used for cooling and combustion.  Inexpensive, stone simple to maintain. When run off of liquid propellant the compression stroke has, in effect, already been done. Should be crazy efficient at small scale.

For those with minimal experience with piston ICE's, with constant rpm and load the complexity of 'breathing' and mixing are simplified and efficiency can approach the theoretical Carnot limits. Get rid of the compression stroke, add in the perfectly characterized cooling requirements, and it's better yet.


The major trade to look at is tapping unvaporized propellant vs increased efficiency. I noodled feeding it with boiloff but the cooling gets tricky and the compression stroke shows up again. Maybe gas fed can work, maybe not.

Being a simple easily maintained system, it's good for Mars use too.


some related info

https://www.ulalaunch.com/docs/default-source/extended-duration/development-status-of-an-integrated-propulsion-and-power-system-for-long-duration-cryogenic-spaceflight-2012.pdf
Very interesting. I like the idea of eliminating hydrazine, helium, most of the batteries, etc. That document seems to be from about 2011, so I wondered whatever happened to the idea. Looking further, I also found "ACES Stage Concept: Higher Performance, New Capabilities, at a Lower Recurring Cost," Section IV: Integrated Vehicle Fluids (IVF), Jonathan Barr, ULA, 2015, which was a little easier read, albeit less detailed.

ULA abandoned ACES in 2020 in favor of the Centaur V, but I can't find any indication whether Centaur V uses the internal-combustion-engine approach of IVF or not. It certainly offers long-duration missions with multiple relights though.

If you put something like this on Starship, I'm wondering where the exhaust would go. Some of the documentation for ACES makes it sound like it used the main engine bell. Does that make sense?
The two red thingies on opposite sides are the units. There are little nozzles extending from them. KISS. If they do another three vacuum engines on SS it'll get crowded but still workable.


The engineering team for this system could put three support gearheads in hog heaven.
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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1330 on: 08/17/2022 06:58 pm »
Hmm. Looking at the pic flashed an idea. Use three units evenly spaced. Three rotating cranks. Three sources of mild torque. The nozzles are intended for settling thrust but can be used to add to the crank torque. Between the two there would be some fine low propellant cost attitude control.



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Offline Twark_Main

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1331 on: 08/17/2022 08:40 pm »
 
The tiles mentioned were not really intended or explored for EDL. I wonder if anybody's been looking at different fillers. If the heat shield tiles had a Y2O3 glaze they might be able to thin them for lower mass.


Edit to add: Y2O3 is hydrophobic. That's a big thing for the tiles. Not a total solution but a step in the right direction.
I think the trouble is that the heat-shield tiles need to be emissive in the range from about 1 to 8 microns. That rules out coating them with anything like Y2O3. Or anything else that reflects most solar energy, for that matter.
Maybe I'm misunderstanding. See pg3, bottom chart showing a piece of the Y2O3 transmission spectrum. I'd cut n paste but it's not cooperating. [size=78%]https://iopscience.iop.org/article/10.1088/1757-899X/1240/1/012001/pdf[/size]


The chart shows low transmission from about 2 to 10 microns. I've assumed this to mean it readily adsorbs these wavelengths which should also mean it readily emits at these wavelengths. Wrong?


I've tried looking up an emission spectra and hit paywalls and yttria mixed with other things. Also, why 2-10 microns? Isn't this a bit past the far UV? I thought the ideal emission range was in the near IR.
Ah. In this case, low transmission means it reflects those wavelengths, which means it is almost completely non-emissive in that range. Otherwise it wouldn't look white in the visible.

The problem is that the heat tiles get up to 1650 Kelvin, which means their emission curve (see the chart I posted two pages back) has a lot of overlap with the solar one. That chart shows that over 90% of the IR spectrum at 1650 is between 1 and 8 microns. That has way too much overlap with the solar spectrum. Solar white, in particular, is super reflective from 1/4 micron to 8 microns.

That means you can't make a single kind of tile that serves both purposes.

One obvious solution here is...

don't use a solar white paint with a cutoff at 8 microns. Use something with a different cutoff.

Based on your earlier graphs, the ideal cutoff wavelength for a "designer" selective surface material would be somewhere around 1-1.5 microns.

Edit: it seems that Z-93 paint (which SpaceX has used before) has a cutoff around 3 microns. Getting closer!

Tiles can't simply be painted (or can they? ???), but that's not my point. Rather, this is intended to show that all solar selective surfaces don't have the same cutoff at 8 microns.

« Last Edit: 08/17/2022 10:45 pm by Twark_Main »
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Offline InterestedEngineer

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1332 on: 08/17/2022 11:27 pm »
The tiles mentioned were not really intended or explored for EDL. I wonder if anybody's been looking at different fillers. If the heat shield tiles had a Y2O3 glaze they might be able to thin them for lower mass.

Why not paint the top of Starship white, leave the tiles black, and point the white side at the sun or other radiating entity?

The white will reflect the heat.

The black tiles will radiate some heat out, which by design they are quite good at.

So will this work?

At solar incidence of 1360 W/m^2 and reflectivity of 98% on the white top, 27 watts/m^2 emission would be needed of the tiles, giving an equilibrium temperature of ~150K, above 112k boiling point of methane.  Close, but no cigar, though it would reduce the evaporation rate of the methane by about 8/27 = 30% as compared to the entire Starship being white.  (8W is tile emission at boiling point)

In LEO while on the sunward side the tiles getting earth radiation, at a rate of 400W/m^2.  An hour soak would impart 1.44MJ on each square meter of tile, and the tiles can store 9MJ of heat per square meter before heating up the back side of the tiles (i.e. the mat and stainless steel and thus the fuel) significantly.

Alas, I lack the knowledge to figure out how hot the outside of the tiles get when there's 1.44MJ of energy stored per square meter of tile, so I can't figure out whether that will radiate off while in the shade of the earth.  Anyone got a curve or equation for shuttle tile soak, heat conduction, and radiation?

The LEO scenario can't be better than deep space, and all white would eliminate 392 W/m^2 from earth radiance while on the sunward side of the earth.  Maybe not worth breaking out the shuttle performance curve references and solving a dynamic heat equation.

So for no modification saving painting the top white, one gains a 30% reduction in boil off in deep space as compared to an all-white Starship and at least 7 free orbits of the Earth before having to boil off methalox. 

So definitely helps the deep space scenario, probably worse for LEO.

But it is almost free of major design changes.
« Last Edit: 08/17/2022 11:33 pm by InterestedEngineer »

Offline Greg Hullender

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1333 on: 08/18/2022 12:38 am »
One obvious solution here is...

don't use a solar white paint with a cutoff at 8 microns. Use something with a different cutoff.

Based on your earlier graphs, the ideal cutoff wavelength for a "designer" selective surface material would be somewhere around 1-1.5 microns.
Yes, but then you give up on the ability of Solar White paint to keep the inside of a tank at 50 K. I'm not sure how much warmer it would be with a 1.5 micron cutoff, but my guess is you're talking dry ice, not LOX.

A lot depends on what your goals are. If you want a system to passively keep cryogens liquid even in full sunlight, then you need that 8 micron cutoff. But if you're just trying to reduce the costs of cooling, then, sure, any old white paint is probably fine.

Offline Twark_Main

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1334 on: 08/20/2022 08:14 am »
No no, by "optimum" I mean that a cutoff at 1-1.5 microns will result in the coldest equilibrium temperature. Colder than 8 microns.

The optimum spectral strategy AIUI is to be 100% reflective in parts of the electromagnetic spectrum where incoming flux exceeds black body emission, and 100% emissive otherwise.

If the vertical axis is spectral power (ie the area under the curve is power), the ideal wavelength cutoff is simply where the curves cross.
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Offline Greg Hullender

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1335 on: 08/20/2022 05:59 pm »
No no, by "optimum" I mean that a cutoff at 1-1.5 microns will result in the coldest equilibrium temperature. Colder than 8 microns.

The optimum spectral strategy AIUI is to be 100% reflective in parts of the electromagnetic spectrum where incoming flux exceeds black body emission, and 100% emissive otherwise.

If the vertical axis is spectral power (ie the area under the curve is power), the ideal wavelength cutoff is simply where the curves cross.
Ah. No, the curves I showed above are normalized so the area under each one is 1. If you look at the unnormalized curves, the radiance from the sun is overwhelming and the curves don't cross at all.

Offline Twark_Main

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1336 on: 08/22/2022 10:28 am »
No no, by "optimum" I mean that a cutoff at 1-1.5 microns will result in the coldest equilibrium temperature. Colder than 8 microns.

The optimum spectral strategy AIUI is to be 100% reflective in parts of the electromagnetic spectrum where incoming flux exceeds black body emission, and 100% emissive otherwise.

If the vertical axis is spectral power (ie the area under the curve is power), the ideal wavelength cutoff is simply where the curves cross.
Ah. No, the curves I showed above are normalized so the area under each one is 1. If you look at the unnormalized curves, the radiance from the sun is overwhelming and the curves don't cross at all.

Did you account for the view factor?

You're not comparing 1 square meter of the Sun's photosphere with 1 square meter of Starship's exterior. You're comparing the hemispherical thermal emissions from Starship (view solid angle = 2 pi steradians) with the insolation from the Sun (view solid angle = 6.794◊10−5 steradians).

That gets you the radiant balance for a surface under direct perpendicular sunlight.

Then derate the insolation to account for orbital night (~1/2), the projected geometry of a cylinder (1/pi), and vehicle pointing (for the tank wall this is sin(θ), where θ is the angle between the nose pointing direction and the Sun).

Plus add the emitted heat and reflected light from the Earth, averaged over one orbit. The emitted heat is simply a ~250 K blackbody emitting 235 watts per square meter, derated 50% for view factor. The reflected light can be approximated as Lambertian solar reflector (black body temperature = 6000 K, times the Sun view factor above) with a reflectivity of 31% (Earth's mean albedo), plus 50% derate for view factor, and 1/pi for Earth's projected geometry.

Then see where the curves cross. ;)


Edit: if the surface is at radiative equilibrium, then normalizing the area under the curves to 1 should work, actually. The catch is, you have to make sure the chosen surface temperature for Starship is indeed the correct equilibrium temperature.

Hopefully this helps!
« Last Edit: 08/22/2022 12:38 pm by Twark_Main »
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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1337 on: 08/23/2022 09:23 pm »
Then derate the insolation to account for orbital night (~1/2), the projected geometry of a cylinder (1/pi), and vehicle pointing (for the tank wall this is sin(θ), where θ is the angle between the nose pointing direction and the Sun).

Plus add the emitted heat and reflected light from the Earth, averaged over one orbit. The emitted heat is simply a ~250 K blackbody emitting 235 watts per square meter, derated 50% for view factor. The reflected light can be approximated as Lambertian solar reflector (black body temperature = 6000 K, times the Sun view factor above) with a reflectivity of 31% (Earth's mean albedo), plus 50% derate for view factor, and 1/pi for Earth's projected geometry.

Then see where the curves cross. ;)

The view factor for Earth-to-Starship in LEO is roughly 45%, irrespective of orientation.  I was kinda surprised by this.  See here.

If you point the nose (or the tail, I guess, although that's were the LOX tank dome is), at the sun, the flux should be close to a point-source at infinity projected onto the nose cross-section, which is SolarConstant * π4.5≤.  No view factor hand-wringing required.

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1338 on: 08/24/2022 08:07 am »
Then derate the insolation to account for orbital night (~1/2), the projected geometry of a cylinder (1/pi), and vehicle pointing (for the tank wall this is sin(θ), where θ is the angle between the nose pointing direction and the Sun).

Plus add the emitted heat and reflected light from the Earth, averaged over one orbit. The emitted heat is simply a ~250 K blackbody emitting 235 watts per square meter, derated 50% for view factor. The reflected light can be approximated as Lambertian solar reflector (black body temperature = 6000 K, times the Sun view factor above) with a reflectivity of 31% (Earth's mean albedo), plus 50% derate for view factor, and 1/pi for Earth's projected geometry.

Then see where the curves cross. ;)

The view factor for Earth-to-Starship in LEO is roughly 45%, irrespective of orientation.  I was kinda surprised by this.

Yep. I came to the same conclusion.


Doing (roughly) the above math, I don't know where this 8,000 nanometer spectral cutoff comes from. By my curves, to minimize tank heating the surface should ideally be maximally reflective through the entire infrared band.
"The search for a universal design which suits all sites, people, and situations is obviously impossible. What is possible is well designed examples of the application of universal principles." ~~ David Holmgren

Offline Greg Hullender

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Re: Starship In-orbit refueling - Options and Discussion
« Reply #1339 on: 08/24/2022 10:21 pm »
Doing (roughly) the above math, I don't know where this 8,000 nanometer spectral cutoff comes from. By my curves, to minimize tank heating the surface should ideally be maximally reflective through the entire infrared band.
Well, there's this quote from the guys who came up with Solar White:

"First, assume that a perfect coating was developed with a cutoff at about 4 Ķm, so that only 1% of the Sunís energy was absorbed, i.e. a ratio alpha/epsilon = 0.01. For a sphere the temperature now drops to 88 K, below the 90 K needed to maintain LOX, but still too high to run a superconductor. But if we can find a material with a transition wavelength at about 8 Ķm, where only 0.1% of the Sunís energy is absorbed, then the sphere temperature will drop to about 50 K. This would not only allow superconductors to operate, but would allow LOX storage to occur at higher density and at lower pressure. Figure 7 shows the temperatures that could be achieved if a perfect material were available to coat a sphere at 1 AU from the Sun."
(Cryogenic Selective Surfaces: Final Report on a Phase I NIAC Study, p. 10, February 2016, Robert C. Youngquist and Mark A. Nurge)

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