Okay, some basic physics:
The temperature of a spherical object, evenly heated by incident sunlight and cooling by reradiation, is given by the equation:

T = T_s x ([1-A]/4)^0.25 x (R_s/d)^0.5

where T_s and R_s are the temperature and radius of the sun, A is the albedo and d is the distance from the Sun. You can find this in any basic astronomy textbook, since it relates to planetary temperatures.

Plug in the numbers for an object that reflects about a third of incoming radiation (not particularly shiny) and you find that:

T ~ 250K

Well below freezing.
An object needs to be pretty much black as asphalt (albedo 8%) to raise its equilibrium temperature to freezing, at Earth's distance from the Sun.

Grant Hutchison

So I guess the question should be, "How was the Apollo spacecraft heated?"

Sorry, I've been trying to edit my above post to improve the layout and to add a phrase, but the edit function keeps hanging up.
I'll fix the layout for readability later, but what I was trying to add was:

So basic physics gives us an excellent reason to assume that an unheated Apollo capsule would fall below freezing. It therefore appears that we do need some specifics of Apollo design if the problem is to be considered further.

Grant Hutchison

If someone wants to get nitty gritty I'll mention that each astronaut put out about 490 kilojoules of heat an hour. (Assuming they didn't gain or lose weight on the mission.)

Grant:

Does your calculation result in an average temperture for the sphere? After all, moon rocks get much hotter after sitting in the sunlight for a few weeks. Many of them are lighter in color than asphalt. However, the rocks sitting in the shade are getting quite cold.

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Guesstimate. I'm not much of an orbits guy.

Almost certainly. The CSM had a lot more electronics Than either Mercury or Gemini.

Gotta love that 2/60,000 air conditioning.

(Note: Kitten-like typing may be detected. Sorry if I missed any "typos".)

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Yup.

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And you, to whom adversity has dealt the final blow
With smiling [faces] lyin' to ye' everywhere ye' go
Turn to, and put out all your strength of arm and heart and brain
And like the Mary Ellen Carter, rise again.

Somebody in the about BAUT forum posted a work-around. Click edit, and then click "go advanced". That seems to work.

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I was just sitting here contemplating the immortal words of Socrates who said, "I drank what?"

"Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot." --Carl Sagan "Pale Blue Dot"

It does. Or rather, an average infrared luminosity. (Luminosity varies with the fourth power of temperature.)
It assumes a sphere intercepts radiation over a cross-sectional area of πr² and reradiates a black body spectrum uniformly over its surface area, 4πr². The ratio between these two gives us the factor of 4 sitting on the bottom of the albedo section of the equation. Lumpy objects will generally have a higher ratio of radiating area to interception area, and so may equilibrate to lower temperatures.
Of course, in the real world, something the size of a moon or planet will be able to develop areas of its surface which are locally hotter and colder than the average, just so long as the complicated temperature distribution results in the right amount of infrared reradiation to maintain equilibrium.

[I still can't get the edit function to work, and now I've noticed a misplaced decimal in my equation. If I can ever get back to it, I'll edit the original, but meanwhile here's the corrected version (the typo was in the exponent of the albedo section):

T = T_s x ([1-A]/4)^0.25 x (R_s/d)^0.5

Sorry!]

Grant Hutchison

Thanks! I've now fixed the original, too. My error is in any case carefully preserved for posterity by being quoted in Polite Reasonable Rabid D's post.

Grant Hutchison

Are you using the "quick" edit? That seems to hang quite often. Go to the "Advanced" editor, and save your changes there.

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The Leif Ericson Cruiser

A lot of the discussion refers to "the spacecraft" as if it were a single object. When considered thermally, "the spacecraft" is a collection of objects, each in a specific heat-transfer context. The outer skin, the inner skin, the enclosed air, the windows, the frame, the wiring, the coolant, and so forth are all objects that behave thermally in complex and interactive ways.

While basic heat transfer describes how heat transfers within and between objects, the overall picture of the actual thermal situation of anything as detailed as a spacecraft is not implied at all reliably from the simple equations. That's like saying that since "basic" physics describes one rock atop another, anyone with that knowledge can build Chartres cathedral.

In fact the thermal design of spacecraft is its own field. Clearly "basic" knowledge isn't enough to practice the field, otherwise the various texts, papers, and courses on the subject would be a waste of time and paper.

In practice, understanding heat transfer in a complex composition such as a spacecraft indeed involves basic constitutive relationships, but modeled on the small scale incorporating the actual geometry, relationships, and properties of the components. So while a basic equation can give you the equilibrium temperature of a simple object in a simple radiative environment, the thermal profile of a spacecraft has no closed form and requires iterative models that can be solved only by fast computers and a lot of patience.

"How was the spacecraft cooled?" implies it was naturally hot. A better question is, "How was the spacecraft temperature controlled?"

I can go on and on about that. First we should talk about heat rejection. In space you often reject heat by radiation. Something that's hot will radiate its heat away as electromagnetic energy. Slowly, but surely. So if you have a radiator (not an automotive radiator but a true one) you can face it away from the sun and let heat radiate away into the blackness of space. Often you need two radiators on opposite sides, so that if one is facing the sun and can't effectively radiate, the other can.

The service module had opposing radiators. The fuel cells had their own separate radiators.

So then you need to get the heat from where it is to where it can be rejected. That's best done by a liquid coolant that's pumped in a loop between heat sources and the radiator. Heat always flows from hot to cold, so if the coolant comes out of the radiator freezing cold, heat will naturally flow into it without much coaxing. Grab a metal faucet tap with the cold running and see how long you can hold onto it.

Heat might come from absorption from the sun. It might come from electronic equipment. It might also come from the astronauts' metabolism. If you can get it into the coolant, you can reject it to the radiator on the dark side of the ship.

In practice heat didn't come from the sun on Apollo. The reflectivity of aluminized Kapton varies from about 0.45 to about 0.80 depending on manufacture. Of aluminum itself, up to 0.9. The spacecraft just isn't going to absorb a lot of heat all over.

Electronic equipment was the biggest heat producer on Apollo. Old 1960s and 1970s electronic components, remember.

Humans are finicky. They need an air temperature within a fairly narrow band in order to remain healthy and productive. So for Apollo there was a special problem in keeping their air mass at an appropriate temperature. If you blow the air past an exchanger, you can either suck heat out of it (if the exchanger coils are cold) or put heat into it (if the coils are hot). For Apollo, the same coolant loop was used for cabin air temperature control as for sucking heat away from electronics. A thermostatic switch operated a solenoid valve that piped the cabin heat exchanger to the upstream leg (i.e., right after the radiator, before the electronics blocks) to cool the air, and to the downstream leg (i.e., after the electronics, before the radiator) to heat it.

Without the electronics operating, there was no way to add heat to the air by that mechanism.

But that's not the only way the air could be heated. The CM had five windows, at least one of which would probably be admitting sunlight. Light streams in through the windows and shines on cabin interior surfaces, where it warms them radiatively. Those surfaces in turn transfer heat convectively to the air. That's not a lot of heat compared to what's transfered by the ECS exchanger. But if that suddenly doesn't work, the second-order greenhouse effect may become the first-order effect.

When the Apollo 13 astronauts put shades over the window to try to sleep, the sun no longer shone in. The lit surfaces no longer were warmed by the sunlight, and no longer transferred heat to the air. Even with all the insulation and thermal design, you can't practically eliminate all the conduction paths from the inner structure to the outer skin. And the vast majority of the outer skin that doesn't have a view factor to the sun will radiate and cool. Heat from attached structure conducts to it. And heat from adjacent cabin air will convect/conduct to that structure. Thus at the air/structure interface, the heat transfer reversed. That's why the temperature dropped significantly in the cabin.

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I would hate to live the rest of my life knowing I had done that to you. So I went back and moved the decimal point. Was that it, or was there something else?

You know, I never really thought about it until you mentioned it, but why would a radiator need a fan?

To keep those pesky space bugs from glomming onto the radiator?

All seriousness aside, I think that's one of the common layman misunderstandings. The radiator in a car is not a true radiator in the sense that it employs radiative heat transfer in order to reject heat. In fact it's a heat exchanger that uses forced convection to draw heat from the radiator coils. So when someone hears that the service module had "radiators" and he hears that convective heat transfer to the ambient doesn't work in space, he might wonder what's up. The radiators in the service module were true radiators in that they simply got hot and glowed away the heat as infrared light.

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How efficient is that - in space?

That was it.
Now the only evidence that I ever erred is the very large fuss I made about it.

Grant Hutchison

May I make a friendly suggestion. I did not like IDW's of a private discussion, but maybe we could try half way. There is a lot of stuff here answering his question. I think the ball is in his court. Might I suggest we all go do other things for the moment, and let him respond upon his return.

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How efficient is that - in space?

The short answer is "not very." Radiative heat transfer in general is not a very efficient means compared to forced convection, and forced convection in turn is not very effective compared to conduction. These differences can be orders of magnitude for real-world problems. We use radiative heat transfer in space because it's practically all we have available.

But when you add "in space," you bring up the point that in space radiative heat transfer is, pound for pound, more efficient there than, say, on Earth. That's because one of the many factors that affects the ability to radiate heat in practice is the incoming radiant heat from the environment, especially from nearby surfaces that radiate. Deep space is the perfect heat sink for that property. If your radiator faces deep space, there is no incoming light to fall on the radiator. If it faces a strong reflector such as the nearby Earth, or a strong emitter such as the sun, your ability to reject heat through it suffers a lot.

This was actually a problem on one of the later Apollo missions. One of the radiators on the LM faced upward, ostensibly toward relatively deep space. But in one case light reflected from a lunar mountain fell on the radiator and restricted its efficiency.

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Try what? So far, this is a topic right out of Q&A. Someone asked a question and everyone who thinks they can help provide an answer is answering, as they should, and then people who think they have spotted problems in other answers pipe up, and people ask each other to fill out details, or answers inspire deeper questions, and off we go just like BAUT is supposed to work.

Nothing here is broken -- except maybe for the choice of the subforum for posting. I don't see a conspiracy claim.

IDW shouldn 't have started a Q&A thread if IDW didn't want a Q&A thread.

There is no ball. There is no court. There is no game.

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In post #8 IDW contends that "the spacecraft would be unable to shed heat in the vacuum of space through the conversion of heat energy buildup from Solar radiation and internal heat sources into thermal radiation which the spacecraft can shed in space."

Sounds like he's saying the Apollo spacecraft couldn't have worked, although everyone believes it did. Sounds like a conspiracy theory to me.

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You might have missed this:

(emphasis added)

This led to my questions:

What would stop Apollo from radiating to space? What makes it different from other spacecraft or the Earth for that matter?

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The Leif Ericson Cruiser

I truly hate to add to what may be perceived as a growing dog pile here, and I only speak in hopes of clarifying what I believe is the underlying question by the OP.

To wit: in other threads at other times Warrior has indicated that he either does not believe in radiative heat transfer, or that he believes it is an effect of too small an order to be important in the thermal design of spacecraft.

I will not put words in his mouth. What I would like to respectfully suggest, however, is that we back off and allow him to clarify the point in his original post that he wishes to draw our attention to. If it is, as I believe, what I have indicated above, then detailed discussion of thermal design is basically a sideline to the subject of this thread.

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"You keep using that word. I do not think it means what you think it means."

That just looks like more of a technical question to me, in the form of a "contention". It's a common form in Q&A. Does IDW not seek a correction to the statement?

Is it supposed to be the conspiracy claim?

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I think now would be a good time for IW to explain exactly why the temperature management techniques employed would not have worked as designed...perhaps after having a look at something like this.

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Brett
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I believe it is part of it, yes. But I agree with nomuse, and will wait for IDW to clarify his position.

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The Leif Ericson Cruiser

Your right when you claim all that is required is an elementary knowledge of thermodynamics.

That's not what I think Moose claiming. I paraphrase his answer as, "If you insist on a simplified explanation for how the Apollo CM was cooled, then the simple answer is 'by radiation.'" I don't see anything that implies Moose believes such an answer would be complete. The error here is yours in insisting that only vague, simple explanations are allowed. Moose was simply giving the answer that fit your artificial restrictions.

If someone asked me for an "elementary physics" answer for how an airplane flies, the answer might be, "Because the wings generate lift when air flows over them." That would be a correct answer given within the scope of the restrictions in the question. But that acquiescence doesn't mean the totality of airfoil design can be expressed in "elementary physics," nor that the extremely sexy design of the Boeing 787 Dreamliner's wing can be confirmed or invalidated or even understood solely from those principles.

Doesn't Jay possess such knowledge?

I do, as well as a fairly well-developed understanding of the thermal design of spacecraft and how it can or cannot be considered addressable from an "elementary" physics point of view. I also have an understanding of the details of the Apollo spacecraft systems' thermal design. I also supply tools and expertise to other engineers that facilitates the thermal analysis of their mechanical designs, including for spacecraft.

I am not alone in that knowledge, as has been clearly demonstrated.

Two things though, the car is under the protection of the atmosphere and the magnetosphere...

Would it help to tell us the absorption of those media in thermal wavelengths?

...and air molecules are moving over it to cool it.

No. Air molecules are moving over it to provide a heat transfer mechanism. Without more detail in your example, more consideration of the context, and more rigor in the mathematics and physics, you can't presume heat is conveyed solely away from the car over all applicable time. What about a car parked in the shade?

You're on the right track in trying to account for the ways in which your example might differ from the situation faced by an Apollo spacecraft, but you haven't gone far enough nor considered the problem broadly enough to make it a workable comparison.

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My beliefs are different, I guess.

That's completely understandable, if you feel you can't help without more information.

But, I don't think it should stop anyone else from offering answers, or asking other questions of IDW or other participants. I don't think anyone should feel compelled to wait for a nonexistent ball to return.

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Is it supposed to be the conspiracy claim?

IDW claimed before at GLP that the account of the Apollo 13 experience is not credible because it describes a physically inexplicable thermal situation for the spacecraft. In a post in the other thread at BAUT he referred to the Apollo 13 account not being accurate or credible. Although he has not renewed that claim explicitly here, it appears he intends to continue to argue, as before, that the Apollo 13 spacecraft should have become very hot, not very cold. Hence the leading question in this topic, "How was the Apollo spacecraft cooled?" (emphasis added) when a more appropriate question would ask how it was heated.

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