Talk:Solar greenhouse

/Archive 1

Future of this article
This article only got created because of the Great Greenhouse effect war. Nonetheless it has some useful info. What should happen to it? Much of the how-do-GH's-work is redundant, because of the GHE page's current state. William M. Connolley 2005-06-29 21:24:45 (UTC).


 * The article does have useful content on the details of greenhouses. It should be more tightly linked to the regular greenhouse page and de-coupled from the greenhouse effect page. The overheavy reference section needs to be weeded to focus more on the greenhouse details and delete those only dealing with the climate aspects. -Vsmith 30 June 2005 01:28 (UTC)

The claim that the greenhouse effect works by blocking convection is absurd. That's like saying a tea kettle works by blocking drainage. It says nothing about what drives the temperature up. (With your windows and doors closed, your home also acts as a barrier to convection, but that doesn't make it a greenhouse.) I first encountered this claim on a web site funded by the oil industry that professed to "explain" the greenhouse effect but only clouded the issue (If you'll excuse the expression). --MiguelMunoz 08:47, 28 July 2006 (UTC)


 * The claim is correct. Please see the greenhouse effect article for details. This was discussed extensively there - please go and read the discussion there William M. Connolley 10:26, 28 July 2006 (UTC)


 * I read all of his contributions, but there is no contribution with those numbers, nor is there one that refutes (or even addresses) my claim. I maintain my position. The claim is absurd. If you disagree, you're welcome to point out the flaw in my reasoning. The claim is equally wrong on the greenhouse effect page. --MiguelMunoz 18:23, 28 July 2006 (UTC)


 * You're wrong' but the place to debate it is the GHE page, not here William M. Connolley 20:20, 28 July 2006 (UTC)


 * The question in place can be easily solved by experiment. Any surface can block convection, but certain surfaces deal with IR radiation differently. Gerhard Gerlich, Professor for Mathematical Physics at the TU (Technical University) of Braunschweig, Germany, most recently wrote a long paper to disprove the global warming hypothesis, in which as an aside he revisited the glasshouse debate. He pointed to experiments made by R.W. Wood already in 1909, in which Wood had built two identical boxes as "model greenhouses" and covered one with a glass shield and one with a sheet made of rock salt (NaCl) which does not absorb IR. Surprisingly the salt covered box had become slightly warmer, resulting from the fact that solar light reaching the earth still contains an own portion of IR (which is kept out of the glasshouse by the glass). Wood then blocked out incoming IR by installing another glass plate as a filter for inbound solar light. After this modification both boxes heated to a point of about 55°C, with the difference between them below 1°C. This means that the glasshouse effect is mainly due to blocking of convection, with the radiation portion to be considered neglectable.--Kermecke 10:04, 12 August 2007 (UTC)


 * Gerlich is a nutter, though he has read Wood correctly. Gerlichs paper is trash. A colleague of mine read it and decided it was probably malicious, ie deliberately misleading, rather than merely confused, as I though. Either way its not a suitable ref for wiki. Back to Wood, you'll find his (perfectly valid) expt already described on the GHE page William M. Connolley 15:19, 12 August 2007 (UTC)
 * William, this lemma here is about warming in a glass house, which Gerlich correctly describes, so he is an absolutely valid source for the topic. So what is your objection against mentioning him? That he is a strong and vocal opponent against the global warming dogma which OTOH is - as far as I understand it from your intro - your income base as a climate modeller? Taking out Gerlich as a source here because of your (or your buddy's) opinion regarding a different topic means censorship. This should not be the Wiki way. I am happy to discuss with you views on GW issues and Gerlich's arguments at a separate place. - Cheers - Klaus --Kermecke 08:07, 13 August 2007 (UTC)

I took G out, as I said, because he is a nutter. The fact that he got one thing right doesn't make him any less a nutter; his paper contains numerous errors and is not a useful source of information. Also, this isn't the right page for this - the correct page is greenhouse effect William M. Connolley 20:36, 13 August 2007 (UTC)
 * William, you belong to a group of closely aligned people who publish their shared views on a website called "Real Climate", on which you and your colleagues claim to be something close to the only serious climatologists on the planet. A large number of scientists including Professor Gerlich critize your scientific positions and offer different views. So you are party to this dispute and not the referee, and it might create concerns in the scientific and analyst community if you go on to surpress different opinions by calling them names and censoring any hints to inconvenient scientific sources.--Kermecke 21:45, 13 August 2007 (UTC)


 * The Gerlach paper was not a source used in writing this article. The Wood experiments are well referenced elsewhere as used in the writing of the article. The introduction of a paper discussing Falsification of the Atmospheric CO2 Greenhouse Effects... is not needed here as the article is not about the climate greenhouse effect, rather about how a glasshouse works. The inclusion after the fact of this redundant reference would appear to be pushing an unrelated pov here or just spam. Now please keep the discussion civil and cease making COI accusations - keep this discussion page on track and about glasshouses. Vsmith 00:59, 14 August 2007 (UTC)
 * I had added the Gerlich reference as a prep to edit the main article later which admittedly I had not done yet. So your first point is valid. However, if I invested the time and edited the article, certain people would remove the Gerlich ref again anyway, wouldn't they? --Kermecke 10:00, 15 August 2007 (UTC)
 * Yes, because its trash. We can, if you really want to, discuss the virtues of the article, but please do it in the right place, ie GHE not here William M. Connolley 19:55, 15 August 2007 (UTC)
 * As expected, and that would be a clear breach of Wikipedia's COI policy. BTW, Gerlich thinks that your (RealClimate) positions are wrong (he too likes strong language!). However, he does not censor or suppress the stuff you write. Matter of fact is that his article contains a detailled physical analysis how a glasshouse works. This makes it a valid source for this topic here.--Kermecke 10:33, 16 August 2007 (UTC)
 * Surprise surprise. Wurbling about COI is dull. G's paper contains too much trash to be linked by wiki; if it says anything new that Wood didn't say, I missed it William M. Connolley 20:23, 16 August 2007 (UTC)

I fully agree that claiming greenhouse effect is not exsistent in greenhouse is absurb.

Greenhouse warms up by sun, but it keeps the temperature up by preventing *all* means of thermal transfer. This includes also preventing radiation. If it would not, it would quickly cool down to the environment temperature (just like cheap plastic film greenhouses do..). AFAIK, no one has ever replicated the Woods experiment, so can it really be used as a reference? Not in any self-respecting site!

So the claim is incorrect. —Preceding unsigned comment added by 82.128.226.51 (talk) 15:43, 31 January 2009 (UTC)

—Apis (talk ) 17:57, 31 January 2009 (UTC)
 * This seems to be a reoccurring discussion. The bottom line is that the threshold for inclusion in Wikipedia is verifiability, not truth. So whatever you (or I) believe doesn't matter. Instead we have to cite reliable sources, and there are several that claim that this is the case. Unless someone can provide sources of similar quality saying otherwise, we shouldn't change the text.

POV fork?
I hope no one will immediately brand this page a POV fork and vote it into deletion:
 * 1) There is no NPOV dispute about it going on right now, that I know of.
 * 2) It is a legitimate spinoff of the Greenhouse article (the one about plants in a building with glass walls and roof). --Uncle Ed 17:46, 23 August 2006 (UTC)

Added 2 pictures with extra notes on other uses
Following was added:

.



Include the other uses in article or in the other greenhouse-article. Perhaps a rewrite is necessairy.

KVDP (talk) 14:58, 5 April 2008 (UTC)


 * I'm not sure a white plastic greenhouse actually *is* a greenhouse William M. Connolley (talk) 21:12, 5 April 2008 (UTC)


 * I've deleted the white plastic pix. The glass house pictured definitely *is* a greenhouse, so I've moved that up. Does the white plastic one "A solar greenhouse works by letting in solar radiation and trapping the energy from that radiation to increase and maintain the internal temperature" - or is it, as its description says, to keep the seeds moist? William M. Connolley (talk) 22:23, 18 April 2008 (UTC)

Smell test
I applied the smell test to the statement "Thermodynamically isolate the system to stop convection and conduction from equalizing the inside temperature with the outside temperature" and got back "it stinks." As a description of what tents, houses, greenhouses, Fedex shipping packages, etc. accomplish for their contents this is pure and utter obfuscation. This sort of pretension to scientific legitimacy has no place in Wikipedia. Wake up and smell the flora in the greenhouse, this emperor has no clothes. As Westley said in The Princess Bride, "Anyone who says different is trying to sell you something." --Vaughan Pratt (talk) 05:05, 7 November 2009 (UTC)

By way of expansion on this, why not simply say something along the following lines. ''A greenhouse is a building exposed to sunlight and having limited or no air circulation to the outside for the purpose of maintaining a warm and humid environment suitable for plants. Greenhouses are normally constructed with glass walls and roof. Most forms of glass are transparent to incoming shortwave sunlight (400-2000 nm wavelength) and opaque to outgoing longwave thermal emission (10-30 microns), thereby enhancing the warming effect of the greenhouse. Glass with the opposite behavior would cause cooling, although any glass with that property used for a solar greenhouse would be prohibitively expensive by comparison with conventional air conditioners.'' --Vaughan Pratt (talk) 20:28, 8 November 2009 (UTC)


 * I'm not really sure what you're arguing here. Greenhouses are normally constructed with glass walls and roof is wrong, so we shouldn't say it - they are commonly constructed of plastic which is fairly transparent to IR. Glass with the opposite behavior would cause cooling - you mean, opaque to visible but transparent to IR? This may or may not be so - the statement isn't very clear - but it appears to be irrelevant to the article William M. Connolley (talk) 21:30, 8 November 2009 (UTC)

OK, who wrote:


 * A greenhouse covering which is more transparent to the solar radiation band and less transparent to the thermal radiation band will result in a temperature higher than the surrounding environment, and a greenhouse covering which is more reflective of solar radiation and more transparent to thermal radiation will lower the temperature relative to the surrounding environment. 

It doesn't look right to me, and I don't think the ref supports it. Indeed it sez ''Regardless of the chemical composition of plastic film, its form or its pigmentation, plastic mulched soil is always warmer, on the average, than bare soil. ''

This looks like the Great GH wars all over again, it which case it gets firmly stomped on William M. Connolley (talk) 21:39, 8 November 2009 (UTC)
 * Agreed, in fact that was what prompted my annoyed first remark before I calmed down a bit with my expansion on it. I came here after reading The heat comes from sunlight's infrared spectrum, which is used in the heat lamps that keep McDonald's french fries warm at Conservapedia, which is so laughably wrong that I suspect it's one of the many articles planted by anti-conservapedians to make Conservapedia look silly, which more earnest Conservapedia editors are perfectly able to do on their own without that sort of assistance.  (The proportion of solar radiation at heat lamp wavelengths is less than .01% of what warms greenhouses.)  I wanted to check that at least Wikipedia was able to get this right, but got annoyed when it became obvious the anti-warming proponents had being having a field day with this article.


 * Windows that are more reflective of solar radiation and more transparent to thermal radiation are hundreds of dollars for a few square centimeters and are intended for laboratory use. The zinc selenide windows used with CO2 laser applications are somewhat cheaper but have around 70% transmissivity between 600 nm and 20 microns, whence they block about 40% of the incoming spectral energy (below 600 nm) altogether and absorb a further 40% of the remainder (between 600 nm and 20 microns), while passing 60% of the outgoing longwave thermal emission.  Without doing the math I would guess that overall this would tend to heat a greenhouse made of zinc selenide windows.  More aggressive blocking below 2 microns while passing most of 5-20 microns might cause cooling.  But even if it did that would count as WP:OR unless it were sourced somewhere.  I'm very dubious.  In any event no greenhouse in the world cools its interior this way when the Sun is shining on it, no one could afford such a thing, except maybe Bill Gates to prove a point.  So who exactly is this article serving by claiming otherwise?


 * Regarding your question about my proposed definition, where have you been able to get IR-transparent plastic that is sufficiently strong and cheap as to be practical for greenhouses? I would love to get my hands on it.  By IR we're talking about thermal emission from a greenhouse operating at below 320 K (115 F), namely in the neighborhood of 15 microns. That would be great stuff if it existed!  I do however agree with your remark about irrelevance and would be more than happy to see that bit simply deleted. --Vaughan Pratt (talk) 01:31, 9 November 2009 (UTC)


 * I just noticed you deleted For the traditional case of a warming greenhouse, such as with a glass covering, a covering material is chosen which will absorb some of the outgoing IR and radiate a portion of it back into the greenhouse environment to reduce radiative energy loss to the sky from the amount that the ambient environment experiences. The use of insulation and more infrared-absorbent glazing enhances the effect by reducing heat loss by conduction and IR radiation. Major deletions of this kind based on your own private opinions (which also strike me as technically uninformed) without first discussing them on the talk page is the height of rudeness on Wikipedia.  Have you never previously been blocked for this sort of behavior before?  --Vaughan Pratt (talk) 01:48, 9 November 2009 (UTC)


 * I'm widely regarded as an expert in this area, and can quote you arbcomm to prove it. You *are* aware of the pre-history of all this, aren't you? William M. Connolley (talk) 08:10, 9 November 2009 (UTC)
 * If by "this area" you mean greenhouses then apparently greenhouse experts aren't expected to be familiar with the optical properties of plastic in the far infrared. I'm not an expert in greenhouses myself (my original training was in physics, though my wife's a botanist and she's dragged me through plenty of greenhouses), but I do know from experience that no kind of plastic is transparent to IR unless it's less than about .1 mm thick.  Most greenhouse walls I've seen, whether glass, polycarbonate, or whatever, seem to be sturdier than that.
 * What is true is that greenhouse walls are designed to block heat loss via all three of radiation, convection, and conduction, especially important in winter where heat loss matters the most. The considerable variation in wall materials makes it impossible to give definitive ratios between these three, and the best one can say about radiation is that blocking IR enhances the warming effect, the wording I proposed above.  The paragraph you deleted seemed perfectly correct in that regard, although the wording was somewhat stilted.
 * Regarding my complaint about your revert, being bold is fine when adding material and fixing minor obvious mistakes, but not for deleting an entire paragraph that someone (not me in this case) worked hard on in the past, especially when your rationale is based on incorrect information. In such a situation the normal action is to raise the concern on the talk page so as to give reasonable notice of a proposed deletion on that scale.  Don't the efforts and opinions of other Wikipedia editors mean anything to you?
 * One advantage to an article polished by consensus instead of by fiat is that it becomes more resistant to subsequent tampering, since there is then a whole community with a vested interest in seeing that propagandists of the kind you were having to defend yourself against single-handedly in 2006 don't subsequently hack away at their jointly agreed-to effort.
 * But now that you've drawn the prehistory to my attention I see that Wikipedia put you under a revert ban in 2006. Would you say you are more or less aggressive today about unilaterally reverting whole paragraphs than in 2006?   --Vaughan Pratt (talk) 01:16, 10 November 2009 (UTC)

==Blocking IR does not enhance the warming effect== (Broke long section into two at this point, reindented accordingly.) --Vaughan Pratt (talk) 04:49, 14 November 2009 (UTC) (Not funny, don't try to change the subject please. —Apis  (talk ) 07:34, 14 November 2009 (UTC))

This: "blocking IR enhances the warming effect", I believe is wrong, although I'm not entirely sure what you mean. If you want to reduce radiation losses in a greenhouse you would probably want to use an IR-reflective material, not simply something opaque. A comparison with the greenhouse effect would be incorrect for several reasons. You have misunderstood the bold policy, it's fine to 'boldly' remove sections if you are convinced it will improve the article. If another editor disagree with that decision, you can then discuss it on the talk page, there is no need for drama here. If you have issues with Williams current or previous editing style you can take it up (politely) on his talk page, it is off-topic here in article space. —Apis (talk ) 08:36, 10 November 2009 (UTC) —Apis (talk ) 06:07, 11 November 2009 (UTC) —Apis (talk ) 09:48, 12 November 2009 (UTC) —Apis (talk ) 08:09, 13 November 2009 (UTC)
 * By "blocking" I meant not transmitting, that is, the combined effect of reflection and absorption. In the case of plastic I don't know the ratio since most data for plastic reports only transmittance.  However the ratio is irrelevant when the window is not a good thermal conductor, because the absorbed heat will stay on the absorbing side of the window resulting in a thermal gradient across the window.  When the inside of the window reaches equilibrium it then becomes equivalent to a perfect reflector because absorbed-in balances emitted-out (back into the greenhouse) independently of the reflecting behavior of the window.
 * Why "several reasons?" One of them already seems to be wrong.  What's another?
 * "it's fine to 'boldly' remove sections if you are convinced it will improve the article." Wouldn't that tend to promote edit wars?  Most participants in edit wars can be assumed to be trying to "improve the article."  Improvements on that scale ought to be discussed first on the talk page with reasonable notice.  A remarkable amount of editors' time has been wasted by other editors who don't follow that policy.
 * "If you have issues with Williams current or previous editing style [...] take it up on his talk page." My issue is with the paragraph he's reverted in this article, which was fine from the standpoint of its physics, if not its English, and had no reason to be removed.  He was the one who asked whether I knew about the pre-history of this article, which he did here so I responded to it here.  Looking at his talk page just now, it looks like a bit of a war zone itself so unless there's a very good reason to go there I think I'll steer clear of it, thank you.
 * "it is off-topic here in article space." Sternly spoken.  You'd make a great village constable.  --Vaughan Pratt (talk) 19:58, 10 November 2009 (UTC)
 * Yes, the blocking part was relatively clear, It was the warming effect I was referring to. Not all that surprising, blocking ir-radiation will actually keep the greenhouse cooler during day (by blocking out sunlight). And no, black surfaces don't turn into reflectors when they reach equilibrium, even if glass would have been an insulator (which it's not). You would also have to take into consideration latent heat transfer, convection and conduction transferring thermal energy to the wall material. Why would people trouble themselves to produce and buy expensive reflective glazings if it is "irrelevant"?
 * Normally you make an edit, if another editor don't agree with that edit he can discuss it on the talk page; or he can revert the edit and/or then discuss it on the talk page. Reverting back and forth endlessly is disruptive of course, and that's what's referred to as an edit war. Deleting text that you believe is incorrect and lacks proper references is perfectly normal (if it's done in good faith obviously). All data stays in the page history, so it's not like there is any risk of loosing anything permanently.
 * Apis: "Not all that surprising, blocking ir-radiation will actually keep the greenhouse cooler during day (by blocking out sunlight)." Ok, so maybe I was wrong that the Conservapedia article on greenhouses was written by a troll.  You're claiming the same thing that that article did, namely that the Sun heats by far infrared radiation.  Evidently more people than I realized are confused about radiation.  As it is clear that I'm not going to be able to persuade you otherwise simply by arguing with you, go find a grad student or professor in a reputable physics department and ask them whether the bulk of the radiation energy from the Sun is coming from visible-plus-near-IR or the far infrared (which is the IR we're talking about in this discussion, namely 15 microns---the near IR is the range from 700 nm to 3 microns roughly).  Let me know the outcome.  (I loved the "not all that surprising" touch---I was surprised.)
 * The reason I didn't suggest you calculate this factoid yourself from Planck's Law and the Sun's temperature of 5778 K is that if you were capable of doing so you would have done so already. You evidently don't understand black body radiation.
 * Regarding the number of reverts before one can declare an edit war, admittedly I play it safe with fewer reverts than others, namely none. (Wikipedia has never imposed a revert ban on me because I imposed it on myself years ago.  That hasn't stopped me from contributing a great amount to Wikipedia.)  What I don't understand is why anyone would revert an entire paragraph before giving a week's notice in the talk page.  The only conceivable reason would be that one more week of having that faulty paragraph deluding the world would be sufficient to undermine Wikipedia's reputation for infallibity.  It is that sort of reasoning that leads to edit wars.  There should be no unilateral reverts on the naive ground that the revert would improve Wikipedia.  Obvious vandalism is an entirely different thing.  --Vaughan Pratt (talk) 04:25, 12 November 2009 (UTC)
 * I didn't claim that "the bulk of the radiation energy from the Sun" is coming from the far infrared. What I said was that if you remove a part of the incident radiation into a greenhouse you will reduce the "warming effect" from that radiation. (Besides, a majority of incident radiation is coming from the the atmosphere not the sun.) From a greenhouse perspective you are only interested in radiation that is necessary for photosynthesis. Ideally you would want to reflect all other wavelengths in order to better control the greenhouse climate, but that isn't how a traditional greenhouse work.
 * Regarding Wikipedia policy, I personally believe that, if you had to wait a week before making an edit, wikipedia progress would stop. But a better place to discuss this would be on Village pump (policy).
 * Regarding your "if you remove a part of the incident radiation into a greenhouse you will reduce the warming effect from that radiation," it's also true that if you shade yourself from the moon you will reduce the warming effect of moonlight.  The full moon being at 396 K, the far-IR component of moonlight (i.e. neglecting the considerable visible sunlight reflected from the moon) is (5778/396)4 = .0022% of sunlight at the top of the atmosphere.  (I don't mind confessing that the atmosphere's impact on that ratio is above my pay grade and you may well have a better idea of that amount.  On the other hand the reflected visible sunlight should augment that .0022% considerably.)  I mention this to put in perspective the relative far-IR and visible components of insolation.  As can be seen from the lower table at Percentiles section of the Planck's law article, 99.9% of the radiation from the Sun is below 10 microns while about 78% of the Earth's radiation is above 10 microns.  So a window with a step-function transmittance that is 100% below 10 microns and 0% above allows 99.9% of the incoming solar radiation to enter the greenhouse while preventing 78% of the greenhouse's internally generated thermal emission from leaving.  Besides its (important) role in keeping out cooler air, such a window also serves as a very effective one-way radiation barrier admitting incoming radiation while blocking outgoing.
 * On your "a majority of incident radiation is coming from the the atmosphere not the sun," I take it you consider the function of a parasol is to shade one from the atmosphere rather than the sun. --Vaughan Pratt (talk) 19:18, 12 November 2009 (UTC)
 * Contrary to what you seems to believe, I do understand the model you are thinking of very well. My point is that such a model is too simplified to say anything useful about a real greenhouse. It doesn't take into account convection and latent heat transfer to the glass, nor the geometry of the greenhouse or radiation from the atmosphere (and so on). Perhaps if you had a flat greenhouse in space...
 * You wrote "blocking ir-radiation will actually keep the greenhouse cooler during day (by blocking out sunlight)" and "a majority of incident radiation is coming from the the atmosphere not the sun." I argued against both these statements.  If as you claim your understanding is correct then what is your argument for them?
 * You also wrote "such a model is too simplified," citing "latent heat transfer to the glass." Are you talking about phase change, and if so can you quantify the change to show that it is sufficiently significant to be relevant?
 * A model is only "too simplified" when there exist effects that interact with the model to invalidate its implications. It seems to me that the effects you cite should be orthogonal to the mechanisms we were discussing previously and therefore would not invalidate them.  Why do you think otherwise?  --Vaughan Pratt (talk) 20:28, 13 November 2009 (UTC)

Back to the article
Reading this whole discussion, I think that it's drifted a little away from the substance of the article, but I see nothing that is a valid refutation of this paragraph:


 * For the traditional case of a warming greenhouse, such as with a glass covering, a covering material is chosen which will absorb some of the outgoing IR and radiate a portion of it back into the greenhouse environment to reduce radiative energy loss to the sky from the amount that the ambient environment experiences. The use of insulation and more infrared-absorbent glazing enhances the effect by reducing heat loss by conduction and IR radiation.

So I added it back in. I realize that may be controversial, but I'm hoping it will direct attention back to articulating what, if anything, is wrong with it.

I'll also note that I'm having a similar discussion with Apis over at Talk:Low-emissivity if anyone cares to join that conversation.Ccrrccrr (talk) 02:14, 14 November 2009 (UTC)
 * Thanks, Ccrrccrr. I didn't want to undo that revert without first discussing it, glad you agree with me.
 * But lots of luck preventing Apis from re-reverting it. He claims that he understands Planck's law, but it's clear from his many remarkable assertions about radiation that either he has never read up on Planck's law or was incapable of grasping its consequences.  Yet he is certain he is the expert on radiation, and that those trained in optics are talking through their hat.  He therefore has no qualms about engaging in edit wars, which he justifies on the ground that if one couldn't unilaterally revert paragraphs whenever one thinks they're unreasonable, "Wikipedia progress would stop."
 * In fact the opposite is true: Wikipedia progress stops when editors have to take time off to spar with guys like him who go round deleting any and all paragraphs that don't match their confused understanding of the world.
 * I'd say we have a prime candidate for a revert ban. Let me talk to someone about that.
 * It would also be good if Wikipedia had a faster way of identifying these types so they don't waste people's time as much. --Vaughan Pratt (talk) 04:49, 14 November 2009 (UTC)

—Apis (talk ) 07:34, 14 November 2009 (UTC) —Apis (talk ) 13:23, 14 November 2009 (UTC) —<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 07:34, 14 November 2009 (UTC)
 * (Edit Conflict) Sigh, now you are just being insulting and abusive. I presume you think that anyone that doesn't agree with you shouldn't be allowed on Wikipedia.
 * Your model has great educational value, but it is invalid in describing a real greenhouse because there are other mechanisms that transfer energy to the glass, such as convection and... yes phase change... you see, moisture in the ground will evaporate and then condense on the glass. Convection means that "bubbles" of hot air rise from the ground and move up to the roof in the greenhouse where it will warm the glass as well (and "bubbles" of cold air move down and cool the ground). This alters the glass temperature and thus invalidates your model. As does your assumptions on greenhouse geometry (i.e. a flat surface above another flat surface). As do your assumption that the only radiation source outside the greenhouse is the sun. So you see, there are many variables in how a greenhouse works.
 * Besides, many greenhouses have problems with them becoming too hot! this hypothetical extra "warming" is likely more of a nuisance. In the perfect greenhouse you want to insulate it so you can keep an ideal plant temperature level and still let in a maximum of light that is active in plant photosynthesis (i.e. the point of letting in light isn't to heat the greenhouse).
 * You suggest we include this text based on your model, that would be original research.
 * Regarding this: "On your "a majority of incident radiation is coming from the the atmosphere not the sun," I take it you consider the function of a parasol is to shade one from the atmosphere rather than the sun." It should be obvious that you use a parasol to shade one from the sun, since that is one tiny spot in the heavens where a large fraction of incident radiation is coming from (although it's not where the majority of radiation energy is coming from, (which, again, is the atmosphere)).
 * You also appear to have misunderstood what I said about editing and what reverting means. Part of normal editing is removing things that are wrong/misleading and incorrectly sourced. Mr Connolley deleted a paragraph which he motivated both on the talk page and in the edit summary, that is not the same as reverting. The only one who's been reverting edits so far is Ccrrccrr. Which is fine by the way, if he feels what he is doing is what is best for Wikipedia (e.g. done in good faith), and not to make a point or escalate an edit conflict (which unfortunately is rather common).
 * "if so can you quantify the change to show that it is sufficiently significant to be relevant?" It should be obvious to anyone who has basic physics knowledge that this could be significant. How big this effect will be in reality obviously depends on many factors such as moisture content and ambient temperatures etc. The water drops on the glass would at the same time make the surface more opaque (in the ir-spectrum) further complicating matters. It's also difficult to estimate convection effects. This is why I think your model is too simple. I'm not the one who want to include dubious statements into the article so it seems to me like "the burden of evidence" is on you to show that these factors (and the others I mentioned) are irrelevant.
 * I just noticed that Apis managed to squeeze two independent fallacies into a single sentence: "And no, black surfaces don't turn into reflectors when they reach equilibrium, even if glass would have been an insulator (which it's not)." That glass is not an insulator will come as shocking news to many professional societies involved with glass.  Regarding the former statement, if a surface is emitting the same energy at the same wavelength as it is absorbing, in what sense does that not constitute reflection?  Were you intending to distinguish specular from diffuse reflection, or what? --Vaughan Pratt (talk) 05:44, 14 November 2009 (UTC)
 * (Edit Conflict: please it is extremely confusing and misleading when you keep editing previous text and adding new headings etc.) Not a thermal insulator that is. The other part about reflection shouldn't be taken out of context. I was trying to point out how your analogy was irrelevant to what you where trying to say, to be honest it wasn't entirely clear what you meant since it makes no sense in that context.


 * While at equilibrium, watts in equals watts out. That is, in a body at equilibrium, the entire body absorb energy at the same rate it loose it, that is not the same as reflection at all. Reflection means that the radiation is not absorbed but rather "made to change direction", see Reflection (physics).


 * blocking ir-radiation will actually keep the greenhouse cooler during day (by blocking out sunlight). I was trying to move away from this statement since I felt it was a bit nit-picky with regard to what was implied. My hope was that it would lead to a clarification of what was meant, and then hopefully some sort of reflection and realisation that this is perhaps a more complicated topic after all, apparently that didn't work very well. It was hard to be more specific because it wasn't clear what was meant to begin with.


 * I hope everyone agree that it is true though, if you block (as in reduce) part of the incoming spectrum then you will reduce the "heating". This is the same as using a parasol to shade the sun.


 * The incorrect assumption that is being made is that the ir-black greenhouse covering is going to reduce the energy transfer out of the greenhouse. But as I have been trying to point out, that is not a valid assumption since there are other mechanisms than radiation that transfer heat to the glass. In this case a black covering might increase the energy loss not reduce it!


 * A large part of the solar radiation comes from the IR-spectrum (I did not say far-IR mind you), and although I'm no expert on the absorption spectra of greenhouse glass (or plastics) I seriously doubt that in reality it is anything like 100% in FIR area and 0% everywhere else. For example, glass tends to "block" much UV-light as well (also reducing heating).


 * Regarding the composition of the radiation spectrum from the atmosphere, it is mainly IR, but likely vary a lot e.g. depending on cloud cover and temperature. I do not comprehend how anyone can think it's fine to leave out the largest source of incident radiation from the equation?

—<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 13:07, 15 November 2009 (UTC)
 * "Warming" isn't really what one is looking for in a greenhouse but rather insulation. Greenhouses often become too warm during direct sunlight (because of too much incident radiation, while at the same time preventing convection), which is why you add reflecting curtains and open little windows in the roof to allow hot air to escape etc.

...but I see nothing that is a valid refutation of this paragraph
I've reverted it. As I explained before; this is the original problem. The extensive stuff by VP doesn't help; hopefully we can discuss this here without too much noise. If that fails (as it very likely will) I suggest you come to my talk page and we can have a nie quiet chat William M. Connolley (talk) 10:35, 14 November 2009 (UTC)


 * Thanks for the new section. Let's agree to keep the comments in this section focused on the article, and refrain from any comments about editors.Ccrrccrr (talk) 22:57, 14 November 2009 (UTC)

Aside: lead references to other articles

 * One side issue is the part in the lead that I deleted, referring the reader to other articles for more detail. I didn't find anyone arguing for them on this page--perhaps there's an old discussion I missed?  It seems to me that, rather than more information on the topic of solar greenhouses, those have more information on radiation effects on the Earth's climate.  It seems strange to have that in the lead, as it's tangential, not background on this.  I would think more background for this might be solar radiation or thermal radiation.  Was there a reason to keep that in, or did it simply come along for the ride in the revert of the other stuff?Ccrrccrr (talk) 22:57, 14 November 2009 (UTC)


 * Did you miss Greenhouse_effect? William M. Connolley (talk) 23:26, 14 November 2009 (UTC)
 * I did see that--sorry I should have explained. It refers back to this article as the main article.  So referring people to that section would seem to set up a set of circular references.  If there is info there that isn't explained enough here, we should explain it here, well, and make sure we don't leave the reader with misconceptions, if this is to be the main article on the topic, which seems like the right choice to me.  I wouldn't object to putting that in a "see also" list at the end.  Ccrrccrr (talk) 23:51, 14 November 2009 (UTC)
 * No, you have to actually read what it says in that section William M. Connolley (talk) 09:02, 15 November 2009 (UTC)


 * I have read it. I think it's good. I don't see how that changes the circular reference problem.Ccrrccrr (talk) 14:15, 15 November 2009 (UTC)
 * Sorry, I assumed that If there is info there that isn't explained enough here, we should explain it here, meant you hadn't read it. Yes there is stuff there that isn't explained here, and no it belongs over there not here. GH is the technical article that explains how the greenhouse effect works and distinguishes it from how real greenhouses work. This article is about the very limited subject of greenhouses-for-plants. Yes there is a circular ref problem; I've have a go at sorting that out now William M. Connolley (talk) 17:34, 15 November 2009 (UTC)
 * Done. Now Greenhouse_effect etc William M. Connolley (talk) 17:40, 15 November 2009 (UTC)
 * Good, thanks. Now I'll edit the lead to reference that appropriately as a source for the distinction not for more detail on the description of how a solar greenhouse works.Ccrrccrr (talk) 18:18, 15 November 2009 (UTC)

Back to discussion of disputed paragraph
I just scanned the above discussion, and I really can't find a description of the problems in the disputed paragraph, without being cluttered with descriptions of the problems with their fellow editors.


 * For the traditional case of a warming greenhouse, such as with a glass covering, a covering material is chosen which will absorb some of the outgoing IR and radiate a portion of it back into the greenhouse environment to reduce radiative energy loss to the sky from the amount that the ambient environment experiences. The use of insulation and more infrared-absorbent glazing enhances the effect by reducing heat loss by conduction and IR radiation.

Are there complaints that something is actually incorrect there, or is the complaint just that it's undue weight on a minor effect? Since it's a widely discussed phenomenon, I would think it would be better to describe it correctly and point out how minor it is than to keep silent on it. My other complaint would be that "from the amount..." isn't very clear. I think that would be better worded as "to reduce radiative energy loss to the sky compared to the radiative energy loss to the sky experienced by things outside of greenhouses. Ccrrccrr (talk) 23:09, 14 November 2009 (UTC)

—<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 07:15, 15 November 2009 (UTC)
 * As I have been trying to point out, the model on which you base these assumptions is wrong. Among other things, you cannot ignore other mechanisms that transfer heat (energy) to the glass. Besides this "solar heating" effect is not why you have glass in a greenhouse in the first place. You use glass to insulate it while still allowing in light that is necessary for photosynthesis by the plants. You don't "choose" an ir absorbing material. If you want to insulate radially you would choose an ir reflective material (this is what's referred to as low-e, or low-emissivity coating). As I've also tried to point out, adding glass will block many parts of the sunlight (such as UV), actually reducing the incident radiation. This is not a problem though, since you don't choose the glass for heating but rather to insulate while still letting in photosynthetically active light, of which for example UV is not. We shouldn't try to add any information based on armchair science and grade-school explanations of the greenhouse effect (which refer to a planetary phenomena involving a "high-emissivity" atmosphere and is really quite complex). Besides the term "radiate back" is more nonsense, the glass does not radiate back the radiation it absorbed (which stops existing the moment it is absorbed), it radiates because of it's temperature.


 * Thanks, and sorry to make you repeat the work of writing that out for me when you've already done a lot of typing on this page. And important issue you raise is whether solar heating is important, or if we are mainly interested in glass because it transmits well for photosynthesis.  As Vaughan raises below, there are two articles, solar greenhouse and greenhouse.  From the lead of this one, I gather that we are taking solar greenouse to mean one that is intended to be kept warm by solar radiation.  So I do think discussions of solar gain are relevant.


 * As for the model being wrong because it leaves out some effects, neither I nor the article is attempting to describe a full model of a greenhouse, and I don't have any hope that someone would be able to predict the temperature inside a solar greenhouse from modeling these phenomena alone. If proceed based on deleting anything that is incomplete, we'd delete everything in the encyclopedia.  I think valid reasons for deleting things would be if they were incorrect or unimportant.


 * It's true that it's not the same radiation that "radiates back" from glass. Rather it's the energy.  The radiation is absorbed, which raises the temperature, which leads to radiation leaving the glass.  It's also true that total radiation from the glass is a result of temperature which is a result of all heat transfer mechanisms, including convection and condensation.  The fact that there are multiple steps going on, and other energy transfers going on at the same time, does not make "radiate back" nonsense.  But I do see your point that it's perhaps oversimplified.


 * So here's an attempt to address these issues.


 * Typical solar greenhouse covering materials, such as glass, absorbs far infrared (FIR) radiation emitted by surfaces inside the greenhouse. After the glass is warmed by this radiation and by other effects, it radiates a portion of the energy absorbed back into the greenhouse. This reduces radiative energy loss to the sky compared to radiative energy loss to the sky from the surrounding environment.  In the FIR band, a 0.1 mm polyethylene film as is commonly used in greenhouses transmits about 80% FIR radiation, as opposed to 3% for glass (, Table 5, p. 12).  For this reason, IR absorbing additives are sometimes used in films for greenhouses.  One experiment showed a 13% reduction in night supplemental heating requirements when such films were substituted (, p. 13)


 * Comments?Ccrrccrr (talk) 14:50, 15 November 2009 (UTC)

—<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 15:54, 16 November 2009 (UTC))
 * The problem with that model is that it is incorrect in describing greenhouses, because it ignores important factors.
 * Maybe this is clearer: The model is incorrect because it makes invalid assumptions.


 * Regarding solar gain. First: the point in having glass is to let light in for photosynthesis, otherwise you would keep the plants in a well insulated basement and perhaps heat it with solar panels (but more likely use what's most economical).


 * The heat caused by the sunlight is usually way too much during normal daylight, which is why you need to put a lot of effort into cooling the greenhouse to maintain temperature.


 * During night however you loose the heat source and since a normal greenhouse is poorly insulated you start loosing a lot of energy to the cooler outdoor environment and the temperature drops. In cold climates you might have to add additional heating and insulation during night to maintain a productive plant environment.


 * So, indeed, the solar heating, if limited, might be beneficial. But it's not the reason you use a transparent cover material. The discussion on solar gain can be summarised as "During daytime, the sun heats the inside of the greenhouse", that would be fine by me.


 * Regarding the suggestion. It is WP:OR and misrepresents the source. You are trying to extrapolate from a single data point. While indeed a carefully constructed covering might utilise an ir-black surface to improve insulation (I'm not arguing against that), the source doesn't say that this is universally true (quite the contrary). Since it depends on many complicated factors.


 * If you read what little the source says about this "cloud nine" covering from monsanto company, you'll notice that it is a double layer plastic covering. That means less thermal conduction through the wall and thus the insulating effect from ir-blocking additive would be more dominating. If you read the entire reference you will notice it goes to lengths to explain all the factors I have mentioned above (and more). Another problem is your first quote deals with single layer plastic, and it's not clear if it's the same as the monsanto covering in the second quote. A third problem is that we get no information on how big the effect is, unfortunately a 13% reduction in night supplemental heating could mean anything from almost nothing to a huge amount unless we know what the total is. A fourth problem is that the source deals with "Long Wavelength Transmittance (>2800 nm)" which isn't quite the same as FIR (15-1000 µm according to CIE).


 * If we where to try and elaborate on this it would unfortunately end up being way too technical I think. Since the article doesn't discuss more important factors when it comes to insulating a greenhouse it would also be completely out of proportion (not notable).

—<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 11:33, 16 November 2009 (UTC)
 * (Most importantly it does not prove what I believe some are trying to claim here, i.e. that there is a considerable "greenhouse effect" going on in normal greenhouses, which according to experiments does not appear to be the case. And it is important we don't fortify this misconception.)

Greenhouses as plant habitats
(Prefatory remarks. First of all I'm not clear why there are two Wikipedia articles on greenhouses, this one and Greenhouse.  This one was started in 2005, three years after the other one.  Was it intended to serve a different purpose?  Second, there seem to be two communities with opposing points of view on how greenhouses work, at least at this article.  In such a situation I feel uncomfortable making any changes to the article itself not arrived at by consensus, and have therefore from the beginning confined my input on this article to this talk page, with my main goal being to see what consensus if any can be arrived at.  A secondary goal is to contribute to the clarification of any difficult points that might arise concerning the interplay of heat transport mechanisms and optics, the basic nature of which has not changed significantly since I graduated in physics in 1966, though I surprise even myself that I can still remember that much of it. One reason the topic is controversial is that the relevant mechanisms are sufficiently complicated as to make it hard to summarize them all in a few succinct paragraphs, whence the excessive length of the following, for which I have to apologize. Finally I would like to understand the relationship between the two greenhouse articles before attempting to do anything with either.)

The discussion in the foregoing sections is from the point of view of the notion of "greenhouse" as a concept in its own right without regard to application. There is however another point of view, that a greenhouse is a house modified for other purposes than housing humans. The modification is to replace the opaque walls and roof of a human habitat with glass (or nowadays plastic to save money, but before the 20th century plastic was not the option it is today when fabricating greenhouses).

Both kinds of house maintain their warmth by containing the air. Moreover human houses nowadays tend to use considerably more insulation than greenhouses. Hence the observations about greenhouses that they keep their interior warm by containing the air with insulating walls is even more true for houses, which have considerably more insulation.

So what's the big deal with glass? Why not wood, or bricks, for example? I asked my wife this question. (Her background: her father is from a long line of prominent horticulturalists in Holland and the US, and she herself has two master's degrees in botany from respectively Macquarie University and Stanford University.) She said that the main effect would be that the plants would die for lack of photosynthesizing sunlight. "Plants?" I asked innocently, feigning surprise. "What plants? This Wikipedia article on greenhouses says nothing about greenhouses being for plants, or for anything else for that matter.  It just talks about how greenhouses keep their interior warm."

"Gardeners" and "the plants" are referred to mysteriously near the end, but with no explanation of their involvement. Maybe something could be said along those lines?

My next question to her was, "If what they need is sunlight, why not just put the plants outdoors?" Her answer: "Greenhouses permit growing plants in climates and seasons otherwise unsuited to those plants, for example tropical orchids, so-called 'hothouse tomatoes' out of season, etc. This requires good climate control for optimum conditions, for example if the greenhouse gets too hot one might open a few windows, or during a particularly hot season temporarily whitewash some of the windows."

This dual role of catering for both other climates and other seasons is very interesting, and surely deserves mention. Note that in both roles the object is to elevate the temperature inside, not lower it.

Had a horticulturist written this article it might have ended up with quite a different slant!

I then asked, "Do greenhouses trap either sunlight or heat?" Her answer: "We were taught in college [she majored in botany at Swarthmore in 1966] that light comes in at short wavelengths, which become long when radiated back out, and is thereby trapped by the glass which passes only short and not long." She added, "We didn't think to question this." (Are students questioning this statement in botany classes these days? Anyone here taken a botany course recently?)

My wife took only took one physics course at Swarthmore, whereas I took four years of physics at Sydney University, with the third year being half physics and half maths and the last year being all physics, no other courses at all. So I guess it falls to me to pick up the story at this point.

An underlying principle of houses, arguably the principle, is that they serve to control the climate within, keeping out precipitation and extremes of temperature. They also provide some privacy. At some point additional functions like lockable doors and windows, not to mention drawbridges, for keeping out unwanted visitors were added, but climate control can be seen already in primitive villages that make no effort to lock doors. Before the invention of air conditioning, climate control focused largely on raising rather than lowering the inside temperature.

So it is with greenhouses, with the twist that the photosynthesizing inhabitants need an enclosure transparent to the photosynthesizing portion of sunlight. Chlorophyll for example uses blue and red light, reflecting the unused green light. Hence it would be ok to have either a clear roof or a magenta one (which would pass red and blue), but not a green one, which would block the red and blue essential for photosynthesis.

So naturally one uses glass, at least prior to the 20th century when transparent plastics started to become available, the double-paned-window concept (whether for glass or plastic windows) became popular, and low-e coatings were invented to amplify the greenhouse effect (though not terribly practical for greenhouses themselves) by reflecting instead of absorbing the long-wavelength light trying to escape to the sky.

Prior to the 19th century no one knew that light had wavelengths, nor that thermal radiation was simply light at a wavelength inversely proportional to the temperature. So of course greenhouse designers prior to the 19th century would not reason that glass would be suitable for greenhouses on the ground that it blocks long wavelengths. Instead they would simply build transparent shelters for plants aimed at furnishing them with adequate sunlight while providing similar climate control to that enjoyed by humans in their houses. As pointed out above the climate control is crucial, as the two canonical examples of greenhouse use demonstrate, growing tropical plants in a temperate climate, and growing vegetables out of season, meaning in winter. In both these examples the goal is to heat the greenhouse. A common synonym for "greenhouse" is "hothouse;" if the purpose of a greenhouse were to keep plants cold it would be called a "coldhouse."

However they would certainly have noticed that greenhouses accumulated heat in a way that opaque houses did not. "Obviously" this resulted from the exposure to the Sun that glass provided, which would accumulate in an enclosure with limited circulation, often to the extent that windows would have to be opened in the middle of the day to keep down the heat, at least in summer. (In winter it becomes necessary to bring in auxiliary heating equipment.)

At the beginning of the 19th century Thomas Young discovered and measured the wavelength of light. The wave theory of light quickly supplanted the corpuscular theory of light that had dominated 18th century physics thanks to Newton, and was developed to an extraordinary degree of understanding throughout the 19th century.

The wave theory of light equipped physicists to see that the heating of greenhouses might get some assistance from the tendency of glass to transmit at least 80% the energy in solar radiation while blocking (by either reflection or absorption) almost 100% of the energy in terrestrial thermal emission, whose wavelength is very close to twenty times that of solar radiation. Exactly how much is what I'll try to assess here.

(Note that it is energy that heats, contrary to the understandably widespread but incorrect view, perhaps fostered by fluorescent lighting, that visible light only lights and that heating is the job of infrared. In fact energy increases with increasing temperature, to such an extent in fact that a white-hot object radiates much more visible energy alone than the total energy including infrared radiated by the same object when merely red-hot, thanks to Stefan's law which says that radiance is proportional to the fourth power of the temperature.  Hence if the temperature, and hence frequency, is multiplied by 1.414 (&radic;2) to get from red-hot to white-hot, the power is increased fourfold.)

These transmittance and blocking percentages are easily deduced from the many tables scattered around the web giving the transmittance of various kinds of glass and plastic as a function of wavelength. (Bear in mind that such tables are often given for thicknesses on the order of .1 mm while construction-grade glass or plastic will be 20-40 times that, with an exponential (and hence huge) decrease in transmittance as per Beer's law.)

The insolation (incoming sunlight) passes through the glass roof and air and is absorbed by the greenhouse floor. The glass will be heated to some degree depending on the percentage of insolation it absorbs, but not the air, which lacks sufficient optical depth. To avoid having to deal with a reflection term let's assume the floor is a perfect absorber, i.e. black. (For less black floors you're on your own but feel free to take the calculations below as a guide.) Furthermore let's assume the floor is perfectly insulated from the earth for maximum warmth; picture it as say a 1 mm thick sheet of black-painted copper on a 3 cm thick bed of styrofoam.

The floor will continue to absorb energy as long as the Sun continues to shine on it, and will therefore grow hotter.

But the hotter the floor gets, the more heat it loses. Having disposed of most of the conductive loss with the styrofoam bed, the main direct losses are (1) convective (warming the air in the greenhouse) and (2) radiative (back through the glass into the sky).

1. Since the air is trapped this limits the convective loss to that required to bring the greenhouse air volume to the temperature of the floor. This loss would converge to zero as the air approaches the floor temperature, were it not for the glass conducting some of that heat to the outside. (Opening the windows on the other hand vastly increases convective loss.)

2. If the Sun filled the whole sky the floor would eventually reach the temperature of the Sun. But it doesn't, and the floor will instead reach a more terrestrial equilibrium temperature. Compared to the greenhouse floor, the Earth isn't as black, isn't as well insulated from the ground below, and has ample convective cooling, so we can expect the greenhouse floor to be somewhat hotter by 1 pm than the nearby ground.

At noon the floor is getting the full glare of the Sun, and being only 1 mm thick can respond pretty rapidly to it.

Now so far we've only quantified the transparency of the greenhouse to insolation, which we mentioned at one point as being over 80% so let's go with that figure. We also mentioned radiative loss, but did not say how much escaped from the greenhouse through the glass. Let's consider two cases here, one in which 80% of the terrestrial radiation is transmitted and one in which 1% is transmitted. The former might be reasonable for a greenhouse roof made of saran (I saw figures on this a while back but couldn't locate them just now), the latter for a 5 mm thick sheet of glass or transparent plastic.

There is also convective heating of the inside of the glass by the interior air and convective cooling of the outside of the glass by the exterior air. Glass at a thermal conductivity of around 1 W/M/K has 400 times the thermal resistance of copper, making it a good insulator, but that of styrofoam is 30 times that of glass making it a wonderful insulator, which is why a styrofoam cup of hot coffee is less painful to hold than a glass one, which in turn is much less painful than a copper one.

The 1 W/M/K conductivity of glass means that a one-meter cube of glass will exhibit a 1 K temperature differential along the direction of 1 watt of heat flow, and hence a 1000 K differential when 1000 watts flow. Hence two points 5 mm apart along this flow will see 5/1000 of 1000 K or a 5 K differential. That is, if a 5 mm thick sheet of glass is conducting heat at a power density of a kilowatt per square meter of that glass, there will be a 5 K (9 degrees Fahrenheit) temperature drop across the glass. 1000 W is going to turn out to be roughly the power density needed to reach equilibrium. Hence the greenhouse glass, despite being a thermal insulator technically, is a fairly good conductor in this setting. This means that heat convected to the walls and roof of the greenhouse is essentially immediately available for further convection by the outside air, i.e. the glass acts as an effective heat exchanger. On a windy day the outside air will dramatically cool the glass, but in the absence of any wind a layer of hot air will accumulate over the greenhouse mirroring the trapped air inside and resulting in less effective cooling. In either case the trapped air inside provides a measure of insulation much greater than that of the glass.

Double-paned glass is a much better insulator, with various tricks for improving the insulation but typically with about 40 times the thermal resistance of single-paned glass thanks to the combination of two layers of glass and a layer of air thick enough for good insulation but not so thick as to permit setting up eddy currents moving considerably faster than simple diffusion. With that increase double-paned glass can maintain a temperature differential of 200 K at 1000 W/m^2. Some greenhouse manufacturers offer double-paned polycarbonate plastic with a 6 mm air gap which is somewhere in between in thermal conductivity.

Now let's put all this together. To keep things simple let's assume a floor one meter by one meter. Insolation at the top of the atmosphere is 1366 W/m2, which the atmosphere cuts down to about 1000 on a clear day. This warms the floor until equilibrium is reached, namely when the floor is shedding 1000 watts, namely by convection and radiation (since we've ruled out conduction to the ground below).

If it were just up to radiation, we'd have to radiate away the incoming 1000 watts. Stefan's law gives &sigma;T4 as the power density in watts per square meter of a blackbody radiator at T degrees Kelvin. Setting this equal to 1000 and solving for T we obtain an equilibrium floor temperature of 365 K or 92 C, just under boiling point. (For comparison and further perspective, had we taken the full brunt of the 1366 W without benefit of the atmosphere the floor would have to be 395 K or 122 C, which just happens to be within a degree of the peak temperature at the surface of the moon, so we're clearly on the right track with these calculations.)

If the greenhouse retains any of this, some of it will circulate back to augment the 1000 W from the Sun. For example if 200 W is added to the Sun's contribution in this way the floor rises to (1200/&sigma;)0.25 = 382 K or 110 C. Ignoring convection, this is roughly the effect of the 20% not transmitted by our 80%-transmittance Saran wrap.

At such a high temperature convection inevitably sets in, driven by strong eddy currents created by the high temperatures and high heat flux. If glass were a perfect insulator this would not help and the floor would reach 110 C. However if the single-paned glass roof were to conduct say 500 W via a temperature differential across the glass of 2.5 K, only 1100-500 = 600 W would need to be radiated, accomplished when the floor rises to 50 C.  (With radiation down to 600 W, I've approximated the 20% retained by the Saran wrap as 100 W instead of 200 W, giving 1000+100=1100 W. I've also ignored the walls; imagine a greenhouse whose roof area is much greater than its wall area.)

However relying on convection to transport 500 watts from the floor to the roof without using a fan is wishful thinking. Hence we can expect the floor to heat up to somewhere in between 50 C and 110 C, with convection nevertheless playing an important role in getting the temperature well below 110 C. Unfortunately estimating how far below is beyond my primitive calculating skills, perhaps someone else sees how to do this.

The point here is that even when the greenhouse roof is 80% transparent to all radiation including far infrared, the greenhouse still gets quite hot. This is the point being made by those who insist that greenhouses don't exhibit the greenhouse effect.

We're now in a good position to calculate what happens when we block 99% of the outgoing far infrared radiation while still admitting most of the incoming radiation. This will entail thicker glass or plastic, which will reduce the incoming heat to say 800 W (80% of the 1000 W hitting the top of the greenhouse), which will make things a little cooler.

But now we are trapping 99% of the heat being radiated by the floor. If we used perfect low-e glass, which reflects far infrared while transmitting sunlight, the floor's radiation would be reflected back to the floor. It would then be dependent entirely on convection to shed its heat. Again I can't calculate this, but one can easily imagine the floor rising to 150 C or more when convection is all that's available. which would then get very hot.

If however we just use plain glass, most of the heat will be absorbed by the glass rather than reflected to the floor, which will then rise in temperature until it is in equilibrium with the floor on one side and the immediate outside on the other. Being so hot, the glass will send roughly equal amounts of heat to the outside air and the inside, so only half the heat that low-e glass returns to the interior.

If it is double-paned however, the added insulation will reduce the contribution to the outside, and the glass will heat mainly the interior of the greenhouse, which will accordingly get extremely hot, essentially in the same way low-e glass does. Again no exact figures, these are hard to compute (for me anyway), for this one should resort to thermal computation software. However even at this crude qualitative level, I find myself wondering how much additional benefit a low-e coating can give over ordinary double- or triple-paned glass. Presumably some, but my intuition is that it is not all that much more. And this after paying a lot of money for low-e glass for my house a few years ago. Now my curiosity has been really aroused.

What this discussion does make clear however is that the opacity of glass and plastic to the far infrared radiation being given off by the hot floor is fundamental to all of this discussion about what drives heating of greenhouses. I am mystified that anyone could have a model of these mechanisms that denies this! --Vaughan Pratt (talk) 11:17, 15 November 2009 (UTC)


 * First, I agree that it's bizarre that there are the two articles. This one presumably is about greenhouses that are primarily warmed by the sun as opposed to those that are primarily warmed by fossil fuels or the like.  But I'm not sure it's easy to draw the line.  Another possibility is to have an article about glass-enclosed add-ons to other buildings that are not particularly intended to grow plants, but instead are intended to collect solar heat, that can then be vented into the main building when the heat is both available and needed.  I think we should either get rid of this article, or have it focus more on getting solar heat gain while avoiding heat loss.


 * I appreciate that attempt to construct a model. As you acknowledge, there are lots of limitations of the model, and I don't think it's worth hashing them out further.  I will suggest, however, that if you are interested in playing with this stuff more, one thing you might check out if the free software WINDOW from LBL:

Or this list of whole-building simulation packages, many free:  Another that isn't on that list is eQuest. 


 * The sad thing is that even if you do a bunch of great work with that stuff, it will remain OR, and won't be admissible in the article. But it could be used on the talk page as evidence of what is worth pursuing and what is nonsense.


 * By the way, I think that the idea of there being editors that thing greenhouses work one way, and others that think they work another way is a little overstated. I think everyone agrees that two effects are absolutely essential for getting solar warming beyond the solar warming experienced outside: stopping convention and allowing solar radiation in.  The dispute is as to whether the fact that glass absorbs FIR is a) of major importance, b) of minor importance but worth mentioning, or c) of such small importance that describing it as a real effect is dangerously misleading, or d) just plain wrong.  My position is b).  Ccrrccrr (talk) 15:20, 15 November 2009 (UTC)
 * First, thanks for the pointer to WINDOW, Ccrrccrr, which I'll follow up on. Second, the other article is quite explicit that it is solely about solar-heated greenhouses, with no mention of any other heating methods (despite the fact that solar-heated ones do use other methods especially in winter). Third, my intent with going into the theory in such detail was not to propose any of it for the article, which I would think was way beyond the scope of a simple article on greenhouses, but to give my understanding of where I agree and disagree with the other parties who feel they have a vested interest in this article.  I am only interested in feedback authoritatively correcting, fine tuning, and/or expanding on the calculations I exhibited, not in feedback of the form "you're wrong and I'm right."  Fourth, absent any obvious difference in objective between the two greenhouse articles, it may be worth posting a proposed merge at both articles, discussion of which would include the logistics of the merge.
 * Regarding your concern about WP:OR, what did I write that was in contravention of it? All I did was compute values from well established formulas for the purposes of illustrating points that are obvious consequences of those values.  According to WP:OR, "This policy does not forbid routine calculations, such as adding numbers, converting units, or calculating a person's age, provided editors agree that the arithmetic and its application correctly reflect the information published by the sources from which it is derived."  Had I gone beyond that by proposing numbers for the values for which I could not at the time offer a routine calculation, I would consider that WP:OR, but where did I do that?  All the values I computed for either specific values or bounds on ranges thereof are routine calculations for any senior majoring in physics.  If some trigger-happy reverter wants to revert material based on such computations because he feels they are in error, we can then jointly take the dispute to an independent subject authority for adjudication.  In fact I would say Apis's unwarranted reverting of evidently correct material (none of it written by me) constituted WP:OR in that he is making original claims about established facts that he views as mistaken.  Science advances by (inter alia) correcting established but mistaken facts, but it constitutes OR when Apis takes it on himself to judge established facts as mistaken.  Evidence for such error must come directly from authoritative scientific sources and not indirectly through non-authoritative sources such as Wikipedia articles written by anonymous editors.
 * Regarding your assessment of FIR as of minor importance to the operation of greenhouses, can you actually quantify that or do you mean that you don't consider how greenhouses work to be relevant to the article? If the former, you would need to support Connolley and Apis by demonstrating that the effect is indeed minor or negligible.  I have seen no convincing calculations of the relevant contributions to that effect by either of them and it would therefore be irresponsible to simply take their word for it that FIR is of minor importance.  --Vaughan Pratt (talk) 04:36, 16 November 2009 (UTC)

''First of all I'm not clear why there are two Wikipedia articles on greenhouses, this one and Greenhouse. This one was started in 2005, three years after the other one. Was it intended to serve a different purpose? Second, there seem to be two communities with opposing points of view on how greenhouses work, at least at this article.'' - yes indeed. This one was started as a POV fork during an edit war by someone subsequently arbcomm sanctionned / banned - I forget the details. See-also. Hopefully you're not planning to start up the greenhouse wars again; that would be a very bad idea. I see that your wife was taught the wrong answer; alas, since you've just said the opacity of glass and plastic to the far infrared radiation being given off by the hot floor is fundamental to all of this discussion about what drives heating of greenhouses. it looks like you've found the wrong answer for yourself. You need to read the GH article, where all this is explained William M. Connolley (talk) 17:27, 15 November 2009 (UTC) —<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 11:59, 16 November 2009 (UTC)
 * William, I appreciate your openness and blunt style, which is more to my taste than that of Apis, who conducts his aggressive reverts behind a mask of anonymity. But how is it that you can remember how greenhouses work but not that Cortonin forked an article on 16:25 3/17/05 and you promptly joined him in expanding on that fork?  Cortonin's punishment for the ensuing edit wars was heavier than yours, but you weren't let off completely yourself.  You still haven't answered my earlier question on this page as to whether you're more or less of a reverter today than back then, but judging from your response here it sounds like you have no regrets about the past (perhaps because you can't remember it, as per your claim), and therefore have no intention of behaving any differently than before.  Arbcomm's phrase "often without giving adequate explanation for the reverts" is particularly telling here.
 * Regarding your other remarks, of the general form "you're wrong and I'm right," in the absence of any convincing corroborative detail external to Wikipedia to back them up I will follow Ccrrccrr's advice to simply ignore them. Despite having edited many dozens of articles, quite a few completely from scratch, I have never engaged in an edit war and don't propose to do so here, so you can set your mind at ease there.  --Vaughan Pratt (talk) 06:28, 16 November 2009 (UTC)
 * If you're going to try to be unpleasant, you neeed to do better research: Requests_for_arbitration/Climate_change_dispute_2 William M. Connolley (talk) 08:37, 16 November 2009 (UTC)
 * My apologies, your recollection is not as bad as either of us had thought. What changed their mind?  I seem to recall something about Wales stepping in here.
 * I don't mean to seem like an unpleasant investigator here, but I do care about getting the story about greenhouses straight. If you have advice on how to accomplish this while minimizing hurt feelings (both yours and mine) I'm all ears.  --Vaughan Pratt (talk) 09:37, 16 November 2009 (UTC)
 * Here's a start: WP:CIVIL
 * I'm not following, help me out here. At WP:CIVIL it says "Where the uncivil comment is yours, any of these options will help to reduce the impact: ...Strike it out (using HTML strikeout tags ), to show, publicly, that you withdraw the comment."  But when I offered to do so at my  talk page and asked if that would be ok, you said you would object, albeit not strenuously.  How can I follow WP:CIVIL when you don't operate according to its guidelines yourself?  I'm sorry you feel this way. --Vaughan Pratt (talk) 07:30, 17 November 2009 (UTC)

Is FIR-blocking a minor or major contributor to greenhouse action?
(This section is intended as a replacement for the preceding section by shortening the main reasoning while bringing in additional material. While shorter than its predecessor, it is still quite long, which I put down to the complexity of the relevant physics.)

I'm not the botany expert in my family, that would be my wife, who is descended from a long line of Dutch nurserymen and horticulturalists and whose life has revolved around plants since before high school. She has a master's degree with a botany concentration from Macquarie University and a master's degree with a concentration in ecology from Stanford University.

When I asked her whether greenhouses trap either sunlight or heat, she answered that she had been taught, at every level of her education, by all her professors, in both Australia and the US, that sunlight is readily admitted to the greenhouse at short wavelengths, which become long when radiated back out, and are thereby trapped by the glass, which passes only short and not long wavelengths.

Prior to the politicization of greenhouse warming, it would seem that no one had ever even thought to challenge this completely straightforward and elementary account of how greenhouses work, which is in complete accord with every property of the relevant radiations and materials involved with greenhouses known to both physicists and biologists.

I'm the physicist in our family, having taken an honours degree in physics (a five year program whose final year was nothing but physics courses), followed by a master's degree. Both programs were within Sydney University's School of Physics, with the latter concentrating on computer science, at that time considered a program within physics.

My understanding of plants and their needs is as limited as my understanding of physics is extensive. Having had occasion to design windows to pass far infrared radiation (FIR), namely in the neighborhood of 10 microns, I'm very familiar with the difficulty of coaxing FIR through any kind of material capable of transmitting visible light, whether glass or plastic. That said, Saran wrap passes FIR fairly well, so it is plausible to me that a greenhouse constructed from one layer of Saran wrap would allow the FIR to escape.

The point of a greenhouse however is to duplicate other climates and other seasons, typically tropical climates in a temperate zone (think orchids) and the summer season during winter (think hothouse tomatoes). In both those examples the goal is to retain heat. Hence in those examples (there are other examples where cooling is the goal), constructing a greenhouse from Saran wrap in order to permit more FIR to escape would seem counterproductive. It would also be architectural folly, since the Saran wrap would tear in the first strong breeze.

Prior to the development of construction-grade transparent plastics, greenhouses, or hothouses as they are called in some parts of the world, were always constructed of glass. Ordinary glass is largely transparent to the energy-bearing (heating) portion of sunlight but essentially totally opaque to the far infrared energy radiated by objects at terrestrial temperatures such as the interior of a greenhouse. The advent of plastic windows did not change this because optically transparent plastic is no different from optically transparent glass in its essentially total blocking of FIR.

98% of the heating energy of sunlight is between .251 microns wavelength (near-ultraviolet, visible light starts at .410 microns) and 3.961 microns (near infrared). 98% of the heating energy of the thermal emission from the interior of a greenhouse is between 5.2 microns and 81.7 microns.

Remarkably, both glass and transparent plastic are essentially transparent over the range .251 to 3.961 microns, and essentially opaque over the range 5.2 to 81.7 microns.

By the middle of the 19th century physicists had realized that this tendency of glass to pass visible light while blocking far infrared would result in the walls and roof of greenhouses trapping the incoming insolation and preventing it from escaping in any form other than reflected light along with conduction through the glass mediated by convection in the air on either side of the glass.

The mechanisms by which incoming radiation is turned around and radiated back out are two-fold: reflection and absorption. Reflected radiation returns at the same wavelength as it arrived while absorbed radiation is re-radiated at about twenty times the wavelength of the incoming radiation. A greenhouse with a light interior will tend to reflect, one with a dark interior will tend to re-radiate at twenty times the wavelength of the incoming radiation. The objects in a greenhouse including the floor are sufficiently dark overall that the reradiated longer wavelengths will be a significant component of the total energy trying to escape from the greenhouse, a nontrivial detail in the construction and operation of greenhouses.

A century and a half after this principle had been grasped, elaborated, and digested, anthropogenic global warming became a political hot potato. One of its many victims was this 150-year-old understanding of the mechanism of how greenhouses worked. Anyone who understood that mechanism was well equipped mentally to see how Earth was threatened by the encroachment of greenhouse gases.

It may be entirely unfair to the industrial complex, but I can't help thinking that among the many strategies employed by these anthropogenitors (if I can coin a word as yet completely unknown to Google, meaning those bearing the burden of the responsibility for anthropogenic global warming or AGW), aimed at sowing fear, uncertainty, and doubt in the general public's mind about the culpability of said anthropogenitors, is one of downplaying the role of infrared-blocking by actual greenhouses. If greenhouses aren't really capable of greenhouse warming, then maybe the anthropogenitors aren't really doing anything like it either. We would then have a range of opinions about how greenhouses work where in the preceding 150 years there was only one.

The question I would like to raise here is, do we have a genuine scientific insight into the real mechanism by which greenhouses work, or has science merely fallen victim to the anthropogenitors who don't appreciate the spotlight science has suddenly shone on them and who, to mix metaphors, are now darting for cover like cockroaches using every available tool in their propaganda arsenal.

This question cannot be answered by a simple assertion of opinion, which has been the dominant approach followed to date in the four-year history of this article, but only by theoretical or experimental demonstration of the relevant quantities. --Vaughan Pratt (talk)


 * When I asked her whether greenhouses trap either sunlight or heat, she answered that she had been taught, at every level of her education, by all her professors, in both Australia and the US, that sunlight is readily admitted to the greenhouse at short wavelengths, which become long when radiated back out, and are thereby trapped by the glass, which passes only short and not long wavelengths. Prior to the politicization of greenhouse warming, it would seem that no one had ever even thought to challenge this completely straightforward and elementary account of how greenhouses work, I'm sure your wife is a very nice person. But she is a botanist, and she was taught by botanists. As for the ranting about politicisation, leave it out guv. Just read the science; its linked from the article, but here it is direct so you have no more excuses: http://www.wmconnolley.org.uk/sci/wood_rw.1909.html William M. Connolley (talk) 10:10, 16 November 2009 (UTC)
 * Certainly Wood's reputation is beyond any possible reproach. But besides this one article in a 1909 issue of the Philosophical Magazine, has anyone else duplicated Wood's experiment and drawn the same conclusion?  Given that he gave neither the dimensions of the enclosure nor of the glass, it would be impossible to duplicate as conducted anyway.  This is not how experiments are usually conducted and described, and it is strange that a physicist of Wood's stature would take so little care with it.  If his conclusion were correct, surely someone else would have repeated his little experiment with greater care in order to verify it.  Have they?  Otherwise we have only his bald assertion that this is what he observed.  He could have made any number of errors in performing and interpreting his single experiment.  His remark at the end does little to increase confidence in the care he took with his experiment: "I do not pretend to have gone very deeply into the matter, and publish this note merely to draw attention eto the fact that trapped radiation appears to play but a very small part in the actual cases with which we are familiar."  For all we know he repeated it a year later when challenged, got entirely different results, and everyone lost interest in the matter.  This is far too little experimental evidence from which to draw a solid conclusion. --Vaughan Pratt (talk) 11:01, 16 November 2009 (UTC)


 * Is FIR-blocking a minor or major contributor to greenhouse action?


 * The answer is: it depends on many different factors.

—<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 11:54, 16 November 2009 (UTC)
 * I assure you I am not an "AGW denier", but we should stick to the facts and the science and leave the politics out of it. And if it's true what you say, there "is far too little experimental evidence from which to draw a solid conclusion" then all the more reason to leave these claims out of the article.
 * That's not what I said. I said this (referring to Wood's experiment) is far too little experimental evidence.  Taking someone's words out of context so as to give them a different meaning is political method, not scientific method.  Citing Wood's experiment is a legitimate scientific datapoint, albeit a very inconclusive one for my money.
 * I agree that the scientific facts take precedence in answering the question I posed. But it is naive in such discussions to ignore the enormous pressure that has been brought by business interests to influence in their favor the scientific status of everything related to greenhouse warming.  If the situation were a mugger pointing a gun at you, would you insist that all discussion of the mugger be confined to the ballistics of his assault, or would you permit speculation about his motives?  If you were a very polite muggee you might preface any such speculation with "It might be entirely unfair to this shooter, who may be just out to practice his marksmanship and is merely pointing his gun my way by coincidence."  (Note that I prefaced my more speculative remarks in this way above.)  But would you then take politeness to the next level and refrain from speculating on more sinister motives?
 * In this case the coincidence is that attention is now being drawn to this obscure experiment, a hundred years later, at the same time that AGW is under assault by business interests and their supporters. Like you I don't believe in denying AGW, but unlike you I also don't believe in denying that there are people motivated by other than scientific curiosity to manipulate our understanding of warming whether global or greenhouse.
 * It would be fascinating if Wood's hunch and little experiment were borne out by closer examination, and I would then be delighted to see that canard shot down like a duck (there is in fact an etymological connection though not quite that one). Not that I have any grudge against this particular belief, in fact I've been rather attached to it, but if it does turn out to be a canard then bang, good riddance.
 * Meanwhile the main differences I see between citing Wood's isolated experiment purporting to undermine well over a century's understanding of greenhouse operation and citing Miskolczi's isolated calculation purporting to show AGW is not caused by CO2 is that Miskolczi has not yet shown himself to be of Wood's calibre, and that Miskolczi's calculation is referenced more often in ostensibly reputable circles, both for and against, see e.g. for an instance of the former.  In science the majority opinion among reputable scientists rules, and I don't understand the motivation for carving out an exception for Wood any more than I see doing so for Miskolczi.  Granted Wood's reputation gives him an edge but if that were a sound argument we would have to deny that God plays dice on the ground that Einstein denied it.  Just because the Pope turned out to be more fallible than Galileo does not make prominent scientists infallible.
 * But perhaps I just have an overly suspicious mind, the mugger really is just out for practice. --Vaughan Pratt (talk) 19:33, 16 November 2009 (UTC)

—<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 23:55, 17 November 2009 (UTC)
 * I have no doubt there are many with a hidden political and/or economical agenda here on Wikipedia, just as everywhere else. It bothers me as much as it seems to bother you. Much of wikipedia policies regarding content deal with these issues. Wikipedia try to represent the "generally" accepted knowledge (in the scientific community where applicable) about a subject and not the objective "truth".
 * My point exactly (about consensus vs truth). Wood may have discovered the truth but that doesn't make it the consensus view.  Both my wife and I were trained, respectively in the US and Australia, to believe in the infrared theory of greenhouses.  No one so far has pointed to any evidence of a major sea-change there in either botany or physics.  Even though I think of myself now as a theorist shoring up the missing analysis of Wood's experiment (I do hope I'm not the first), that's still nowhere near a quorum.  If there's a strong-willed minority on Wikipedia that wants to override that quorum in the interests of truth over consensus, you can sign me up for the truth side even though this is against Wikipedia policy.  --Vaughan Pratt (talk) 05:51, 18 November 2009 (UTC)
 * Apis: The answer [to this section's question] is: it depends on many different factors. Do you know that for a substantive fact, or are you using the word "depend" in a way that would make the temperature of the earth depend on radiation from the moon (which it does)?  If the former, can you back it up?  Otherwise it's a vacuous statement since almost every phenomenon in nature can be shown to depend on many different factors.  --Vaughan Pratt (talk) 22:35, 16 November 2009 (UTC)

—<span style="color: rgb(5, 85, 5);">Apis (<span style="color: rgb(5, 85, 5);">talk ) 23:55, 17 November 2009 (UTC)
 * You are right and I did mean notable factors. Insulation is one important factor in greenhouse design. This can be achieved in several different ways, in which absorbing thermal radiation can play a notable role if utilized properly. 0.1 mm single layer polyethylene plastic film has a transmittance of 0.80 for λ > 2.8 µm, and this is a common greenhouse cover material. If you use many insulated layers, the insulation effect from IR-blocking can be notable, thus motivating IR-blocking additives in the plastic. Using low-e (reflective) multilayer glazing would be even better but probably too expensive to be economical. And then there is the woods experiment mentioned previously. I would be sceptical to using a single layer ir-black cover since the surface area of the covering typically is larger than the radiating surface inside the greenhouse. I suspect that might even increase radiation loss in worst case.
 * Ok, I'm missing something here. Wood showed that there was no difference in temperature when a non-IR-blocking material such as rock salt is replaced by an IR-blocking material such as glass.  You seem to be claiming that if you increase IR blocking in plastic it will increase temperature.  How do you reconcile that with Wood's experiment?  Does IR blocking work differently in plastic than glass, or what?
 * On your second point, while you're right that a larger covering surface allows more heat to flow out, it also allows more heat to flow in. How do you show that the increase in heat out is greater than the increase in heat in when you increase the covering surface?  --Vaughan Pratt (talk) 05:51, 18 November 2009 (UTC)

Here's a possible way out from this seemingly gridlocked discussion: If I understand correctly, Apis states that in a greenhouse with single-layer glazing, it doesn't make a significant difference what the ratio of λ > 2.8 µm IR absorbed vs. transmitted. However, with multi-layer glazing, other heat transfer is reduced greatly, so how λ > 2.8 µm radiation interacts with the glazing becomes a factor that could be worth considering. Whether that's true depends on what your threshold for "significant" is, but it's not an unreasonable assessment. Combine that with the fact that double glazing is pretty important for making a solar greenhouse (meaning heated by the sun) work in a cold climate (if it's not a cold climate this becomes a non-issue), and you have a pretty clear case that it's an important factor to discuss in the article. Of course, double glazing is even more important to discuss in the article and I don't see that in there anywhere! Ccrrccrr (talk) 12:52, 18 November 2009 (UTC)
 * Yes! You understood my reasoning perfectly (well, enough to draw the correct conclusions from it, certainly.) I wish everyone else debating this stuff could see all this as clearly as you, apparently it's even beyond that brigadier general chap who seems to be short a harvester or whatever, and he's supposedly an actual academic.  If Wood had come up with this insight in 1909 he might have noticed that double or triple glazing enhanced the greenhouse effect to the point where even he would have to agree that it was appreciable.  I wish you luck in persuading the other editors of this.  I'm of the opinion that only the serious professionals have the ability to judge these things, of which there seems to be an equally serious shortage here.  I think this line of reasoning needs to be heard and judged in a forum better qualified than the consensus opinion of Wikipedia editors.  --Vaughan Pratt (talk) 07:31, 19 November 2009 (UTC)

Making sense of Wood's experiment
Now that User:William M. Connolley has thrown down the gauntlet of Wood's experiment, I've been trying find some, even a little, theoretical support for Wood's intuition and empirical observation that the temperature of a greenhouse depends very little on whether its transparent covering passes far infrared (FIR). Any serious mismatch between experiment and theory calls into question either the experiment or the theory. It's all very well for Wood to attribute his insight to intuition, but when that intuition gives wildly different answers from the formulas, then either (i) the formulas are wildly wrong, or (ii) the theorists are applying the formulas wildly incorrectly, or (iii) the experimentalists (in this case Wood) have overlooked some phenomenon in their experiment.

There is no reason to suspect (i), which leaves (ii) and (iii). Initially I was leaning towards (iii) because I simply could not come up with any evidence for (ii).

The sticking point for me has been that the interior of Wood's box, being at 55 C, must radiate away $$\sigma T^4$$ = 650 W/m2 or so, as a necessary consequence of Stefan's law, using $$\sigma$$ = 5.67&times;10-8 and T = 328 K.  Sunlight arriving at the box is roughly 1000 W/m2, which to achieve equilibrium must therefore be the total power density leaving the box. The latter can be partitioned into radiation reflected from the two sides of the glass covering, which I'll take to be 4%+4% = 8% or 80 W for typical glass reflecting normally incident radiation. This leaves 920 W to be either absorbed by the cover or transmitted into the interior of the box; I'll assume that only 20 W is absorbed (reasonable for sufficiently clear and thin glass) and take 900 W for the latter.

The 900 W entering the box has to return as 650 W of radiation in order to satisfy Stefan's law at 55 C, whence by equilibrium the remaining 900 - 650 = 250 W must be all convection, these being the only two available transports.

Wood did not account for that 650 W. He did not even bring it up as a concern, suggesting that he was going on pure intuition and experiment without doing the calculations that led (or misled) everyone else into arriving at an entirely different conclusion, and therefore not noticing that huge 650W discrepancy.

The mystery is, how can the two boxes be the same temperature inside when the window of one box blocks the 650 W of radiation while the other passes it? Why is there no heat build-up in the blocked box? Very mysterious. --Vaughan Pratt (talk) 12:30, 17 November 2009 (UTC) To summarize the situation, we have an empirical observation by a most distinguished experimental physicist that is in violent disagreement with the predictions from the theoretical modeling done by the 19th century physicists who first considered this possibility after realizing that light had wavelengths. Ordinarily this sort of discrepancy between theory and experiment would be followed up by careful repetitions of the experiment in combination with re-examination of the model. If repeated experiments yield the same observations, suspicion falls on the model, and the usual outcome is some improvement to the model offering a theoretical explanation of the empirically observed phenomenon. Physics is not a Procrustean bed that tries to force experiments to go the way theory predicts (or shouldn't be, though it often is).

For some reason this seems not to have happened here, at least as far as Jones and Henderson-Sellers were able to determine from their extensive research into the "History of the greenhouse effect" cited by Connolley at. Perhaps no serious physicist could be persuaded there was anything at stake here, or perhaps no one had taken the trouble to calculate the exact temperature difference that the accepted model of greenhouse warming was predicting, which is much larger than what Wood found, or perhaps they saw the discrepancy but put their faith in the model and paid no attention to this mid-career (41-year-old) experimentalist.

As might be deduced from the first half of this section, I felt I was closing in on the answer when I wrote the above, but wasn't confident about it, so I decided I'd better sleep on it in order to be sure it was right. A night's sleep turned out actually to be very productive, giving further theoretical insights explaining Wood's experiment.

Let me start from the conclusions and work backwards to my reasoning. Feel free to challenge any of this at any level of detail. One assumption I'll make, based on Wood's stellar reputation as an experimental physicist (literally---astrophysics was a main area for him), is that he conducted his experiment very carefully, his too-casual reporting of it and his disclaimer "I do not pretend to have gone very deeply into the matter" notwithstanding. I'll infer from that that the 1 K temperature difference he referred to, which he seemed to think of merely as experimental error, was actually very meaningful. For the purposes of the following I'll assume it was exactly 1 K with the glass box being hotter; it's too bad he didn't attempt to measure the difference more precisely. I'll further assume conductivities of 1 and 6 W/m/K for respectively glass and rock salt, per my copy of the 2000-page Chemical Rubber Publishing Company's Handbook of Chemistry and Physics (old-fogey force of habit, I could have looked online). These are approximate per the tables, being somewhat variable; in a more carefully designed experiment Wood could have measured them more precisely had it occurred to him that they might be needed.

The conclusions:

1. There need be no convection at all inside the boxes to explain the transport of heat from the black-painted bottom of each to its window. Wood would have observed precisely the same outcome had he pumped the interiors of both boxes down to a vacuum, and moreover independently of where he positioned the thermometer inside each box. (This is a gedankenexperiment that assumes sufficiently rigid and airtight materials, permissible for the purposes of a mere gedankenexperiment.)

2. The thickness h of the two windows Wood selected (recall that they were the same thickness) can be computed from Wood's reported observations as 1.1 mm. This is implausibly thin, so either the temperature difference was larger than Wood reported, for example 2.0 degrees would give a more plausible 2.2 mm, or the theoretical explanation below is incomplete, or Wood had some reason to select unusually thin glass, or maybe his entire setup was smaller than one would visualize from his offhand account, which omitted all dimensions.

Here's my proposed model accounting for Wood's observations. Both boxes are acting as essentially blackbody radiators of far infrared, FIR. However although they converge to almost the same temperature they do so for somewhat different reasons. I'll start with the box with the glass window.

The glass window being opaque to FIR, it is itself a black body at those wavelengths and the cavity between it and the black cardboard below instantly fills with FIR radiation at 55 C, bringing the entire contents of the box to a uniform 55 C. This is true whether or not any air is present; whatever air is in the box will instantly heat to 55 C itself without the usual delay associated with convective heating since every molecule of air will be uniformly subjected to this trapped radiation at 55 C (328 K) not interact significantly with the trapped radiation but will be heated by convection from the hot surfaces.

The inside surface of the glass window is heated entirely by radiation at 55 C. The rest of it is then heated entirely by conduction directed outwards. (Recall that, except for some minor possible absorption, the glass window is transparent to sunlight, which therefore cannot be heated from outside.) The thermally conducting power density P in W/m2 is directed outwards and is given by the formula P = &kappa;D/h where &kappa; is the thermal conductivity of the window in W/m/K, D is the temperature differential across the window in degrees Celsius, and h is the thickness of the window in meters, confirmable by checking the dimensions of the units. Hence h = &kappa;D/P = 1/900 m or 1.1 mm when &kappa; = 1 W/m/K, D = 1 K, and P = 900 W.

Once this 900 W has been safely conducted through the glass it is then free to be radiated and convected away. We can compute the former as 650 W by Stefan's law, and infer the latter as 250 W, this being what convection needs to make up in order to discharge the entire incoming 900 W back out into the environment when equilibrium has been reached (which will be solely the time needed to heat the glass to 55 C).

This model attributes all of the temperature difference observed by Wood to the thermal conductivity of glass without reference to rock salt's thermal conductivity, which happens to be six times higher but it could have been six times lower and it would have made no difference. Here's the corresponding story for the box with the rock salt window.

Like the glass-windowed box, this one develops 55 C radiation in its cavity too, and likewise it sends all 900 W of it out the window. The key difference is that, whereas this 900 W had to be conducted through the glass window, here it simply radiates through the window! Other than that everything remains the same. Negligible conduction across the window occurs, and it therefore develops a negligible temperature differential. This is why the temperature difference between the boxes can be taken as a good proxy for the temperature differential across the glass window alone.

This detailed explanation of Wood's experiment is surely of sufficient interest in its own right that, had any theoretical physicist in the past hundred years taken the trouble to examine the matter and work out why Wood saw what he did, that explanation would surely have accompanied Wood's offhand report of his one observation in any citation of evidence against the conventional wisdom that greenhouses achieve their temperature to a significant degree by trapping FIR.

So: what is the answer to the question of the preceding section? Answer: it's a trick question, because it begs the question of whether infrared trapping has any impact. For glass that is sufficiently thin and/or thermally conductive it has no perceptible impact at all! For 3 mm (1/8") glass of thermal conductivity 1, typical for windows, it will add 3 degrees to the temperature. Refinements of this model may reveal an even smaller effect, but this is already far smaller than is predicted by failing (as I did myself) to recognize that the glass itself is a black body radiator at FIR.  So even though glass is a thermal insulator, having 1/40 the conductivity of say copper, for the purposes of modeling windows it is not unreasonable to refer to it as a conductor as has been suggested here, the physical definition notwithstanding.  --Vaughan Pratt (talk) 21:51, 17 November 2009 (UTC) As a postscript it occurs to me that some may be wondering why the rock salt window is considered merely a transmitter and not itself a black-body radiator, since there is no significant physical difference between the radiation coming out of it and that from the glass window.

The difference is that the black-body spectrum of the radiation from the rock salt window came from inside the box, whereas that from the glass window was shaped by the window itself.

Had the cardboard in both boxes been painted with a kind of paint that radiated FIR in a narrow band, say at 14 microns because it was constructed of millions of CO2 nanolasers (a science fiction fantasy), only the glass window would emit black-body radiation because it had to convert the outbound FIR to thermal heating of the glass, then reconstruct it as radiation on the other side, where it will have no memory at all that the energy used to be coherent. The rock salt window on the other hand will pass the coherent FIR straight through unmodified, which is not black-body radiation by any stretch of science fiction. It is like the difference between postman Rocky S. who delivers the coherently-written Amazon book you ordered and postman Glassy I. who substitutes his own incoherent ramblings.

It might also be worth pointing out that all of the physics in this model is confined to optics, radiation, and heat conduction. The uncontroversial observation made earlier that "it depends on many factors" can therefore be sharpened to the more informative "it depends on three factors." No thermodynamics, electromagnetism, classical mechanics, quantum mechanics, gravity, or climate physics enters into the model at all. One could add them, but only at the expense of subtracting from the simplicity of the model, which they would only complicate to no significant advantage. --Vaughan Pratt (talk) 22:22, 17 November 2009 (UTC) Another postscript occurs to me. At Connolley asks the excellent question "Why is his second to last paragraph wrong?" In light of the above analysis, it is clearly naive to identify a one-degree difference with no difference, since the difference can be made very large simply by making the glass windows very thick: if each millimeter adds a degree, thickening the glass to an inch raises the temperature 28 C. So Wood's inference of no significant effect of CO2 on global warming breaks down even before taking convection effects into account.

There is furthermore no counterpart in the atmosphere of an obligingly conductive thin layer of glass: the heat leaving the Earth is dependent on making its own way through the atmosphere using only radiation and convection, without the benefit of conduction enjoyed by the heat escaping from a greenhouse. As CO2 blocks progressively more of the radiation path, the effective thermal resistance (inverse of conductivity) of the atmosphere as implemented by convection, multiplied by its many kilometers of thickness, makes "conduction-via-convection" a formidable barrier for heat transport not even remotely comparable to a 1/8" sheet of glass. --Vaughan Pratt (talk) 23:49, 17 November 2009 (UTC)


 * I must admit all of Wood's experiment seems to miss a major point about a greenhouse as far as I'm concerned. During he day one opens the vents to stop it overheating. During the night the vents are closed and the greenhouse keeps the plants warm. I'd have thought that on a clear night a cover that let infrared through easily would be more likely to let plants frost up. So having glass that lets through the light for the plants to grow yet acts as an insulator and stops infrared radiation sounds a good idea to me. As to Wood the real question is why a cover that stops infra red still let the inside get so hot. This is all OR by the way so you won't be say it in an article, I guess it can help with getting through the jungle of obscurantism that has been growing round the greenhouse effect though. Dmcq (talk) 10:06, 19 November 2009 (UTC)


 * Right. Most fuel use in heating greenhouses is at night.  So how quickly it cools at night is at least as important as how hot or quickly it heats during the day.  The "real question" of why a cover that stops IR still let the inside get hot is easy--the glass lets the vast majority of the IR spectrum in the sunlight through.Ccrrccrr (talk) 02:09, 20 November 2009 (UTC)
 * Dmcq, that's a great point about night time behavior, I hadn't thought to consider it. (Also about OR, with which I fully agree---fortunately talk pages aren't held to the same high standard of WP:V as articles, which makes it possible to evaluate alternative perspectives to test whether there's any new consensus that might form and what support exists in the literature for it.)  Presumably the diurnal variation of the interior of a greenhouse is considerably greater than its exterior; however if one works with the daily average instead of the noonday behavior, how different does that make the impact of IR-blocking?
 * The one thing about an opaque window is that unlike a transparent window it heats up by absorption (assuming it's not a perfect reflector) until the radiation-side surface is at the same temperature as the radiation (radiation does have a well-defined temperature even when not a black-body spectrum). If it's a thermal conductor to the extent that glass is, namely about 1 W/m/K, the opposite surface then warms up too and starts radiating.  If the power density is half a kilowatt/m2 (as for a box at 306.4 K = 33.4 C), the temperature gradient at equilibrium across glass that is fully opaque at that wavelength is .5 degree per millimeter.  This is so little that even at night IR-blocking accomplishes little because the heat can get through the blocker by conduction instead of radiation with negligible loss, and turn back into radiation on the other side.  So one way or another a thin layer of glass is leaky whether it is leaking via transmission or conduction.  An IR-blocker needs to be fairly thick in order to have a significant temperature drop across it sufficient to keep the interior of the greenhouse warm.
 * Regarding "the glass lets the vast majority of the IR spectrum in the sunlight through," Ccrrccrr, one thing to keep in mind here is that Wood found it necessary to put a sheet of glass in front of the rock salt window to stop it getting hotter than the box with the glass window. What this tells is that glass blocks some solar radiation (else putting the glass ahead of the rock salt wouldn't have accomplished anything).  Just how much is impossible to tell from Wood's sparse documentation.  However it can be calculated using Planck's law and an assumed glass cutoff at 2.8 microns: about 5% more of the insolation is blocked than if the cutuff were at say 5 microns, consistent with your "vast majority."  In that case Wood's extra glass window should only have decreased the incoming power density for the rock salt box by 5%, but perhaps that was what Wood needed to avoid the embarrassment of having the rock salt box hotter instead of colder than the glass box when he noticed it happening.  Sounds like Wood made up the rules as he went along.  --Vaughan Pratt (talk) 06:35, 20 November 2009 (UTC)


 * If you have a thin sheet like you say that conducts heat well but is opaque to the radiation, and there is no air conduction!, then the sheet should heat up to an intermediate temperature from the radiation on both sides. Therefore the temperature of the ground underneath would only rise in temperature about a half as fast as it would otherwise. It would also cool only about half as fast at night. Dmcq (talk) 13:42, 20 November 2009 (UTC)


 * I think this is the same thing that Dmcq is getting at: Vaughan says, "An IR-blocker needs to be fairly thick in order to have a significant temperature drop across it sufficient to keep the interior of the greenhouse warm."  But that's not the way it works in practice.  If you have a reasonably thin IR blocker (absorber or reflector) made of a moderately heat-conductive material, the what limits the heat flow out is primarily the heat transfer processes (by radiation and convection) to the inside surface of the thin sheet, and the heat transfer processes from the outside surface to the ambient.  A very crude rule of thumb is that the heat transfer coefficient is about 5 to 10 W/(square meter K) including convection and radiation for building size and temperature sorts of things.  In other words, RSI 0.1 to 0.2.  5 mm (thick) glass is RSI 0.005.  The thermal resistance of the glass is not important regardless of whether the thin layer transmits, absorbs, or reflects IR. Ccrrccrr (talk) 15:00, 20 November 2009 (UTC)
 * Well, this is fascinating. I will go and measure these things to see what actually happens. :)  (It rained a lot today, the weatherman says Tuesday will be the next sunny day.  Though I suppose rainy days should also be of interest.)
 * Granted convection acts slowly in transferring heat to a thin sheet, but radiation heats the surface instantly, what takes time is conduction through to the other side. I would expect convection to be irrelevant here because the air is merely sitting around in the box/greenhouse passively waiting to be warmed up by the intense radiation, which quickly brings the entire interior of the enclosed box to the same temperature.  While I agree with Dmcq's reasoning that the sheet will "heat up to an intermediate temperature from the radiation on both sides," that's the average sheet temperature.  I would expect the sheet, once it has reached equilibrium, to exhibit a temperature gradient across it, with its inside temperature equal to the surface temperature of the box below, and its outside temperature being a few degrees lower and radiating away the heat of the sheet at that outside temperature.  (By "thin" I have in mind a couple of millimeters, though I'll play around with this up to 15 mm.)
 * Ccrrccrr, could you please explain your "what limits the heat flow out is primarily the heat transfer processes (by radiation and convection) to the inside surface of the thin sheet, and the heat transfer processes from the outside surface to the ambient" in more detail? In your account does the heat get from the inside to the outside surface by conduction?  If so does that conduction obey Fourier's law, and if so what temperature drop across the sheet would you infer?  If not how does the heat cross that barrier?  --Vaughan Pratt (talk) 08:50, 21 November 2009 (UTC)


 * Replying directly to the above: No, I don't want to explain in more detail. Instead I'll refer you to a reference:  .  Yes, heat gets from inside to outside by conduction and the temperature drop across the sheet would be very small.  Let's say the temperature difference between inside and outside was 20.5 C.  And let's say inside film resistance was 0.13 RSI; outside 0.07 RSI.  Total 0.205, including 0.005 for the glass.  Voltage divider law says drop across glass itself is 0.5 C.


 * I must recommend reading up on this stuff rather than thinking out load on talk pages and asking us to teach you.Ccrrccrr (talk) 03:49, 22 November 2009 (UTC)
 * We may be talking at cross purposes. I don't have any problem doing these calculations: your reference at  uses Fourier's law (which they write as q/A = (Tin - Tout)/Resistance which is equivalent to what I wrote) the same way I do, with the same numerical results for any given values of the parameters.  I wasn't asking for help, I was asking how you drew your conclusion, which didn't make sense to me.  (Next time I'll say "Really?" instead of "this is fascinating" which might not convey the irony as well.)  There is no "thinking out loud," I did the calculations and put them and my conclusions up.  I stand by them; if you see an error anywhere please point it out.
 * Talking about errors, there seems to be a discrepancy in the emissivity of glass between Wikipedia's Low-emissivity article and your reference (2nd paragraph after the section "Heat Flow Across an Air Space): the former says 0.95 and the latter 0.9.  It's a routine exercise to compute the emissivity of glass from first principles; when one does so assuming a refractive index for window glass of 1.54 it comes to 0.954, so my vote goes for the Wikipedia value.  The only way I can see them getting 0.9 is if they were talking about a wavelength of radiation for which the glass in question is transparent, for which the emissivity is 0.91 (since the 4% reflection at the other side will be added to the 4% on the first side).  --Vaughan Pratt (talk) 22:39, 22 November 2009 (UTC)
 * (I just noticed one error I made: I should have said the air inside was warmed by convection, not sure what I was smoking when I said by radiation.) --Vaughan Pratt (talk) 22:58, 22 November 2009 (UTC)
 * It might help clarify my main point if I agree that the temperature drop across the regions on each side of a window can be substantially more than that across the actual glass (assuming single glazing). My point is that the fact that the glass itself blocks IR does not necessarily mean that the glass blocks heat transfer, which the very low temperature drop across the glass itself supports.  (Bear in mind that it is the glass itself that is credited with blocking IR, not the media on either side, which would make their own contribution to thermal resistance whether or not the glass blocked IR.)  I had the feeling that you (Ccrrccrr) had agreed with me on that detail, but I may have spoiled that by going into unnecessarily complicated detail, for which my apologies.  --Vaughan Pratt (talk) 06:51, 24 November 2009 (UTC)
 * I was assuming the sheet was so thin the temperature differential across it would be very small. Consider it as a sheet of metal for instance. And I was ignoring convection or conduction on either side which is a huge assumption, I was just considering radiation. As far as I can see a sheet like that should halve the rate of heat transfer. Dmcq (talk) 16:57, 21 November 2009 (UTC)
 * I was thinking of "thin sheet" in the sense of a greenhouse window. Metal behaves very differently from glass and your intuition that the temperature difference would be small for a thin metal plate is spot on because metal has 20-40x times the thermal conductivity of glass.  A thin sheet of metal is a dead short thermally, whence the two sides will have the essentially same temperature unless the power flux is huge.  (Open and short circuits mean the same thing for thermal conduction as they do for electricity. Ohm's law is the electrical counterpart of Fourier's law, with voltage difference in place of temperature difference,  resistance in place of thickness divided by thermal conductivity, and dQ/dt interpreted as rate of charge flux (current I) in amps instead of rate of heat flux in watts.)  Another difference from glass is that if it's shiny, as metal tends to be, then it's a good reflector and a bad radiator, whereas glass that is opaque at the wavelength in question (here FIR) is a bad reflector and a good radiator (a good reason to use a glass stovetop).  So while your intuition about heat transfer across a thin sheet of metal is good, in order to apply it to glass you have bring in those large factors.
 * For a plate in contact with air, there is nothing to conduct to beyond the plate (either side), leaving just radiation and convection. In the case of Wood's experiment, if for the sake of an exact answer we assume a uniform 55.00 C measured at the outside surface of the window and a refractive index of 1.50 for the window (whether glass or rock salt) at that wavelength (making the emissivity 1 - ((1.5-1)/(1.5+1))2 = 0.960), we can then use Stefan's law to calculate very precisely that the outside surface of his window must radiate at 5.6704&times;10-8&times;.960&times;328.154 = 631.2 W/m2, neither more nor less.  (If we couldn't calculate it that precisely with those assumptions, physicists would have no justification for giving the Stefan-Boltzmann constant 5.6704&times;10-8 to such high precision!)  If we further assume an incoming flux of 900.0 W/m2 of solar radiation transmitted into the box by the window (i.e. after reflection of 4%+4% and neglecting absorption of solar radiation by the glass), then for equilibrium the convection must be 900.0 - 631.2 = 268.8 W/m2.  No guesswork, estimation, or complicated convection modeling needed, just the above assumptions including knowledge of all numbers to high precision.  This neglects various (hopefully small) leakages and reflections, which in principle can be made arbitrarily small by careful design.
 * With glass carrying that power density (picture the equivalent electrical circuit) and say 2 mm thick, the thermal resistance will be high enough to develop 2.2 C across the plate. At 15 mm it should be 17 C.  But that's just theory, which is notorious for being way off sometimes on account of some major overlooked factor.  I'm going to go outside and measure it empirically now, today turned out to be a gorgeous day with no breeze or clouds to inject thermal noise.
 * When theory and experiment agree, no third party can outvote them. When they don't agree, no third party has enough weight to break the tie convincingly (though the right-wing press would have you believe otherwise) and the only solution is to bring theory and experiment back into agreement.  --Vaughan Pratt (talk) 19:56, 21 November 2009 (UTC)


 * I think I've lost track of what you're trying to say. Could you explain it to me simply please? What will you be able to conclude one way or the other? Dmcq (talk) 20:50, 21 November 2009 (UTC)
 * How are you with Ohm's law? With that analogy, copper is low resistance and glass is 40x higher in resistance.  I'm treating the heat flux as a current source rather than a voltage source because in equilibrium the heat flux is known and the temperature drop across the glass is unknown (what we're trying to solve Fourier's equation for).  We know what the heat flux has to be, namely the incident sunlight.  Solving, we find that the temperature drop across common glass is roughly 1 C per millimeter of glass thickness.  The outside surface must be the same temperature at equilibrium regardless of the glass thickness, since that's determined by radiation and convection from that surface regardless of the inside temperature of the box/greenhouse.  Conclusion: every millimeter added to the thickness of the glass adds a degree to the temperature drop across the glass, and therefore to the interior temperature (since the outside of the glass stays constant).  --Vaughan Pratt (talk) 22:31, 21 November 2009 (UTC)
 * I should add that that 1 K/mm drop was for a kilowatt of heat flux through a square meter of glass, e.g. a skylight with the Sun overhead on a clear day. At a more typical 200 watts say, the drop would be 0.2 degrees/mm.  --Vaughan Pratt (talk) 06:51, 24 November 2009 (UTC)