Guest Post by Willis Eschenbach
I stumbled across a lovely article about the Saharan silver ant over at phys.org. These ants have special hairs that reflect strongly in the visual and radiate strongly in the infrared. They show a photo of the ant hairs under a couple different amounts of magnification:
Figure 1. Photograph from the phys.org article on the Saharan silver ants and their hair.
The article says:
Saharan silver ants (Cataglyphis bombycina) forage in the Saharan Desert in the full midday sun when surface temperatures reach up to 70°C (158°F), and they must keep their body temperature below their critical thermal maximum of 53.6°C (128.48°F) most of the time. In their wide-ranging foraging journeys, the ants search for corpses of insects and other arthropods that have succumbed to the thermally harsh desert conditions, which they are able to endure more successfully. Being most active during the hottest moment of the day also allows these ants to avoid predatory desert lizards. Researchers have long wondered how these tiny insects (about 10 mm, or 3/8″ long) can survive under such thermally extreme and stressful conditions.
Using electron microscopy and ion beam milling, Yu’s group discovered that the ants are covered on the top and sides of their bodies with a coating of uniquely shaped hairs with triangular cross-sections that keep them cool in two ways. These hairs are highly reflective under the visible and near-infrared light, i.e., in the region of maximal solar radiation (the ants run at a speed of up to 0.7 meters per second and look like droplets of mercury on the desert surface). The hairs are also highly emissive in the mid-infrared portion of the electromagnetic spectrum, where they serve as an antireflection layer that enhances the ants’ ability to offload excess heat via thermal radiation, which is emitted from the hot body of the ants to the cold sky. This passive cooling effect works under the full sun whenever the insects are exposed to the clear sky.
They describe how the hairs “keep [the ants] cool in two ways”—by reflecting the visible light, and by strongly emitting in the thermal infrared.
Curiously, however, nowhere do they mention the importance of a third cooling method that I noticed as soon as I looked at their photograph—the shape of the hairs ensures that more energy is radiated upwards than is radiated downwards. I had never considered that such a thing might be possible. The silver ants have a layer of hairs above their skin which selectively radiate more thermal energy away from the skin than towards the skin. Amazing.
The hairs can do this because, as shown in the right half of Figure 1 and as described in their caption to Figure 1,
a) the hairs have a roughly triangular shape in cross-section and
b) the flat side of the triangular cross-section of the hairs is towards the skin and
c) the two upper sides of the hair are “corrugated”, increasing the surface area facing skywards.
The net result of all of these acting together is to minimize the surface area of the side of the hair facing the skin, and to maximize the surface area of the sides facing the sky. Energy will be radiated from the hair surfaces at some rate per square unit of surface area (e.g. watts/square metre). So the larger the proportion of the hairs’ surface area facing the sky, the greater the proportion of energy radiated skywards versus back towards the ant.
How large is the imbalance in radiation likely to be? Well, the triangular cross-section of the hairs in the picture are about equilateral (three sides the same length). This would mean twice the area pointing skywards as is pointing towards the ant’s skin.
However, there would still be some loss back to the ant’s skin from some portion of the radiation from the tilted upper surfaces of the hairs. Some of that sideways/downwards radiation would be absorbed by the adjacent hairs, however. And some of that back-radiation would be offset by the increased skyward-facing surface area resulting from the corrugation of the upper surfaces of the hairs.
So overall those lesser effects might cancel out in whole or in part, and thus it seems like the layer of ant hairs will emit something like up to twice as much radiation out towards the sky as it does towards the ant’s skin. As is often the case, nature shows the way … what an ingenious cooling method.
And what, you might ask, do Saharan silver ants have to do with climate science?
Well, looking at the cross-sections of the hairs making up the layer shown in the right half of Figure 1, I was reminded of the shape of a cross-section through a layer of tropical cumulus clouds. In particular, I realized that:
a) tropical cumulus clouds have a roughly triangular shape in cross-section and
b) the flat side of the roughly triangular cross-section of the clouds is towards the surface and
c) the upper sides of the clouds are “corrugated”, increasing the surface area facing skywards.
Just sayin’ … it’s something I wouldn’t have guessed was possible, that an absorptive atmospheric layer of clouds could radiate perhaps up to twice as much thermal radiation upwards as it radiates downwards.
I do so enjoy climate science, there are so many amazing things for me to learn about.
w.
PS: My usual request—if you disagree with someone, please quote their exact words that you disagree with. That way, we can all understand exactly what you object to.
About 33 years ago I built a house in New Orleans with a steeply pitched galvanized roof over an air space shaped like an equilateral triangle with an insulated attic “floor” above the living space below. I remember being shocked that the air space under the roof remained just about outside air temperature on even the hottest sunniest days. From the outside it was apparent that the roof was reflecting most of the sunlight, at times projecting light strongly on nearby structures. Convection carried heat within the airspace upwards away from the living area below, released the heated air at the peak and drew outside air into bottom of the airspace, which then washed over the insulation. The metal roofing readily conducted heat from the warmer side to the cooler.
At the time I congratulated myself for being so smart, but I guess mother nature had beaten me by a few million years, at least.
That’s where the missing energy is! The ants are reflecting it back into space! But… oh, noooooooooo…. the ants are dying. I found one dead one on one day and four dead ones the day after. I fitted an exponential curve to the data and concluded that at this rate the ants will become extinct within a decade. Nature Paper is pending! It has been pre-approved by my mates who do the reviews. No probs!
This will cause a global catastrophe. Only one thing can save us now. I must get more funding for my research which will include 50 trips abroad each year to enjoy dinner and wine.. er, I mean, to present my results .. well look, don’t worry about all of that, just remember that if you don’t give me more money you are a hater.
You wouldn’t want to be called a nasty name, would you? No! I didn’t think so. So there you go. Give me the money!
Let me see if I can’t explain what I mean by example. Imagine a very small star hanging in space. It has a vertical pillar next to it which is three sided. A cross section of the situation looks like the left side of this figure:
Let me compare that to the star whose cross-section is shown in the right side of the picture, which has a vertical pillar next to it with two nearly flat and roughly parallel sides.
Now the question is, will the temperature of the pillars be different in the two cases? Assume that the pillars are the same temperature throughout the cross-section, such as if they are superconducting or very small in dimension.
I say yes, the columns will have different temperatures. Both are absorbing the exact same amount of energy from the star. But they have very different total surface areas. Absorbing the same amount but having different surface areas means that the equilibrium radiation per square metre must be less, and thus the temperature must be less.
However, note that this does NOT mean that if placed in an isothermal container it would force a thermal differential. It does NOT violate any laws of thermodynamics.
Despite that, the two columns end up at different temperatures … which in turn implies a different cooling rate for the two situations, a difference based entirely on the shape of the pillar.
Which is what I’ve been saying all along, but folks said was impossible. The radiation away from the star is different than the radiation back towards the star.
w.
Willis: Your ant hairs are not triangular columns in space. Although they reflect most SWR, the ants are surrounded on all sides by incoming LWR. Absorptivity = emissivity at LWR wavelengths. While they are “cooling” themselves by emitting LWR, they are “warming” themselves by absorbing DLR from the atmosphere and OLR from the ground.
One can maximize the AREA exposed to the weaker DLR by slanting surfaces facing the sky, but the radiative flux is given by Lamberts cosine law (area times cosine of the angle) and is constant no matter how much you slant the surface.
Thanks, Frank, but that’s changing the goalposts. What I was told was that the shape of the hairs didn’t matter at all in a purely radiative situation. Not one bit. It was solely a matter of the cross-sectional area, that was all that counted.
So now, if I understand it, you agree with me that the columns would take up different temperatures specifically because of their different shapes. And while you are right that there are other things happening with the ant, my point remains.
The shape of the columns/hairs affects the rate of radiational heat loss.
The shape affects the rate of heat loss by doing what folks told me upstream was impossible—the triangular shape in my figure just above has a larger radiating area facing away from the heat source than does the flat shape. As a result, it is able to lose heat faster by radiation alone than if it were a flat shape.
w.
Willis,
You can do some arithmetic on this. Suppose the triangle is equilateral. Then yes, it radiates 3/2 times the flat shape at the same temp – 3 sides instead of two.
But suppose there are 3 triangles in a row. Radiation is the same as the convex hull, and the perimeter is 7; 3+2+2. Flat would be 6=3+3. So the radiation is 7/6.
And suppose there were 100. Ratio is (100+2+99=201/200). Getting close to 1. If you are concerned only about upward radiation, the ratio is 101/100. Once you are talking about a surface material, it is virtually 1.
Willis – it’s complete OT here … but … given your recent look at UAH data I cannot help thinking that there’s another satellite dataset that could do with a bit of an exposé given that the normal mission eye candy is extremely sparse (and what has been released is seemingly almost wholly at odds with in particular- NASA models) It honestly looks like an opportunity for WUWT folk to get a jump on the herd….
I’ve looked and there are calibration issues – but – nitpicking absolute values cannot detract from what look like dynamic features and distributions that are new …
Willis: When I wrote at 12:11 am, I had missed the part of your reply near my original comment. Near your original reply, I wrote: “Doubling the surface area doesn’t help at all, since one surface of the the hair points back towards the ant’s body, returning just as much radiation to the ant in that direction as it radiates away from the ant in the other direction.”
Your figure with a star and a flat or triangular column isn’t relevant to this situation.
I also wrote: “Furthermore, unless these ants are – like Willis and Higley7 lost in outer space with radiating fins – any surface from which they emit LWR is a surface that will also absorb LWR (emissivity equals absorptivity). That includes DLR from the atmosphere and OLR from the surface of the desert.”
Your figure with a star and a flat or triangular column isn’t relevant to this situation either. In fact, you have illustrated a situation in outer space – the “unless” that qualified my statement. (Higley7’s comment discussed space.) Your illustration may be relevant to comments others have made, but not mine.
Before we can tell whether any change or modification will warm, cool or leave the temperature of an object unchanged, we need to consider all of the routes by which energy can enter and leave that object. The current discussion seems to be restricted to radiative transfer of energy. Question: If I cut a sphere into two hemispheres, their total surface area will increase by 50%. If I move them far apart compared with their size, will their increased surface area cause them to cool off more quickly? Answer: You don’t know, until you specify the surroundings. If the sphere and hemispheres had been in the freezer and were now in an ordinary room at 20 degC, the two hemispheres will WARM up faster than the whole sphere. In empty space, the two hemispheres will cool off faster than the whole sphere – unless they are already at the same temperature as or colder than the cosmic microwave background (2.7 degK).
The subject to this post – the goal post – was triangular hair on an ant in a desert. The ant radiates infrared proportional to the fourth power of its body temperature. The top half of the ant receives weaker DLR from the cooler sky above. The bottom half of the ant receives stronger OLR from the hotter ground. Whatever emissivity may be, it effects both incoming and outgoing fluxes equally. I don’t believe the orientation of triangular hair or a change to round hair will make any difference in THIS situation.
Consider a figure with two infinite planes at temperatures T1 and T3 with a triangular column in between at an equilibrium temperature T2. Point the vertex towards or away from the warmer plane (T3). Does T2 change? Now make the column circular. Actually, even a simple situation like this one may require a long calculation involving “view factors”.
http://webserver.dmt.upm.es/~isidoro/tc3/Radiation%20View%20factors.pdf
The view factors for “Patch to infinite plate” may make the problem easier.
Nick Stokes June 23, 2015 at 3:16 am
Nick, you are a piece of work. This is why discussing things with you is so unpleasant.
You never, ever admit that you were wrong.
In this case, you claimed over and over that geometry (the shape of the hairs) makes absolutely no difference. None.
Now, having noticed that you were 100% wrong, you’re trying to to get people to not notice your error by coming back to lecture me on the subtle differences based on the number of hairs … nice try.
I think I’ll wait to discuss this with you further until you actually admit that you were totally wrong, that what counts is NOT just the cross-sectional area. I don’t think you are capable of actually admitting you were wrong.
But I could be wrong, and I’d be happy for you to prove me so …
w.
Willis:
And that is absolutely correct when talking about the radiative power as would be observed by a point in space hanging out anywhere around the exterior of the enclosed volume or area. So long as the material is Lambertian, or Lambertian with respect to the wave lengths we’re interested in, this remains true. As you noted, of course, not all materials are Lambertian with respect to all wavelengths. And not noted is that emitters need not be Lambertian either; the sun is not for example. But keeping with simplicity we’ll simply call it Lambertian just for the envelope sketch you’re after.
Yep, obviously. This is a common bit of garble that arises in physics when everything is treated as a dimensionless point, even when it should not be. By sheer obviousness, if a body is radiating x photons per second per meter squared, then doubling the meters squared doubles the total x. That makes absolutely no difference to the observed radiative power of course.
And now that Nick has stepped up to the plate, let me finish some of his notes for you. His golfball example from StackExchange is valid, but not germane. The strict point we are interested in here is how many photons per second go which way with respect to a horizon line. How many go up and how many go down. This is not relevant for any sphere as it is perfectly rotationally symmetric with respect to any plane; and the putative triangle is not.
So assume we posit our nifty isosceles hanging in space above a surface, and let us only look at how many photons go which way with respect to a horizon line parallel to the base, one edge, of the triangle. For convenience we’ll simply state that each point on the circumference radiates 1 photon per second per nominal degree. As all sides are equal length, we’re only concerned about what fraction of any single 180 degree sweep per face cross that horizon line. As the base is parallel, then we just call it 180 photons. The other two sides are equal but opposite with respect to the horizon line. If the faces were perpendicular to the horizon line we’d get 90 up and 90 down. But as they as canted back 30 degrees from perpendicular, each will send 120 up and 60 down. (with respect to the base.) Your sums here are obvious as 300 down and 240 up.
So can a Lambertian emitter with respect to a horizon line show differential in what quantity of radiation goes where with respect to that horizon line. Obviously. Geometry matters when geometry matters. And so long as we’re talking about up and down radiation, geometry matters. You can offset some of the detriment that would occur with the ‘pointy bit up’ if we note that we don’t have a horizon line, but a triangle above a cylinder (cross sectionally) but I highly doubt you’ll find the elevation you need with clouds to make this go away. (The ant analogy being understood here as the pointy bit being the up direction.) But flip it upside down and you’re on track for interesting things.
Happy hunting. And a healthy kudos for Nick and everyone else that stepped up to the plate.
Jquip June 23, 2015 at 10:43 am Edit
Mmm … I pointed out not once but several times that I was NOT “talking about the radiative power as would be observed by a point in space”. I reiterated that instead of radiative power, I was talking about a flow situation involving a solid object interrupting the radiative heat loss from a warmed object.
As a result, I fail to understand what your statement has to do with anything under discussion.
I did much more than note that all materials are not Lambertian. I pointed out that some materials are specularly reflective in the frequencies of interest. This means that all bets are off regarding the uniform radiation that everyone (including you) assumes is happening, and that the idea of “Lambertian” goes out the window entirely. Does the thermal radiation coming off the brass plate in the right half of the picture below look Lambertian to you?
So no, we can’t just assume for simplicity that the surfaces are Lambertian, and I’ve said that several times as well. As long as the reflectivity is non-zero we can have unevenly distributed radiation coming off of a solid object, something that y’all keep saying doesn’t happen. You’re 100% right … but only in Lambertia, which near as I can tell is a country in BlackBodyLand.
Here on this planet nothing is truly Lambertian, everything is at least somewhat reflective even in thermal radiation, and from the looks of the photomicrographs, the ant hairs are likely to be reflective as well.
The difference between an imaginary horizon and the horizon of the actual earth when looking from 10 km up is a couple of degrees, from memory. Small enough to ignore in first cut analyses at any rate.
Thanks, jquip, for your clear post. I’d have more kudos for Nick if anyone at any time had ever heard him admit he was wrong. But I thanked him for raising the issue when he first raised it.
w.
Willis,
“In this case, you claimed over and over that geometry (the shape of the hairs) makes absolutely no difference. None.”
I think you should follow “My usual request—if you disagree with someone, please quote their exact words that you disagree with.”. I said, rather carefully:
” Corrugations don’t change that, unless they increase the area subtended by the object. “
You are increasing the area subtended by an object, from line segment to triangle. I am calculating the effect of that.
You said
“So overall those lesser effects might cancel out in whole or in part, and thus it seems like the layer of ant hairs will emit something like up to twice as much radiation out towards the sky as it does towards the ant’s skin. “
I am pointing out that the view factor issue is dominant, and the factor is nothing like twice. With n parallel hairs, it’s 1+1/n. The ants have a lot of hairs.
Nick Stokes June 23, 2015 at 12:24 pm
Glad to, Nick. Here was your first reply to the issue.
Nick Stokes June 22, 2015 at 1:15 am
Regards,
w.
Willis,
You wrote: “Despite that, the two columns end up at different temperatures … which in turn implies a different cooling rate for the two situations, a difference based entirely on the shape of the pillar.”
That is true for this diagram.
“Which is what I’ve been saying all along”
No, it isn’t. An ant does not have just one hair, so you also have to consider the interaction between the hairs. So change your diagram into two walls extending to infinity horizontally for the diagram oriented as shown. Both walls present a flat surface toward the star, but one presents a corrugated surface “upward” (away from the star). The two walls will be at the same temperature. Half the radiation emitted from the upper surface will hit another part of the upper surface and be re-adsorbed, so the net emission will be the same.
The issue is not the number of hairs an ant has. It is that people have been saying over and over that the shape of the hair didn’t matter for the radiation.
Now that I have shown that the shape DOES matter for the radiation, now you and others want to claim that it’s not the shape, it’s the number of hairs, or it’s the arrangement of the hairs, or something else.
Look, Mike, you and Mosh and Nick were wrong about whether the shape affects the radiation. It is NOT, as you and others claimed, merely a matter of the cross-sectional area perpendicular to the field of view.
Now, I’m willing to discuss this further. But not with folks who won’t admit that they were wrong. Here’s you, Jeff Id, and Mosh:
Mike M. June 22, 2015 at 8:00 am Edit
So you were 100% wrong, the shape is involved in radiative as well as convective heat transfer, and it would NOT violate the Second Law.
Here’s Jeff Id, with more of the same nonsense about how the shape makes absolutely no difference, just the projected surface area. And he was 100% wrong:
Jeff Id June 22, 2015 at 11:43 am
And here is the “me too” from Mosh, who also was 100% wrong ..
Steven Mosher June 22, 2015 at 12:52 pm
So I’m waiting for you guys to man up and admit you were wrong. Nick Stokes won’t do it, but I had hoped for better from you. You accused my claims of violating the Second Law … you gonna man up, or hide with Nick?
w.
Willis,
I will not admit to being wrong for the most fundamental of reasons: I AM RIGHT. And so is Nick, and Mosher, and Jeff. I wrote “If Willis is right, the outer surface cross section looks like a triangle wave. Now draw an imaginary surface that just touches all the peaks of the triangles.” Obviously talking about a collection of closely spaced objects, not a single hair. And when you wrote “The silver ants have a layer of hairs above their skin which selectively radiate more thermal energy away from the skin than towards the skin” you were pretty obviously not talking about a single hair.
It is one thing for us to be unable to convince you or for you to be unable to convince us. But for you to insult us because we won’t bow down before the Great and Mighty Willis is beneath you. Or should be.
Willis,
Yes, the triangle will radiate more effectively and stay cooler in the configuration you show. You have expanded the outline. The body is convex, and there is no view obstruction. But in the triangle case, some of the radiation goes back below the base line.
There is a discussion here that is on point.
The more precise version of my claim that corrugation doesn’t help is that a body of uniform temperature absorbs and emits in just the same way as its radiative profile. That is, the envelope of all straight lines in space that touch the surface. In 2D that is the convex hull; in 3D it is a bit more complicated. It’s what a CAT scan would make of a totally absorbing body.
The thing about 2LoT, which Jan also referred to, is that a complex surface is subject to the same sort of 2LoT restriction as Kirchhoff’s Law. If something improves its emissivity, then the absorptivity has to follow. But a black body already absorbs every ray that encounters its radiative profile, so the emissivity can’t improve.
Of course, if you do expand the profile, then you are likely to absorb more as well as emit. In your case, you have made it one way, and that is probably more applicable to clouds. A big isolated cloud will radiate more than a small one. But if you are looking at a whole bank of clouds, a bumpy surface doesn’t make a difference.
Here’s a bit of reasoning on the triangle. The total radiation is what observers can pick up. Say the triangle is equilateral. An observer vertically above, or up to 30° each side, sees an outline equal to the base, and could not tell the difference. But from 30 to 90°, he sees a larger profile – ie receives more radiation. Total radiation above the plane is greater.
But suppose there were three adjacent triangles. It’s only when the observer is so low in the sky that he sees the closest peak in line above the farthest base point that he can distinguish the triangles from the flattened version. So the radiation discrepancy is much less. And when it starts to look like a ripply surface, virtually none.
Like I said, Nick, I doubted greatly that you had the blanquillos to admit you were wrong. So far you’re proving me right.
Before, you were claiming that the geometric shape of the hairs made no difference at all. None. It was a matter of basic physics.
Now, you say it makes a difference, but that the difference depends on the surroundings … well, duh. Thanks for telling me what I already know.
I’m still waiting, however, for you to admit that you were 100% wrong about how the geometric shape was immaterial. All I’ve gotten so far from you is tap dancing. Impressive tap dancing to be sure … but no admission of error.
w.
Willis,
“Before, you were claiming that the geometric shape of the hairs made no difference at all. None.”
Again, please follow your request and quote my exact words.
Duh – OCO-2 data being sat on until Paris is done and dusted ?
Willis, if you have vertical angle of incidence of the impinging suns light (almost in the Sahara), from an equilateral triangular surface, reflection is very strong by bouncing horizontally from one hair surface to the adjacent hair surface and straight back up into a clear sky. That they are silver is a measure of the efficiency of this effect. I would say that this surely is by far the major (90%[?]) effect. It is the icing on the cake that the hairs also serve to reduce heat further and the source of nature’s detailed wonder that she experimented on improvements possibly over millions of years to get this model.
It makes me think that not only do we wonder about phenomena and incessantly inquire by experimentation to find out what makes things tick, but even nature doesn’t know what works without constant experimental adjustment until they get the model (almost) ‘right’. Humbling to think that’s how we ourselves got to the here and now. Moreover, nature does it with millions of different species and she’s still rejecting her work for better – will we ever reach a perfect ecology?
Willis:
You stated “As a result, it is able to lose heat faster by radiation alone than if it were a flat shape.”
Isn’t it more correct to say that the rate of energy lost is independent of shape (LW out will always equal radiation adsorbed)? What IS dependent is the temperature of the emitter. More radiating area for LW reduces T required to drive the flux
Paul, it seems like you’re talking about the rate of energy loss per square meter, and I’m talking about total energy loss … but it’s not clear.
w.
I am talking about total energy loss. In your example of equilateral triangles imagine 900 watts per square meter in from SW, then each surface radiates 300 watts per square meter of LW. If it was a flat profile it would be 450 watts per square meter of LW per surface. If it was a square it would be 225 of LW per surface. Total energy rate out isn’t any more or less regardless of surface configuration. Sum up all the surfaces and they have to total to 900. Surface rate out changes
Temperature of the hair is what changes dramatically. It goes down in proportion to number of surfaces doesn’t it? Temperature at any arbitrary area of surface will be only high enough to drive the flux out of that arbitrary area.
From the ant’s body perspective, a triangle generates the least ‘down welling LW’ flux to its exoskeleton. That’s the ant’s goal, right?
[assuming anything greater than triangle create new issues]
Frank: you said…
“The ant radiates infrared proportional to the fourth power of its body temperature.”
Body temperature is most likely not the ‘hair’ temperature. The body is only connected to each hair by its attachment point and it is probably not a great conductor. The ‘hair’ is effectively a surface that is mostly isolated from the body. The ant is radiating LW from its body of course but I’d wager that this is a very small proportion of what is coming from its radiating surface.
Ever pet a cat that’s been laying in the sun? Fur gets real hot. Kitty is just toasty warm. Same principle.
paulatmisterbees commented: “Body temperature is most likely not the ‘hair’ temperature. The body is only connected to each hair by its attachment point and it is probably not a great conductor. The ‘hair’ is effectively a surface that is mostly isolated from the body. The ant is radiating LW from its body of course but I’d wager that this is a very small proportion of what is coming from its radiating surface.”
I agree with you that I over-simplified this part of the problem to focus on Lambert’s cosine law and other factors that control radiative heat transfer under these circumstances: reflection of SWR, OLR from below, DLR from above, emission from ant itself. Distinguishing between the ant’s triangular hair and the ant itself – which is triangular in Willis’s latest scheme – doesn’t change Willis’s incorrect reasoning.
Hi Frank:
If you think about the totality of the little guys life, he actually spends most of his time in the sand, not on the sand. So it might well be that most of his adaptations have to do with shedding heat while underground. He seems to manage life above ground, in part, by screaming around to get his/her work done before his radiation budget blows up.
I think his reasoning is fine but perhaps semantics have tripped us up. His triangle example contains this…
“Despite that, the two columns end up at different temperatures … which in turn implies a different cooling rate for the two situations, a difference based entirely on the shape of the pillar.”
It seems like a conflation of coolness (meaning reduction in temperature) with cooling rate. I take ‘cooling rate’ meaning as identical to loss of energy. He explicitly says in the example the correct implications of differing surfaces will effect surface loss rates resulting in reduction in temperature.
I agree completely with this but suggest that ‘cooling rate’, at least as I take it to mean energy rate, is not a function of surfaces. In fact total energy loss rate can’t have anything to do with surface configuration. It has to balance the incoming.
What is the energy loss rate of an infinite plate of superconductor? It’s the same as the energy rate being fed to it. What is its temperature rise? Nada. What is its cooling rate? Same as its heating rate. But is it cool? Yes, cooler than it would be if it was as big as the ant.Is it cooling? No. It never heats up.
Damn English anyway. That’s why these things are better communicated with equations.
Interesting side note:
I did a project once with a brilliant officer from the South Korean Navy. He couldn’t speak a lick of English and my Korean was limited to kimchee. We were modeling dredge spoil flows for the Army Corps of Engineers; heavy duty math and programming was involved. You don’t want the flow to be back to the channel you just dug out, right?
We did the whole project by ‘talking’ in FORTRAN on a blackboard. Fun times and no mistakes (fingers crossed here).
“Saharan silver ants (Cataglyphis bombycina) forage in the Saharan Desert in the full midday sun when surface temperatures reach up to 70°C (158°F), and they must keep their body temperature below their critical thermal maximum of 53.6°C (128.48°F) most of the time.”
If the air temperature of the surroundings is 70 °C the ant will also have this temperature after some time by thermal convection. The hairs are only delaying this process of establishing thermal equilibrium. As the emissivity in the IR of the surroundings is near one radiative cooling of the ant cannot be better than the surrounding desert.
I am surprised no one has brought up the aspect of this being a bit like Willis’s Steel Shelled Planet example, besides the reflectivity issue… only in reverse. That is, not keeping heat in by multiple layers between the ants body surface and the outside but this time the constant energy source being from the outside inward.
Willis, do you see some parallel there?
Sorry to come to this thread so late.
Interesting, but the first thing that occurs to me is- what clues do we get from the described lifestyle of these ants? Seems likely that the ants are designed to survive relatively short forays in the most extreme heat. Therefore likely that whatever physical adaptations we are looking at, are designed to slow up the acquisition of an untimately unsurviveable air temperature. So the physical properties we are examining will be to do with reflectivity/insulation rather than any equilibrium radiative properties.
Not sure Willis’s links to cloud shapes stand up, but intriguing nonetheless
Fascinating subjects and I have not read all the comments but does anyone know what the hairs on the bottom of the ant look like along with the feet “pads”? It would seem like that if the mechanism is correct then the hairs on the bottom would different in configuration that what is on the top.
Seems likely the triangular hairs evolved for a reason and quite likely Willis has arrived at a correct explanation for an unusual situation. Frank and Nick just want to argue for the sake of doing so.
Larry: Since Willis writes so compellingly and occasionally brilliantly, I’d prefer to believe that everything Willis writes is right (probably unlike Nick). Unfortunately, none of us is always right and spreading incorrect information is not good for the skeptical cause.
https://en.wikipedia.org/wiki/Lambert%27s_cosine_law
https://en.wikipedia.org/wiki/View_factor
OK, here is an experiment that doesn’t involve outer space. Two identical rooms separated by a wall with a radiator built into it such that one side radiates into room A, the other into room B. The room A side of the radiator is ‘corrugated’ and the room B side is flat – to simulate the upper and lower sides of the silver ant-hair. If the radiator is left to run for a couple of hours, will room A be warmer than room B? If so, doesn’t Willis have a point?
mcdodwell,
Nice thought experiment.
“If the radiator is left to run for a couple of hours, will room A be warmer than room B? If so, doesn’t Willis have a point?”
To answer your second question: Absolutely. That is how I understood Willis’s original claim.
To answer your first question: If heat transfer from the radiator is by radiation only, then the two rooms will end up at the same temperature.
He didn’t specify reaching equilibrium. If Room A reaches that point faster, and the time required for Room B to match is greater than a couple of hours ….
mcdodwell,
Your nice, clear thought experiment deserves a more careful answer than my previous post.
To understand the issue, we need the concept of convexity. An object is convex if a straight line between any two points on its surface lies entirely within the object. The extension of such a line outside the object will not intersect the object.
If we have a convex object, a photon emitted from the surface will travel in a straight line and will not strike the surface of the object. In that case, more surface area means more emission, assuming that other factors, such as temperature and emissivity, are the same.
If an object is non-convex, then there will be some pairs of points on the surface such that a line between those points lies outside the object. Some photons emitted from the surface will travel along such lines and will be re-adsorbed by the object. Thus, the net emission from the object will be less than would be calculated from its surface area.
How much less? I am not absolutely certain of this, but I think the answer is that you draw the convex object of minimum surface area that just encloses the non-convex object.
The wall in your thought experiment is non-convex. The convex object that just contains it has flat surfaces on both sides: on side B, matching the flat surface that is already there; on side A, just touching the peaks of the corrugation. Both flat surfaces have the same area, so the net emission is the same on both sides.
The ant hairs are individually convex, so in isolation they emit more than, say, a circular hair of the same cross section. But Willis postulated that the shape assists the radiative cooling of the ant as a whole and the ant is most certainly not convex. So what matters is the surface that encloses the ant as a whole. That is independent of the shape of the hairs.
“If the radiator is left to run for a couple of hours, will room A be warmer than room B?”
The thought experiment can be used to show the thermodynamic issue. Suppose you didn’t apply power to the radiator, but it conducts internally. That is actually what we have here; the hairs don’t have their own power source. It still radiates; just less because it is cooler. Would room A be warmer than room B? If so, you could run a heat engine using the difference.
You might say, well, you could easily silver one side so it radiates less. But that is where Kirchhoff comes in; absorptivity also has to drop, so there is no difference in net flow. So if it was a black surface, and you corrugate one side, if that increases the emissivity the absorptivity has to rise. But it can’t. It was already totally absorbing all incident radiation.
Interesting adaptation.
Reminds me of Caribou/Reindeer living on the tundra and boreal forests (summer>winter).
Their hair is hollow which provides some insulation.
I will jump in with another possible use for corrugated hollow “hairs” which are highly reflective and triangular in cross section.
Suppose that a live ant could nest two layers of the hair before going out in the sun, bottom layer with apexes pointed “up” and top layer with apexes pointed “down”. They would form a largely hollow sheet with diagonal interior walls. This should be highly resistant to heat flow, almost like a thermal bottle, yet somewhat flexible as each triangular element could slide past is neighbors in two directions, and the corrugations would allow each hair side to bulge to allow movement in a third direction.
Eventually, however the ant would still become hot and race back to the cool inside the nest. Once inside, if the ant could slightly lift one layer of hairs, or cross one layer in relation to the other, the diagonals would open up and allow for the circulation of air from the hot body of the ant to the cooler surroundings.
As soon as the ant had cooled it could again seal its thermal insulation and return outside.
Of course this is simply the wildest speculation…. like climate science in miniature.
I’m not sure why the hairs’ turning or adjusting to face the sun requires a power source. Does heliotropism require it? The Aristotelean theory was that the sunflower’s head is making passive adjustments… maybe this has been disproven.
Willis, you say: “Curiously, however, nowhere do they mention the importance of a third cooling method that I noticed as soon as I looked at their photograph—the shape of the hairs ensures that more energy is radiated upwards than is radiated downwards.”
Gee, you don’t think the reason why these scientists didn’t mention the importance of your third cooling method is simply because … it’s not an issue.
You even quoted the correct point from the article: “c) the two upper sides of the hair are “corrugated”, increasing the surface area facing skywards.”
Indeed, what’s important from an evolusionary perspective is to increase the surface area “facing skywards”. Because that’s the way the radiation cooling the ant is moving. It’s about maximising its radiant heat loss. Conversely, the undersides of the hairs are flat so that they lie parallel to the ant’s body, making the transfer of energy by radiation from the body to the hairs as effective as possible.
The hair layer (and the air gap between it and the ant’s body) would also insulate against the searing heat being radiated and conducted>convected from the ground and up towards the ant. Working much like the loose garments worn by desert people during the day.
“Yu’s group discovered that the ants are covered on the top and sides of their bodies with a coating of uniquely shaped hairs with triangular cross-sections…”
Presumably, there are no hairs on the ant’s underside, which is exposed to the searing heat upwelling from the burning sand, but which is also in shadow. Whatever is going on with the shiny hairs on the ant’s back, something else is happening on its underside, where conditions are different.
But it would be nice to have a good image of the critter’s ventral surface, and a peek at the various structures of the exoskeleton there, before saying much more.
Yeah, that’s actually true. So no hairy insulation against searing surface heat going on after all. Interesting.
Air is not a good thermal conductor, but there are other parts to the puzzle. Note my bold below in this short excerpt from a NY Times article about the Sahara silver ants, from 1992. Dr. Wehner’s work includes peeling the eyeballs of these ants, but my question is: are the ants really climbing the vegetation to cool off? Or are they just getting their bearings?
Undaunted by their task, these desert ants literally rise to the occasion, hauling themselves up out of their burrows on limbs nearly a quarter of inch long, a great length for an ant. Just by raising themselves a quarter of an inch above the ground, the ants can cool their bodies by nearly 30 degrees Fahrenheit, since even this small distance affords a measure of protection from the surface’s intense heat.
The silver ant, which of all the desert ant species endures the highest temperatures, must periodically find and climb small stalks on which to cool off before continuing its hunt. On the top of a flower stalk, the ants can often be seen stretching their front legs skyward to reach the cooler air. The Swiss biologists have found that the cooling-off spells on these refuges are vital if the ant is survive the heat on its long hunting expeditions.
The silver ant’s search for cooler vantage points can complicate the biologist’s task, since the ants rush to climb anyone who comes close to them. “We have to be quite careful of the ants when we do our measurements,” Dr. Wehner said. “They will run towards you and climb up onto you as the tallesest thing around.”
NY Times
Science
Life at the Extremes: Ants Defy Desert Heat
By CAROL KAESUK YOON
Published: June 30, 1992
http://www.nytimes.com/1992/06/30/science/life-at-the-extremes-ants-defy-desert-heat.html?pagewanted=1
Well, I dunno. I’m not an ant, but I do live in a desert. This is the first I’ve heard that reaching for the sky aids in cooling off, but I’ll give it a try next time I start to overheat. Then I’ll prolly make an antline for the nearest shade, let the hot air out of my ballcap, and have a big glug of water.
It is interesting to note that the photograph reveals (with a little imaging) what appears to be protein striations that wrap around the folicle in a spiral. Their width appears to be around 318 nm and are embedded in a semi-clear sheath. Submicron studies on a single follicle would seem to be something that might reveal some interesting results.
On reflection from clouds. Light reflection from clouds is still not well understood. Even knowledge about water molecule size, mix, altitude, evaporation, temperature, sunlight distribution, bandwidth absorption/reflection, atmospherics etc. when mixed with system dynamics yields a fairly empty set between the braces. So little time so much to know…,
Willis, here is another incredible evolutionary story. The corals in the Red Sea fluoresce at night.
Quite magical
http://www.washingtonpost.com/news/speaking-of-science/wp/2015/06/24/scientists-discover-an-unexpectedly-beautiful-rainbow-of-fluorescent-corals-in-the-red-sea/
One hypothesis was that they might create these pigments for sunscreen, but very little light reaches these depths in the Red Sea.
http://www.nature.com/news/radiant-reefs-found-deep-in-the-red-sea-1.17840
Joanne Ballard
Willis: I’ll make one more try explaining why various commenters don’t believe the shape of the hair on the ants or the shape of any other part of the ant makes any difference for radiative cooling.
Your ants do not live in space. In your illustration, the triangle receives radiation from a POINT-SOURCE and increasing the surface area pointing away from that source increases radiative cooling. This doesn’t happen on the surface of the earth. The ants receive thermal IR from all directions in the environment and emit in all directions. The ants can reflect SWR; but they can’t emit LWR without absorbing it, because emissivity = absorptivity at all wavelengths.
The ant emits eoTb^4 in all directions, where Ta is the surface temperature of the bug and e is the emissivity of the ant’s surface. Let’s first simplify the environment that is radiating towards the ant. From the ant’s perspective, 50% of the environment consists of hot desert sand (blackbody equivalent temperature of Ts) emitting OLR and the other 50% is from the cooler atmosphere emitting DLR (with a blackbody equivalent temperature of Ta). From a mathematical perspective, we can say that the ants live between two infinite planes: one at Ts and the other at Ta. Since these planes are infinite, the distance from the ant to the plane turns out to be irrelevant.
“Flat ants”: Let’s first imagine that our ant is effectively flat and horizontal. In the absence of other mechanism of heat transfer (no conduction or convection, 100% reflection of SWR), conservation of energy demands that the temperature (Tb) of the ant in radiative equilibrium with its environment satisfy the following equation:
eTb^4 = 0.5*Ta^4 + 0.5*Ts^4
“Triangular Ants”: Now let’s imagine that our ant is an equilateral triangular or covered with equilateral triangular hairs. Will the ant receive less flux from the hot surface and more flux from the cool atmosphere if we point the vertex of the triangles at the cooler sky. The view factors for a small patch of plane surface in the vicinity of an infinite plan can be found at the link below and it helps to look at the diagram there. When the angle between the two planes is B, the front side (Ff) and backside (Fb) view factors are
Ff = 0.5*(1+cos(B))
Fb = 0.5*(1-cos(B))
http://webserver.dmt.upm.es/~isidoro/tc3/Radiation%20View%20factors.pdf
For radiation from the ground, the face of the triangle parallel to the ground has B = 0 and receives all radiation on the “front side” and none on the “back side”. The other two faces have B = 60 deg and receive radiation on the “back side”. Remember: The ground is an infinite plane, not a point source, and the “upward facing” sides of the triangle receive some radiation from the ground on their “back side”! The bottom side of the triangle has a view factor from the ground (infinite plane) of 1 and the two top sides of the triangle have view factor of 1/4 each. By expanding the above flat ant into a triangle, it receives 50% more radiation from below when the radiation source is an infinite plane (but no more radiation when the source is one point)!
If the triangle is rotated so that the vertex faces the ground, there will be two faces with view factors of 3/4 and one face with a view factor of 0. Rotating the triangle doesn’t change the total view factor from the ground (or the sky) when the sources are infinite planes (not single points).
Rotating “Flat Ants”: If we go back to the above “flat ant” model and rotate the ant 90 degrees so it is perpendicular to the ground, it will receive half as much radiation from the ground on each of two faces compared with how much it received on one face when it was horizontal. (IF the ground were a point source, a “flat ant” would receive zero on both faces when vertical.) No matter what angle you rotate the “flat ant”, it receives the same amount of radiation from a source that is an infinite plane. This example most clearly illustrates the point Nick and others have been trying to make. You can’t escape expose to radiation by changing the angle of a face when the radiation is coming from all directions or from an infinite plane.
IF the face or faces of the ant that are facing the hot ground have low emissivity/absorptivity and the faces or faces of the ant facing the cool sky have high emissivity/absorptivity, THEN the ant can gain an advantage. However, this advantage can be gained by both flat and triangular ants.
Any other examples of triangular hairs anywhere? Only on these extremophile ants? That is a very expensive genetic trick which must have an adaptive thermodynamic purpose. Likewise the corrugation. However it works–it obviously works. –AGF