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If the basic requirement for the function of a Stirling engine is a heat source and a heat sink, other than the occasional rain, bat droppings and roof rats, why couldn't one use ambient temperature as the heat source and the much colder sky, via radiative cooling, as the heat sink, to move a Stirling engine to almost perpetually produce power?

Current local weather, in Taylor, Arizona: 23:30 MST, 7°C, 62% humidity, 1°C dew point, clear skies
Effective sky temperature, with a 25° compound parabolic aperture, -106.18°C
Stagnation temperature of radiator (after losses): -64°C
Carnot efficiency, with a radiator at -26°C: 11.8%
Engine efficiency, as a percentage of Carnot: 45%
Total efficiency: 5.3%
Heat radiated, net after losses, with the radiator at -26°C: ~100W m^-2
Heat radiated, net after losses, with the radiator at 7°C: ~225W m^-2
Engine output: 5.6W m^2

For background, see U.S. Patent 4624113, University of Chicago representing Argonne National Laboratory, on behalf of USDOE (assignee), 1986.
For the math, see Smith-2009
For adjustments for humidity and cloudiness see Berdahl-Martin.

The net radiated output is dependent on the radiator temperature. At the stagnation temperature the net output is zero. Surely, a Stirling engine can be tuned for a specific ΔT. Will the radiator equalize at the optimum output temperature?

Are there any other issues?

Edit: Added the radiated power for a radiator at ambient, for comparison.

Edit: The calculated losses are conservative, per Smith, using air between the radiator and the cover. I haven't done the math for a partial vacuum between the radiator and cover, per Argonne patent, but the losses should be less. I haven't found a mathematical model for that calculation yet.

Of course, there will always be a crossover point for maximum power output vs. ΔT vs. Stirling engine Carnot efficiency vs. radiator temperature vs. weather conditions vs. radiator surface area. Raise the Carnot efficiency to a more optimistic 58% of Carnot and tune it for a larger ΔT for a greater Carnot efficiency, because more power.

We currently have a 200W solar array with average daily solar insolation of 5.5 hours for an average (rated) output of 1.1kWh. Of course, rated output is not true output. To compete with solar (based on rated output), working 24 hours daily (most of the time) the Stirling sky engine only needs to produce 45W continuously, so if it can net 10W average output per square meter of radiator it would require less than 5m^2 of radiator.

Also, there is wiggle room with the viewing angle of the compound parabolic emitter array, but a smaller viewing angle will increase the height of the compound parabolic shape, which presents other challenges.

Also, coupling the sky emitter on the cold side with a solar collector on the hot side could be a lot of fun, but that would require a larger battery bank to store the energy when the sun is shining.

Houston, we have a...

The losses in the compound parabolic emitter must be reduced for this idea to be practical for producing power from ambient heat. With current local temperature at 6°C and a dew point at 2°C and with the radiator at -26°C, before losses the net radiated output is 149.3W m^-2. That's awesome. However, estimated losses include 7.8W mirror losses, 29.9W cover losses, 1.36W spectral losses and 16.1W non-radiative losses, reducing net output to 94W m^-2. That sounds super, too, but Carnot efficiency is at 11.5%, and losses in the SE and generator knock that down to 6.7W m^-2 (at a very optimistic 58% of Carnot). This is at the crossover differential for the ambient temperature, the point at which net radiated heat and Carnot efficiency balance to give the highest output for the SE.

To top that off, the compound parabolic reflector with a 30° viewing angle will have a diameter at the top that is twice that of the radiator, and the ratio of the area of a circle to the area of the square in which it fits brings the total space occupied by the one square meter radiator up to 2.56m^-2. I'd need to cover the entire 47.57 m^-2 roof of the cabin with compound parabolic dishes to get 100W out of the SE.

Optics for Passive Radiative Cooling has a suggestion for altering the compound parabolic shape to fit a square for better space utilization. I haven't done the math, but I don't like how it would affect output, when we're pinching Watts.

If the SE was good enough to give me 75% of Carnot at the generator--dream on--that only adds another 2W m^-2. Not much can be done about the cover losses without using Saran Wrap, which is impractical. Not much can be done about the mirror either.

That leaves the non-radiative losses, which I've already lowballed at .5W m^-2 °C, because I thought Smith's guarded suggestion of 1.5W m^2 °C was too high. The vacuum per Argonne will undoubtedly reduce it further, but I still need a model to say how much. The thermal conductivity of the cavity wouldn't change much without high vacuum, which is impractical due to practical construction materials, so it will come down to the convective coefficient. Argonne didn't quantify the vacuum in its model or provide any mathematical model for the determination that the invention could achieve 40 to 80°C below ambient without producing condensation on the cover. Again, high vacuum would be impractical for the materials that are described for the invention, so convective coefficient must be key. Reducing the non-radiative losses by 50% only gives us another Watt for a very efficient SE.

Though it is possible to produce energy from ambient heat with this method, it might only be practical for a trickle charger. For 45W output with a very efficient SE it would require an array of CPEs covering an area of 17m^-2. I'd better look at the math in combining a solar collector and CPE.

Does anyone have any suggestions for squeezing more power out of thin (ambient) air with this thing?

I apologize for the book. I thought it might help someone.

I had another thought. Allow me to think aloud.

Reducing the non-radiative losses makes the CPE more efficient, which changes the balance, which changes the crossover differential. Cutting the non-radiative losses to .25W m^2 moves the optimum radiator temperature to -29°C, which gives an output of 7.32W m^-2, giving only a .8W gain.

If you had a cold store with a sufficient heat capacity and thermal mass, you could take it down to the stagnation temperature for greater Carnot efficiency. Of course, it would be cyclical, and it would need to be insulated very well.

Water might work, if you can contain it without breakage as the ice expands the volume.The Four Mile Island Icebox

Of course, the specific heat of water is so high that it might take too long to take it down to temperature. Maybe a junkyard engine block would work, but heat exchange would be easier with a block of ice.

Edit: I'll have to do the math.

Edit: It would also require starting and stopping the SE cyclically without losing too much heat between the warm and cold side, to allow the efficient cyclical cooling of the cold store.

While spending time around the refrigerator doing helium balloon experiments I noticed that another experiment I had totally given up on has come back to life.


I had tried growing calcium crystals by mixing lime and vinegar and letting it sit in a bowl until crystals form. It is supposed to only take a few days. After over a week nothing happened even though almost all the vinegar had evaporated. I just left it on top of the fridge and forgot about it.

I was searching for previous posts about sky cooling or passive radiant cooling and found this old thread.

Anyway, I embarked on this calcium crystal growing project because I was reading a paper somewhere, a long time ago now, (or maybe it was a video?) that these type of crystals make a good pigment for a sky cooling paint because of how super white, like snow crystals they are.

Then looking up about the crystals I found information on how to grow them.

I have a bunch of bags of agricultural dolomitic crushed lime left over from another project so thought I'd give it a try.

Not a single bit of crystal had formed when I finally gave up.

But wow, this stuff is really bright white!

https://crystalverse.com/limestone-and- ... -crystals/

Interesting video:

https://youtu.be/2iwXdGxyzYw

I like the water wave in a bottle bit at about 4:00

Kind of how I picture the energy flow in a Stirling engine.

If you want to skip to the water wave part:

https://youtu.be/2iwXdGxyzYw?t=237