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So let's say I have a super cooling "battery" basically a brick that cools anything that touches one end of it to ~0k. Now, using handwavium I can thermally isolate it so that it doesn't just cool everything infinitely. What I want to know is:

given this "cooling battery" what is the best way to create lift using WW2 era technology?

There can be some flex there, since my civilization is supposed to be slightly more advanced than others of the time, but nuclear solutions are a no go, since that would have too much impact on the outcome of the war. Some ideas I've had are

Temperature Gradient Turbine

Put our super cooling battery on one side of a tube, and a heat source on the other, the difference in temperature will cause the air to move around the tube. Place a turbine inside the tube, and you have thrust.

Explosive Sublimation

Use our super cooling batter to produce a brick of frozen Hydrogen, put this in a tube and take away the battery, the Hydrogen will begin to rapidly expand, if a hole is left in the bottom of this tube, we have thrust.

Super Cooled Environment

If we cool the air around our pilot, or only on the top of a pair of wings, will that have a noticeable effect on flight? Note: This idea is a long shot, I'm just trying to think outside the box, or tube as the case may be

Ideally I'd like something as rooted in hard science as possible, with certain amounts of handwavium applied where necessary (eg. creating containment fields for our super cooled air, preventing humidity from forming huge blocks of ice)

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  • $\begingroup$ Aren't you afraid that this super cooling battery could change the outcome of war ? With a simple fan you've got yourself some kind of an ice gun, you can make ice walls in minutes, freeze enemies in seconds... $\endgroup$ – everyone Aug 8 '17 at 8:40
  • $\begingroup$ Theoretically, yes, but, for the purposes of the story, I want to use it to make a jetpack. It actually isn't a huge plot point, I just wanted to know if flight is one of the many wacky things that super cooling can accomplish. The only reason I care about nuclear is because of its historical significance $\endgroup$ – Devon Muraoka Aug 8 '17 at 8:52
  • $\begingroup$ It is thermodynamically very difficult to have such an heat sink. Given enough energy you could have a rod with one cold and one hot extremities. Resulting usage would be very different, but the thing would be more plausible. $\endgroup$ – ZioByte Aug 8 '17 at 13:00
  • $\begingroup$ What you are calling a super cooling "battery" is a heat sink that transfers any heat it gains instantaneously to somewhere else, preferably an infinite distance away. Essentially it's a thermal teleportation device. $\endgroup$ – a4android Aug 8 '17 at 13:52
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For your last idea I don't see how it can work at all. But I also see a major problem with the first two ideas: environmental air is never fully dry air, but alway bear some water in it.

This means that as soon as you cool it down (and you state you are cooling it around 0 K) that humidity will produce ice which will end up clogging any piping you have.

This will happen also with the heating of frozen hydrogen (by the way, considering hydrogen is pretty scarce in our atmosphere, can't you use another gas?), which will enclose in pretty thick layer of ice (see example of a nitrogen vaporizer in the picture below)

enter image description here

What you can try is to have a battery expecially meant for humidity removal before the inlet of your circuit, and a good set of heaters to remove the ice layer from the outside.

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You could look into the effects of Quantum Levitation, also known as the "Meissner Effect". Basically, if a superconductor is sufficiently cooled and can be kept cool, which because of your "cold battery", it can, it can cause this levitation effect.

What this can allow is a form of travel across a rail at ridiculously high speeds, completely free of all friction. Like a hovertrain, but way better.

For actual flight, "Pre-Cooled Jets" work by cooling the air intake, so that relatively little fuel is required to generate the same amount of thrust as a normal jet while using less fuel. One of the issues with normal jet packs is that they are incredibly fuel inefficient, so if you were to supercool the air going in, you could actually solve that efficiency problem. The other issue is that they're incredibly loud, but that doesn't stop them from flying.

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  • $\begingroup$ Pre-cooled jet engines are, dare I say it, cool. Plus one because it warmed the cockles of my heart. $\endgroup$ – a4android Aug 8 '17 at 13:47
  • $\begingroup$ Pre-cooled jet engines were cool before it was cool ;) $\endgroup$ – DisturbedNeo Aug 8 '17 at 13:50
  • $\begingroup$ When you say loud, are we talking louder than a normal jet engine? If so, why? $\endgroup$ – Devon Muraoka Aug 8 '17 at 17:37
  • $\begingroup$ "They are loud (about 160 decibels—enough to rupture an eardrum)" $\endgroup$ – DisturbedNeo Aug 9 '17 at 8:32
  • $\begingroup$ It's just over half as loud as a passenger jet taking off, I believe (which is somewhere around 300 decibels next to the source), but of course a Jet Pack is supposed to be a personal device and is a fraction of the size of a passenger jet. The pilot would need ear protection, and you're not gonna be able to sneak up on anybody. $\endgroup$ – DisturbedNeo Aug 9 '17 at 8:34
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Starting with the ideal gas equation.

The four gas variables are: pressure (P), volume (V), number of mole of gas (n), and temperature (T). Lastly, the constant in the equation shown below is R, known as the the gas constant, which will be discussed in depth further later:

PV=nRT

So as you decrease temperature you decrease pressure. If you decrease temperature all the way to the condensation point that decreases pressure a lot.

Next: airplane wings. Airplane wings work by producing decreased pressure over the wing as compared to under the wing. The pressure under the wing lifts the wing and thus the plane.
from http://www.explainthatstuff.com/howplaneswork.html enter image description here

A plane wing generates decreased pressure via differential airflow speeds. But you could generate differential pressure by cooling the air on top of the wing. Instead of rapid airflow decreasing pressure atop the wing, you would cool the air to decrease the pressure.

So: a plane which does not need to move forward to stay aloft. It could silently hover.

A wing is structured to guide airflow. The wing of your cold hoverplane does not need to be structured that way. A circumferential "wing" occupying the entire top of a circular vehicle might be better as lift could be delivered evenly around the circumference of the vehicle. The cold low pressure air atop the vehicle would produce condensation within it, causing the vehicle to be enveloped in a cloud when underway.

enter image description here from http://www.thelivingmoon.com/43ancients/04images/Earth/Eyes/Lenticular_UFO_001.jpg

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    $\begingroup$ Would you not want to have heated air over top to reduce pressure and colder, denser air underneath the wing to support it? $\endgroup$ – Thucydides Aug 9 '17 at 0:53
  • $\begingroup$ I was thinking about just that @Thucydides. Intuitively what you say makes sense. But the ideal gas law says increase temperature = increase pressure and vice versa. Maybe that is if you hold volume stable, which would not be the case here. If volume is allowed to increase (like it would) I think you are correct. $\endgroup$ – Willk Aug 9 '17 at 3:45
  • $\begingroup$ @Thucydides - the relevant law is Amontons's Law: Given a constant number of mole of a gas and an unchanged volume, pressure is directly proportional to temperature. But the cool gas in the atmosphere immediately contracts in volume with the result that the same volume is denser. Denser air over means relatively more buoyancy for wing and air under which will tend to rise - float - up through denser cold air. $\endgroup$ – Willk Aug 9 '17 at 18:08
  • $\begingroup$ Wings work via Bernoulli's principle, where the faster flowing air over the upper surface reduces the pressure, while the slower moving air provides the lift (attempting to push into the area of lower density). The only way things can work in reverse is a hot air balloon, the warm air displaces the colder air and the balloon rises. You are confusing an aerostat for an aerodyne. $\endgroup$ – Thucydides Aug 10 '17 at 0:02
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As the question is written, the main application is using the supercooling pack to manipulate the Carnot Cycle to increase the efficiency of the engine (note, this works for any heat engine, so the answer would apply to a steam engine, a diesel engine or a Stirling Cycle engine, among others).

The Carnot Cycle is based on the idea:

Carnot's theorem is a formal statement of this fact: No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.

enter image description here

Carnot's Equation

This can be diagrammed as such:

enter image description here

Carnot engine diagram (modern) - where an amount of heat QH flows from a high temperature TH furnace through the fluid of the "working body" (working substance) and the remaining heat QC flows into the cold sink TC, thus forcing the working substance to do mechanical work W on the surroundings, via cycles of contractions and expansions.

For a jet engine (Brayton cycle), the supercooling of the intake air helps increase the power by increasing the mass flow of the engine. A similar effect is used in some engines by water injection (overspray), once again increasing the mass flow and decreasing the compressor outlet temperature, so you have two places where a supercooling brick can be used to increase the power output of a small backpack sized jet engine.

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