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Similar to my previous thread. In my setting, wizards from a pre-industrial fantasy world come to real life. One of these wizards is a cryomancer recruited by the US military and tries out his talents against modern forces. His favorite spell is freeze ray. How it works is that he has a magic staff. The large staff unleashes a cold beam at mach 1 that covers whatever it hits in thick ice (1° Kelvin).

This warlock unleashes his freeze ray at various vehicles in the current US military. He flash freezes ground vehicles, aircraft, and even naval vessels. Would the freeze ray be effective against any of these targets? By effective, I mean that either the vehicle is disabled, the vehicle is destroyed, or the crew inside the vehicle are severely wounded or even killed.

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    $\begingroup$ Is suspect given about half an hour and a basic Stirling engine, your cryomancer could single-handedly revolutionize energy production. That sounds a lot better for Uncle Sam than zapping a few tanks. $\endgroup$
    – Cadence
    Commented Mar 17, 2023 at 22:08
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    $\begingroup$ 1° Kelvin is waaayyyy colder than you think it is. Heck, hydrogen freezes at *14° K, and helium freezes at *0.95° K. -40F would be just as effective. $\endgroup$
    – RonJohn
    Commented Mar 18, 2023 at 6:17
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    $\begingroup$ How does the spell works precisely? Does it lowers the temperature of the whole target to 1K or simply convers it with ice at 1K? In this latter case, what is the thickness of the ice? $\endgroup$ Commented Mar 18, 2023 at 10:21
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    $\begingroup$ what kind of ice are wetalking about? water or frozen atmosphere? $\endgroup$
    – ths
    Commented Mar 19, 2023 at 0:39
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    $\begingroup$ @AncientGiantPottedPlant You're assuming the mages continue producing as the price goes arbitrarily lower. If they were clever, they'd form a cartel and fix the price at a "reasonable" level. (And if anyone tries to undercut them, that's where the freeze ray comes in!) $\endgroup$
    – Cadence
    Commented Mar 19, 2023 at 10:21

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It would immobilize or destroy just about anything other than nuclear powered ships.

The big issue I see it causing is simply engine air intake and exhaust. Even tanks need this, so covering a tank in a thick layer of ice would shut down the engine and therefore the tank. Aircraft would have it even worse, as you would shut down the engine, add a bunch of weight and ruin its wing lift all at the same time (while also probably preventing the pilot from ejecting, unless the blast of the ejection seat is powerful enough to break through the ice).

I imagine you'd also see immediate mechanical failure, like axles being suddenly frozen solid. You could probably calculate what torque overpowers what thickness of ice but I'd say just play it how you want it, if the ice is thick enough to freeze mechanics or not.

A nuclear powered ship would presumably be the least impacted, since its power plant could continue to operate while the ice melted, though I doubt they'd be firing anything anytime soon.

1 kelvin is so extreme that you might cause other issues, though. I'm imagining the videos of dunking things in liquid nitrogen, which makes them brittle. I'm not sure how much thickness of ice leeches out how much temperature from how much metal at what speed but I could imagine causing permanent damage if you hit a turret with a freeze ray and the turret tried to rotate. It might just shatter something important in the effort.

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    $\begingroup$ This cold ray would affect a nuclear wessel just like any other ship, if for no other reason than nuclear wessel are mostly not nuclear. Maybe radioactive decay would keep the very immediate area warm, but 1° Kelvin is really cold; I bet all the water would freeze, all the piping, containment units, etc would become brittle and shatter, etc. $\endgroup$
    – RonJohn
    Commented Mar 18, 2023 at 6:10
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    $\begingroup$ @RonJohn I kinda wonder about temperature transmission rates. OP didn't specify ice thickness but I dunno how it would be calculated anyway. What thickness of 1 degree Kelvin ice drops the temperature of a tank or ship by how many degrees over what period of time. Like okay, the ice surely damages the outside, but if you're 10 feet inside a ship, do you even notice? I wonder if the ice would explode from contacting such a relatively "hot" surface... $\endgroup$
    – JamieB
    Commented Mar 18, 2023 at 6:16
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    $\begingroup$ I wonder if the ice would explode from contacting such a relatively "hot" surface (10 feet inside the ship)... Honest question: are nuclear wessels any warmer than non-nuclear vessels? I don't think so, since burning kerosene to boil water into steam is just as hot as using uranium to boil water. $\endgroup$
    – RonJohn
    Commented Mar 18, 2023 at 6:22
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    $\begingroup$ @RonJohn By hot, I mean the surface of the ship/tank/etc at 300K (about 80F, assuming a pleasant spring day) coming into sudden contact with ice at 1K. Probably does bad things to the metal. I wonder what happens to the ice? $\endgroup$
    – JamieB
    Commented Mar 18, 2023 at 16:05
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    $\begingroup$ at 1 Kelvin the "ice" might well be frozen air. $\endgroup$ Commented Mar 20, 2023 at 6:38
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Yes, Extremely Effective

There are 2 things (and a bunch of secondary things) that would make a Freeze Ray against vehicles terrifying.

Shrinkage

No, I'm not talking about that kind of Shrinkage, I'm talking about Metal Shrinkage. When metal gets cold, it contracts. Sometimes this is used deliberately for things like Interference fitted bearings. However, think of all those moving parts that have a range of tolerances to work properly, not all Materials shrink at the same rate and by the same amount.

That means all those tolerances that are required for the vehicle to function are now out of whack and the Machine will quite literally grind to a halt.

Brittleness from the Cold

Combine this with the above Shrinkage - Components are now under significantly more stress and have less strength - they will tear themselves to pieces and shatter. Shattered components = machiney-no-worky.

Other interesting things:

Condensation turning to Ice - think of the Accuracy International L96 Rifle - The Swedes liked it, but in very cold weather -40 arctic conditions, the moisture in the air would condense on the Bolt, freeze and lock it in place.

This is without the shrinkage and brittleness.

This would happen all throughout the vehicle.

Weight - Ice weighs quite a bit - Ships have to keep on top of their de-icing, lest they become too top-heavy and capsize in rough seas, Aircraft need to be De-Iced in part due to the weight.

even the mighty US Carrier could be brought Lo by such a weapon

Aerofoils and rotor blades - Ice ruins those specifically designed shapes, which is the other reason why aircraft need to be de-iced, if you distort the aerofoil enough, the wing doesn't produce lift and the aircraft falls out of the sky.

People - Just look at the German Army's invasion of Russia in WW2 for how Cold effects people. It's not very nice.

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    $\begingroup$ Forget vehicles. It would just kill the people inside from the air they breathe. $\endgroup$
    – DKNguyen
    Commented Mar 17, 2023 at 20:50
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    $\begingroup$ Haha, shrinkage. $^{\text{(that means willies, guys.)}}$ $\endgroup$
    – Daron
    Commented Mar 17, 2023 at 21:14
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Lets do some back-of-the-envelope math. A decent summer day might be 82 degrees F, which is 301 Kelvin. Your freeze ray drops the temperature of the target to 1 Kelvin, for a delta of 300 K.

The coefficient of linear thermal expansion indicates how much a material changes length due to temperature changes. The coefficient for steel is $12\times10^{−6}$, which means a change of 300 K would result in a contraction of 3.6 mm per meter. Materials like aluminum would contract twice as much, and glass contracts around half as much. Those numbers don't sound too significant, but the overall effect can be huge where you have dissimilar materials connected to each other. One shrinks more than the other, and the end result is that both materials end up damaged or warped. The bolts holding them together can be sheared in two. This process also happens over an unbelievably short time period, so any materials that aren't extremely good conductors of heat will have colder spots and warmer spots that contract at different rates resulting in material fatigue and possibly even cracks.

The coeffecient of volume expansion is the same thing, only in three dimensions. For gasoline it's $950\times10^{−6}$, which means the liquid in your tank and fuel lines now takes up more than 25% more space than it did a minute ago. All of your fuel lines have burst, and your engine block has most likely cracked open. Any other vehicle system involving a lubricant or operating fluid (brakes, steering, etc.) suffers the same fate.

Many materials become very brittle at low temperatures. The ductile-to-brittle transition for steel occurs around 173 K. Many metal components in the vehicle would crack and shatter due to becoming brittle while simultaneously suffering strain due to temperature contraction.

None of this actually matters, of course. A sudden transition to 1 Kelvin would kill the vehicle's operators almost instantly, and the vehicle is more or less worthless without anyone operating it.

The type of vehicle really doesn't matter. There isn't much that can survive at 1 Kelvin and of the few things that can, vanishingly few can survive a sudden transition to 1 Kelvin. Land vehicles would be practically stopped in their tracks as the grease around their axles froze and their moving parts stopped moving. Aircraft would be dangerous to freeze because their engines would go out but they would maintain their existing speed and trajectory, becoming an uncontrolled projectile (possibly carrying explosives). Watercraft are particularly vulnerable because once their exteriors become brittle, you can freeze the water around the ship, squeezing it with ice and shattering the hull. Be particularly cautious if you attempt to freeze something like a guided missile. The stress of freezing may be sufficient to activate the trigger mechanism, and the missle can explode faster than you can freeze it (particularly for a nuclear explosion that can generate heat faster than you can freeze it away).

The only military vehicle I can think of that might stand a chance would be something with a directed energy weapon (like a plasma railgun or high-powered laser) that could return fire, generating enough heat to counteract the cold beam. It wouldn't hold for long, but all it has to do is buy enough time for the weapon to strike and kill the cryomancer.

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    $\begingroup$ Doesn't gasoline contract when it cools/freezes instead of expanding? $\endgroup$
    – Shalvenay
    Commented Mar 18, 2023 at 4:28
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    $\begingroup$ OP seems to indicate the magic only covers the target in 1K ice, not uniformly shock its temperature down to 1K. Thermal conductivity matters now, and hard shields will certainly protect occupants. The rate of cooling load (and damage) is also limited by the volume of ice available. Definite instakill against aircraft, much less clear against a land tank. $\endgroup$
    – obscurans
    Commented Mar 18, 2023 at 6:33
  • $\begingroup$ @obscurans you're unlikely to hit a flying aircraft with something that travels at the speed of a handgun round. $\endgroup$
    – fectin
    Commented Mar 19, 2023 at 23:29
  • $\begingroup$ A nuclear weapon wouldn't detonate if simply shattered by ice. $\endgroup$
    – jdunlop
    Commented Mar 20, 2023 at 20:24
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It depends on how the spell really works.

From your description I get two possible situations:

  1. Target is frozen to 1K instantly AND covered with thick ice at the same temperature.

  2. Target is not frozen, but instantly covered with thick ice at 1K.

The scenarios are quite different.

In the first case the target is with most probability destroyed (barring some counter magic): at 1K the crew would die instantly, all electronics will be shattered by thermal stresses and even the component materials (even most metals) would become so brittle they will shatter easily (maybe also from the sheer weight of the tank). Moreover most chemical reactions will effectively stop.

In the second case, it depends heavily on the thermal shielding of the tank and the total mass of the ice produced. The 1K ice will begin drawing thermal energy from the environment (outer side) and from the tank (inner side), rising its temperature and lowering the tank temperature in the process. This process continues until the tank, the ice and the external environment reach thermal equilibrium. It's quite a difficult calculation to perform without knowing the actual construction of the tank, but in the end, it depends on the relative thermal capacities of the mass of ice and of the tank.

If there is enough ice to bring down the temperature of the tank to dangerous level (for the materials and/or crew), then it would be an effective spell.

Keep in mind that the freezing effect will cool down the tank from outside, so before the thermal equilibrium is reached, the outer tank parts will be cooled faster, so the first parts affected are the outer joints (e.g the joints between tracks elements, for example), which could become stuck due to thermal shrinkage, and maybe break if the tank was moving.

To put some numbers in: the specific heat for ice is about 2.1 kJ/(kg K), whereas that of steel is about 0.42 kJ/(kg K). The specific heat means how much energy is needed per kilogram to raise the temperature of the material by 1K. So assuming the tank has a mass of 10t = 10000kg and it can resist up to -30°C and the ambient temperature is 20°C, you need to lower its temperature by 50K.

This requires 0.42 * 10000 * 50=210MJ of energy to be transferred to the ice. Assuming the mass of ice is 1000kg, for it to reach -30°C (243K) it would take a temperature increase of 242K, so the energy required is: 2.1 * 1000 * 242=508MJ.

So yes, 1000kg of ice would be sufficient to make 10t of steel to go below -30°C. The problem is that this is at thermal equilibrium and doesn't take into account the time needed and any sort of thermal insulation or heating system the tank could have.

Moreover there is also the heat exchanged with the environment (part of the ice will increase its temperature drawing heat from the atmosphere instead of from the tank).

Keep also in mind that ice is a good thermal insulator (think igloos) so the inner layer of ice will slow down heat transfer from the outside layers. So covering an object in super-cool ice is not an efficient strategy to cool it down quickly (it would be much more efficient to expose the tank to a freezing wind).

In the end, it would require quite a lot of ice to cool it down, and it won't be quick. Most probably, once you burden the tank with some additional tons of ice, it will stop in its tracks just for the sheer weight of the ice.

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    $\begingroup$ I am talking about scenario #2, where the target is covered in thick ice on contact. As for how much ice or the cone of the beam, I'm not a chemistry major so I just left leeway with that. I don't want to give out numbers that seem silly on inspection. $\endgroup$
    – Rhymehouse
    Commented Mar 19, 2023 at 19:19
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    $\begingroup$ I'm missing scenario #3: The surface of the target is rapidly cooled to 1K, causing the atmosphere to condense and freeze onto it. The ice that is formed then 'shields' the target from the ray, causing the ice to rapidly grow outwards, without drawing all that much heat out of the target. This also means that the ice only contains a little water-ice, and is mostly nitrogen and oxygen. $\endgroup$
    – AI0867
    Commented Mar 20, 2023 at 10:27
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    $\begingroup$ @Rhymehouse: You should edit your question to make that clear. Its current phrasing left us guessing whether the layer of ice was formed directly by the magic, or if it was a symptom of the target itself being super-cooled (either surface layer or all the way through.) As you can see from multiple answers, it wasn't clear to anybody, and still isn't without finding this comment under one of the answers. $\endgroup$ Commented Mar 20, 2023 at 10:33
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I can see a couple limits to the mage. For example, military planes fly very fast, very high. Regardless of how effective the spell is, eyeballing a death ray at a supersonic target 50,000 feet up in the sky is a tall order.

Tanks and ships aren't as fast, but can also hit from many km away, and are (un)surprisingly good at evading incoming projectiles.

Another foil for the mage could be how clever the beam is. If it hit a fly on the way to a tank, would it freeze the fly and stop there? If it hits a track, would it freeze the whole tank? Again unsurprisingly, military stuff is very good at figuring out when stuff is flying towards it, and shooting back at what's coming. If a small counter missile or reactive armour intercepts the magic beam, I'd imagine it would freeze but stop the beam, effectively making that magic useless.

The second issue comes from how the spell works. If it is even slightly subject to real physics, then some military vehicles might be able to survive. All materials (especially thick armour) have properties called thermal mass and thermal conductivity.

  1. If the beam can immediately cool down any target's entire mass to 1k, then yes, no chance of survival, but that is so op that you'd have to worry about the mage missing the shot and freezing the whole planet.
  2. If the beam acts like a cold object coming in contact with the target, then it might be fairly survivable. Recall thermal mass. Regardless of how cold the beam is, it's gonna take some time for the whole object to become cold. Depending on internal heating and thermal mass, it might be able to keep vital elements hot enough to function. It only needs a few seconds to shoot back at the mage for it to end the threat.
  3. The beam's own thermal mass is also interesting. Can it freeze a tank with the same effort it freezes a whole ship? Would the mage need to put in more effort to freeze a whole skyscraper? If the mage can instantly and effortlessly freeze a plane carrier then there is not much that can stand in his way. Except for some very pissed entrophy law bringers.
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It Freezes Them

A still frame from Austin Powers: The Spy Who Shagged Me (1999) where Austin is frozen solid, like in a cryogenic tube. There is a text that says: "I've been frozen for 30 years. I've got to see if my bits and pieces are still working."

In the short term, your vehicle is frozen in place. The wheels cannot turn because they are encased in ice. The guns will not work because the shells go boom when they hit the ice and then the tank itself goes boom.

Once the cold seeps deep inside the vehicle, the crew turn into icicles. That is if they don't suffocate first. The internal combustion engine gets cold and turns off. Any bits and pieces that are still moving either stick together or become brittle and break.

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Yes, definitely it would disable them if not outright destroy them.

All modern military equipment is dependent on electricity, power sources, and electrical conductivity.

At 1 degree Kelvin, we are talking about principles of low temperature conductivity. Resistance values are substantially reduced. Capacitors charge essentially instantaneously. Coils produce almost instantaneous field strength changes. Induced voltages would be, well, extreme. Electrical motors would have unimaginable torque and speed. Batteries would not work, generators would freeze up. Anything electrical would become non-functional.

Not to mention that this equipment is not made of a homogenous material, the components would not contract at the same rate. Nothing would fit properly. Every shaft and gear would bind. Combine this with the huge torque of the super conducting motor windings, and the brittleness of material at this temperature, and everything that moves would fracture and disintegrate.

For all the freeze ray was able to lower the temperature, I am afraid you would paradoxically end up with a very melted piece of equipment from all of the energy released.

Incidentally, a 'freeze ray' would NOT project 'cold', it would super-absorb 'heat'. Seems to me that whatever was at the ray source would have to cope with extreme heating, at the least.

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    $\begingroup$ Once the excess heat brings things back up to normal temperature, the resistance will drop again, and it stops overheating. $\endgroup$
    – Daron
    Commented Mar 17, 2023 at 21:14
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    $\begingroup$ @Daron So when you turn a stove element off, the stove element instantly cools? $\endgroup$ Commented Mar 17, 2023 at 21:57
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    $\begingroup$ @Daron That is not a genuine answer. $\endgroup$ Commented Mar 17, 2023 at 22:43
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    $\begingroup$ Pure copper doesn't superconduct at 1K, or any temperature. It does conduct better, by some ratio (copper.org/resources/properties/cryogenic has a graph with multiple curves, IDK when the factor of 10 or the factor of 2000 would apply). But circuits designed to have resistors will use things like carbon films which also don't superconduct. And inductance doesn't drop to zero as temperature falls, you still have at least the the vacuum level, although that could be much lower than ferrite cores. But anyway, you don't have instantaneous changes in currents or magnetic fields. $\endgroup$ Commented Mar 20, 2023 at 10:47
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    $\begingroup$ That means the current goes UP by between ten and 100 times - if resistivity of copper wires was the only thing limiting current, then yes. But that's very unlikely. I should have looked up cryo temperature behaviour of various common resistor types, like carbon. Also, for motors, back-EMF from the motor spinning will balance the input voltage. In a normal DC motor, making all the wiring superconduct would reduce resistive losses to zero, down from maybe 50% or something? (electricaleasy.com/2014/01/losses-in-dc-machine.html). So current might double until the motor sped up $\endgroup$ Commented Mar 20, 2023 at 13:43
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I believe that most answers have already covered all possible sides of the issue from the perspective of physics, and they have summarised it in two major classes:

  1. When the mage's beam, travelling at Mach 1, hits anything in its path, it instantly lowers the temperature of that 'anything' to 1ºK. The result: immediate breakdown of whatever is hit (vehicles will still continue to move, according to their momentum; explosives may still get triggered, especially on missiles; laser beams, by themselves, will not be affected, but the laser gun — and its operator! — will); all occupants inside whatever vehicle they are will immediately die (no life is possible at 1ºK, especially a sudden drop to 1ºK, as it is implied). That is the 'no fun' scenario.
  2. The mage's beam instantly covers the object hit by it with a layer of ice at 1ºK. In this scenario, things are more interesting (from the perspective of the narrative, that is!), because you have to account for thermal transference issues. Most vehicles would be stopped in its tracks pretty quickly, but most of their internal equipment (including its crew!) will have a chance of survival. Then the issue here will mostly be how thick the ice will be when it hits the target and how quickly the mage can replenish it; also, how accurate his aim will be (think of hitting a missile travelling at Mach 2.5 with a narrow beam which travels at Mach 1 — how fast and often can the mage keep the target in his sights to be able to create enough ice to cover the missile, disable it, make it fall to the ground, and neutralise its explosives?)

Now, obviously we're talking magic here. Nevertheless, for the sake of the narrative to at least induce some suspension of disbelief, I would expect the Sanderson's Three Laws of Magic to be followed, at least to a degree. Here are some thoughts:

  1. 'Cold rays', as so well explained by @justin-thyme-the-second, are in fact 'super heat-absorbing rays'. One assumes that the staff will be made of a material that can absorb as much heat as possible without getting too hot to handle; however, it's one of the interesting limits that might get used in the narrative — how much heat can the staff absorb until it becomes too hot to handle? Or even explode? Or at the very least, it might have to discharge the heat in a parallel dimension somewhere (think 'Hell' — where all magic staffs from cryomancers discharge their accumulated heat...) but has to do that periodically. This places an interesting limitation on the way the cryomancer is able to freeze targets — he may be able to catch a few tanks and airplanes and missiles, but when it comes to aircraft carriers, he might have to give the staff some time to discharge all that heat. Of course, as a last recourse, the warlock might just hurl the fully-charged staff to a large target (think of a full-scale naval base!) and let it explode in a thermonuclear explosion. Bye-bye staff, yes, but at least the wizards' quest might be completed in that extreme way.
  2. If the staff actually emits a ray, then there is a problem: as the super heat-absorbing ray travels across the atmosphere, it will, naturally enough, freeze the air around it instantly. So the ray will be a physical rod of frozen air (attracting water condensation along its course), connecting the warlock with the target; at some point, of course, this rod will break. Also remember that it's travelling at Mach 1 — I can only imagine (but not calculate, my mastery of physics is not enough for that) the incredible tensions placed on the frozen rod. I would guess it would break almost immediately — and, not being in touch with the ray's source, it would harmlessly sublimate into air again (not to mention that the sonic boom — or crackle — due to hitting Mach 1 will propagate along the whole rod, making it break even faster). Now, this might not be a problem: one can assume that this process of flash-freezing the air and the breaking-up of the rod might happen almost instantly (and thus be only seen as some special effects, as the air freezes and breaks apart in an instant, travelling along the path of the ray). That, for instance, would allow an 'invisible' ray to become 'visible' (similar to how a laser will get reflected by dust, thus revealing its path) — enough for the warlock to guide it and acquire aims! — and therefore give a good explanation on the visibility of the ray (and make for good narrative infodump). There are a few catches, though: Mach 1 is fast, but not instantaneous, which means that the military will be able to target the ray and track its progress (hypersonic missiles can also been brought down, so one assumes that the current military has ways to track them down at those speeds), and trace it back to where the cryomancer is; the cryomancer will have to have line-of-sight to his targets (or else he won't see the ray!), which also means that those 'targets' have a line-of-sight to him; and, as a slight twist which might be used on a special setting, the ray will be invisible outside an atmosphere — but nevertheless still work, of course!
  3. A corollary to the above: if the warlock puts the staff in contact with a water body, there will not be a 'ray', so to speak: water will get frozen in a circle/sphere with the staff at its centre, spreading out at Mach 1. That will surely be a way to literally freeze the aircraft carrier in its tracks — by freezing the water around it! However, there is again a limit to how large an area (or, more correctly, a volume) of water that the staff can freeze by absorbing its heat; and the further the ice sheet travels, the more heat needs to be absorbed, with a cubic power function — i.e. going from 1 metre of frozen ice to 2 metres requires eight times the absorption of hit, not twice, meaning the staff will get quickly 'full' (on the naval base thermonuclear explosion scenario above, the easiest way for the wizard to hit it is just to throw the staff into water as close as possible, activate the staff, and let it absorb heat from the water until it explodes — thus first freezing everything and afterwards blowing everything up).
  4. Now here is one of the pet peeves I have about how the staff works. Never mind the difficulty of hitting a supersonic airplane with a supersonic ray (which is not instantaneous and therefore requires very accurate aiming, far beyond the skills of a regular human without technological means — and the further away the airplane is, the harder it will be. And no, you do not want to get the airplane too close to you!), or how fast the cryomancer will need to be to switch his targets when multiple missiles, artillery shells, and rounds of ammo are all shot at him. Even assuming superhuman capabilities — if he is a cryomancer, maybe he can also freeze time itself? — this will be no mean feat, because the cryomancer must constantly evaluate the speed and distance to multiple targets, while balancing the need to allow the staff to periodically discharge its heat into the parallel dimension and wait a bit until the staff is operational again. In other words: to fight an army, you will need an army of cryomancers as well, perfectly coordinated among themselves (because the army will be!). One thing is to freeze down a handful of tanks with a 'surprise attack', but once the cryomancer is identified as the source of threat, he'll have to deal with hundreds or thousands of damage-inflicting long-range weaponry, all of it impossible to evade with merely human speed, coming at him from all sides — and airborne! — and responding differently to how the ray works. For instance, when freezing a missile's guidance electronics, the missile will not immediately fall to the ground (due to momentum, inertia, etc.), but may be incapacitated and miss its target (best-case scenario) without exploding, or exploding in a harmless (non-radioactive) way. But what about a 'dumb' artillery shell, thrown ballistically at the cryomancer? The ray may freeze it on the air (remember, however, how fast it will be!), and that instant freeze may also break down the metal itself (thoroughly deforming it, as if it had been melted down, as explained on the other comments), but remember that it will be encapsulated in a shell of frozen air, keep its mass and overall shape, and still continue to fall towards the wizard at roughly the same speed as before. In other words: the wizard cannot protect himself (or his team mates) from, say, a machine gun spewing hundreds of shells per second. He might try to freeze the gun instead — but good luck at doing that while being under constant enemy fire! (one might imagine the cryowizard using sharp-shooter tactics, stealthfully approaching the enemies and freezing their guns one by one, instead of the 'all-out attack', expecting to be able to 'freeze away' whatever is thrown at him).
  5. The second pet peeve is more complicated: how does the wizard designate a target? In other words: the ray, once emitted from the staff, will travel in one direction at Mach 1, freezing the air on its path, until... what? The ray certainly can go through a tank and emerge from the other side and continue to hit tanks along its path... until... what? Does the wizard need to activate/deactivate the ray? If so, it means that it will be much, much harder to coordinate multiple attacks or defenses that occur simultaneously. Freezing a lot of empty aircraft on a runway would be no big deal for the wizard. But if the aircraft are all airborne and firing missiles and ammo against the wizard, at the same time engaging in evasion techniques... the staff is not a 'fire-and-forget' tool, or is it?
  6. But wait, there is more! One assumes that the way the ray works is similar to how the contemporary military 'illuminate' targets with laser beams, to mark them for over-the-horizon precise artillery shelling (for instance). Laser travels at the speed of light through the air, not Mach 1; and it's relatively easy to know when it 'hits a target', because it will reflect it (and metal reflects much better than, say, a patch of rough ground) and, of course, it will not be able to go through the target. This makes it perfect for precise aiming for sharpshooters. Now the magic super heat-absorbing 'cold ray' hardly works that way: it freezes everything it comes in contact with. Even if one might artificially assume that some things freeze much faster than others (which is certainly true of, say, metal man-made objects, compared to freezing a mountain made of rocks), and for all purposes any enemy vehicles/artillery will be made of metal, it's nevertheless hard to define exactly 'what' a target is. An airplane on an otherwise empty bit of sky is easily labeled as a 'target' (not considering that it moves very fast, which is a separate issue), because, well, it's all air except for the bit of metal suspended in that air. One assumes that the cryomancer will know precisely when the ray hits the airplane in order to know when he can deactivate it (no need to further extend the ray). But what about a nest of machine guns inside a bunker partially sunken in the surrounding ground? Because the cryomancer will very likely not have a clear line-of-sight inside the bunker (which would give him the chance to freeze guns instead), he could attempt to freeze the whole bunker instead. The problem here is when to stop! Concrete walls are similar to the mountain they're built into, so effectively the wizard would need to absorb a huge quantity of heat of all that mass — and never know when to stop. Imagine bunkers with corridors dug deep into the mountain, which the soldiers can use either to run away or to move to other bunkers, out of the sight of the wizard, in the hope of catching him by surprise by attacking from a completely different direction. How could the cryomancer deal with this? He can, of course, freeze the whole mountain — but will the staff be able to handle all that heat? Even if it does, one might assume — per Sanderson's laws — that it would take a lot of time for the heat to get discharged, during which the cryomancer would be vulnerable (and quite visible on the battlefield). Most likely, however, there will be limits to how much the staff can absorb before exploding; and even a clever cryomancer attempting just to freeze selected spots on the mountain — not the whole of it — might be easily eluded by enemy soldiers moving around out of sight (especially if there are a lot of them — and there will be!). So, sure, the narrative might call for the cryomancer to freeze a tree near the bunker's entry, causing it to fall and effectively block the view; or provoking an avalanche by selectively freezing some patches of ground and some cherry-picked rocks conveniently located above the bunker, expecting everything to get covered in ice, mud, broken trees and rocks, and so forth. That's something that a cryomancer might be able to pull off, if he has the element of surprise on his side, and he's not in the middle of a hot battlefield full of flying objects aimed at him. In other words: no, the cryomancer cannot 'wave his staff' at the whole battlefield — mountains, valleys, rivers, bunkers, machine guns and their operators, tanks, airplanes, missiles, artillery shells — and expect everything to be instantly frozen.

So... here is where Sanderson's laws of magic come in. You'll have to figure out the following:

  • Will the ray freeze everything in its passage, or just some materials? If the ray will not freeze the atmosphere (say, it freezes only metals/rock/wood etc.), will it be visible? If not, how will the wizard know where the ray is, in order to aim it properly?
  • How will the staff discharge the heat it has absorbed? How fast is that operation? What will be 'depleted' (if anything) during that operation? What happens if the cryomancer neglects to discharge the heat periodically — will the staff become simply too hot to handle, or will it explode, releasing a thermonuclear blast?
  • Does the cryomancer need to activate and deactivate the ray? Consider how this will affect a) the ability to get a 'fix' on a flying target also travelling at Mach 1 or even much faster; and b) dealing with the 'knowing when to stop' scenario.
  • Can the cryomancer activate multiple rays at the same time? (and selectively deactivate them, as they reach their targets) If yes, how will that affect the staff's ability to absorb — and discharge! - heat?
  • What is the range of these rays? Since they might be able to go through everything (if the cryomancer does not deactivate it after reaching its intended target)... will it be possible to, say, freeze patches of the Moon? (although at Mach 1, it would take quite a long time until the staff reaches the Moon) Or even the Sun, for all purposes...
  • Does the 'cold ray' travel in a straight light? Is it affected by gravity or electromagnetic fields? Assuming 'no' on all these questions, how often can the cryomancer change its direction (remember — the ray keeps travelling at Mach 1, even if the cryomancer changes its direction, so a ray with lots of bends and curves will be quite hard to aim accurately!)? This would effectively mean that the ray behaves as a remote-controlled missile, with the difference that there is no camera mounted on the missile, so the cryomancer will need to 'guide' it merely relying on 'line-of-sight' adjustments — incredibly hard to do at a distance! Think of hitting airborne objects a few km away — the wizard will be able to see them, send a ray towards them, and adjust its aim... until the ray is so far away that the slightest 'correction' will make it miss the target... and as it goes further and further away, the wizard will have a 'flattened' view of the target and much less 3D clues to know how exactly to 'bend' and 'twist' the ray to be able to hit the targets — which are moving at supersonic speeds, mind you!
  • Can the ray be deflected in any way? Since it's not instantaneous, and visible (as it freezes and sublimates air around its passage), it can be 'hit' with whatever might deflect it. Even if it does not respond to any physical laws, consider the following scenario: shoot a thermonuclear missile on the same path as the ray, moving at the same speed. Difficult to achieve, yes, but modern electronics are up to the challenge. This would mean that the ray will now be constantly absorbing heat from the missile, quickly overheating the staff before the ray hits its intended target. The cryomance now has the option of letting the ray continue on its path — and absorb the extra heat, to critical levels — or to deactivate the ray, and try again. Which would only get the military to shoot another missile in the same way. It would be a question of what would come first: the cryowizard's ability to control the staff; the staff's ability to discharge heat; or the military's supply of missiles getting exhausted. Also note that even if the cryomancer is able to change the ray's direction 'on flight', this would not be a problem for the missile — its electronics are way faster at responding to sudden change than a human's nervous system, so it would always keep on track. (BTW, as we can see today in Ukraine, it is possible to shoot down hypersonic missiles with contemporary technology, and yes, that actually means shooting a supersonic missile at precisely the right moment against another supersonic or even hypersonic missile — all that in fractions of seconds — so the wizard's 'cold ray' would be comparatively easy to target in this way)
  • What happens if the staff is activated and immersed in a body of water?
  • Ditto but by placing the staff in contact with the ground
  • What happens when the cryomancer drops the staff? Will whatever rays have been emitted continue to move in the same direction?
  • What happens when the cryomancer moves? So far, I have only considered that the cryomancer is in a static position while aiming his ray (which also means he's quite vulnerable). But consider a very long ray — used to shoot down an unsuspecting aircraft many kilometres away. What happens to the ray when the wizard moves the staff? Does it move with the staff? If so, consider a many-kilometres-long ray — what happens to it, if it is not connected to the staff any longer? Does it dissipate on its own and the cryomancer needs to create a new ray? This makes for interesting narrative twists, as the cryomancer will be quite good in a mêlée (since the rays cast will be very short and hit their targets very quickly; so even moving the staff around will not make a huge difference), which would be the intended purpose of the staff on a medieval-fantasy scenario, while it would be not as effective for sharpshooting targets at a long distance, because the cryomancer would have to be perfectly immobile to have a chance at such a shot...
  • How much do these wizards know about contemporary military weaponry, anyway? If it's the first time they encounter a modern military, most of the weaponry would be completely baffling and not even recognised as weaponry, anyway. I mean, an isolated soldier, with a helmet (helmet = soldier) and a machine gun (similar to a crossbow, but much deadlier), might be adequately identified as an 'enemy'. A flying airplane — especially one not yet engaged in the attack — might just be some sort of magical metallic object of unknown purpose. A tank will not be recognised as a weapon at all — until it starts shooting. While a conventional ballistic artillery cannon might be vaguely described as 'a war machine throwing metallic rocks very far away and very quickly' and therefore seen as a threat — a modern, rocket-based artillery gun will hardly be identified, even when it starts shooting — at least, before it becomes obvious that the rockets are not 'firework' but intended to strike targets very precisely. A warship, by contrast, will immediately be 'understood' as such; but an aircraft carrier, which will send out swarms of metallic flying objects, might be completely baffling — at least, until those airplanes come closer and start shooting missiles (but by then it's too late!).

I'm sure there are plenty of other questions that would require answers to deal with most, if not all, scenarios. But I hope that the ideas above, plus the physical limitations already explained by others in this thread, will help you to flesh out your narrative.

In conclusion: while it seems that the cryomancer will have a huge advantage on a contemporary battlefield — because he will be able to 'freeze in its tracks' anything that is thrown at him — this is only true if only one (or at least a very small amount) enemy weapon is thrown at him at the same time.

So, he might stop one (or possibly even two or three or four) tanks in his tracks; but not a full platoon, especially if he doesn't have line-of-sight to all units (while they will have visuals of him, via imagery coming from satellites/surveillance airplanes in real time).

He might freeze down a supersonic airplane, kilometres away (while it is still harmless to the cryomancer and his team), especially if the pilot has no clue about what is happening to him; this will require the wizard to be very immobile for an extended period of time, but, having the element of surprise, he'll be able to do so. He will not be able to defend himself from a platoon of aircraft shooting air-to-ground missiles and rounds and rounds of ammunition against the cryomancer, while at the same time engaging in complex evasive maneuvers to avoid being hit by the 'cold ray'. In fact, he wouldn't stand a million-to-one chance to survive more than a few seconds.

While he might not have the power, mana, or whatever ability he 'spends' to activate the ray to freeze an entire aircraft carrier and its crew, he might attempt to freeze the water around the aircraft carrier instead. That would 'freeze it in its tracks' — for a while. It would also deplete the magic abilities of the wizard, or at least require a lot of heat to be discharged by the staff, during which the military will not be asleep. They will throw everything they have at the cryomancer, while patiently waiting for the ice to thaw around the carrier (the carrier might not work any longer, though; and part of its crew will have died, but possible not everybody).

So, yes, a cryomancer would be a formidable opponent in the battlefield, but not an invulnerable and invincible one. His powers give him an edge, sure, when the element of surprise is on his side; but he simply cannot keep an army at bay.

Not unless, well, you completely ignore any of the laws of magic, and just tell the readers that the cryomancer is invulnerable, e.g. his aim is always accurate, merely by looking at an aircraft the staff will immediately send a perfectly-aimed, bended ray to freeze it, and the staff is directly connected to another dimension where it can constantly discharge heat at will, all the time, without any interruption. One can also assume that the cryomancer can freeze time itself, allowing him to carefully prepare a full set of rays to hit multiple targets with infinite precision, and, once time is 'thawed' again, all are hit simultaneously and any threat can be overcome this way. Last but not least, the cryomancer is also clairvoyant, in the sense that he can 'travel' along the cold ray and know exactly when to twist or turn in order to make precise adjustments to its path and hit exactly what it intends to hit.

Well, that would make him omnipotent and invulnerable. But what would be the fun in that? :-)


P.S. An earlier inspiration I had for this answer was that the staff would not really 'cast a ray' per se, but rather shoot some form of super heat-absorbing pellet instead, which would 'implode' when hitting a hard target, absorbing all its heat (and then explode as a consequence). This would arguably be better in terms of narrative, and deal with issues such as how the 'ray' is aimed (it is not — the pellets behave according to ballistics), how many rays there can be (one pellet is shot and the wizard decides its direction — and can shoot as many as he wishes, all it takes for things to work is to have a good aim!), how far they can go (again, a pellet would just be a bullet for all purposes, and what works for bullets will work for 'cold pellets' as well), and so forth. It would neatly cover most of the aspects of a 'cold ray' while avoiding the questions related to the heat sink (which one assumes that it's somehow 'in' the staff itself, or at least is 'part' of the staff in some way).

However, a pellet-shooting staff is not what the OP describes as the 'cold ray', so I had to rethink a bit how to properly balance it out assuming that the ray itself is as immaterial as, say, light, and thus its usage is more similar to the way a laser pointer works than to the way a missile-throwing device does...

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I am going to throw out somewhat of a frame challenge to this question.

'Heat' is not a separate 'thing'. Temperature is a property of matter, directly related to it's state (solid, liquid, gas). Without matter, there can be no temperature. 'Hot' and 'cold' are only artifacts in our mind, constructs to describe certain sensory information. Unfortunately, the terms 'heat', 'temperature', 'hot' and 'cold' are very often (still) confabulated into false or fake concepts.

Without some form of matter, there can be no temperature, no 'hot' or 'cold', any more than there can be a 'solid', 'liquid', or 'gas' without some form of matter. A vacuum in space can have no temperature, because there is no matter to apply this property to. In this sense, 'cold' is like talking about 'red'. There has to be something that has the property 'red'. The property 'red' in and of itself, in isolation, does not exist.

There can be no such thing as a 'cold ray' without there being some form of matter that the cold is a property of. This wizard has to be projecting some 'thing', some 'matter' (even be it 'ether') that has the property 'cold'.

There is another option. That is, the 'ray' does not go from the wizard to the object, but the reverse. Somehow, the spell is able to convert the vibrating heat energy of the molecules of the equipment into some form of EM energy, and beam that back to the staff, or the wizard can cast a spell that causes the layer of atmosphere surrounding the object to do the same (meaning this spell is worthless in space). The surrounding atmosphere would then, through conduction, draw heat out of the target. So, now the question that is begged to be asked is 'does the spell continue to draw energy out of the layer of atmosphere, or are normal principles of thermodynamics now to play out?'

Here, a brief history of thermodynamics that outlines the historical misconception of 'heat' in popular mythology..

Up until the mid-1800's, the concept of heat as a 'thing' prevailed. Just as fire was an element and not an artifact of combustion, somehow heat was some form of material or ether or some 'thing' that could move around of its own accord. It was not just a property of matter; it had an existence in and of itself. It is easy to see how they could have this concept, since most of their experiences with heat had something to do with it 'coming out of something', either logs in a fire, a volcano, or the Sun. When you burned a log, you liberated this thing called 'heat' and it was able to cook your food, destroy a building, or cause ice to melt. The concept of 'fire' as an 'element' that was released was very much a part of this. Fire and heat were mysteriously, mystically linked. Such ideas as the conservation of heat were unknown, because it seemed to be something that was extracted and then used up. When one got heat from a log, nothing got cooler.

This concept sufficed as an explanation right up to the invention of the steam engine. Not the invention of the engine itself, but the desire to optimize the work it could do. The time period around the 1850's was marked by a tremendous competition between England and France into the mastery and perfection of this technology and the idea that work could be obtained from the transfer of heat. It is not just a coincidence that the theories of thermodynamics of Carnot, Maxwell, August Krönig, Ludwig Boltzmann and Rudolf Clausius among others came about in this time period. It was all about the power of steam to build a strong industrial base. The country that mastered it would be the dominant driver, and it was a national priority to understand it. The age of mastery over steam, in many respects, provided the impetuous for the age of physics. There was unabashed support at the governmental level for any research into it.

The work of Clausius, in particular, building on Carnot, developed the idea that heat was something that flowed from a high heat pressure (high temperature hot) to a low heat pressure (low temperature cold), and thus what was hot became cooler, what was cold became hotter, until equilibrium was reached. But what about the log that produced this heat? Where in the log did it come from? The log got smaller as heat came from it. Where does conservation of matter come in? It is obvious the log is being destroyed. (Of course, the idea of using the term 'pressure differentials' was not directly referenced, full apologies to Boyle, and even Boyle did not relate gas pressures to 'vibrating moving atoms' colliding, Rutherford having not yet been born).

But even though during this period the world of physics moved closer and closer to the understanding that heat was a property of matter, not something distinct from matter, and the kinetic theory of gasses took shape, it was not quite there yet. Heat was regarded as a means to an end, and that end was work. To Maxwell and others, heat that was created or released or produced from combustion, and not used to do real work, was a waste and contributed to inefficiency. Heat energy was conserved once it was released, and then moved from the air to water and steam, but the energy not converted to work was lost, never to be recovered again. How to console this alleged reality with the laws of conservation of matter and energy? The solution, of course, was this misdirection called 'entropy' that became a term physicists bandied about, changed the definition to suit, used to patch the holes in the theories, and thus allowed then to go to sleep at nights.

It was not until Rutherford, and the beginnings of the understanding that heat was a measure of the vibrations of atoms, did heat begin to become a 'property of matter'. The idea of the kinetic theory of heat truly matured. There was no separate 'thing' or 'energy' or 'heat' that existed, except that it was an inherent property or result of the vibration of atoms that made up matter. Without these atoms vibrating, there was no heat.

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  • $\begingroup$ Late comment, but if you read the OP, the freeze ray shoots out ice at 1 Kelvin. $\endgroup$
    – Rhymehouse
    Commented May 13 at 4:56

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