Hello readers! Today we’re taking an analytical dive into the feasibility of ‘ice magic’, which I am defining as the ability to conjure solid ice out of thin air. This frosty power is found in traditional fantasy and in superhero genres, from Elsa in Frozen, to Todoroki in My Hero Academia, to Frozone in The Incredibles (just to name three examples). Each of these characters can create icy formations from the air around their hands, and so my question is this: where does the ice come from?
My assumptions
I am going to approach this question having made two key assumptions. Firstly, I am assuming that users of ice magic can lower the temperature of their surroundings. For me, this is the ‘magic’ part, where no scientific explanation is required. The characters are clearly biological heat sinks of some kind, and I won’t ask how (maybe another time).
My second assumption is that these characters cannot create something from nothing – i.e., they cannot conjure ice molecules into existence. To some, this could also be excused as ‘magic’, but for me, the creation of matter crosses a line. I like to imagine that even fictional universes contain a finite amount of energy that can neither be created nor destroyed. Therefore, the only way that Elsa or Frozone could create ice from thin air is to freeze the water that already exists around them.
The limits of ice magic
Most franchises make no effort to explain ice magic, probably because a hyper-detailed lecture segment on thermodynamics would scare their audience away. I, however, trust that my audience is made from sterner stuff, so here we go.
Ice powers are presented to us in various ways, but it is common to see characters freezing objects in their hands, firing jets of snow and ice from their palms, or creating ice formations in the air around them. Based on our key assumptions, this should only be possible if there is a sufficient amount of water available in their surroundings – and though this is believable in some cases, it is less believable in others.
One example of a ‘believable’ case is a scene in Frozen where Elsa runs across the surface of a lake, freezing the water beneath her feet. In this scenario, there is plenty of water available for her to freeze. All she has to do is lower the temperature of her surroundings by absorbing the heat, and the water will turn to ice, simple as that.
However, other presentations of ice magic are far less believable. Across the superhero genre, characters can summon icy weapons, shields, and platforms out of thin air, and in Frozen, Elsa manages to manufacture an entire palace made of ice. This type of magic will form the focus of the rest of this post, and my specific question is this: does air really contain enough water for superheroes to make icy objects?
Step 1: How watery is air?
The air around us contains water vapour, which is just water in its invisible, gaseous form. One way of describing this water content is the absolute humidity, often given as the mass of water within a cubic metre of air (e.g., 5 g/m3). However, there is a limit to how much water vapour the air can hold. If this limit is reached, the air becomes saturated, forcing any additional water vapour to condense back into liquid droplets. Therefore, another way of describing the water content of air is the relative humidity, which gives us an indication of how close the air is to being saturated (e.g., 80%).
The maximum amount of water that the air can hold depends on its temperature. Hot air can hold a lot more water than cold air; for example, air at 30 °C can hold a maximum of 30.34 g of water per cubic metre, but the same volume of air at 0 °C can only hold 4.85 g. Already, we can see that the temperature and the humidity of the air will limit the amount of ice that any given superhero, ice queen or wizard can draw from their surroundings.
Step 2. Getting water out of air
In order to get water out of the air, we can reduce its temperature. For example, if we take one cubic metre of saturated air at 30 °C and reduce its temperature to 0 °C, suddenly it can only hold 4.85 g out of its original 30.34 g. The excess 25.49 g of water vapour is forced to turn back into liquid – a process with which we’re all familiar, because this is what causes condensation to from on cold surfaces on hot days. Just by lowering the temperature of the air, our fictional characters can extract water, then freeze it.
Step 3. How much ice can we make?
The volume of ice that can be made depends on two things: the amount of air available, and its humidity. For most characters using ice magic, their area of influence is close to their body – probably not much more than a few cubic metres. In terms of the humidity of their surroundings, no character is likely to face temperatures higher than 40 °C, when each cubic metre can hold up to 51.08 g of water. This, then, provides a reasonable upper bound on the amount of ice we can extract. In fact, if our fictional character drops the temperature of their surroundings from 40 °C to -40 °C, they can take almost all 51.08 g of water out of the air.
Luckily, most icy characters are immune to feeling the cold, and they could put up with these ridiculously low temperatures. Once they freeze the water, the ice will expand by around 9%, meaning that each cubic metre of air would yield approximately 56 cm3 of ice. This (by rough estimation) is about the volume of a Mars bar. Slightly less than expected? That’s modern Mars bars for you.
Step 4. Reflect on the impossibility of Elsa’s ice palace
Even from optimistically humid starting conditions, our calculations suggest that thin air can only yield a measly amount of ice. This undermines many scenes involving ice magic, and none more so than Elsa’s castle in Frozen. In this case, the starting temperature of the air is unlikely to be much higher than zero, and so Elsa would only be able to extract up to 5.29 cm3 from each cubic metre. This is barely larger than a standard 4×2 Lego brick. Therefore, we can only conclude that she would be hard-pressed to finish anything larger than the Official Disney Ice Castle Lego Set 43197 by the time she has finished singing about letting go. And I don’t care if she’s the queen; she should have got planning permission for that castle before building it. It’s one rule for them, one rule for the rest of us…
Still, there are certain factors that could help our fictional characters out of their construction conundrums. Firstly, the air around them is unlikely to be stationary. Once they have extracted their measly Lego brick of ice, the depleted air will be blown away, and new, saturated air will be blown in to take its place. The speed at which they can construct icy objects will therefore be limited by the air replenishment rate – or, in other words, by the wind speed.
Step 5. Ice cubes in a hurricane
If the wind is blowing at 2 m/s (a gentle breeze), then each cubic metre of air surrounding our superhero/wizard/ice queen will be replenished every half-second (roughly). Just a breath of air movement will allow our characters to keep building, and their building rate will be controlled by the wind speed.
To take this example to the extreme, imagine our character in hurricane winds of 30 m/s, surrounded by fully saturated air at 40 °C. From these starting conditions, they could generate nearly 30 Mars bars of ice per second from each cubic metre of air within their sphere of influence. This would be an awful lot of Mars bars, and an impressive amount of ice, but as we know, most wielders of ice magic aren’t forced to rely on tropical hurricanes.
In fact, rather than icy characters gaining strength in hot, humid locations, they are often shown to become weaker. This suggests that reducing the temperature exacts too great a toll on their powers, or that their icy creations would melt too quickly. However, if lowering the temperature is no great object, then the best place to create sprawling ice objects would be the hot, humid tropics. The worst place for our character to end up would be a desert, with air devoid of water. If you took Elsa and Frozone on a trip to the dry valleys of Antarctica, they would be unable to make anything out of ice, unless they could extract the water from their own bodies. Even in such a cold location, they would be rendered powerless – but at least they wouldn’t be too fussed about the temperature.
In summary…
Even with exaggerated inputs into our calculations, the maximum volume of ice that can be drawn from thin air is much less than films, comics and anime would have you believe. Of course, it could well be that our initial assumptions are wrong. Perhaps these characters can create matter at a click of their fingers. Perhaps they are drawing water from a wider field than I give them credit for – and they might even be messing with molecular interactions and chemical reactions in ways that I (and probably their creators) hadn’t considered.
In any case, I hope you enjoyed this brief exploration into the infeasibility of ice magic. If you’re the type of person who enjoys an overly detailed magic system with a relatively robust physical basis, then I’ll point you politely in the direction of Highmoor, the first novel in a high fantasy series that I’m writing. It’s actually available for free on Amazon until the 28th August, so you can make the most of that offer if you move quickly. Happy reading, and I’ll be back with another post next week!
The more detailed maths…
To generate the figure above, I used the Buck equations, which relate the partial pressure of water vapour (i.e., the pressure the water molecules exert on their surroundings) to air temperature. There are two versions of these equations, for above and below 0 °C:
Pw (T>0 °C) = 0.61121 exp[(18.678 – [T / 234.5]) * (T / [257.14 + T])]
Pw (T<0 °C) = 0.61115 exp[(23.036 – [T / 333.7]) * (T / [279.82 + T])]
(Note that Pw is in kPa and T is in °C)
I then calculated the maximum water holding capacity of air by dividing the partial pressures by temperature and by the specific gas constant for water, which is 461.5 Jkg-1 K-1:
Max. holding capacity = 10^6 * Pw / (T * Rw)
(Note that max. holding capacity is in g/m3, and that Pw is still in kPa).
C. W. Clayton 