Hello readers! This is an old post that I unearthed while tidying up the blog, so I have streamlined the structure and removed the spelling errors in order to share it once again. These calculations come from June 2023, and were originally tied to a post that discussed the properties of lava. At the time, I was playing lots of The Legend of Zelda: Tears of the Kingdom, and the lava physics stood out to me as being particularly un-lava-like. There were a number of issues, including its suspiciously watery viscosity, but one particularly unlikely mechanic that caught my attention was the ability to form floating rafts of solid rock by spraying the lava surface with water.
Of course, lava-water interactions such as these are nothing new to video games. Those of us of a certain age will be very familiar with making obsidian in Minecraft by pouring buckets of water on lava. Similar water-lava solidification mechanics exist in 3D Mario games, older Zelda games, and even in Stardew Valley. But how feasible is this? Can you freeze the surface of a lava flow by using water, and could you use this as a pathway, or as a raft?
To answer these questions, I’m going to run some simple calculations for energy transfer between water and lava. This will give us some idea of how much water we need, how much solid rock we could produce, and whether it would be a good idea to stand on such a rocky crust if the opportunity arose (always no).
A warning before we go any further: I will be talking about some basic game mechanics from The Legend of Zelda: Tears of the Kingdom. I’m not going to mention the story, and I’ll only mention locations that have been established in previous instalments in the series.
Lava in Hyrule
I recently encountered my first lava in Tears of the Kingdom (henceforth abbreviated to TotK). It was displaying classic video-game-lava behaviour by flowing in a neat channel through a building, with a bright, incandescent surface of yellowy-red. It was very pretty and very fun, but it would have been neither of these things had realism played a role during game development. There are numerous problems with the lava depicted here – if it’s even lava at all.
The first problem with this lava is that it has a glowing surface that is entirely uniform across the channel. Real lava channels will rarely display glowing colours across their width, unless they are very close to the volcanic vent. This is because lava is incredibly hot (typically 1000-1200 °C for basaltic eruptions), and it loses huge amounts of heat from its surface via radiation into the atmosphere. When the surface cools down, it stops glowing; in fact, the yellowness of the lava is related to its temperature. The lava surface will develop a semi-solid crust very rapidly, which will hide the glowing material beneath. If you look at footage of lava flows (such as the recent ones in Iceland), you will often only see glowing lava at the edge of the channel, where the crust is continuously torn apart.
The second problem with this lava is how close we can get to it without burning. As mentioned, lava is incredibly hot. If it hasn’t developed a surface crust, then it will be radiating huge amounts of heat – plenty enough to give Link severe burns (Link is the main character, for those that don’t know). In real life, geologists have to dress up in reflective silver suits and use very long sticks if they want to collect samples from an active flow, but video games almost always ignore radiative heat loss. I can walk Link right up to the edge of the lava, and he doesn’t seem to be showing any ill effects. This game even has a temperature gauge in the corner, telling us that we’re still an appropriate level of cool (all thanks to Link’s fancy footwear).
There are other issues too, such as the lava splashing like water when we drop things into it (such as ourselves – oops), and the way that all the fluid in the channel moves at a constant speed, rather than moving fastest in the centre and slowest at the walls. I’d love to know what the walls and floor are made from, to withstand the temperature of the lava but remain cool enough for Link to stand on. However, these design decisions were almost certainly made to save the animators and programmers a lot of time and effort – because let’s face it, do we want the lava to be realistic, or to be fun?
The power of water
As in many games before, TotK features a mechanic whereby water can be used to cool down the surface of lava and form solid platforms. So, although radiative heat losses are entirely overlooked, water-driven heat losses are integral to the gameplay. The question is this: do the lava-water interactions occur in a physically justifiable manner? And if not, how far are they from reality?
The physical process of cooling lava with water feels very intuitive, and in terms of gameplay, it is a very rewarding mechanic. In nature, water can be an effective way of cooling molten rock; for example, lava erupted underwater loses heat far faster than lava on land, because water is very efficient at carrying heat away. Submarine lavas can sometimes cool down so quickly that crystals don’t have time to grow, which is how we end up with volcanic glass. If we’re feeling generous, then Minecraft’s obsidian formation is almost accurate. Almost.
Most games greatly exaggerate the power of water. In TotK, a fountain from a small hydrant can create a solid lava crust that is thick enough for Link to stand on without falling through or sinking. Remember, the water from the fountain not only has to turn the lava surface from a liquid into a solid, but then from a very hot solid into one Link can actually stand on without setting fire to his fetching furry footwear. Is this realistic? Let’s find out.
Changing state
What happens when we pour water on lava? Energy will be transferred from the lava into the water, so the lava will cool down. We want the lava to turn from a liquid into a solid, while the water heats up, turns to steam, and wafts away. These simple steps outline the problem that we are aiming to solve.
Let’s assume that we start with water close to its freezing point, around 0 °C. A very simple equation can tell us the amount of energy required to raise 1 kg of water to 100 °C. Another very simple equation tells us the amount of energy required to turn the 100 °C water into steam (see the Appendix for details). We find that turning 1 kg of near-freezing water into steam will take 2.7 MJ of energy from the lava. The next step is to calculate how many kilograms of water are required to bring the lava below its solidification point.
I’ll assume that our lava is starting at 1200 °C, and that it solidifies at 1000 °C. As such, we can calculate that 1 kg of lava releases 0.64 MJ when it solidifies. By taking a ratio of the energies exchanged by the water and lava, we find that 1 kg of near-freezing water can solidify 4.2 kg of lava. But this is only half the story.
Cooling down
Our previous calculations only bring the lava down to 1000 °C, which is far too hot to stand on (even with our sturdy but stylish boots). We therefore need to calculate the energy required to reduce the temperature of the solid lava from 1000 °C to 40 °C (again, see the Appendix for details). With this extra stipulation, we find that 1 kg of water can only produce 1.5 kg of rock cool enough for Link to stand on.
How much water do we need?
The lava platforms produced in the game appear to be about 2 m x 2 m in area, and around 0.2 m thick. If we assume the density of our lava to be 2700 kg/m3, the value for natural basalt, this means that it would take 1440 kg of near-freezing water to produce the platforms we see in the game. Does this tally with the flow rate of the tiny water fountains? It doesn’t look that way.
For illustrative purposes, let’s consider a UK fire hydrant, which has a minimum flow rate of 8 kg/s. At this rate, it would take 3 minutes to form our lava platform (actually, it would take much, much longer than this – but we’ll get to that in a minute). By our current calculations, we would require a flow rate of around 140 kg/s to get lava platforms spawning as fast as they do in the game. For comparison, the water cannons used to dispel riots are usually only 20 kg/s. The fountains in TotK could never freeze lava at the speed presented, unless they are emitting a liquid well below 0 °C, or the lava isn’t actually lava at all.
Some caveats…
Before you go running off to your nearest basaltic fissure with water buckets and heavy duty wellies, we need to discuss the limitations of our calculations. We made some heavy assumptions; for example, that all the energy from the water transferred cleanly and evenly into the lava. Unfortunately, this sort of energy transfer is implausible. Water will hit the surface of the lava, and once this goes solid, it will shield the molten material beneath it. The only way for the lava to keep cooling down is for heat to be conducted from its interior through the solid crust – and this will take a very long time, because the solid crust is a very good insulator. In short, we will be waiting much longer than three minutes for our lava crust to be thick enough to stand on (even if we used a water canon).
It is also very unlikely that we could generate a stable platform. The near-instantaneous conversion of water to steam often produces explosive results, which would launch fragments of lava considerable distances, as well as breaking up the crusts as they form. It would be very silly to stand close to this lava-water interaction.
One final issue worth mentioning is that once lava solidifies, it will have a higher density than the molten material around it. The only way that sinking would be avoided is if the platform incorporated a huge amount of steam on the inside – which might be possible, given the last point about explosivity. If the platform is 50% air pockets (like a really crunchy Aero bar), then it would only take 720 kg of water by our flawed calculations. However, the platform would have to contain significantly more bubbles than the lava around it in order to float. Link should tread with caution.
In summary…
Lava in video games rarely behaves like lava in real life. This is mostly because games are designed to be fun and engaging, which means that the more boring aspects of reality are dropped, while the exciting ones are exaggerated. However, I wonder if some of the physics are overlooked through ignorance rather than creative choice – after all, most people won’t have learnt about lava at school. Indeed, most people will have seen more fictional lava than real lava, and so their understanding and expectations are based on falsehoods, however fun and engaging these might be.
As always, you have to suspend your disbelief to enjoy video games, and the level of suspension depends on the game. For TotK, we must accept that Link can create a solid platform of basalt in ten seconds, step onto it without catching fire, and then sail it across a lake of lava. It is ridiculous, yes – but it is also a lot of fun. Thanks for reading, and have a lovely week!
Appendix:
The change in energy dE caused by a change in temperature dT is given by
dE = m*c*dT
where m is the mass of the object, and c is its specific heat capacity. The values of c for water and lava are 4200 J/kg K and 1200 J/kg K respectively.
The energy E required for an object to change state is
E = m*L
where L is the latent heat. The latent heat of vaporisation of water is 2.3*10^6 J/kg, and the latent heat of fusion for lava is 4*10^5 J/kg.
The energy required to raise 1 kg of near-freezing water to boiling point is 1*4200*100 = 4.2*10^5 J. The energy required to turn this boiling water into steam is 2.3*10^6 J, so the total energy needed is 2.7*10^6 J. This energy is going to be taken from the lava, cooling it down and turning it into rock.
Assuming that our lava is starting at 1200 °C, and that it solidifies at 1000 °C, the energy required to reduce 1 kg to solidification point is 1*1200*200 = 2.4*10^5 J. The energy released when it solidifies is 4.0*10^5, so the total energy released by 1 kg of lava is 6.4*10^5 J.
By taking a ratio of the energy required to turn water into steam, and the energy released on turning lava into rock, we find that 1 kg of water can solidify 4.2 kg of lava.
If we add the extra stipulation that the lava must cool from 1000 °C to 40 °C, we use the first equation again (1*1200*960 = 1.2*10^6 J). Therefore, the total energy required to bring 1 kg of lava from 1200 °C to 40 °C is 1.8*10^6 J, and by taking new ratios of the energies, we find that 1 kg of water can produce only 1.5 kg of cooled, solid lava.
C. W. Clayton 