THE SCIENCE OF DRAGON FIRE IN GAME OF THRONES
Warning: this article contains spoilers for the final episode of Game of Thrones. If you don’t already know why Bran Stark came all this way, turn back now.
It’s been a while now since Game of Thrones aired its blazing, tyrannical, and controversial finale. Even before the molten slag that used to be the Iron Throne was able to cool, fans around the world flooded the internet with their myriad opinions of the episode and the show as a whole. Reactions to the final season can safely be described as conflicted, with many fans angry over what they consider bad writing or inconsistent character choices. What everyone can agree on is that the show gave its viewers a visual spectacle unlike any other show on television.
Let me start by being upfront: I love Game of Thrones and it is very easy for me to suspend my disbelief to enjoy the magic-filled story it tries to tell. Despite my buy-in as a lifelong fan of fantasy and storytelling, I still find myself viewing aspects the the story through a scientific lens. Even the most directly magical parts of the show aren’t immune; in fact, they might be the most fun to deconstruct! There was an especially dramatic moment in the finale that blew me away and left my mind racing for the weeks that followed. The now iconic scene in which Drogon, enraged by the death of Daenerys, unleashes his fiery wrath upon the Iron Throne and reduces it to a smoldering puddle immediately caught my attention as a great chance to learn exactly how powerful dragons in this story can be. So, what does science have to say about the most fearsome creatures in Westeros? Let’s find out.
It’s All About Mass
I know what you’re probably thinking. “We saw him destroy an entire city single handedly and you’re stuck on melting a pointy chunk of metal?” and my answer is, yes! Not because it simply looked cool–though it definitely looked cool–but because I realized that I could use this clip and a bit of thermodynamics to discover just how terrifyingly powerful a dragon’s fiery breath really is.
Before we can learn anything about the dragon fire, we must learn about the Iron Throne itself. According to show legend, the throne was forged from the 1,000 swords that the first Targaryen King, Aegon the Conqueror, took from the lords he defeated in battle. Littlefinger of course claims there aren’t even 200 blades. The actual number of swords in the Iron Throne doesn’t much matter for our purposes; we will need to assume that the name isn’t a complete misnomer and that the throne is basically pure iron (After all, it isn’t called the 0.5% Carbon Steel Throne). Knowing the material is a vital step because it gives us much-needed information on the physical properties of the throne—density, melting point, etc. But we’re getting ahead of ourselves. Before we can use any of this information we need to know something else: Exactly how massive is the Iron Throne?
The easiest way to find this out would be to get the throne itself and just weight it, but I see some issues with that plan and 99% of them are that it doesn’t exist. The next best thing is to get a replica of the throne, find out how big it is, and then calculate how much something the same size made of iron would weigh. We’re in luck, too! HBO actually sells a full-size replica of the Iron Throne and it only costs…$30,000. Okay so scratch that plan. Let’s go with something more budget friendly. How about an officially licensed 4” scale replica of the throne that only costs $30? This should work just fine (note: don’t try explaining to your significant other that this a great deal because technically you’re saving $29,970).
You may be thinking at this point, “That’s cute and all, but how is this tiny thing going to help us know anything about the real Iron Throne?” Well, I’m glad you asked! We can measure the volume (the amount of 3-dimensional space an object occupies) of this model and scale it up proportionally to find the volume of the bigger version.
We’ll do this by using an old, reliable scientific technique called the water displacement method. It’s a great way to find the volume of solid objects that have complex, irregular shapes like the throne. The theory behind the technique is simple: when you submerge an object in a liquid, it displaces a volume of liquid equal to the volume of the object. You experience this phenomenon when you climb into a bathtub and notice that the water level rises as you put more of your body under the water. It was this exact experience that allegedly made Archimedes shout “Eureka!” as he came to this realization. In the pictures below, notice how the water level inside the beaker rises considerably after we submerge the model in it.
(3) Water is moved from the beaker to the graduated cylinder until it is back to the original level.
Then we remove water until it’s back to the original water level. The amount of water removed—shown here in the graduated cylinder to the left—is equal to the volume of the scale model. The graduated cylinder has more precise measurements than the beaker and using it we can see that the amount of water displaced by the throne is almost exactly 75 milliliters (mL)–for water, 1 mL is equal to 1 cubic centimeter (cm3)–so the volume of displacement is 75 cubic centimeters (cm3) and therefore our scale model of the Iron Throne has the same volume. From now on we are going to call that value V1.
Our next step is to use our measurement to calculate the volume of the full-size throne which we will call V2. Measuring the height of our scale model we see that it is 9.37 centimeters tall–let’s call that value L1. Thanks to this awesome diagram, we know that the actual Iron Throne is 2.18 meters tall–this value can be called L2. That gives us a scale ratio of about 23.27:1 where for every centimeter of height of our model, the full-size throne has 23.27 centimeters of height. In short, the real throne is 23.27 times bigger than our model.
It would make sense then that V2 would be equal to 23.27 times the V1 right? Well it turns out that doesn’t really work. That calculation would just be us finding the volume of 23.27 of our scale models stacked on top of one another.
Despite maybe making sense at first glance, that calculation doesn’t work for us because we are trying to find out the Iron Throne’s size in three dimensions and that means we must use a mathematical principle called the Square-Cube Law. The law can be summed up like this:
When an object undergoes a proportional change in size, its new surface area is proportional to the square of the multiplier and its new volume is proportional to the cube of the multiplier.
Mathematically it looks like this:
If we plug in our measured values to the above equation, we find that V2 = 0.946 m3. There it is, the volume of the actual Iron Throne! The next step is to use that to find out the mass of the throne, which isn’t too difficult if we use the following equation where m is the mass of the throne, D is the density, and V is the volume:
The density of Iron 7.874 g/cm3 and we just found that the volume of the throne is 0.946 m3 so if we plug in those values we find at last that the Iron Throne is a hefty 7,446 kg (16,415.64 lbs). That’s an insanely heavy chair! It’s over four times as heavy as the average American car and it even outweighs an African bush elephant, which Cersei was ever so disappointed she didn’t get to see.
This gives us everything we need (mass, material, melting point) to calculate the energy Drogon released when he destroyed the throne.
Burn Baby Burn
In normal, solid metals the atoms are arranged in a 3-dimensional crystalline structure in which each atom is constantly vibrating in every direction. That motion has energy and when we take the average of that energy in an object, we call it temperature. When you add more energy to this structure in a form such as heat, these atomic vibrations will increase along with the temperature of the solid. If you continue adding energy, the atoms will eventually vibrate so much that the bonds between them begin to break down. The atoms that were rigidly held together in place by these bonds are able to move more freely around each other. This is what is happening when an object undergoes a phase change from solid to liquid.
The amount of energy that these structures can store depends on the atoms and the connections between them and can vary wildly between different substances. The energy per unit mass required to raise the temperature of an object by one degree Celsius is called its “Specific Heat Capacity” and is mathematically represented by the letter c.
However, simply heating a solid to its melting point is not enough to turn it into a liquid; there is an additional energy input required to induce a phase change from solid to liquid or a liquid to a gas. You’ve probably noticed that when you step out of a shower you usually feel cold. This is due to the water on your skin evaporating. The water droplets are absorbing the heat needed for this phase change from your skin (the same process our bodies use to cool off on a hot day by sweating). The energy per unit mass required to change a specific material from the solid to liquid state is called its “Latent Heat of Fusion,” and is mathematically represented by the letter L.
Now that we know the theory behind them, here are two simple equations that we will use. In these formulas, Q is the energy and ΔT is the change in temperature.
The first is the Specific Heat Formula, which will tell us how much energy it would take to heat the Iron throne from room temperature (20 °C or 68 °F) all the way up to the melting point of iron (1538 °C or 2800 °F). The second is the Phase Change Formula, which will tell us how much energy it would take to change the throne from solid to liquid. Using the mass for the Iron Throne we calculated in the previous section and the thermal properties of iron that I found on this site, we find that the amount of energy required to completely melt the Iron Throne is 6.81 billion (1,000,000,000) joules or 6.81 gigajoules (GJ). Whoa.
Drogon has more energy than a bolt of lightning inside of him; the average lighting bolt only contains 1 GJ of energy. A ton of TNT releases 4.184 GJ when it explodes and under controlled conditions a single kilogram of TNT can completely destroy a small vehicle. A 125-ton Boeing 767-200 flying at 192 m/s (≈ 430 mph) has 3 GJ of kinetic energy. The energy that Drogon emits when destroying the throne is over three times more than the payload of a Tomahawk Cruise Missile! Dragons are weapons of mass destruction indeed.
What makes Drogon’s feat even more impressive is how quickly he accomplished it. Drogon managed to completely melt the Iron Throne in just 30 seconds. In physics, the amount of energy transferred per unit time is called power. Drogon’s power output is at least 227 megawatts, enough to power tens of thousands of homes. You could harness his fire and it would be enough to power the Large Hadron Supercollider (the largest machine in the world) AND the entire CERN facility at peak usage! It also appears that dragons in Westeros are able to breath fire for extended periods of time without much of a problem. They are basically small, mobile coal power plants that run on sheep.
Who would’ve thought that anything could make dragons more impressive than they had already proved to be? In a show where we’ve seen them destroy entire armies, cities, and even a giant magical ice wall, we couldn’t appreciate their true power until now. With an immense supply of energy stored inside them, the technological applications of dragons are far more valuable than anything destructive. It turns out Daenerys was using her dragons all wrong! Instead of using them to burn her enemies, she should have hooked them up to a heat engine and they could have provided electricity to all of Westeros. It would have had a happier ending, at least.
To continue learning:
Heat vs Temperature: https://bit.ly/2oYYWBm
Specific Heat Capacity: https://bit.ly/1nc2dUS
Heat Capacity and Melting Points: https://bit.ly/2p9TDfh
Latent Heat of Fusion: https://bit.ly/1h9SgH1
Thermal Properties of Iron: https://bit.ly/2FhtwN6
Calculation: https://bit.ly/31H7IEu
