biology, Dragons, physics, thought experiment

Dragon Metabolism

As you might have noticed, I have a minor obsession with dragons. I blame Sean Connery. And, because I can never leave anything alone, I got to wondering about the practical details of a dragon’s life. I’ve already talked about breathing fire. I’m not so sure about flight, but hell, airplanes fly, so it might be possible.

But I’ll worry about dragon flight later. Right now, I’m worried about metabolism. Just how many Calories would a dragon need to stay alive? And is there any reasonable way it could get that many?

Well, there’s more than one type of dragon. There are dragons small enough to perch on your shoulder (way cooler than a parrot), and there are dragons the size of horses, and there are dragons the size of cathedrals (Smaug again), and there are, apparently, dragons in Tolkein’s universe that stand taller than the tallest mountains. Here’s a really well-done size reference, from the blog of writer N.R. Eccles-Smith:

dragon-size-full-chart

The only downside is that there’s no numerical scale. There is, however, a human. And, if you know my thought experiments, you know that, no matter what age, sex, or race, human beings are always exactly 2 meters tall. Therefore, the dragons I’ll be considering range in size from 0.001 meters (a hypothetical milli-dragon), 1 meter (Spyro, number 3, purple in the image) to 40 meters (Smaug, number 11), and then beyond that to 1,000 meters, and then beyond to the absolutely ludicrous.

As a starting-point for my estimates, I’m going to take the path of least resistance: I’m going to assume that dragons are endothermic like humans, with a similar resting metabolism. For my calculations, I’m going to try out two different sets of assumptions. The first assumption relies on the “metabolic equivalent,” a unit which measures (approximately) metabolic output for various activities. It’s equivalent to 58.2 watts per square meter, and I’m just going to apply it to the approximate surface area of the dragon in question. To estimate that surface area, I’m going to calculate the surface area of its bounding box (the smallest box the dragon could squeeze into) and multiply by a correction factor (between 0.5 and 1), to account for the fact that dragons are less boxy and more round.

For the second round of calculations, I’m going to go by metabolic power per unit mass. My baseline is a 70 kg human with a 100-watt metabolism (the human body is pretty damned efficient, all things considered…), which comes out to 1.5 watts per kilogram. To get the mass, I’m going to find the volume of the bounding box, multiply by 0.8 (since, even packed tight, the dragon’s not gonna fill the whole box), and then multiply by 1 gram per cubic centimeter (the approximate density of ordinary tissue).

Pok, the Milli-Dragon

He doesn’t live by the sea. He lives in a wizard’s ear, because he’s only a millimeter long. I just made all that up, but it kinda sounds like something the late (aww….) Terry Pratchett would’ve come up with.

Either way, Pok weighs 800 micrograms, and only consumes between 1.2 microwatts (calculating by mass) and 52.5 milliwatts (calculating by surface area), which is less than the power consumption of an average LED. Worst-case scenario, Pok needs 0.00721 Calories per day (notice the capital C; it makes a difference). That comes out to a whopping 5 milligrams of lean meat per day. A literal morsel: a cube not even 2 millimeters across. Smaller than a pea. (For those interested in such details, I’m using WolframAlpha’s calorie values for goat meat, since goat is lean and lower in Calories than beef or pork, and will therefore give me upper-limit estimates. I’m also assuming a meat density of 1 g/cc.)

Pok is about the least-demanding pet you could ask for. Give him a cricket or a fly per day, and he’ll probably be happy. Whether you actually want a fire-breathing dragon that can fly into your ear (or nose, or lungs) is up to you.

Bok, the Chicken Dragon

Bok comes from mythology. She only appears once, in a written transcription of a proto-Norse folktale from Østergaard, a small island between Iceland and Norway, where she was the messenger and companion for Sköll, the sun-chasing wolf.

Nah. I’m kidding. I made that up. Sorry. Guess I’m in butt-head mode today…

Bok is the product of my damaged mind. She’s about the size of a chicken (or the size of a Microraptor, a cool four-winged flying raptor). Part of my life as a suburban farmboy (my life is weird) is spent tending to chickens. No microraptors, unfortunately. Either way, from that I know two things: 1) Chickens really like pecking humans in the ass, and 2) Chickens (and, by extension, microraptors) are about 30 cm along their longest axis, and perhaps 20 cm along their other axes. That makes for a surface area (after multiplying by 0.75, since none of my chickens are cuboids), of 0.240 square meters. That makes for an energy consumption (at rest, which means 1 metabolic equivalent) of 14 watts by area. I calculate Bok’s mass at 9.6 kg (21 pounds). That’s a lot heavier than most chickens, but I’m assuming dragons are going to be a lot denser than your average avian. Either way that makes for 14.4 Watts by mass. Vigorous activity (jogging, high-intensity cycling, very energetic sex, being Bruce Lee, flying around and breathing fire) consumes about 8 times as much power.

At rest, Bok runs at 14.4 watts (about the same as an LED lightbulb) and needs 297 Calories per day (208 grams, of meat). But if Bok spends 40% of her day running around like an idiot and biting things (which is what chickens do, in my experience), then I have to re-do the math. It’s easy: it’s basically just a weighted average:

297 Cal/day (at rest) * 0.6 (proportion of the day) * 1 (1 metabolic equivalent) + 297 Cal/day * 0.4 (rest of the day) * 8 (high-output exercise) = 1,128 Cal/day.

That’s 789 grams (a pound and a half) of meat per day. That’s more goat than you get in most curries, but it’s not ludicrous (although it’s almost as big as the alarming 48-ounce porterhouse steak). But seeing as Bok only weighs 10 kilograms at most, it’s not really that far off. I would guess my chickens eat at least a quarter of their own bodyweight in feed per day (plus table scraps, flies, dirt, poo, and any mice that happen to wander into the coop).

Spyro

I’ve never played Spyro. I never had a PlayStation. I’ve probably played about 45 minutes of Playstation 1 in my entire 28-year life. It seems like Spyro was a pretty cool game, though. I mean, at the very least, it’s got dragons, which counts for a lot in my messed-up ledger.

But I’m not here to talk about retro games. I’m here to talk about dragons. (I feel like a 10-year-old every time I say that.) From the comparison picture above, I’m putting Spyro at about 60 cm x 60 cm x 60 cm (he’s less elongated than most dragons). That makes for a surface area of 1.62 square meters, and a mass of 130 kilograms. His resting metabolism, therefore, is between 31.5 Watts (a third of a human’s) and 195 Watts (two humans’ worth). At rest, he’ll need up to 4,030 Calories per day. From here on out, I’m gonna assume 25% of Spyro’s day is spent in vigorous activity, so the weighted average gives us 11,082 Calories per day, which comes out to 7.75 kg of meat per day.

I’d like to detour for just a moment to talk about Michael Phelps. Never thought I’d say that… But anyway, according to Fox, Phelps’s diet during training racks up 12,000 Calories. Because I’m a bit of a pig, I’m jealous of his diet. I quote now (almost) directly from that article: For breakfast, Phelps has 3 fried-egg sandwiches with lettuce, tomato, and mayonnaise; 1 5-egg omelet; 1 bowl of grits; 3 slices of French toast with powdered sugar; 3 chocolate chip pancakes; and 2 cups of coffee. I’m jealous: that sounds like an amazing breakfast. But I’m not an Olympic swimmer, so if I went on the Phelps diet, I’d rapidly swell to fill the entire house.

Draco from Dragonheart

I love Dragonheart. It’s got everything I love about 90s fantasy movies. Whoever decided to cast Sean Connery as the voice of a dragon, I take my hat off to you. It’s a good thing they never made a shitty sequel, right? Right? RIGHT???

Ahem. Anyway, Dragonheart is probably one of the reasons I’m still obsessed with dragons to this day. In my mind, Draco is everything a dragon ought to be: he’s big, powerful, majestic, intelligent, and he’s got an attitude. To double-check the accuracy of that dragon-comparison chart, I’m imagining Draco holding Dennis Quaid in his mouth. No, that’s not a weird fetish (well, it probably is, actually, but it’s not my weird fetish). If you’ve seen the movie, you’ll know why. I think the chart might be low-balling Draco’s size a little bit. I’m going to say he’s as long as a shipping container. That is to say, 12 meters. (I’m now imagining a dragon with YANG MING tattooed on his side. I really need to get more sleep.)

Now, unlike Spyro, Draco is much longer than he is wide or high. Let’s say 6 m x 4 m x 4 m. You’ll notice I halved the length. That’s because, if he curled his tail up, he could fit in a box half his length. These are the kind of snap decisions you have to make in thought experiments. Anyway, that’s a surface area of 128 square meters (which is a power of 2, which is one of those things nerds like me can’t help but notice). He masses about 76.8 metric tons.That’s within the range of estimated dinosaur masses, which makes sense, since Draco is built like and about the same size as a large dinosaur.

Going by surface area, Draco is running at 7,450 Watts. Going by mass, he’s burning 115,200 Watts. You may notice a slight massive discrepancy. I’m more inclined to believe the 115 kilowatt figure, since that’s about the power output of a medium-sized car or truck engine. And a truck pulling a moderate load seems like about the kind of power a dragon would expend at minimal effort. This is complete guesswork, of course, but give me a break–I don’t have access to a dragon. Unfortunately.

Therefore, from now on, I’ll be dispensing with the metabolic equivalent model. There are three reasons: 1) I’m lazy, 2) It was already a stretch to apply that model to anything other than a human being, and I’ve already stretched way beyond that, and 3) Since, according to thought-experiment tradition, I’m working with pessimistic numbers, I’ve gotta go with the mass. The mass scales proportional to the cube of the length, while the surface area scales in proportion to the square of the length, so the mass is always going to be bigger from now on.

Anyway, getting back on track: Draco burns 115 kilowatts at rest. That’s 3,200,000 Calories. That’s a shade over 2,200 kilograms of goat. That’s a lot, but it’s not that unreasonable, if you think about it: it just means Draco has to eat one cow per day, or fifty peasants.

Of course, that’s only if he’s lying in his lair all day. Which he’s not doing, if he’s going out eating cows and peasants. Let’s dial back our numbers: let’s assume that Draco conserves energy (which he’d have to), and he only spends 1/8th of his day (12.5%) doing vigorous (8 times resting metabolism) exercise (chasing peasants, eating cows, menacing Dennis Quaid, making me cry). That’s 6,000,000 Calories per day. Now he needs 4,200 kilograms of meat per day. Two cows, four goats, maybe six sheep, or eighty-five peasants. (In a horrifying alternate universe, that’s the Michael Phelps diet.)

Smaug the Terrible

Do you have any fucking idea how much I was hoping for a movie adaptation of The HobbitThe Hobbit was my first taste of Tolkein, and in my mind, it’s still by far the best thing he’s ever written. The Lord of the Rings series were good books, and epic in the truest pre-Internet sense. But The Hobbit is better-paced, with a lighter-hearted style, less dense prose, and a grand adventure.

And do you have any fucking idea how disappointed I was in the movie adaptation? For one thing, it only needed to be one movie. Peter Jackson, I love you for the original Lord of the Rings trilogy, but I’m gonna shove a giant weta up your ass for trilogy-ing The Hobbit. The dwarves were ridiculous and the movie was too damn long, too grim, and paced pretty badly, compared to the book. At least, I think so. I haven’t taken any pains to remember the movie, partly because I was really bored with Peter Jackson Peter Jacksoning so hard.

Okay. Hold on. Give me a moment…

Okay. I’m back. I spent fifteen minutes swearing, punching walls, and popping blood pressure pills. But I’m done ranting now. For real. This isn’t gonna be one of those comedic endings where I’m done ranting right until the end, when I suddenly shout “MOTHERFUCKER!” like Samuel L. Jackson, and start cappin’ fools. I’m not here to complain about movies. I’m here to be happy about dragons.

Anyway. Here’s a picture of Smaug (from the movie) preparing to mate with a 747.

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(Source.)

Okay, okay, he’s not actually going to boink the 747. (Not that far-fetched, though, according to the Internet. If you’re brave, and over 18, and it’s legal for you to look at dirty pictures, and you’re not at work, and you’re morbidly curious like me, Google “dragon car sex”.)

Sorry. Got distracted. Stupid Internet. Anyway, a 747 is about 70 meters long. Smaug’s a little longer than that. Say 100 meters, with a 75-meter-long bounding box. The cabin is around 6.5 meters in diameter. Looks to me like Smaug is wider than the cabin, but probably not too much wider than the landing gear. Let’s say his smallest dimension is 15 meters. His mass, therefore, is 0.8 * 75 meters * 15 meters * 15 meters * 1 g/cc = 13,500 metric tons, or 13.5 million kg. At 1.5 Watts per kilogram, he has to produce 20.25 megawatts just to stay alive. No wonder Smaug spent so much time hanging out in his lair. We’ll use the same figures we used for Draco: 7/8ths of his time, he’s just lying around; the other eighth, he’s doing vigorous 8-metabolic-equivalent activity. That almost doubles his energy demand, from 20.25 megawatts to 30.8. There aren’t many powerplants that have been built that can deliver that much power in such a small space. To give you an idea of Smaug’s energy needs, he’s gonna need at least one Los Angeles-class submarine nuclear reactor. His Calorie requirement comes to 785 million Calories per day. Remember back in the day, when McDonald’s restaurants used to have that “Over 1 Billion Served” thing on their billboards? Well, they could’ve supplied a few thousand dragons at best, at that rate. Although, given my experiences with McDonald’s food, we’re gonna have a few thousand dragons with diarrhea, which is another kind of nightmare altogether. So let’s not feed our dragons cheeseburgers. Let’s feed them goat. Here’s where the trouble starts. He needs 550 metric tons of goat. That’s 275 cows a day, or over 11,000 peasants. No wonder everybody wanted Smaug dead. He needs nine shipping containers stuffed full of meat every single day. There’s a reason he created a whole patch of desolation, I suppose.

Before I move from the slightly-ridiculous to the completely ridiculous, let’s talk about heat. As Randall Munroe of XKCD pointed out (much more eloquently, to nobody’s surprise), if you’ve got a certain amount of power being generated in a system, that amount is eventually going to have to leave that system as waste heat.

Smaug needs 20.25 Megawatts. Smaug’s bounding box has a surface area of 4,650 square meters. I’m not going to multiply by 0.75, because when it comes to radiating heat, he’ll have his tail extended, and so he’s better approximated as a cuboid than as a compact cylinder. It’s the same reason my chickens hold their wings out when it’s really hot: expose more area to radiate more heat.

Smaug’s in trouble: he’s gotta radiate 4.4 kilowatts per square meter, which means his skin’ll be so hot that you could cook a steak on his back or, if you’re living in a Ray Bradbury nightmare, use him to set books on fire.

But I’m neglecting another important factor: those wings I was talking about. Dragons have big membranous wings, stretched with skin. Just like elephants’ and rabbits’ ears, that skin makes for an ideal radiator. From the image, I’ll guess that Smaug’s wings, fully extended, are 100 meters from root to tip and have a mean chord (width) of 50 meters. That’s 5,000 square meters. I’m going to multiply that by 0.75, because Smaug’s wings have those little concavities at the back (there must be an anatomical name for those…), so they’ll have a smaller area than the rectangle that contains them. Still, that’s 3,750 square meters. Actually, it’s 7,500, since both the top and bottom can radiate. That gives a total wing surface area of 15,000 square meters. That lowers his radiant flux to 1.35 kilowatts per square meter, and his skin temperature to a still-lethal but more sensible 120 C. He’s gonna need a lot of frills up and down his back to dissipate the remainder, but it’s probably doable. He’s certainly gonna have to be able to run hot, though: he’s likely to build up heat in his interior, since it can’t be transported instantly to his surface. Maybe that’s why dragons breathe fire: a weird cooling system.

Zil the Nightmare

There are no pictures of Zil. Not because he’s some sort of Lovecraftian abomination, but because I just made him up, and as you’ve already seen, I can’t draw dragons to save my life.

Zil is the last thing you want to see looming over your village. Here’s what he looks like about to eat a 747:

Zil vs 747

(Dragon silhouette is from deviantart; plane silhouette is royalty-free clipart.)

Zil is horrifying. You can’t kill him. Not because of protective magic or anything, but because no medieval projectile can penetrate far enough into his body to hit a vital organ. You’re gonna have to wait until you’ve developed gunpowder and/or railguns to take him down, and do you really think a dragon this size is gonna give you the chance to develop gunpowder and/or railguns?

Fully extended, Zil is 1,000 meters long. Squished into his bounding-box, he’s only 750 meters long (yet again, “only”). A 747 has a wingspan of 64.4 meters, and from the picture, Zil’s body is much wider than that. Let’s say 150 meters, since he’s got a lot of tail and wings to squish in there. He’s got a total surface area almost the size of Vatican City. He masses 13.5 million metric tons. Heavier than any aircraft, train, or ship we’ve ever built. Heavier than the Great Pyramid of Giza. Heavier than most skyscrapers. That’s a lot of dragon (which sounds like a gross innuendo). How much energy does he need?

Well, at 1.5 watts per kilogram, that’s 20.25 gigawatts. Feel free to insert your own Back to the Future joke. He needs almost as much power as China’s massive Three Gorges Dam produces. That’s over 20 modern CANDU nuclear reactors, or ten large coal-fired power plants. Zil’s definitely not gonna want to be active more than 1/8th of the day. Actually, because he’s a big beast and he doesn’t wanna die of overexertion, let’s say he restricts his vigorous activity to 1/10th of the day. His power requirement then becomes 34.43 gigawatts. That’s 711 billion calories per day. Evey day, Zil needs the equivalent of 709.8 kilotons of TNT, which is 47.3 Hiroshima bombs. Every damn day.

My intuition tells me there’s no way a creature like Zil could survive. Not with a human-type metabolism, anyway. But, for completeness, I’m going to go ahead and do the numbers for his food intake. He’s going to need 497,200 metric tons of goat per day. If you want to feed him (although why would you? He’s a civilization-killing nightmare! You monster!), you’d have to deliver his supper in a converted supertanker. He’s going to need almost a quarter of a million cows per day, or almost 10 million peasants. If he lived today (which he doesn’t. You can tell by the fact that you’re not dead), he’d eat the entire human population within two years. But you might have noticed there aren’t many dragons around now. Judging by fantasy tropes, I’d guess that the last dragons died out around 1300 AD (or CE, or whatever the hell you want to use…why are there always so many damn units and suffixes?) According to the U.S. Census bureau, there were less than half a billion people on Earth in 1300. Zil could very easily have eaten the entire human population in two months. An animal that size is the ecosystem equivalent of a black hole: it just dominates everything in the vicinity.

Zil’s planform area (the area of his silhouette) fits into a square 750 meters by 750 meters. I’d say he fills that square halfway, so his planform area is 281,250 square meters, and his total radiating area (excluding things like frills, but including the wings) is 562,500 square meters. To get rid of all that heat, he’s going to have to radiate at 619 C, which is almost hot enough to melt aluminum. He’d glow a dim cherry-red. You could probably forge steel just by sticking it in his mouth (although you can only do that once). Not that it matters: he’s already eaten you.

Ridikulaus, the Mountain

Ridikulaus is another dragon I made up. Sitting up, he stands 12 kilometers tall. Why 12 kilometers? I dunno. Why am I 0.00185 kilometers tall?

Okay, okay, the real answer is that, above 12 kilometers, the air gets very, very cold and very, very thin, and there aren’t many large organisms (humans and their balloons and shit aside) that fly that high, even briefly. I don’t want Ridikulaus to suffocate every time he sits up.

His bounding box is 12 kilometers long (naturally) and 1.2 kilometers wide and high. He weighs 12.96 trillion kilograms, or about 13 billion metric tons. He makes up over one-eighth of Earth’s total biomass (including ridiculously prolific critters like bacteria, krill, and algae). He needs 19.44 terawatts of power, which is quite a bit more than all of humanity is using at the moment. That would put him at a 0.72 on the Kardashev scale (which is a nifty unit used to measure the level of development of advanced civilizations, by power consumption). That is to say, he needs more power than our power-hungry 2016 information-age civilization. How many Calories per day is that?

Well, it’s kinda silly to use a unit like Calories on this scale. But when have I ever had a problem with silliness? That’s 401.5 trillion Calories per day. That’s a quarter of a billion metric tons of goat meat every single day. That’s over 140 million cows per day, or 5.6 trillion peasants. Which is a shame, because even though most human beings who ever lived were peasants (in the sense of being subsistence farmers), they only total up to something around 100 to 200 billion. Ridikulaus really is a destroyer of worlds. Not in some vague cosmic sense or in the sense of a nebulous magical evil. He’s a destroyer of worlds because he fucking eats them barren. Oh, and by the way, his skin is hotter than a bonfire and glows a bright red-orange, and can burn a person to death by radiant heat alone. You know, in case things weren’t bad enough.

Hjúki, Daughter of the Moon

Hjúki’s one of those mythological figures that frustrates me, because she’s interesting (being the daughter of Máni, the Norse personification of the Moon), but there’s almost nothing written about her. All we know from the Prose Edda is that Hjúki is the dragon whose egg is the moon, and who will hatch at the time of Ragnarök, and will go on to slay one of the Norse gods, although the Prose Edda doesn’t say which one. It just calls her “god-slayer.”

Oh, sorry, did I say Norse mythology? I meant “bullshit I made up.” I know it makes me look like a slimy jerk when I do that, but I didn’t do it to trick you. I did it because, cool as Norse mythology is, I think my version’s cooler. And if stealing from the lumber-rooms of mythology was good enough for Terry Pratchet (his words), then it’s good enough for me. So, Norse mythology, I’m stealing your cool names and your grand themes and outlandish gods, and I’m putting them into my own bizarre mythology. A mythology in which Hjúki is the dragon who lives inside the moon, and is waiting for the Last Day to come up on the calendar, so she can hatch and come eat the Earth.

I know it’s absurd to try and work out her metabolism. I mean, come on, she’s so big she’s got her own surface gravity. Her greatest enemy wouldn’t be medieval warriors on horseback. It’d be hypervelocity space junk. But what the hell, I’ve come this far. Might as well finish.

I’m going to skip the whole bounding-box thing. Hjúki lives inside the moon, so I’m just gonna say she makes up 90% of the Moon’s mass (she’s very dense, for a dragon). That’s 66 billion trillion kilograms. At a human metabolic rate, she needs 99 billion terawatts. She’s not consuming nearly that much right now (in my imaginary mythological world), because she’s deep in hibernation. Human beings have yet to discover her, although they’ve gotten clues, in the form of peculiar mass concentrations beneath the lunar surface, which make low lunar orbits unstable. When she wakes, though, she will burn hotter than the sun (over 15,000 Kelvin). Just looking at her will blind you, and standing near her will scald you to death in seconds. She eats her own weight in matter every day, so once she hatches, she’ll devour the Earth within three months.

Actually Hjúki fits pretty well into both Judaeo-Christian and Norse mythologies: an awe-inspiring being of light who can destroy the whole world with little to no effort. Who burns bright enough to blind, and who descends without mercy on all people, regardless of race, sex, age, or wealth. A final judgment.

Don’t worry–I don’t take myself nearly that seriously. I’m just enjoying weaving a mythology around a planetoid-sized dragon. Although, you’ve gotta admit, Hjúki’s more plausible than a lot of that weird-haired guy on Ancient Aliens says…

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2 thoughts on “Dragon Metabolism

  1. Heat dissipation sounds like the reason dragons breathe fire. Of course it might be some kind of hypergolic reaction, but venting excess metabolic heat is more likely! 🙂

    • Of course, natural selection really likes multiple-purpose solutions, so it could be a bit of both: The dragon expels air, and glands mist that air with a volatile liquid which evaporates and carries off heat. And, since a lot of volatile liquids are highly flammable, it just ignites the vapor to get a second use out of it 😀

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