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The Physics of Dragonfire

Last year, I wrote a post about the physics of the plasma-temperature dragonfire from Dwarf Fortress. Today, because my frontal lobes are screwed on backwards, I wanna work out whether or not biology could produce a plume of 20,000-Kelvin plasma without stretching credibility too far. I have a hunch that the answer will be disappointing, but my hunches are usually wrong. Must be those faulty frontal lobes.

The first thing we need to work out is how much power we’re going to need to heat all that air. Let’s say dragonfire comes out of the dragon’s mouth at 50 meters per second (111 mph, about as fast as a sneeze or a weak tornado). As a rough approximation, let’s assume that a dragon’s mouth has a cross-sectional area of about 0.0600 square meters (about the area of a piece of ordinary printer paper). This is one of those nice situations where we can just multiply our two numbers together and get what we’re looking for: a flow rate of 3.120 cubic meters per second.

So here’s what we know so far: we’ve got a dragon breathing 3.120 cubic meters of air every second. That air has to be heated from 300 Kelvin (roughly room temperature) to 20,000 Kelvin. The specific heat capacity of air is close to 1,020 Joules per kilogram Kelvin over a pretty wide range of temperatures, so we’ll assume that holds even when the air turns to plasma. That means that every second, our dragon has to put out 79.96 million Joules, or 22.2 kilowatt-hours. But we’re not talking about hours here. We’re talking per second. That’s 79.96 megawatts, which is almost twice the power produced by the GE CF6-5 jet engines that power many airliners. That’s a lot of power.

But, much to my surprise, there are some fuels that can deliver that kind of power. Compressed hydrogen burning in pure oxygen could do it. Except I’m basing that assumption entirely on the power required. There’s a lot more physics involved than that. The highest temperature that a combustion reaction can reach, assuming no heat loss, is called the adiabatic flame temperature, and although this is an impressive 3,500 Kelvin for a well-mixed oxy-hydrogen flame, that’s nowhere near the 20,000 Kelvin we need. The only fuels with higher energy densities than hydrogen are things like plutonium and antimatter, and for once, I’m going to be restrained and try not to resort to antimatter if I don’t have to. Let’s see if there’s another way to do it.

In my previous post on dragonfire, I described Dwar Fortress’s dragon’s-breath as a medieval welding arc. So to hell with it–why not use an actual welding arc to heat the air? Well, it turns out that something like this already exists. It’s called an arcjet. Like VASIMR, it’s one of those electric-thruster technologies that has yet to get its day in the spotlight. But arcjets have found another purpose in life: allowing space agencies to test their reentry heat shields on the ground. Here’s a strangely satisfying video of one such arcjet heater being tested on an ordinary metal bolt:

That certainly looks like how my brain tells me dragonfire should look, but from a little research, it seems that the Johnson Space Center’s arcjet only puts out something like 2 megawatts, thirty-five times less than the 79 we need. According to these people, the arc in an arcjet thruster can reach the 20,000 Kelvin we need, but it seems pretty likely that the actual plume temperature is going to be a lot lower.

And besides, our dragon’s powerplant has to be (relatively) biology-friendly, since it has to be inside a living creature. The voltages and currents needed to run an arcjet would probably make our dragon drop dead or explode or both.

So, as much as I hate to do it (I’m kidding; I love to do this) I’ve gotta turn to antimatter.

Antimatter is the ultimate in fuel efficiency. Because almost all of the universe is made of matter (and nobody really knows why), if you release antimatter into the world, it’ll very quickly find its matching non-anti-particle and annihilate, producing gamma rays, neutrinos, and weird particles like kaons. The simplest case is when an electron meets a positron (its antiparticle). The result is (almost) always two gamma rays with an energy of 511 keV, meaning a wavelength of 2.4 picometers, which is right on the border between really high-energy X-rays and really low-energy gamma rays.

This presents yet another problem: hard x-rays and soft gamma rays are penetrating radiation. They pass through air about as well as bullets pass through water (which isn’t an amazing distance, I’ll admit, but I’m still not about to sit in a pool and let someone shoot at me). At 511 keV and ordinary atmospheric density, the mass attenuation coefficient (which tells you what fraction of the radiation in question gets absorbed after traveling a certain distance) is in the neighborhood of 0.013 per meter, which means a beam of 511 keV photons will get 1.3% weaker for every meter it travels.

Working out just what fraction of these photons need to be absorbed is a bit beyond me. If the radiation has to be 1,000 times weaker, it’ll have to pass through 1.6 meters of air. That sounds to me like it’d be enough to burn our dragon’s tongue right off. And indeed, if we run the equation a different way, we see that, after traveling through 30 centimeters (about a foot) of air, the gamma rays will still have 25% of their original strength. I’m trying very hard not to imagine what burning dragon teeth would smell like.

But there’s no reason our dragon has to be making its death-dealing plasma out of air. Water is the most common molecule in biology, so why not use that instead? A 511 keV photon can still travel over 10 centimeters in water, but that’s a heck of a lot better than the 150 centimeters we were looking at before.

Of course, we can add a dash of metal atoms to the mix to absorb more of the x-rays and protect our poor dragon from its own flame. The heaviest metal found in organisms in large quantities is iron, usually in the form of hemoglobin. So let’s just throw some hemoglobin in that water, handwave away how the dragon is producing so many positrons, and call this experiment a success.

Well, it’s not a total success, since what I just described is essentially a dragon vomiting a jet of blood and then turning that into scalding-hot plasma. No wonder everybody’s scared of dragons…

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The Phantom haunts the CT scanner.

In a previous post, I mentioned how cool it was that “The Curse of Dimensionality” is actually a legitimate phrase used in computer science. You know what else is a cool and entirely legitimate phrase? Nothing can prepare you:

X-ray Phantom

That sounds incredibly creepy. It sounds like an alien menace out of the best kind of terrible mid-’80s sci-fi. Just say it out loud: “X-ray Phantom.” A creature built from photons which can pass through anything less substantial than ten centimeters of lead and can burn the skin from your flesh if it touches you.

But if there are any radiologists reading this, then you already know what an X-ray phantom is. And you already know that it’s creepy enough without any sci-fi embellishment whatsoever. People of a nervous disposition, don’t look down:

(Source)

An X-ray phantom is a model designed to match, as closely as possible, the structure and density profile of the human body. Since X-ray phantoms are standardized, if you put one in a CAT scanner and get a different picture than you expected, you know it’s a problem with your scanner, not the subject. Plus, I imagine they’re very helpful for radiology students, since they let them practice scanning things without irradiating actual people for no reason, which is a pretty rude thing to do.

But I can’t think about how useful X-ray phantoms are. I can only think about how fucking creepy they are:

(Source)

I don’t know about you, but I’m getting a kind of RealDoll vibe from this one. Except it looks less like a RealDoll and more like one of those horrifying budget sex-dolls you see if you wander into the wrong side of the Internet. You know, the kind that consist of a disembodied silicone pelvis with nothing but genitalia. Except I wouldn’t recommend using an X-ray phantom as a budget sex doll, because according to the seller of that last one, the bastard costs 18,900 Euros. Dear oh dear.

But the horrifying perverse vibe I get from that X-ray phantom is nothing, nothing at all, a drop in the bucket, an atom in a star, compared to the horrifying perverse vibe I get from our last phantom. Children and people with weak constitutions, do not look down:

(Source)

This is an X-ray phantom used in dentistry. But I cannot look at this phantom without first bursting into laughter and then running screaming from the room. I know without a doubt that senior dental X-ray technicians, when they’re working with the trainees, leave this suitcase sitting in the corner without comment, and then, suddenly open it and fold the head out and slam it on the table to see if they can make somebody in the audience pee in their pants.

What I want to know is: who looked at this thing and didn’t think “That’s the creepiest thing since that My Little Pony sex doll”? (Google that if you dare.) It looks like The Giant from Twin Peaks having the best orgasm of his life. Whether that orgasm is related to the creepy rubber phallic thing (which is apparently for holding X-ray film) I don’t know. And I don’t really want to know. But one of the other pictures on the distributor’s website pretty much closes the case on this one:

There are no words.

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