physics, silly

Diets

The 5/2 Diet: Eat as you normally would five days out of the week. Fast (consume no more than 500 Calories) the other two days.

The “Ketosis Diet”: Eat no more than 1200 Calories per day.

The Michael Phelps: Eat no fewer than 12,000 Calories per day.

The ultra-python: Eat normally until age 18. Then, eat 95,000 club sandwiches (36,000 kilograms, 45,291,000 Calories). Fast until age 80.

The that’s-not-how-that-works diet: Eat normally. Following every meal, eat 5 grams of Americium-241. Mix with water or orange juice if desired. Continue until you develop a mutation which allows you to harness radiation directly as an energy source.

The gluten-free-free diet: Not only are you forbidden from eating foods that don’t contain gluten, you must eat lab-grade purified wheat gluten for every meal. Variation: For sufferers of Celiac disease, you may substitute wheat gluten.

The that’s-also-not-how-that-works diet: From Monday to Sunday, you are only permitted to drink that coffee that they dig out of cat poop. On Sunday, eat 134 bananas, in order to reach an average of 2,000 Calories per day.

The Nibbler: Eat four 250-Calorie meals spaced evenly throughout the day. Eat 10 50-calorie snacks, similarly spaced. One of your snacks must be a large pebble.

The Extreme Nibbler: Eat the following meals on a repeating cycle: 10 milligrams sirloin steak, 20 milligrams potato, 100 milligrams spinach. Eat one meal per second throughout the day. If you require sleep, hire a patient Irishman to feed you your meals during the night.

The Heat Death:
Week 1: Eat 2,000 Calories per day. Your Calories should consist of 40% protein, 40% carbohydrates, and 20% fat.
Week 2: Eat 1,500 Calories per day. Your Calories should be divided the same as before.
Week 3: Eat 750 Calories per day. Your Calories should consist of 50% protein, 40% carbohydrates, and 10% fat.

Week 520 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000: Consume radio photon per day. You may consume any photon you like, as long as its wavelength is in the VLF band or lower. If you find this step difficult, you may consume a single lepton once per week. If you can find one anywhere in the diluted, pitch-black expanse.

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Death by Centrifuge

WARNING! Although it won’t contain any gory pictures, this post is going to contain some pretty gory details of what might happen to the human body under high acceleration. Children and people who don’t like reading about such things should probably skip this one. You have been warned.

In my last post, I talked a bit about gee forces. Gee forces are a handy way to measure acceleration. Right now, you and I and (almost) every other human are experiencing somewhere around 1 gee of head-to-foot acceleration due to the Earth’s gravity. Anyone who happens to be at the top of Mt. Everest is experiencing 0.999 gees. The overgrown amoebas at the bottom of the Challenger deep are experiencing 1.005 gees.

But human beings are exposed to greater gee forces than this all the time. For instance, the astronauts aboard Apollo 11 experienced up to 4 gees during launch. Here’s an awesome graph from NASA:

Fighter pilots have to put up with even higher gee forces when they make tight turns, thanks to the centrifugal acceleration required to turn in a circle at high speeds. From what I can gather, many pilots have to demonstrate they can handle 9 gees for 10 or 15 seconds without blacking out in order to qualify to fly planes like the F-16. Here’s an example of things not going right at 9 gees:

Yes, it’s the same video from the last post. I spent fifteen or twenty minutes searching YouTube for a better one, but I couldn’t find it. I did, however, discover this badass pilot in a gee-suit who handled 12 gees:

The reason we humans don’t tolerate gee forces very well is pretty simple: we have blood. Blood is a liquid. Like any liquid, its weight produces hydrostatic pressure. I’ll use myself as an example (for the record, I’m pretty sure I would die at 9 gees, but anybody who wants to let me in a centrifuge, I’d love to prove myself wrong). I’m 6 feet, 3 inches tall, or 191 centimeters, or 1.91 meters. Blood is almost the same density as water, so we can just run Pascal’s hydrostatic-pressure equation: (1 g/cc [density of blood]) * (9.80665 m/s^2 [acceleration due to gravity]) * (1.91 m [my height]). That comes out to a pressure of 187.3 millibars, or, to use the units we use for blood pressure in the United States, 140.5 millimeters of mercury.

It just so happens that I have one of those cheap drugstore blood-pressure cuffs handy. You wait right here. I’m gonna apply it to the fleshy part of my ankle and check my math.

It’s a good thing my heart isn’t in my ankle, because the blood pressure down there is 217/173. That’s the kind of blood pressure where, if you’ve got it throughout your body, the doctors get pale and start pumping you full of exciting chemicals. For the record, my resting blood pressure hovers around 120/70, rising to 140/80 if I drink too much coffee.

The blood pressure at the level of my heart, meanwhile, should be (according to Pascal’s formula) (1 g/cc) * (9.80665 m/s^2) * (0.42 m [the distance from the top of my head to my heart]). That’s 41.2 millibars or 30.9 mmHg. I’m not going to put the blood-pressure cuff on my head. To butcher that Meat Loaf song “I would do any-thing for science, but I won’t dooooo that.” I can get a good idea of the pressure at head level, though, by putting the cuff around my bicep and raising it to the same height as my head. Back in a second.

Okay. So, apparently, there are things I won’t do for science, but there aren’t many of them. Among the things I will do for science is attempting to tape my hand to the wall so my muscle contractions don’t interfere with the blood-pressure reading. That didn’t work out. But the approximate reading, because I was starting to fear for my sanity and wanted to stop, is 99/56. 56 mmHg, which is the between-heartbeats pressure, is higher than 41.2, but it’s in the same ballpark. The differences are probably due to stuff like measurement inaccuracies and the fact that blood vessels contract to keep the blood pressure from varying too much throughout the body.

Man. That was a hell of a digression. But this is what it was leading to: when I’m standing up (and I’ve had coffee), my heart and blood vessels can exert a total pressure of about 131 mmHg. Ordinarily, it’s pumping against a head-to-heart pressure gradient of 41.2 mmHg. But what if I was standing up and exposed to five gees?

In that case, my heart would be pumping against a gradient of 154.5 mmHg. That means it’s going to be really easy for the blood to flow from my brain to my heart, but very hard for the blood to flow from my heart to my brain. And it’s for that reason that the handsome young dude in the first video passed out: his heart (most certainly in better shape than mine…) couldn’t produce enough pressure to keep the blood in his head, in spite of that weird breathing and those leg-and-abdomen-straining maneuvers he was doing to keep the blood up there. People exposed to high head-to-foot gees see their visual field shrink, and eventually lose consciousness altogether. Pilots call that G-LOC, which I really hope is the name of a rapper. (It stands for gee-induced loss of consciousness, in case you were wondering).

You’ll notice that, in almost all spacecraft, whether in movies or in real life, the astronauts are lying on their backs, relative to the ground, when they get in the capsule. That’s because human beings tolerate front-to-back gees better than head-to-foot gees, and in a rocket launch or a capsule reentry, the gees will (hopefully) always be front-to-back. There is at least one documented case (the case of madman test pilot John Stapp) of a human being surviving 46.2 front-to-back gees for over a second. There are a few documented cases of race drivers surviving crashes with peak accelerations of 100 gees.

But you should know by now that I don’t play around. I don’t care what happens if you’re exposed to 46.2 gees for a second. I want to know what happens if you’re exposed to it for twenty-four hours. Because, at heart, I’ve always been a mad scientist.

There’s a reason we don’t know much about the effects of extremely high accelerations. Actually, there are two reasons. For one, deliberately exposing a volunteer to gee forces that might pulp their organs sounds an awful lot like an experiment the Nazis would have done, and no matter you course in life, it’s always good if you don’t do Nazi-type things. For another, building a large centrifuge that could get up to, say, a million gees, would be hard as all hell.

But since I’m playing mad scientist, let’s pretend I’ve got myself a giant death fortress, and inside that death fortress is a centrifuge with a place for a human occupant. The arm of the centrifuge is 100 meters long (as long as a football field, which applies no matter which sport “football” is to you). To produce 1,000,000 gees, I’d have to make that arm spin 50 times a second. It would produce an audible hum. It would be spinning as fast as a CD in a disk drive. Just to support the centrifugal force from a 350-kilogram cockpit, I’d need almost two thousand one-inch-diameter Kevlar ropes. Doable, but ridiculous. That’s the way I like it.

But what would actually happen to our poor volunteer? This is where that gore warning from the beginning comes in. (If it makes you feel better, you can pretend the volunteer is a death-row inmate whose worst fears are, in order, injections, electrocution, and toxic gas, therefore making the centrifuge less cruel and unusual.)

That’s hard to say. Unsurprisingly, there haven’t been many human or animal experiments over 10 gees. Probably because the kinds of people who like to see humans and lab animals crushed to a pulp are too busy murdering prostitutes to become scientists. But I’m determined to at least go through the thought experiment. And you know what, I’m starting to feel kinda weird talking about crushing another person to a pulp, so for this experiment, we’ll use my body measurements and pretend it’s me in the centrifuge. A sort of punishment, to keep me from getting too excited about doing horrible theoretical things to people.

The circumference of my head is 60 cm. If my head was circular, I could just divide that by pi to get my head’s diameter. For most people, that assumption doesn’t work. Luckily (for you, at least), my head is essentially a lumpy pink bowling ball with hair, so its diameter is about 60 cm / pi, or 19.1 cm.

Lying down under 1 gee, hydrostatic pressure means the blood vessels at the back of my head will be experiencing 14.050 mmHg more pressure than the ones at the front. From the fact that I don’t have brain hemorrhages every time I lie down, I know that my brain can handle at least that much.

But what about at 5 gees? I suspect I could probably handle that, although perhaps not indefinitely. The difference between the front of my head and the back of my head would be 70.250 mmHg. I might start to lose some of my vision as the blood struggled to reach my retinas, and I might start to see some very pretty colors as the back of my brain accumulated the excess, but I’d probably survive.

At 10 gees, I’m not so sure how long I could take it. That means a pressure differential of 140.500 mmHg, so at 10 gees, it would take most of my heart’s strength just to get blood to the front of my head and front of my brain. With all that additional pressure at the back of my brain, and without any muscles to resist it, I’m probably going to have to start worrying about brain hemorrhages at 10 gees.

As a matter of fact, the brain is probably going to be one of the first organs to go. Nature is pretty cool: she gave us brains, but brains are heavy. So she gave us cerebrospinal fluid, which is almost the same density as the brain, which, thanks to buyoancy, reduces the brain’s effective mass from 1,200 grams to about 22 grams. This is good because, as I mentioned, the brain doesn’t have muscles that it can squeeze to re-distribute its blood. So, if the brain’s effective weight were too high, it would do horrible things like sink to the bottom of the skull and start squeezing through the opening into the neck (this happens in people who have cerebrospinal fluid leaks; they experience horrifying headaches, dizziness, blurred vision, a metallic taste in the mouth, and problems with hearing and balance, because their leaking CSF is letting the brain sink downwards and compress the cranial nerves).

At 5 gees, my brain is going to feel like it weighs 108 grams. Not a lot, but perhaps enough to notice.

But what if I pulled a John Stapp, except without his common sense? That is: What if I exposed myself to 46.2 gees continuously.

Well, I would die. In many very unpleasant ways. For one thing, my brain would sink to the back of my head with an effective weight of 1002 grams. The buoyancy from my CSF wouldn’t matter anymore, and so my brain would start to squish against the back of my skull, giving me the mother of all concussions.

I probably wouldn’t notice, though. For one thing, the hydrostatic blood pressure at the back of my head would be 641.100 mmHg, which is three times the blood pressure that qualifies as a do-not-pass-Go-go-directly-to-the-ICU medical emergency. So all the blood vessels in the back of my brain would pop, while the ones at the front would collapse. Basically, only my brainstem would be getting oxygen, and even it would be feeling the strain from my suddenly-heavy cerebrum.

That’s okay, though. I’d be dead before I had time to worry about that. The average chest wall in a male human is somewhere around 4.5 cm thick. The average density of ribs, which make up most of the chest wall, is around 3.75 g/cc. I measured my chest at about 38 cm by 38 cm. So, lying down, at rest, my diaphragm and respiratory muscles have to work against a slab of chest with an equivalent mass of 24.4 kilograms. Accelerating at 46.2 gees means my chest would feel like it massed 1,100 kilograms more. That is, at 46.2 gees, my chest alone would make it feel like I had a metric ton sitting on my ribs. At 100 gees, I’d be feeling 2.4 metric tons.

But at 100 gees, that’d be the least of my problems. At accelerations that high, pretty much everything around or attached to or touching my body would become deadly. A U.S. nickel (weighing 5 grams and worth 0.05 dollars) would behave like it weighed half a kilogram. But I wouldn’t notice that. I’d be too busy being dead. My back, my thighs, and my buttocks would be a horrible bruise-colored purple from all the blood that rushed to the back of me and burst my blood vessels. My chest and face would be horrible and pale, and stretched almost beyond recognition. My skin might tear. My ribcage might collapse.

Let’s crank it up. Let’s crank it up by a whole order of magnitude, and expose me to 1,000 continuous gees. This is where things get very, very messy and very, very horrible. If you’re not absolutely sure you can handle gore that would make Eli Roth and Paul Verhoven pee in their pants, please stop reading now.

At 1,000 gees, my eyeballs would either burst, or pop through their sockets and into my brain cavity. That cavity would likely be distressingly empty, since the pressure would probably have ruptured my meninges and made all the spinal fluid leak out. The brain itself would be roadkill in the back of my skull. Even if my ribs didn’t snap, my lungs would collapse under their own weight. The liver, which is a pretty fatty organ, would likely rise towards the top of my body while heavier stuff like muscle sank to the bottom. Basically, my guts would be moving around all over the place. And, at 1,000 gees, my head would feel like it weighed 5,000 kilograms. That’s five times as much as my car. My head would squish like a skittle under a boot.

At 10,000 gees, I would flatten. The bones in the front of my ribcage would weigh 50 metric tons. A nickel would weigh as much as a child or a small adult. My bones would be too heavy for my muscles to support them, and would start…migrating towards the bottom of my body. At this point, my tissues would begin behaving more and more like fluids. This would be more than enough to make my blood cells sink to the bottom and the watery plasma rise to the top. 10,000 gees is the kind of acceleration usually only experienced by bullets and in laboratory centrifuges.

By 100,000 gees, I’d be a horrible fluid, layered like a parfait from hell: a slurry of bone at the bottom topped with a gelatinous layer of muscle proteins and mitochondria, then a layer of hemoglobin, then a layer of collagen, then a layer of water, then a layer of purified fat.

And finally, at 1,000,000 gees, even weirder stuff would start to happen. For one thing, a nickel would weigh as much as a car. But let’s focus on me, or rather, what’s left of me. At 1,000,000 gees, individual molecules start to separate by density. The bottom of the me-puddle would be much richer in things like hemoglobin, calcium carbonate, iodine-bearing thyroid hormones, and large, stable proteins. Meanwhile, the top would consist of human tallow. Below that would be an oily layer of what was once stored oils in fat cells. Below that would come a slurry of the lighter cell organelles like the endoplasmic reticula and the mitochondria. The heavier organelles like the nucleus would be closer to the bottom. That’s right: at 1,000,000 gees, the difference in density between a cell’s nucleus and cytoplasm is enough to make the nucleus sink to the bottom.

I think we’ve gotten horrible enough. So let’s stop the centrifuge, hose what’s left of me out of it, and go ahead and call up a psychiatrist.

But before we do that, I want to make note of something amazing. In 2010, some very creative Japanese scientists decided to try a bizarre experiment. They placed different bacteria in test tubes full of nutrient broth, and put those test tubes in an ultracentrifuge. The ultracentrifuge exposed the bacteria to accelerations of around 400,000 gees. Normally, that’s the kind of acceleration you’d use to separate the proteins from the membranes. It’d kill just about anything. But it didn’t kill the bacteria. As a matter of fact, many of the bacteria kept right on growing. They kept on growing at an acceleration that would kill even a well-protected human instantly. Sure, their cells got a little weird-shaped, but so would yours, if you were exposed to 400,000 gees.

The universe is awesome. And scary as hell.

Actually, I think I’ll let Sam Neill (as Dr. Weir in Event Horizon) sum this one up: “Hell is only a word. The reality is much, much worse.”

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Dragonfire

So, I’ve been playing a lot of Dwarf Fortress lately (which goes a long way to explain the lack of new posts). If you don’t know, Dwarf Fortress is a bizarre and ridiculously detailed fantasy game where you send a squad of dwarves into the wilderness to dig for gems and ore and try to stay alive as long as possible. That’s harder than you might think, since all dwarves are born alcoholics who must have booze to function properly, they’re surrounded by horrible creatures that want them dead, the environment is harsh, and they’re…well, they’re a little dim.

I love Dwarf Fortress. I love it because the creators have put such an insane level of love and detail into it. For example, how many other fantasy games do you know where they actually use the specific heat of copper when calculating whether or not your armor is melting?

But one detail in particular caught my eye: Dwarf Fortress’s temperature system. Temperatures in Dwarf Fortress are, to quote the Wiki, “stored as sixteen-bit unsigned integers,” which means temperatures between 0 and 65,535. The cool thing is that Dwarf Fortress doesn’t use some wimpy unspecified temperature scale. There is a direct correspondence between Dwarf Fortress temperatures (measured in degrees Urist. Don’t ask.) and real temperatures. To convert from Dwarf Fortress temperatures to Kelvins, for instance, just do a little simple math: [Temperature in Kelvins] = ([Temperature in degrees Urist] – 9508.33) * (5/9) . As it turns out, the Urist scale is just the Fahrenheit scale shifted downward by 9968 degrees (which, incidentally, means you can go several thousand degrees below aboslute zero, but that’s an issue for another time).

Better yet, Dwarf Fortress has DRAGONS! I love dragons, far more than any twenty-six-year-old adult male probably should. I turn into a hyperactive eight-year-old boy when I think about dragons. And Dwarf Fortress combines two of my great loves: dragons, and being unnecessarily specific about things. Here’s a typical encounter between a human swordsman in bronze armor (the @ symbol; the graphics take some getting used to) and an angry dragon (the D symbol).

Dragon Fight 1

Round 1. FIGHT!

Dragon Fight 2

The dragon breathes fire. The human’s chainmail pants are now filled with poo.

Dragon Fight 3

The human is engulfed in dragonfire and begins burning almost immediately.

Dragon Fight Aftermath

To nobody’s surprise, the dragon wins. I’d also like to note that this dragon is a real jerk: while his poor prey was burning to death, it swooped in and knocked the human’s teeth out…

Dragon fights in Dwarf Fortress end very quickly. That’s because, as the wiki tells us, dragonfire has a temperature of 50,000 degrees Urist. Which translates to a horrifying 22,495.372 Kelvins (22,222.222 ºC, 40,032 ºF). That’s higher than the boiling point of lead. It’s higher than the boiling point of iron. It’s higher than the boiling point of tungsten, for crying out loud. In fact, it’s sixteen thousand degrees hotter than tungsten’s boiling point. Dwarf Fortress dragons don’t breathe fire like those wimpy Hollywood dragons. They breathe jets of freakin’ plasma. Plasma hotter than the surface of the sun. Plasma almost as hot as a lightning bolt.

With this in mind, we can take a scientific (and somewhat gruesome) look at what happened to our unfortunate human swordsman just now.

From the images above, let’s say the dragon’s plasma jet reached a maximum length of 10 meters before the dragon stopped spitting. Just before it struck our adventurer, it was spread out in a rough cone 10 meters long and 5 meters wide at the base. It was broiling away at a temperature of 22,500 Kelvin. When you’re working with absurd temperatures like this, the radiated heat and light do as much or more damage than the plasma itself. This kind of thing (unfortunately) also happens in more mundane circumstances: when high-voltage, high-current equipment shorts out, it can produce an arc flash, an electric discharge that produces a dangerous explosion, a deadly flash, a flare of plasma, and a shower of molten metal.

Arc flashes are horrifying. They’re a serious source of danger to electrical engineers. They’re also not terribly funny. But they give us an idea of the effects of dragonfire.

At a temperature of 22,500 Kelvin, the front surface of the fireball would radiate about 0.285 terawatts of energy. The formula for a blackbody spectrum tells us that the fireball will be brightest at a wavelength of 128.79 nanometers, which is in the far ultraviolet. That’s more energetic than the ultraviolet light from germicidal lamps, which is already more than enough to cause burns and damage the eyes. So our unlucky swordsman would be looking at instant UV flash-burns.

Lucky for him, he probably won’t have long to worry about those burns. The fireball is radiating at 1.453e10 watts per square meter. If we assume the swordsman knew he was about to fight a dragon and therefore put on some sort of bizarre medieval bronze spacesuit and polished it to a mirror finish. He’s still dead meat: copper, one of the main components of bronze (the other is most often tin) is a terrible reflector at the wavelengths in question here, bottoming out at around 30%. That means our foolish knight is still going to be absorbing 70% of the radiant heat, which will (given a long enough exposure) raise its temperature to around 20,500 Kelvin, more than hot enough to flash-vaporize the outer layers.

But if we’re nice and pretend the knight was smart enough to have his bronze armor coated with something decently reflective at all wavelengths (like ye olde dwarven electropolished electroplated aluminum), he would only absorb about 5% of the incident radiation. Well, bad news, sir knight: your armor’s still heating up to 7,600 Kelvin, which is much hotter than the surface of the sun.

Of course, producing a plume of 22,000-degree plasma takes a lot of energy (I’ll resist the urge to nitpick the biology of that), and even if we put that aside, according to the game’s own internal logic, dragonfire doesn’t hang around very long. Each in-game tick (in adventure mode or arena mode) lasts one second, and our bronze swordsman was only exposed to these ridiculous temperatures and irradiances for around 10 ticks, or 10 seconds. If we consider the fact that the plume of dragonfire is going to lose a lot of energy to radiation and thermal expansion, our knight probably wouldn’t evaporate right away. But he will probably wish to his randomly-generated deity that he did.

Metals are good conductors of heat, and copper is one of the most conductive metals, heat-wise. Therefore, although our knight only got exposed to that horrifying draconic welding arc for a few seconds, his armor’s going to soak up a lethal amount of heat from that exposure. Arc flashes, lightning, and nuclear explosions can cause second- and third-degree burns from just a few seconds’ exposure, so our night is going to be blind and scorched, and then he’s going to poach like an egg inside his armor.

Don’t worry, though–he probably won’t feel it. Unless he has superhuman willpower (and is therefore able to hold his breath while the rest of his body is bursting into flames), he’s going to take a panicked gasp, and that’ll put an end to his battle very, very quickly.

The inhalation of superheated gas kills very rapidly. The inhalation of gas at thousands of degrees (meaning: the dragon’s plume and every cubic centimeter of air in contact with it) kills instantly. So our knight would probably lose consciousness either instantly, or within 15 seconds, which is how long it takes you to pass out when your heart and/or lungs quit working. And what would be left? A knight cooked Pittsburgh rare, wrapped in a blanket of broken bronze welding slag.

So, if you think you’ve outgrown being scared of dragons, imagine this: a scaly reptilian horror older than a sequoia, fixing you with its piercing gaze and then spewing a jet of gas as hot and bright as a welding arc. That’s good–I didn’t need to sleep tonight, anyway…

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Could you kill the human race with a BB gun?

As you might have guessed, this post is heavily influenced by xkcd’s brilliant weekly What-If blog

While pondering meteorites striking the earth with absurd velocities, I got to wondering whether or not you could actually kill the human race with a single BB. Because physics is a frightening place, the answer to questions like this is usually yes.

To simplify the first stage of calculations, we need to know how much energy is required to kill the human race. I will call this constant the “ohgod,” and I will set it equal to the kinetic energy of a 15-kilometer-wide stony asteroid traveling at 22 kilometers per second, which would be more than sufficient to cause a mass extinction which would almost certainly wipe out the human race. One ohgod is approximately 1.283 x 10^24 joules, or about 2.6 Chicxulubs (or, as people who fear the awesomeness of Mesoamerican words put it, 2.6 dinosaur-killers). 

The mass of a BB is surprisingly hard to find, although there is a very handy chart listing the masses of high-end BBs in grains, which can easily be converted to grams. By my reckoning, a standard 4.5-millimeter (0.177 caliber) BB should weigh about 0.4 grams. In order to figure out how fast a 0.4-gram BB would have to be moving to have 1 ohgod of kinetic energy, we must solve the relativistic kinetic energy equation for velocity. The relativistic kinetic energy equation is a little unwieldy:

E = [(1/sqrt(1-v^2/c^2)) + 1] * m * c^2

I actually had to get out pen and paper to solve this equation for v. Here’s my math, to prove that I’m not a lazy cretin:

Image

When I calculated v and plugged my numbers back into the relativistic kinetic energy formula on WolframAlpha, I was greeted with one of the most satisfying things a nerd can ever see: I got back exactly 1.283 x 10^24 joules, which means I didn’t have to do all that algebra again.

As it turns out, in order to have a kinetic energy of a species-killing asteroid, a BB would have to be traveling quite fast. I would have to be traveling at 0.9999999999999999999996074284163612948528545037647345 c, in fact. That speed is slower than the speed of light by only a few parts in 10^22, which is to say by only a few parts in 10 billion trillion. A few parts in 10 billion trillion equates to a bacterium-sized drop of water added to an Olympic-sized swimming pool. Feel free to insert your own joke about homeopathy here.

Our lethal BB would be traveling almost as fast as the fastest-moving particles ever detected. I’m thinking here about the Oh-my-God particle, which was (probably) a proton that hit Earth’s atmosphere at 0.9999999999999999999999951 c. The Oh-my-God particle is faster by a hair. But our BB is still traveling a ludicrous speeds. Light is fast. A beam of light could circle the Earth in 133 milliseconds, which, if you look at reaction-time data, is about half the time it takes a human being to detect a stimulus and for the nerve impulse to travel down their arm and make a muscle contract. Very few physical objects can hold their own against light. But our BB could. If you raced our BB and a beam of light head-to-head, after a thousand years, the BB would only be lagging 3 millimeters behind, which is about the diameter of a peppercorn, which is ridiculous.

But the question here is not “How fast would a BB have to be traveling to have the same kinetic energy as a humanity-ending asteroid.” The question is “Could you actually use a hyper-velocity BB to kill the human race,” which is much more interesting and complicated. 

First of all, the BB would have an insane amount of kinetic energy. E = m * c^2, of course, and from that, we know that our BB’s kinetic energy (its energy alone) would have a mass of 1.428 * 10^7 kilograms, which is about the mass of five Boeing 747 jet airliners. I would have to be a very gifted physicist to tell you what happens when you’ve got atoms with that kind of energy, but I suspect that there would be very weird quantum effects (aren’t there always?) which would conspire to slow the BB down. Because of quantum randomness, I imagine the BB would constantly be emitting high-energy gamma rays, which would decay into electron-positron and proton-antiproton pairs. Which is to say that our BB would be moving so fast that, rather than leaving behind a wake of Cherenkov radiation, it would leave behind a wake of actual physical matter, conjured seemingly from the ether by the conversion of its kinetic energy. 

As for what would happen when the BB actually hit the Earth, that’s beyond my power to calculate, on account of I don’t have access to a fucking supercomputer. But we can assume that the BB would pass straight through the Earth with no physical impact: all of its interactions with our planet would probably be on the level of ultra-high-energy particle physics. And from that, we can estimate its effects.

The BB would cut a cylindrical path 4.5 millimeters across and 1 earth diameter long. If it deposited all of its kinetic energy along this track, it would raise the temperature of the rock by 10^15 Kelvin, which would make it one million times hotter than a supernova, which would most certainly be more than enough to kill all of us and vaporize a significant fraction of the Earth.

But the BB would only spend 44 milliseconds passing through the Earth, and somehow I doubt that regular matter would stop it entirely. Let’s assume instead that only one tenth of its energy got deposited in its track. We’re still talking a temperature a hundred thousand times that in the center of a supernova, which is ridiculous and would, once again, kill us all and peel the skin off the planet.

What if the BB only loses one one hundredth of its energy as it passes through the Earth? Same result: the Earth is replaced by a ball of radioactive lava.

But if, because of its ridiculous speed, it only loses one one millionth of its kinetic energy interacting with Earth, it still heats its needle-thin track to 3 billion kelvin, which is hot enough to fuse Earth’s silicon into iron and produce a violent explosion that would spawn earthquakes and firestorms and might, in spite of the energy losses, kill us all anyway.

But when you consider how much energy even the mighty Oh-my-God particle (which was, let me remind you, moving so fast that light was having trouble staying ahead of it) deposited just by hitting the atmosphere, I’d say the BB would lose quite a bit more than one one-millionth of its kinetic energy on impact. And I’d say that that kinetic energy would be spread over a fairly wide area. I’m thinking it would leave behind a column of hydrogen-bomb-temperature fusion plasma in the atmosphere, then hit the crust and fan out within an ice-cream-cone-shaped volume of the mantle. The nastiness of the results depend entirely on how big an ice-cream cone we’re talking, but it’s likely to be fairly narrow and fairly long, so we’re probably looking at a near-supernova-temperature column of fusing rock plasma with a length measured in kilometers. The explosion would be worse than anything the Earth has ever seen and would, yes, almost certainly kill all of us. If the immediate radiation didn’t get us, then the explosion would expose the mantle and lift enough dust to darken the sky for years.

You know, at the start of this, I thought I had an idea I could pitch to Daisy Outdoor Products. Now that I think about it, I think I’ll put the proposal in a drawer and forget about it.

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