physics, Space, thought experiment

The Moon Cable

It was my cousin’s birthday. In his honor, we were having lunch at a slightly seedy Mexican restaurant. Half of the people were having a weird discussion about religion. The other half were busy getting drunk on fluorescent mango margaritas. As usual, me and one of my other cousins (let’s call him Neil) were talking absolute nonsense to entertain ourselves.

“So I’ve got a question,” Neil said, knowing my penchant for ridiculous thought experiments, “Would it be physically possible to tie the Earth and Moon together with a cable?” I was distracted by the fact that the ventilation duct was starting to drip in my camarones con arroz, so I didn’t give the matter as much thought as I should have, and I babbled some stuff I read about space elevators until Neil changed the subject. But, because I am an obsessive lunatic, the question has stuck with me.

The first question is how much cable we’re going to need. Since the Earth and Moon are separated, on average, by 384,399 kilometers, the answer is likely to be “a lot.”

It turns out that this isn’t very hard to calculate. Since cable (or wire rope, as the more formal people call it) is such a common and important commodity,  companies like Wirerope Works, Inc. provide their customers (and idiots like me) with pretty detailed specifications for their products. Let’s use two-inch-diameter cable, since we’re dealing with a pretty heavy load here. Every foot of this two-inch cable weighs 6.85 pounds (3.107 kilograms; I’ve noticed that traditional industries like cabling and car-making are stubborn about going metric). That does not bode well for the feasibility of our cable, but let’s give it a shot anyway.

Much to my surprise, we wouldn’t have to dig up all of North America to get the iron for our mega-cable. It would have a mass of 3,919,000,000 kilograms. I mean, 3.918 billion is hardly nothing. I mean, I wouldn’t want to eat 3.919 billion grains of rice. But when you consider that we’re tying two celestial bodies together with a cable, it seems weird that that cable would weigh less than the Great Pyramid of Giza. But it would.

So we could make the cable. And we could probably devise a horrifying bucket-brigade rocket system to haul it into space. But once we got it tied to the Moon, would it hold?

No. No it would not. Not even close.

The first of our (many) problems is that 384,399 kilometers is the Moon’s semimajor axis. Its orbit, however, is elliptical. It gets as close as 362,600 kilometers (its perigee, which is when supermoons happen) and as far away as 405,400 kilometers. If we were silly enough to anchor the cable when the Moon was at perigee (and since we’re tying planets together, there’s pretty much no limit to the silliness), then it would have to stretch by 10%. For many elastic fibers, there’s a specific yield strength: if you try to stretch it further than its limit, it’ll keep stretching without springing back, like a piece of taffy. Steel is a little better-behaved, and doesn’t have a true yield strength. However, as a reference point, engineers say that the tension that causes a piece of steel to increase in length by 0.2% is its yield strength. To put it more clearly: the cable’s gonna snap.

Of course, we could easily get around this problem by just making the cable 405,400 kilometers long instead of 384,399. But we’re very quickly going to run into another problem. The Moon orbits the Earth once every 27.3 days. The Earth, however, revolves on its axis in just under 24 hours. Long before the cable stretches to its maximum length, it’s going to start winding around the Earth’s equator like a yo-yo string until one of two things happens: 1) So much cable is wound around the Earth that, when the moon hits apogee, it snaps the cable; or 2) The pull of all that wrapped-up cable slows the Earth’s rotation so that it’s synchronous with the Moon’s orbit.

In the second scenario, the Moon has to brake the Earth’s rotation within less than 24 hours, because after just over 24 hours, the cable will have wound around the Earth’s circumference once, which just so happens to correspond to the difference in distance between the Moon’s apogee and perigee. Any more than one full revolution, and the cable’s gonna snap no matter what. But hell, physics can be weird. Maybe a steel cable can stop a spinning planet.

Turns out there’s a handy formula. Torque is equal to angular acceleration times moment of inertia. (Moment of inertia tells you how hard an object is to set spinning around a particular axis.) To slow the earth’s spin period from one day to 27.3 days over the course of 24 hours requires a torque of 7.906e28 Newton-meters. For perspective: to apply that much torque with ordinary passenger-car engines would require more engines than there are stars in the Milky Way. Not looking good for our cable, but let’s at least finish the math. Since that torque’s being applied to a lever-arm (the Earth’s radius) with a length of 6,371 kilometers, the force on the cable will be 1.241e22 Newtons. That much force, applied over the piddling cross-sectional area of a two-inch cable, results in a stress of 153 quadrillion megapascals. That’s 42 trillion times the yield strength of Kevlar, which is among the strongest tensile materials we have. And don’t even think about telling me “what about nanotubes?” A high-strength aramid like Kevlar is 42 trillion times too weak. I don’t think even high-grade nanotubes are thirteen orders of magnitude stronger than Kevlar.

So, to very belatedly answer Neil’s question: no. You cannot connect the Earth and Moon with a cable. And now I have to go and return all this wire rope and get him a new birthday present.

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Cars, physics, thought experiment

A City on Wheels

Writing this blog, I find myself talking a lot about my weird little obsessions. I have a lot of them. If they were of a more practical bent, maybe I could’ve been a great composer or an architect, or the guy who invented Cards Against Humanity. But no, I end up wondering more abstract stuff, like how tall a mountain can get, or what it would take to centrifuge someone to death. While I was doing research for my post about hooking a cargo-ship diesel to my car, another old obsession came bubbling up: the idea of a town on wheels.

I’ve already done a few back-of-the-envelope numbers for this post, and the results are less than encouraging. But hey, even if it’s not actually doable, I get to talk about gigantic engines and huge wheels, and show you pictures of cool-looking mining equipment. Because I am, in my soul, still a ten-year-old playing with Tonka trucks in a mud puddle.

The Wheels

Here’s a picture of one of the world’s largest dump trucks:

liebherr_t282_1

That is a Liebherr T 282B. (Have you noticed that all the really cool machines have really boring names?) Anyway, the Liebherr is among the largest trucks in the world. It can carry 360 metric tons. It was only recently outdone by the BelAZ 75710 (see what I mean about the names?), which can carry 450 metric tons. Although it doesn’t look as immediately impressive and imposing as the BelAZ or the Caterpillar 797F, it’s got one really cool thing going for it: it’s kind of the Prius of mining trucks. That is to say, it’s almost a hybrid.

I say almost because it doesn’t (as far as I know) have regenerative braking or a big battery bank for storing power. But those gigantic wheels in the back? They’re not driven by a big beefy mechanical drivetrain like you find in an ordinary car or in a Caterpillar 797F. They’re driven by electric motors so big you could put a blanket in one and call it a Japanese hotel room. The power to drive them comes from a 3,600-horsepower Detroit Diesel, which runs an oversized alternator. (For the record, the BelAZ 75710 uses the same setup.)

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biology, Dragons, thought experiment

Even More Dragonfire

Because I like dragons and I can’t help myself. Don’t worry. This one won’t be nearly as long as my usual posts about dragons. If anything, it’s more to show the thought process that goes into my thought experiments.

Let’s dispense with the notion of dragonfire hotter than the surface of the sun, and with biologically-produced antimatter. Let’s pretend that dragons are made of fairly ordinary flesh. They breathe fire from their mouths (naturally), so they’re going to have to be careful not to burn their tongues off. Let’s assume they have funny saliva glands that mist their mucous membranes to stop them getting scalded off by direct contact with hot air and fire. There’s still thermal radiation to deal with.

According to NOAA (who usually talk about weather, but have, in this case, started talking about fire), exposure to thermal radiation at an intensity of 10 kilowatts per square meter will cause severe pain after 5 seconds and second-degree burns (nasty blisters) after 14 seconds. With that in mind, I want to find out how hot dragonfire can be before its thermal radiation is too much for a dragon’s mouth to handle.

Well, let’s assume a dragon’s mouth is a cylinder 1 meter long and 30 centimeters in diameter. Multiply the circumference of that cylinder by its length to get its surface area (minus the ends), and then multiply the area by 10 kilowatts per square meter to get the maximum radiant power that can reach the mucous membranes. The result: 9.425 kilowatts. Now, let’s model the jet of fire as a cylinder (again, without ends) 1 centimeter in diameter and 1 meter long. That cylinder can’t emit more than 9.425 kilowatts as radiant heat. Divide 9.425 kilowatts by the cylinder’s surface area. To stay below 9.425 kilowatts, the jet of flame can’t emit at an intensity higher than 300 kilowatts per square meter. Apply the Stefan-Boltzmann law in reverse to get an estimate of what temperature gas radiates at 300 kilowatts per square meter. That comes out to a disappointing 1,517 Kelvin, which is cooler than the average wood fire.

I’m not satisfied with that, so I’m going to cheat. Sort of. I’m going to assume that the dragon has a bone in its fire-spewing orifice that acts like a supersonic rocket nozzle, which allows it to emit a very narrow, fast-moving stream of burning gas. The upshot of this is that the jet becomes narrower than that of a pressure washer: 1 mm in diameter throughout its transit through the mouth. That’s a bit more encouraging: 2,697 Kelvin, about the temperature of a hydrogen-air flame (which means we can just use hydrogen as the fuel). It’s still nowhere as hot as I want it to be, but I don’t think Sir Knight is going to be walking away from this one.

We could, of course, push the temperature up by taking into account the fact that the dragon’s mouth isn’t a perfect blackbody, and reflects some of the radiation, but like I said, this isn’t a full post. I just wanted to show you guys how I flesh out an idea.

Stay safe out there. And don’t try to breathe fire.

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Cars, physics, thought experiment

Supersonic Toyota? (Cars, Part 2)

A while ago, I wrote a post that examined, in much greater and (slightly) more accurate detail what speeds my 2007 Toyota Yaris, with its stock drivetrain, could manage under different conditions. This post is all about Earth at sea level, which has gotta be the most boring place for a space enthusiast. Earth at sea level is what rockets are built to get away from, right? But I can make things interesting again by getting rid of the whole “sensible stock drivetrain” thing.

But first, since it’s been quite a while, a refresher: My Yaris looks like this:

2007_toyota_yaris_9100

Its stock four-cylinder engine produces about 100 horsepower and about 100 foot-pounds of torque. My drivetrain has the following gear ratios: 1st: 2.874, 2nd: 1.552, 3rd: 1.000, 4th: 0.700, torque converter: 1.950, differential: 4.237. The drag coefficient is 0.29 and the cross-sectional area is 1.96 square meters. The wheel radius is 14 inches. I’m totally writing all this down for your information, and not so I can be lazy and not have to refer back to the previous post to get the numbers later.

Anyway…let’s start dropping different engines into my car. In some cases, I’m going to leave the drivetrain the same. In other cases, either out of curiosity or for practical reasons (a rarity around here), I’ll consider a different drivetrain. As you guys know by now, if I’m gonna do something, I’m gonna overdo it. But for a change, I’m going to shoot low to start with. I’m going to consider a motor that’s actually less powerful than my actual one.

An Electric Go-Kart Motor

There are people out there who do really high-quality gas-to-electric conversions. I don’t remember where I saw it, but there was one blog-type site that actually detailed converting a similar Toyota to mine to electric power. That conversion involved a large number of batteries and a lot of careful engineering. Me? I’m just slapping this random go-kart motor into it and sticking a couple car batteries in the trunk.

The motor in question produces up to 4 newton-meters (2.95 foot-pounds). That’s not a lot. That’s equivalent to resting the lightest dumbbell they sell at Walmart on the end of a ruler. That is to say, if you glued one end of a ruler to the shaft of this motor and the other end to a table, the motor might not be able to break the ruler.

But I’m feeling optimistic, so let’s do the math anyway. In 4th gear (which gives maximum wheel speed), that 4 newton-meters of torque becomes 4 * 1.950 * 4.237 * 0.700 = 21 Newton-meters. Divide that by the 14-inch radius of my wheels, and the force applied at maximum wheel-speed is 59.060 Newtons. Plug that into the reverse drag equation from the previous post, and you get 12.76 m/s (28.55 mph, 45.95 km/h). That’s actually not too shabby, considering my car probably weighs a good ten times as much as a go-kart and has at least twice the cross-sectional area.

For the electrically-inclined, if I was using ordinary 12 volt batteries, I’d need to assemble them in series strings of 5, to meet the 48 volts required by the motor and overcome losses and varying battery voltages. One of these strings could supply the necessary current of 36 amps to drive the motor at maximum speed and maximum torque. Ordinary car batteries would provide between one and two hours’ drive-time per 5-battery string. That’s actually not too bad. I couldn’t ever take my go-kart Yaris on the highway, but as a runabout, it might work.

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physics, thought experiment

The Highest Mountain

One of my favorite things about writing this blog is that it gives me a chance to answer the questions my irritating eight-year-old self wouldn’t quit asking. It’s like an exorcism: I’m putting to rest the ghost of my incredibly nerdy childhood.

Some of those questions have proven more stubborn than others. For instance: How fast can a planet spin? I talked about that in a previous post, but I’m still not satisfied, so trust me, the centrifuge planet will return.

Another of those questions has actually gotten *harder* to answer the more I’ve learned. It was sparked by a poster in one of my classrooms. The class must have been excruciatingly boring, because although I couldn’t tell you what subject it was or who the teacher was, I can picture that poster very clearly in my head.

It must have been a geometry poster, because it had all sorts of different geometric objects on it: A cube, a hyperboloid, a cone, a flat plane, and a sphere. But what caught my eye was that, to demonstrate the shapes of the surfaces, they put maps of the Earth on them. I spent what felt like hours staring at that poster (probably scaring the hell out of the teacher) while I wondered what it would be like to stand on an Earth shaped like a giant Pringle. Recently, the memory of the poster was reignited by the fantastic, infuriating, and pleasantly inexpensive game HyperRogue, which takes place on a hyperbolic plane that’s a bit like the Pringle-shaped surface.

But until I can hunt down a copy of that poster on e-Bay (and worry people by staring at it for many more hours), my questions about life on a hyperbolic planet will have to go unanswered. Instead, I want to put to rest another stubborn question:

WHAT THE HELL IS THE MAXIMUM HEIGHT OF A MOUNTAIN?

Seriously! How high can a mountain get? I’m not sure why I’m so angry about this, but I think it’s because my own attempts to figure it out have been repeatedly foiled, either by circumstance (read: laziness), or by the fact that geology is more complicated than you might think. I’ve tried to write this very post over half a dozen times, and failed every time. Now, though, I think I can finish what I started.

At first, I assumed the only real limit to a mountain’s height would be the strength of the rock it was made of. As we’ll see by the end, that *does* turn out to be the most important limit, but there are a lot of other important constraints.

The phrase “the tip of the iceberg” is one of those cliches that’s been run over so many times it’s almost invisible on the page. It’s like that one pair of underwear that’s so worn out a harem-girl could use it as a really bizarre veil. But you know what? The phrase is still valid. It’s hard to find proper images of what the rest of an iceberg looks like, but we know it’s far bigger than the tip. We know that because of buoyancy.

For an object to float, it has to displace its own weight’s worth of the medium it’s floating in. That means the floating object has to be less dense (averaged over its whole volume) than the medium. This is why you can float a cannonball in a bucket of mercury. It’s also why the ridiculous-looking Civil War ironclads like this

 

The CSS Virginia or Merrimac

The CSS Virginia or “Merrimac” (Source.)

could float. The mercury is almost one and a half times as dense as the iron cannonball. The ironclad is made of thick metal plates, but those plates are wrapped around a large volume of air and humans, making the overall density low enough that it floats. (Apparently, though, its density was only just barely low enough. When the ship was fully-loaded, its upper deck would be covered in a few inches of water, making it the world’s worst submarine.)

You might be wondering why the hell I’m talking about icebergs all of a sudden. I’ll explain in a moment. For now, though, some calculations. Let’s assume a cubic iceberg. The density of sea ice varies depending on the age of the ice (which determines how much dense salt water is trapped in its pores), but let’s say 1.000 g/cc. The density of average seawater is about 1.027 g/cc.

It turns out that, in order to balance its own weight, a cubic iceberg must have over 97% of its edge length submerged. An iceberg that would only just fit inside a stadium (a 100-meter edge length) would stick up a little higher than the average adult man. 97 meters of it would be underwater. “The tip of the iceberg” is a cliche, yeah, but that doesn’t make it wrong.

I imagine many of you are swearing at me right now. I don’t blame you: I went from talking about a weird poster in my elementary school math class, then promised to talk about mountains, then got sidetracked talking about icebergs. Believe it or not, I’m actually getting at something, because, as it turns out, mountains float like icebergs.

“Mountains float like icebergs.” That sounds like it belongs in a really awful poem. But in a geological sense, it’s kinda true. It’s called isostasy. On geologic timescales, solid rock flows like an incredibly viscous fluid. (Technically it’s a rheid or a viscoelastic solid.) The mantle is much dense than the crust. The crust’s density averages 2.75 g/cc, while the mantle-like transition zone supporting it is around 3.40 g/cc. And luckily, it turns out that, in order to find out how deep the roots of a mountain have to go (I stole that phrase from Tolkein, I’ll admit), we can use the same math we used for icebergs. For the densities I gave above, the math says that a mountain’s root (or foundation, if you prefer) has to go 5.231 times deeper than the mountain’s height.

(Before anyone says anything, I *am* aware that there’ll be a contribution from the mountain’s buoyancy in air, but I’ve already digressed too much as it is.)

Does that mean we can have a mountain as high as we want as long as the roots go deep enough? No, unfortunately. The rock that makes up continental crust is fairly strong and solid down to a depth of about 200 kilometers, where the crust gives way to the asthenosphere. Asthenosphere comes from the Greek for “weak sphere.” It’s a good name: in the asthenosphere, rock gets, well, weak. It also gets mushy, a little like clay. It’s not actually *molten* (in fact, most of the mantle isn’t molten, which I’m still really annoyed my geology teachers never told me), but it’s soft enough that it’s likely to flatten out under pressure.

That means that the pressure exerted by the mountain’s weight and the buoyancy force will squeeze the foundation sideways until the foundation’s shallower than the asthenosphere boundary. On the surface, that means the mountain will sink until it’s about one-fifth as high as the asthenosphere is deep. So no mountain on Earth can reasonably reach higher than 38.234 kilometers.

That’s still damned impressive. Even weather balloons would have to steer around a mountain that high, nevermind airliners. You wanna talk about the death zone? The tip of this mountain would be way above the Armstrong limit. Up there, not only is there too little oxygen to support human life, but the pressure’s so low that *water boils at body temperature*, which is bad news to exposed, wet organs like, say, lungs.

Actually, the mountain might be able to go a little higher than this. Our math so far assumes that the mountain is supported only by its foundation’s buoyancy. It’s like a gigantic peg set in a hole in a continent. In reality, the mountain will be anchored to the crust, by friction if nothing else. That crust is just as reluctant to sink as the crust that makes up the mountain, and plus, it’s got a bit of bending strength. After all, the crust is a mass of rock somewhere between 20 and 100 kilometers thick. This so-called “flexural isostasy” (which doesn’t even look like real words, but is). Imagine a yardstick (or meter-stick, if you swing that way) sticking off the edge of a table. It bends some, but holds itself up. That’s flexural isostasy. Its effect is much harder to calculate, but we know it would help support the mountain, so it would make a positive contribution to a mountain’s maximum height.

But like I said at the beginning, isostasy isn’t the real limiting factor. The limiting factor is much simpler: rocks, like the piers of a bridge, can only support so much weight before they crack. No matter how wide your pillar, if you over-load it, the pressure will squeeze its base outward until its outer layer breaks off, putting all the weight on an even smaller cross-section, which increases the pressure and makes the next layer break off, and so on.

Mountains aren’t columns, though. They’re better approximated as cones. Time to dust off my calculus and figure out the pressure on the base of a conical mountain.

It turns out that the pressure doesn’t depend at all on the steepness of the cone’s sides. This makes sense, if you think about it: A narrow pointy mountain has less mass and therefore less weight, but that weight is concentrated on a much smaller area. A broader mountain is much heavier, but it also has a much bigger cross-section. The formula for the pressure at the base of a mountain is dead-simple:

(1/3) * (density of the rock) * (height of the mountain) * (acceleration due to gravity)

If the pressure exerted by the mountain is larger than the compressive strength of the rock (I’m assuming granite for this calculation), then the rock at the bottom will be very likely to shatter and peel off, and over less-than-geologic time, that’ll trigger rockslides that eat away the mountain’s sides until the mountain is shorter and surrounded by a pile of broken rock. And before you try to say we could just build the whole mountain out of broken rock, that won’t work: gravel flows under pressure, so we’d have the same problem.

Granite’s compressive strength is around 130 megapascals, according to the Engineering Toolbox. Plug that into the formula, and we get a maximum height of 14.461 kilometers. That would be an impressive mountain. If it sat where London is, you’d be able to see the summit from Paris. Still, airliners would only barely have to detour around it, and it’s not even twice the height of Mount Everest. Nothing like the insane mountain in that one H.P. Lovecraft story (the physics of which I’ll forgive because Lovecraft is awesome).

But what if we exploited that flexural isostasy by saying the crust around the mountain is just really absurdly thick and strong? No dice. The transition from crust to asthenosphere happens above a particular pressure and temperature, which means a particular depth below the surface. Say we have an Australia-sized plateau that sits twenty kilometers higher than the surrounding crust. That just means that, beneath the plateau, the asthenosphere will start twenty kilometers above the asthenosphere of the normal crust, which means the whole damn plateau will undergo plastic deformation and sink like a deflating marshmallow until it’s close to the same height as the crust around it. That’s hydrostatic equilibrium at work. It’s like trying to build a tower out of mud: for any reasonable height, it’s just going to flatten itself out.

But if you’re like me and you *demand* a really heigh mountain, you could try varying the parameters in the equation. You could build your mountain from something less dense, like ice, which decreases the weight, which seems like it should decrease the maximum height. Unfortunately, not only is ice much weaker under compression than granite, but ice is a rheid, and flows like a liquid under pressure, over shorter-than-geologic timescales. That’s one of the reasons glaciers look like rivers: they almost *are*.

The only other parameter we can control is the acceleration due to gravity. That means that, if you want a really enormous mountain, you have to go to another planet.

Mars proves my point with Olympus Mons, an ancient shield volcano the size of France. It reaches 22 kilometers high. Earth’s highest mountain (measured relative to sea level) is Mount Everest, at 8.848 kilometers.

Mars has two advantages when it comes to building huge mountains: it’s got a lower surface gravity, which means the rock weighs less; and its interior is a lot cooler, meaning the asthenosphere (if it even exists) starts much deeper.

For a long time, Olympus Mons was calle dthe highest mountain in the solar system. That, though, is kinda hard to say with a straight face. Olympus Mons is the clear winner if its altitude is 26 kilometers, which is its altitude as measured from the low-lying plains nearby. Olympus Mons, though, is such a wide mountain that those plains are a thousand kilometers from the summit. At that distance, we’re no longer dealing with “pointy mountain rising above a plain” as much as “lump of putty squished against a globe.” I presume the 22-kilometer height is measured against Mars’s effective sea level or its geoid or something like that, which in my mind is a more sensible way to measure height.

But even though Olympus Mons might still be the tallest, it’s probably going to have to share the title. It almost loses out to the bizarre ridge that runs around [Iapetus’s] equator. Iapetus has always kind of creeped me out. It looks *wrong*. It looks like the ancient seed of a universe-devouring demon-vine. Maybe that’s just me. But either way, the equatorial ridge rises 20 kilometers above the surface, almost dethroning Olympus, and making a visible bump in Iapetus’s silhouette

Iapetus

Iapetus. (Source.)

But Olympus’s best competitor isn’t found on a planet. It’s found on the asteroid slash dwarf planet Vesta: Rheasilvia Mons, rising 22 kilometers above the local topography.

Rheasilvia

Rheasilvia region, with Rheasilvia Mons just above center. (Source.)

This, though, is as much of a cheat as saying Olympus Mons is 26 kilometers high, because Vesta is a very lumpy object, and the local topography of Rheasilvia is (probably) a gigantic planet-shattering impact basin the size of Sri Lanka. It covers most of Vesta’s southern hemisphere, and it’s so big and so deep that it squishes Vesta way out of sphericality, which makes deciding what standard to use when measuring Rheasilvia’s height a little tricky.

Still, Olympus Mons, Iapetus’s creepy Winter Wall, and the apocalyptic mountain on Vesta prove two things: even the most sterile airless bodies are amazing, and that I was right: mountain height is mostly constrained by gravitational acceleration, which determines how high a mountain gets before it exceeds its rock’s compressional strength.

That’s done. Time to go find some more childhood demons to exorcise.

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Uncategorized

Sundiving, Part 2

(NOTE: After re-reading this post in 2021, I’m starting to doubt the validity of the math and physics here. I’m keeping the post up for posterity, but I’m warning you: read this with a very critical eye.)

In the previous post, I figured out how to get a spacecraft to an altitude of one solar radius (meaning one solar radius above the Sun’s surface, and two solar radii from its center). That’s nice and all, but unless we figure out how to get it the rest of the way down intact, then we’ve essentially done the same thing as a flight engineer who sends an astronaut into orbit in a fully-functional space capsule, but forgets to put a parachute on it. (Not that I know anything about that. Cough cough Kerbal Space Program cough…)

The sun is vicious. Anyone who’s ever had a good peeling sunburn knows this, and cringes at the thought. And anyone who, in spite of their parents’ warnings, has looked directly at the sun, also knows this. But I’ve got a better demonstration. I have a big 8.5 x 11-inch Fresnel lens made to magnify small print. I also have a lovely blowtorch that burns MAP-Pro, a gas that’s mostly propylene, which is as close as a clumsy idiot like me should ever come to acetylene. Propylene burns hot. About 2,200 Kelvin. I turned it on a piece of gravel and a piece of terra cotta. It got them both orange-hot, but that was the best it could do. The Fresnel lens, a cheap-ass plastic thing I bought at a drugstore, melted both in seconds (albeit in very small patches), using nothing more than half a square foot of sunlight.

Actually, the area of that magnifier is handy to have around. It’s 0.0603 square meters. On the surface of the Earth, we get (very roughly) 1,300 watts per square meter of sunlight (that’s called the solar constant). To melt terra cotta, I have to get the spot down to about a centimeter across. The lens intercepts about 80 Watts. If those 80 Watts are focused on a circle a centimeter across, then the target is getting irradiated with 770 solar constants, which, if it was a perfect absorber, would raise its temperature to 2,000 Kelvin. If I can get the spot is half a centimeter across, then we’re talking 3,070 solar constants and temperatures approaching 3,000 Kelvin.

And while I was playing around with my giant magnifier, I made a stupid mistake. Holding the lens with one hand, I reached down to re-position my next target. The light spot, about the size of a credit card, fell on the back of my hand. I said words I usually reserve for when I’ve hit my finger with a hammer. This is why you should always be careful with magnifying lenses. Even small ones can burn you and start fires.

The area of a standard credit card is about 13 times smaller than the area of my lens, so my hand was getting 13 solar constants. And even a measly 13 solar constants was more than enough to sting my skin like I was being attacked by a thousand wasps. Even at the limit of my crappy Fresnel lens, somewhere between 770 and 3,070 solar constants, we’re already in stone-melting territory.

At an altitude of 1 solar radius, our Sundiver will be getting to 11,537 solar constants. Enough to raise a perfect absorber to 4,000 Kelvin, which can melt every material we can make in bulk. Our poor Sundiver hasn’t even reached the surface and already it’s a ball of white-hot slag.

Except that I’ve conveniently neglected one thing: reflectivity. If the Sundiver was blacker than asphalt, sure, it would reach 4,000 Kelvin and melt. But why on Earth would we paint an object black if we’re planning to send it to the place where all that heat-producing sunlight comes from? That’s even sillier than those guys you see wearing black hoodies in high summer.

My first choice for a reflective coating would be silver. But there’s a massive problem with silver. Here are two graphs to explain that problem:

(Source.)

Sun Blackbody

(Source is obvious.)

The top spectrum shows the reflectivities of aluminum (Al), silver (Ag, because Latin), and gold (Au) at wavelengths between 200 nanometers (ultraviolet light; UV-C, to be specific: the kind produced by germicidal lamps) and 5,000 nanometers (mid-infrared, the wavelength heat-seeking missiles use).

The bottom spectrum is the blackbody spectrum for an object at a temperature of 5,778 Kelvin, which is a very good approximation for the solar spectrum. See silver’s massive dip in reflectivity around 350 nanometers? See how it happens, rather inconveniently, right around the peak of the solar emission spectrum? Sure, a silver shield would be good at reflecting most of the infra-red light, but what the hell good is that if it’s still soaking up all that violet and UV?

Gold does a little better (and you can see from that spectrum why they use gold in infrared mirrors), but it still bottoms out right where we don’t want it to. (Interesting note: see how gold is fairly reflective between 500 nanometers and 1,000 nanometers, but not nearly as reflective between 350 nanometers and 500 nanometers? And see how silver stays above 80% reflectivity between 350 and 1,000? That’s the reason gold is gold-colored and silver is silver-colored. Gold absorbs more green, blue, indigo, and violet than it does red, orange, and yellow. Silver is almost-but-not quite constant across this range, which covers the visible spectrum, so it reflects all visible light pretty much equally. Spectra are awesome.)

Much to my surprise, our best bet for a one-material reflector is aluminum. My personal experiences with aluminum are almost all foil-related. My blowtorch will melt aluminum, so it might seem like a bad choice, but in space, there’s so little gas that almost all heat transfer is by radiation, so it might still work. And besides, if you electropolish it, aluminum is ridiculously shiny.

(Image from the Finish Line Materials & Processes, Ltd. website.)

That’s shiny. And it’s not just smooth to the human eye–it’s smooth on scales so small you’d need an electron microscope to see them. They electro-polish things like medical implants, to get rid of the microscopic jagged bits that would otherwise really annoy the immune system. So get those images of crinkly foil out of your head. We’re talking a mirror better than you’ve ever seen.

Still, aluminum’s not perfect. Notice how its reflectivity spectrum has an annoying dip at about 800 nanometers. The sun’s pretty bright at that wavelength. Still, it manages 90% or better across almost all of the spectrum we’re concerned about. (Take note, though: in the far ultraviolet, somewhere around 150 nanometers, even aluminum bottoms out, and the sun is still pretty bright even at these short wavelengths. We’ll have to deal with that some other way.)

So our aluminum Sun-shield is reflecting 90% of the 15.7 million watts falling on every square meter. That means it’s absorbing the other 10%, or 1.57 million watts per square meter.

Bad news: even at an altitude of 1 solar radius, and even with a 90% reflective electropolished aluminum shield, the bastard’s still going to melt. It’s going to reach over 2,000 Kelvin, and aluminum melts at 933.

We might be able to improve the situation by using a dielectric mirror. Metal mirrors reflect incoming photons because metal atoms’ outer electrons wander freely from one atom to another, forming a conductive “sea”. Those electrons are easy to set oscillating, and that oscillation releases a photon of similar wavelength, releasing almost all the energy the first photon deposited. Dielectric mirrors, on the other hand, consist of a stack of very thin (tens of nanometers) layers with different refractive indices. For reference, water has a refractive index of 1.333. Those cool, shiny bulletproof Lexan windows that protect bank tellers have a refractive index of about 1.5. High-grade crystal glassware is about the same. Diamonds are so pretty and shiny and sparkly because their refractive index is 2.42, which makes for a lot of refraction and internal reflection.

These kind of reflections are what make dielectric mirrors work. The refractive index measures how fast light travels through a particular medium. It travels at 299,792 km/s through vacuum. It travels at about 225,000 km/s through water and about 124,000 km/s through diamond. This means, effectively, that light has farther to go through the high-index stuff, and if you arrange the layers right, you can set it up so that a photon that makes it through, say, two layers of the stack will have effectively traveled exactly three times the distance, which means the waves will add up rather than canceling out, which means they’re leaving and taking their energy with them, rather than canceling and leaving their energy in your mirror.

This, of course, only works for a wavelength that matches up with the thickness of your layers. Still, close to the target frequency, a dielectric mirror can do better than 99.9% reflectivity. And if you use some scary algorithms to optimize the thicknesses of the different layers, you can set it up so that it reflects over a much broader spectrum, by making the upper layers very thin to reflect short-wavelength light (UV, et cetera) and the deeper layers reflect red and infra-red. The result is a “chirped mirror,” which is yet another scientific name that pleases me in ways I don’t understand. Here’s the reflection spectrum of a good-quality chirped mirror:

(Source.)

Was I inserting that spectrum just an excuse to say “chirped mirror” again? Possibly. Chirped mirror.

Point is, the chirped mirror does better than aluminum for light between 300 and 900 nanometers (which covers most or all of the visible spectrum). But it drops below 90% for long enough that it’s probably going to overheat and melt. And there’s another problem: even at an altitude of 1 solar radius, the Sundiver’s going to be going upwards of 400 kilometers per second. If the Sundiver crosses paths with the smallest of asteroids (thumbnail-sized or smaller), or even a particularly bulky dust grain, there’s going to be trouble. To explain why, here’s a video of a peanut-sized aluminum cylinder hitting a metal gas canister at 7 kilometers per second, 57 times slower than the Sundiver will be moving:

We have a really, really hard time accelerating objects anywhere near this speed. We can’t do too much better than 10 to 20 km/s on the ground, and in space, we can at best double or triple that, and only if we use gravity assists and clever trajectories. On the ground, there are hypersonic dust accelerators, which can accelerate bacterium-sized particles to around 100 km/s, which is a little better.

But no matter the velocity, the news is not good. A 5-micron solid particle will penetrate at least 5 microns into the sunshade (according to Newton’s impact depth approximation). Not only will that rip straight through dozens of layers of our carefully-constructed chirped mirror, but it’s also going to deposit almost all of its kinetic energy inside the shield. A particle that size only masses 21.5 picograms, so its kinetic energy (according to Wolfram Alpha) is about the same required to depress a computer key. Not much, but when you consider that this is a bacterium-sized mote pressing a computer key, that’s a lot of power. It’s also over 17,000 times as much kinetic energy as you’d get from 21.5 picograms of TNT.

As for a rock visible to the naked eye (100 microns in diameter, as thick as a hair), the news just gets worse. A particle that size delivers 110.3 Joules, twenty times as much as a regular camera’s flash, and one-tenth as much as one of those blinding studio flashbulbs. All concentrated on a volume too small to squeeze a dust mite into.

And if the Sundiver should collide with a decent-sized rock (1 centimeter diameter, about the size of a thumbnail), well, you might as well just go ahead and press the self-destruct button yourself, because that pebble would deliver as much energy as 26 kilos (over 50 pounds) of TNT. We’re talking a bomb bigger than a softball. You know that delicately-layered dielectric mirror we built, with its precisely-tuned structure chemically deposited to sub-nanometer precision? Yeah. So much for that. It’s now a trillion interestingly-structured fragments falling to their death in the Sun.

My point is that a dielectric mirror, although it’s much more reflective than a metal one, won’t cut it. Not where we’re going. We have to figure out another way to get rid of that extra heat. And here’s how we’re going to do it: heat pipes.

The temperature of the shield will only reach 2,000 Kelvin if its only pathway for getting rid of absorbed heat is re-radiating it. And it just so happens that our ideal shield material, aluminum, is a wimp and can’t even handle 1,000 Kelvin. But aluminum is a good conductor of heat, so we can just thread the sunshade with copper pipes, sweep the heat away with a coolant, and transfer it to a radiator.

But how much heat are we going to have to move? And has anybody invented a way to move it without me having to do a ridiculous handwave? To find that out, we’re going to need to know the area of our sunshade. Here’s a diagram of that sunshade.

Sunshade 2

I wanted to make a puerile joke about that, but the more I look at it, the less I think “sex toy” and the more I think “lava lamp.” In this diagram, the sunshade is the long cone. The weird eggplant-shaped dotted line is the hermetically-sealed module containing the payload. That payload will more than likely be scientific instruments, and not a nuclear bomb with the mass of Manhattan island, because that was probably the most ridiculous thing about Sunshine. Although (spoiler alert), Captain Pinbacker was pretty out there, too.

The shield is cone-shaped for many reasons. One is that, for any given cross-sectional radius, you’re going to be absorbing the same amount of heat no matter the shield’s area, but the amount you can radiate depends on total, not cross-sectional, area. Let’s say the cone is 5 meters long and 2 meters in diameter at the base. If it’s made of 90% reflective electropolished aluminum, it’s going to absorb 4.93 megawatts of solar radiation at an altitude of 1 solar radius. Its cross-section is 3.142 square meters, but its total surface area is 16.02 square meters. That means that, to lose all its heat by radiation alone, the shield would have to reach a blackbody temperature of 1,500 Kelvin. Still almost twice aluminum’s melting point, but already a lot more bearable. If we weren’t going to get any closer than an altitude of 1 solar radius, we could swap the aluminum mirror out for aluminum-coated graphite and we could just let the shield cool itself. I imagine this is why the original solar probe designs used conical or angled bowl-shaped shields: small cross-sectional area, but a large area to radiate heat. But where we’re going, I suspect passive cooling is going to be insufficient sooner or later, so we might as well install our active cooling system now.

Heat pipes are awesome things. You can find them in most laptops. They’re the bewildering little copper tubes that don’t seem to serve any purpose. But they do serve a purpose. They’re hollow. Inside them is a working fluid (which, at laptop temperatures, is usually water or ammonia). The tube is evacuated to a fairly low pressure, so that, even near its freezing point, water will start to boil. The inner walls of the heat pipe are covered with either a metallic sponge or with a series of thin inward-pointing fins. These let the coolant wick to the hot end, where it evaporates. Evaporation is excellent for removing heat. It deposits that heat at the cold end, where something (a passive or active radiator or, in the case of a laptop, a fan and heat sink) disposes of the heat.

Many spacecraft use heat pipes for two reasons. 1) The absence of an atmosphere means the only way to get rid of heat is to radiate it, either from the spacecraft itself, or, more often, by moving the heat to a radiator and letting it radiate from there; heat pipes do this kind of job beautifully; 2) most heat pipes contain no moving parts whatsoever, and will happily go on doing their jobs forever as long as there’s a temperature difference between the ends, and as long as they don’t spring a leak or get clogged.

On top of this, some heat pipes can conduct heat even better than solid copper. Copper’s thermal conductivity is 400 Watts per meter per Kelvin difference, which is surpassed only by diamond (and graphene, which we can’t yet produce in bulk). But heat pipes can do better than one-piece bulk materials: Wikipedia says 100,000 Watts per meter per Kelvin difference, which my research leads me to believe is entirely reasonable. (Fun fact: high-temperature heat pipes have been used to transport heat from experimental nuclear reactor cores to machinery that can turn that heat into electricity. These heat pipes use molten frickin’ metal and metal vapor as their working fluids.)

The temperature difference is going to be the difference between the temperature of the shield (in this case, around 1,500 Kelvin at the beginning) and outer space (which is full of cosmic background radiation at an effective temperature of 2.3 Kelvin, but let’s say 50 Kelvin to account for things like reflected light off zodiacal dust, light from the solar corona, and because it’s always better to over-build a spacecraft than to under-build it).

When you do the math, at an altitude of 1 solar radius, we need to transport 4.93 megawatts of heat over a distance of 5 meters across a temperature differential of 1,450 Kelvin. That comes out to 680 Watts per meter per Kelvin difference. Solid copper can’t quite manage it, but a suitable heat pipe could do it with no trouble.

But we still have to get rid of the heat. For reasons that will become clear when Sundiver gets closer to the Sun, the back of the spacecraft has to be very close to a flat disk. So we’ve got 3.142 square meters in which to fit our radiator. Let’s say 3 square meters, since we’re probably going to want to mount things like thruster ports and antennae on the protected back side. Since we’re dumping 4.93 megawatts through a radiator with an area of 3 square meters, that radiator’s going to have to be able to handle a temperature of at least 2,320 Kelvin. Luckily, that’s more than manageable. Tungsten would work, but graphite is probably our best choice, because it’s fairly tough, it’s unreactive, and it’s a hell of a lot lighter than tungsten, which is so dense they use it in eco-friendly bullets as a replacement for lead (yes, there’s such a thing as eco-friendly bullets). Let’s go with graphite for now, and see if it’s still a good choice closer to the Sun. (After graphite, our second-best choice would be niobium, which is only about as dense as iron, with a melting point of 2,750 Kelvin. I’m sticking with graphite, because things are going to get hot pretty fast, and the niobium probably won’t cut it. (Plus, “graphite radiator” has a nicer ring to it than “niboium radiator.”)

Our radiator’s going to be glowing orange-hot. We’ll need a lot of insulation to minimize thermal contact between the shield-and-radiator structure and the payload, but we can do that with more mirrors, more heat pipes, and insulating cladding made from stuff like like calcium silicate or thermal tiles filled with silica aerogel.

Of course, all the computations so far have been done for an altitude of 1 solar radius. And I didn’t ask for a ship that could survive a trip to 1 solar radius. I want to reach the freakin surface! Life is already hard for our space probe, and it’s going to get worse very rapidly. So let’s re-set our clock, with T=0 seconds being the moment the Sundiver passes an altitude of 1 solar radius.

Altitude: 0.5 solar radii

T+50 minutes, 46 seconds

Speed: 504 km/s

Solar irradiance: 28 megawatts per square meter (20,600 solar constants)

Temperature of a perfect absorber: 4,700 Kelvin (hot enough to boil titanium and melt niobium)

Total heat flux: 8.79 megawatts

Temperature of a 90% reflective flat shield: 2,700 Kelvin (almost hot enough to boil aluminum)

Temperature of Sundiver’s conical shield (radiation only): 1,764 Kelvin (still too hot for aluminum)

Radiator temperature: 2,600 Kelvin (manageable)

Required heat conductivity: 1,000 Watts per meter per Kelvin difference (manageable)

Altitude: 0.25 solar radii

T+1 hour, 0 minutes, 40 seconds

Speed: 553 km/s

Solar irradiance: 40.3 megawatts per square meter (29,600)

Temperature of a perfect absorber: 5,200 Kelvin (hot enough to boil almost all metals. Not tungsten, though. Niobium boils.)

Total heat flux: 12.66 megawatts

Temperature of a 90% reflective flat shield: 2,900 Kelvin (more than hot enough to boil aluminum)

Temperature of Sundiver’s conical shield (radiation only): 1,900 Kelvin (way too hot for aluminum)

Radiator temperature: 2,900 Kelvin (more than manageable, but the radiant heat would probably hurt your eyes)

Required heat conductivity: 1,400 Watts per meter per kelvin difference (manageable)

Altitude: 0.1 solar radii

T+1 hour, 5 minutes, 25 seconds

Speed: 589 km/s

Solar irradiance: 52 megawatts per square meter

Temperature of a perfect absorber: 5,500 Kelvin (tungsten melts, but still doesn’t boil; tungsten’s tough stuff; niobium is boiling)

Total heat flux: 16.34 megawatts

Temperature of a flat shield: 3,000 Kelvin (tungsten doesn’t melt, but it’s probably uncomfortable)

Temperature of our conical shield: 2,000 Kelvin (getting uncomfortably close to aluminum’s boiling point)

Radiator temperature: 3,100 Kelvin (tungsten and carbon are both giving each other worried looks; the shield can cause fatal radiant burns from several meters)

Required heat conductivity: 1,600 watts per meter per kelvin difference (still manageable, much to my surprise)

Altitude: 0.01 solar radii (1% of a solar radius)

T+1 hour, 8 minutes, 11 seconds

Speed: 615 km/s

Irradiance: 61 megawatts per square meter

Temperature of a perfect absorber: 5,700 Kelvin (graphite evaporates, but tungsten is just barely hanging on)

Total heat flux: 19.38 megawatts

Temperature of a flat shield: 3,200 Kelvin (most materials have melted; tungsten and graphite are still holding on)

Temperature of our conical shield: 2,100 Kelvin (titanium melts)

Radiator temperature: 3,200 Kelvin (tungsten and graphite are still stable, but at this point, the radiator itself is almost as much of a hazard as the Sun)

Required heat conductivity: 1,900 Watts per meter per Kelvin difference (we’re still okay, although we’re running into trouble)

The Sundiver finally strikes the Sun’s surface traveling at 618 kilometers per second. Except “strike” is a little melodramatic. The Sundiver’s no more striking the Sun than I strike the air when I jump off a diving board. The Sun’s surface is (somewhat) arbitrarily defined as the depth the sun’s plasma gets thin enough to transmit over half the light that hits it. At an altitude of 0 solar radii, the Sun’s density is a tenth of a microgram per cubic centimeter. For comparison, the Earth’s atmosphere doesn’t get that thin until you get 60 kilometers (about 30 miles) up, which is higher than even the best high-altitude balloons can go. Even a good laboratory vacuum is denser than this.

But even this thin plasma is a problem. The problem isn’t necessarily that the Sundiver is crashing into too much matter, it’s that it’s that the matter it is hitting is depositing a lot of kinetic energy. Falling at 618 kilometers per second, it encounters solar wind protons traveling the opposite direction at upwards of 700 kilometers per second, for a total velocity of 1,300 kilometers per second. Even at photosphere densities, when the gas is hitting you at 1,300 kilometers per second, it transfers a lot of energy. We’re talking 17 gigawatts per square centimeter, enough to heat the shield to a quarter of a million Kelvin.

This spells the end for the Sundiver. It might survive a few seconds of this torture, but its heat shield is going to be evaporating very rapidly. It won’t get more than a few thousand kilometers into the photosphere before the whole spacecraft vaporizes.

In fact, even at much lower densities (a million hydrogen atoms per cubic centimeter), the energy flux due to the impacts of protons alone is greater than one solar constant. (XKCD’s What-If, the inspiration for this whole damn blog, pointed this out when talking about dropping tungsten countertops into the sun.) At 1.0011 solar radii, the proton flux is more than enough to heat the shield up hotter than a lightning bolt. As a matter of fact, when the solar wind density exceeds 0.001 picograms per cubic centimeter (1e-15 g/cc), the energy flux from protons alone is going to overheat the shield. It’s hard to work out at what altitude this will happen, since we still don’t know very much about the environment and the solar wind close to the sun (one of the questions Solar Probe+ will hopefully answer when (if) it makes its more pedestrian and sensible trip to 8 solar radii.) But we know for certain the shield will overheat by the time we hit zero altitude. The whole Sundiver will turn into a wisp of purplish-white vapor that’ll twist and whirl away on the Sun’s magnetic field.

But even if heating from the solar wind wasn’t a problem, the probe was never going to get much deeper than zero altitude. Here’s a list of all the problems that would kill it, even if the heat from the solar wind didn’t:

1) This close to the Sun, the sun’s disk fills half the sky, meaning anything that’s not inside the sunshade is going to be in direct sunlight and get burned off. That’s why I said earlier that the back of the Sundiver had to be very close to flat.

2) The radiator will reach its melting point. Besides, we would probably need high-power heat pumps rather than heat pipes to keep heat flowing from the 2,000 Kelvin shield to the 3,000-Kelvin radiator. And even that might not be enough.

3) Even if we ignore the energy added by the proton flux, those protons are going to erode the shield mechanically. According to SRIM, the conical part of the shield (which has a half-angle of 11 degrees) is going to lose one atom of aluminum for every three proton impacts. At this rate, the shield’s going to be losing 18.3 milligrams of aluminum per second to impacts alone. While that’s not enough to wear through the shield, even if it’s only a millimeter thick, my hunch is that all that sputtering is going to play hell with the aluminum’s structure, and probably make it a lot less reflective.

4) Moving at 618 kilometers per second through a magnetic field is a bad idea. Unless the field is perfectly uniform (the Sun’s is the exact opposite of uniform: it looks like what happens if you give a kitten amphetamines and set it loose on a ball of yarn), you’re going to be dealing with some major eddy currents induced by the field, and that means even more heating. And we can’t afford any extra heating.

5) This is related to 1): even if the Sun had a perfectly well-defined surface (it doesn’t), the moment Sundiver passed through that surface, its radiator would be less than useless. In practical terms, the vital temperature differential between the radiator and empty space would vanish, since even in the upper reaches of the photosphere, the temperature exceeds 4,000 Kelvin. There simply wouldn’t be anywhere for the heat to go. So if we handwaved away all the other problems, Sundiver would still burn up.

6) Ram pressure. Ram pressure is what you get when the fluid you’re moving through is too thin for proper fluid dynamics to come into play. The photosphere might be, as astronomers say, a red-hot vacuum, but the Sundiver is moving through it at six hundred times the speed of a rifle bullet, and ram pressure is proportional to gas density and the square of velocity. Sundiver is going to get blown to bits by the rushing gas, and even if it doesn’t, by the time it reaches altitude zero, it’s going to be experiencing the force of nine Space Shuttle solid rocket boosters across its tiny 3.142-square-meter shield. For a 1,000-kilogram spacecraft, that’s a deceleration of 1,200 gees and a pressure higher than the pressure at the bottom of the Mariana Trench. But at the bottom of the trench, at least that pressure would be coming equally from all directions. In this case, the pressure at the front of the shield would be a thousand atmospheres and the pressure at the back would be very close to zero. Atoms of spacecraft vapor and swept-up hydrogen are going to fly from front to back faster than the jet from a pressure washer, and they’re going to play hell with whatever’s left of the spacecraft.

Here’s the closest I could come to a pretty picture of what would happen to Sundiver. Why do my thought experiments never have happy endings?

Sundiver Descent Profile SM WM

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The Biology of Dragonfire

In a recent post, I decided that plasma-temperature dragonfire might be feasible, from a physics standpoint. There’s one catch: my solution required antimatter (and quite a bit of it). Antimatter does occur naturally in the human body, though. An average human being contains about 140 milligrams of potassium, which we need to run important stuff like nerves and heart muscle. The most common isotope of potassium is the stable potassium-39, with a few percent potassium-41 (also stable), and a trace of potassium-40, which is radioactive. (It’s the reason you always hear people talking about radioactive bananas. It also means that oranges, potatoes, and soybeans are radioactive. And cream of tartar is the most radioactive thing in your kitchen, unless you’ve got a smoke detector in there.)

Potassium-40 almost always decays by emitting a beta particle (transforming itself into calcium-40) or by cannibalizing one of its own electrons (producing argon-40). But about one time in 100,000, one of its protons will transform into a neutron, releasing a positron (the antimatter counterpart to the electron) and an electron neutrino. The positron probably won’t make it more than a few atoms before it attracts a stray electron and annihilates, producing a gamma ray. But that doesn’t matter, for our purposes. What matters is that there are natural sources of antimatter.

Unfortunately, potassium-40 is about the worst antimatter source there is. For one thing, its half-life is over a billion years, meaning it doesn’t produce much radiation. And, like I said, of that radiation, only 0.001% is in the form of usable positrons.

Luckily, modern medicine gives us another option. Nuclear medicine, specifically (which, by the way, is just about the coolest name for a profession). As you may have noticed by the fact that you don’t vomit profusely every time you go outside, human beings are opaque. We can shoot radiation or sound waves through them to see what their insides look like, but that usually only gives us still pictures, and it doesn’t tell us, for instance, which organs are consuming a lot of blood, and therefore might contain tumors. For that, we use positron-emission tomography (PET) scanners. In PET, an ordinary molecule (like glucose) is treated so that it contains a positron-emitting atom (most often fluorine-18, in the case of glucose). The positron annihilates with an electron, and very fancy cameras pick up the two resulting gamma rays. By measuring the angles of these gamma rays and their timing, the machine can decide if they’re just stray gamma rays or if they, in fact, emerged from the annihilation of a positron. Science is cool, innit?

One of the other nucleides used in PET scanning is carbon-11. Carbon-11 is just about perfect, as far as biological sources of antimatter go. It’s carbon, which the body is used to dealing with. It decays almost exclusively by positron emission. It decays into boron, which isn’t a problem for the body. And its half-life is only 20 minutes, which means it’ll produce antimatter quickly.

There’s one major catch, though. Whereas potassium-40 occurs in nature, carbon-11 is artificial, produced by bombarding boron atoms with 5-MeV protons from a particle accelerator. I may, however, have found a way around this. To explain, here’s a picture of a dragon:

Whole Dragon

No, those aren’t labels for weird cuts of meat. They’re to explain the pictures that follow.

Living things contain a lot of free protons. They’re the major driver of the awesome mechanical protein ATP synthase, which looks like this:

(The Protein DataBank is awesome!)

Sorry. I just really like the way PDB renders its proteins.

Either way, we know organisms can produce concentrations of protons. But in order to accelerate a proton, you need a powerful electric field. The first particle accelerators were built around van de Graaff generators, which can reach millions of volts. Somehow, I doubt a living creature can generate a megavolt.

Actually, you might be surprised. The electric eel (and the other electric fish I’m annoyed my teachers never told me about) produces is prey-stunning shock using cells called electroctyes. These are disk-shaped cells that act a little bit like capacitors. They charge up individually by accumulating concentrations of positive ions, and then they discharge simultaneously. The ions only move a little bit, but there are a lot of ions moving at the same time, which produces a fairly powerful electric current that generates a field that stuns prey. The fact that organisms can produce potential differences large enough to do this makes me hopeful that maybe, just maybe, a dragon could do the same on a nanometer scale, producing small regions of megavolt or gigavolt potential that could accelerate protons to the energies needed to turn boron-bearing molecules into carbon-11-bearing molecules. Here’s how that might work:

Bio-linac

There’s going to have to be a specialized system for containing the carbon-11 molecules, transporting them rapidly, and shielding the rest of the body from the positrons that inevitably get loose during transport, but if nature can invent things like electric eels and bacteria with built-in magnetic nano-compasses, I don’t think that’s too big a stretch.

The production of carbon-11 is going to have to happen as-needed, because it’s too radioactive to just keep around. I imagine it’d be part of the dragon’s fight-or-flight reflex. Here’s how I imagine the carbon-11 molecules will be stored:

Storage Zone

Note the immediate proximity to a transport duct: when you’ve got a living creature full of radioactive carbon, you want to be able to get that carbon out as soon as you can. Also note the radiation shielding around the nucleus. That would, I imagine, consist of iron nanoparticles. There might also be iron nanoparticles throughout the cytoplasm, to prevent the gamma rays from lost positrons from doing too much tissue damage.

Those positrons are going to have to be stored in bulk once they’re produced, though. This problem is the hardest to solve, and frankly, I feel like my own solution is pretty handwave-y. Nonetheless, here’s what I came up with: a biological Penning trap:

Usage Zone

These cells are going to require a lot of brand-new biological machinery: some sort of bio-electromagnet, for one (in order to produce the magnetic component of the Penning trap). For another, cells that can sustain a high electric field indefinitely (for the electric component). Cells that can present positron-producing carbon-11 atoms while simultaneously maintaining a leak-proof capsule and a high vacuum in which to store the positrons. And cells that can concentrate high-mass atoms like lead, because there’s no way to keep all the positrons contained. That’s probably wishful thinking, but hey, nature invented the bombardier beetle and the cordyceps zombie-ant fungus, so maybe it’s not too out there.

The process of actually producing the dragonfire is very simple, by comparison. The dragon vomits water rich in iron or calcium salts (or maybe just vomits blood). The little storage capsules open at the same time, making gaps in their fields that let the positrons stream out. The positrons annihilate with electrons in the fluid (hopefully not too close to the dragon’s own cells; this is another stretch in credibility). The gamma rays produced by the annihilation are scattered and absorbed by the water and the heavy elements in it, and by the time they exit the mouth, they’re on their way to plasma temperatures.

This is not, of course, the kind of thing nature tends to do. Evolution is a lazy process. It doesn’t find the best solution overall (because if you wanna talk about dominant strategies, having a built-in particle accelerator is up there with built-in lasers). It just finds the solution that’s better enough than the competitor’s solution to give the critter in question an advantage. So, although nature has jumped the hurdles to create bacteria that can survive radiation thousands of times the dose that kills a human on the spot, and weird things like bombardier beetles, insect-mind-controlling hairworms, and parasites that make snails’ eyestalks look like caterpillars so birds will eat them and spread the parasites, the leap to antimatter storage is probably asking a bit too much, unless we’re talking about some extremely specific evolutionary pressures.

Which is not to say that nature couldn’t produce something almost as awesome as plasma-temperature dragonfire. Let’s return once again to the bombardier beetle. The bombardier beetle has glands that produce a soup of hydrogen peroxide and quinones. Hydrogen peroxide likes to decompose into water and oxygen, which releases a fair bit of heat (which is why it was used as a monopropellant in early spacecraft thrusters). But at the beetle’s body temperature, the decomposition is too slow to matter. When threatened, however, the beetle pumps the dangerous soup into a chamber lined with peroxide-decomposing catalysts, which makes the reaction happen explosively, spraying the predator with a foul mix of steam, hot water, and irritating quinone derivatives. Here’s what that looks like:

So if nature can evolve something like that, is it too much of a stretch to imagine a dragon producing hydrogen-peroxide-laden fluid, mixing it with hydrogen gas, and vomiting it through a special orifice along with some catalyst that ignites the mixture into a superheated steam blowtorch like the end of a rocket nozzle? Well, look at that beetle! Maybe it’s not as far-fetched as it seems…

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How to Survive 100 Gees (Maybe…)

In a previous post, I discussed some of the gory things that would happen if you put me into a centrifuge and spun it up until I was experiencing an acceleration of 1,000,000 gees.

Now, I’m a science-fiction buff, so I’m all about imagining wild new technologies, but frankly, if I tried to handwave a way to protect myself against 1,000,000 gees, I’d be going pretty far towards the fantasy end of the science fiction-fantasy scale. I’d be far to the right of Firefly, beyond Star Trek, past Star Wars. Hell, I’d probably be closer to Lord of the Rings than to Star Wars.

But I set myself a challenge: figure out a way that a human being could survive 100 gees. That’s 980.665 m/s^2. That’s the acceleration of the Sprint missile, the scary awesomeness of which I’ve talked about before. Here’s the video of it again, because if you haven’t seen it, you should:

I’m obligated to remind you that the tracking shot in that video is played at actual speed. This bastard could accelerate from liftoff to Mach 10 in 5 seconds.

So let’s pretend I’ve invented a handwavium-burning rocket engine that can accelerate my capsule at 100 gees for, say, an hour. In my previous post (and based on experimental data, mostly from race-car crashes), we decided that 100 gees applied over more than a second would be more than enough to kill me. The problem, as I said, is the fact that I have blood, and at 100 gees, even if I was supine (on my back, the ideal position for tolerating accelerations when traveling in the back-to-front direction), that blood would collect at the bottom of my body, rupturing blood vessels and starving the upper parts of oxygen. My heart would almost certainly stop within seconds, either from pure mechanical strain, from the effects of pressure differentials, or because my ribcage caved in and turned it into carne asada.

But I’ve devised some absurd ways to get around this. The first is to put my acceleration couch into a sealed steel coffin (let’s face it, I’m gonna end up in a coffin one way or another; might as well save everybody the cleanup). The coffin will be filled with saline that approximates, as close as possible, the density of my body. Let’s say the coffin is an elliptical cylinder long enough for my body, 1 meter across the short axis, and 2 meters across the long axis. And let’s say I’m positioned so that I’m as close to the top of the tank as possible. (The tank has to be filled right to the brim. If it isn’t, the undulations of the surface will probably be more than enough to kill me.) Let’s say no part of me is deeper than 50 centimeters. At 50 centimeters’ depth, the hydrostatic pressure from my blood would be fifteen times the blood pressure that qualifies as an instant medical emergency: over 3,000 mmHg. More than enough to burst every capillary in my back, and probably the rest of the bottom half of my body.

But when I’m floating in saline that’s very close to the density of my body, the problem all but disappears. In the previous post, my capillaries only burst because they were experiencing a blood-related hydrostatic pressure (sounds like a weather forecast in Hell) of 4.952 bars (just over 5 atmospheres), with only 1.000 bars to oppose it. Things flow from areas of high pressure to low pressure. In this case, that probably means my blood flowing from the high-pressure capillaries through the slightly-lower-pressure skin and out onto the low-pressure floor of the centrifuge.

Suspended in saline, the story is different. The saline exerts 4.952 bars of hydrostatic pressure, exactly (or very nearly, I hope) opposing the pressure exerted by the blood, therefore meaning my heart doesn’t have to work itself to death trying to get blood to my frontal organs.

Speaking of organs, though, my lungs are the next problem. While I’m suspended in saline, they’ll be filled with air. Normally, I like my lungs being filled with air. It keeps me from turning blue and making people cry and then bury me in a wooden box. But air, being so light, doesn’t produce nearly the hydrostatic pressure that saline does, and so there’s nothing to keep my lungs from collapsing. Here’s a brief picture of how the lungs work: your chest is a sealed cavity (if it’s not, you’d better be in the ER or on your way there). The diaphragm moves down when you inhale. This increases the volume of the chest cavity. The lungs are the only part that can expand in volume, since they’re full of gas. That lowers the pressure, which draws air in. Ordinary human lungs weigh something in the neighborhood of 0.5 kilograms. So we know the diaphragm can cope with the weight of 1 kilo. At 100 gees, though, that rises to 100 kilos. Not even Michael Phelps’s diaphragm could make the lungs expand against that much weight.

But fret not! There’s (kind of) a solution! It’s called liquid ventilation, and it’s one of those cool sci-fi things that’s a lot realer than you might think. Instead of breathing gas, you breathe liquid. Normally, that’s bad news (remember the blue and the wooden box and the sad from before?). But certain liquids (for example, perfluorodecalin, a slightly scary-looking fluorocarbon) happen to be very good at dissolving oxygen. Good enough that people and animals have been kept alive while getting part (or, in a few cases, all) of their oxygen from liquid.

There is, however, one snag. Perfluorodecalin is denser than water. Its density is 1.9 g/cc. If the frontmost parts of my lungs are 5 centimeters from the top of the tank, then the hydrostatic pressure from the saline is 0.450 bars. 20 centimeters deeper, at the back of my lungs, the hydrostatic pressure from the saline is 2.450 bars. Meanwhile, the pressure from that heavy column of perfluorodecalin (plus the pressure from the water on top of it) is 4.180 bars. That’s almost a two-fold pressure differential. More than enough to blow out a lung. You might be able to overcome this problem by mixing one part perfluorodecalin with three or four parts high-grade inert mineral oil, but not being a chemist, I can’t guarantee that it’ll end well.

So you know what? Screw the lungs! Let’s just fill ’em with saline! (I wonder how many frustrated respiratory therapists have screamed that in their offices…) Instead, I’m going to get my oxygen the SCIENCE way! That is, by extracorporeal membrane oxygenation. Now, while it might sound like something that would involve a seance and a lot of ectoplasm, ECMO is also a real technology. It’s a last-ditch life-saving measure for people whose hearts and/or lungs aren’t strong enough to keep them alive. ECMO is the ultimate in scary life-support. Two tubes as thick as your finger are inserted into the body through a big incision. One into a major artery, and one into a major vein. The one in the vein takes blood out of the body and passes it through a machine that diffuses oxygen into the blood through a membrane and removes carbon dioxide. The blood’s temperature and pressure are regulated, and usually blood thinners like heparin are added to stop the patient’s blood sludging up from all the foreign material it’s in contact with. Then a pump returns it to the body, well-enough oxygenated to keep that body alive.

There are several hundred problems with using ECMO for ventilation under high G forces. One of them is, of course, that I have to have a tube rammed up my aorta. Another other is that I’d probably have to be anesthetized the whole flight. And yet another is the fact that those tubes and fittings are likely to be significantly more or significantly less dense than saline, and might therefore have enough residual weight (after the effects of buoyancy) to either pierce through my abdomen and into my spine, or float up and pull all my guts out.

So breathing is a problem. But let’s do another hand-wave and say we’ve invented a special polymer that can hold enough oxygen to keep me alive and can dissolve in saline without adding too much density and doesn’t destroy my lungs in the process. There are still problems.

The balance between the hydrostatic pressure exerted by the weight of my body and the pressure exerted by the weight of the saline means there’s either no pressure gradient between body and tank, or the gradient is survivable. But, although most of pressure’s effects depend on pressure differences, some of them depend on absolute pressure. One of those effects is nitrogen narcosis. Air is mostly nitrogen (78% by volume). Nitrogen, being a fairly inert gas, isn’t too important in respiration. But when it’s under high enough pressures, more and more of it starts to dissolve into the bloodstream. If this happens, and then the pressure suddenly falls, it bubbles back out of the bloodstream and you get the horrifying affliction known only as the bends. (Actually, it has lots of different names. Damn. Spoiled my own drama again…) But even if you don’t have sudden pressure drops, when the pressure gets above 2 bars, all that extra dissolved nitrogen starts to interfere with brain function. Since the maximum pressure I’ll be experiencing is about 4.910 bars, Wikipedia’s handy table tells me I’ll probably be feeling a bit drunk and clumsy. When you’re accelerating at 100 gees on top of a magic super-rocket, you really don’t want to be drunk and clumsy.

And it turns out divers who have to work underwater where everything can kill you don’t want to be drunk and clumsy either. But they can’t solve the problem by just breathing pure oxygen. In a normal atmosphere, oxygen’s partial pressure is 0.210 bars. Breathing 100% oxygen at the surface means breathing 1.000 bars. While it’s probably not good long-term, when you’re flying on a super-rocket, “not good long-term” means you can worry about all the other things that are about to kill you.

However, at high pressures, pure oxygen becomes toxic. In a slightly worrying paper from the British Medical Journal, some scientists described how they exposed volunteers to pure oxygen at a pressure of 3.6 atmospheres (about 3.6 bars). Some experienced troubling symptoms like lip-twitching, nausea, vomiting, and fainting after as little as 6 minutes. Even their toughest subject only lasted 96 minutes before suffering “prolonged dazzle” and “severe spasmodic vomiting.” If I was breathing 100% oxygen (in magic-liquid form, of course), some parts of my body would be much higher than that, so I’d be in serious trouble.

But those clever divers have figured out a way around this, too. Sort of. Instead of breathing pure oxygen at depth, they breathe blends of gas containing oxygen, nitrogen, and an inert gas like helium. This means that, for a given pressure, the partial pressure of oxygen will be lower than it would be in an oxygen-nitrogen or pure-oxygen mixture. That saves the diver from oxygen toxicity.

Of course, when you go deep enough, the nitrogen becomes an issue. Very deep divers sometimes breathe a gas mixture called heliox, which is just oxygen and helium (I recognize heliox from reading Have Space-Suit–Will Travel as a pimply, lonely adolescent). Helium has a much smaller narcotic effect than nitrogen. Since I’m going to be experiencing as much as 4.91 bars (let’s call it 5, to be safe), I need to adjust the mixture so that the partial pressure of oxygen stays around 0.210 bars. That means I’ll be breathing a mixture of 96% helium and 4% oxygen.

Because I’m a geek, I know that my lungs can inflate comfortably to 3 liters (they max out at 4 liters). That means, at 4% oxygen, I’ll be getting 120 milliliters of oxygen per breath. When I’m exercising or under severe strain (say, for example, when I’m trapped in a metal coffin at the top of a rocket accelerating at 100 gees), I need 2.2 liters of oxygen per minute. To get that much oxygen when each inhale gets me 120 milliliters requires a respiratory rate of 36 breaths per minute. That’s awfully fast for an adult, and when you consider that I’m either breathing magic low-density fluorocarbons or magic oxygenated saline, that’s a lot of work for my lungs to do, and a lot of wear and tear.

So my conclusion is that, sadly, I won’t be able to strap myself to a speeding infinite-fuel Sprint missile for an hour. But all this math makes me think that it’s probably possible to protect the human body against milder accelerations (say 10 gees) for long periods, using the same techniques. Any fighter pilots who want to climb into a saline coffin and breathe Fluorinert, let me know how it turns out.

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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 your 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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The Land Speed Record that Will Never Be Broken

As I’ve noted more than once, human beings like to make things go really fast. Part of me thinks that’s because we’re hunter-gatherers by nature, and somewhere deep in our limbic systems, we think that if we can make it to Mach 3, we’ll finally catch that damned antelope. The other part of me thinks we like it because it’s AWESOME!

As of this writing, the world land speed record stands at a hair over 763 miles per hour (almost 1228 km/h, or 341 m/s). The record is held by Andy Green and his ThrustSSC. This is the first land speed record to break the sound barrier. I must also note that when I looked at that page, the entry at the top of the “Related Records” section was the world’s thinnest latex condom. I’m starting to wonder what exactly Andy Green gets up to when he’s not cruising through Nevada at Mach 1.002…

But that’s just the record for the fastest land vehicle with a person inside it. The ultimate land speed record, as far as I can tell, is held by a multi-stage rocket sled at Holloman Air Force Base, which deals with creepy secretive things. Their rocket sled reached Mach 8.47, or 6,453 mph (or 10,385 km/h, or 2,885 m/s; why are there always so many damn units…). They’re not saying why, exactly, they’re accelerating a rocket sled to railgun velocities, but they’ve done it.

There’s no theoretical reason a human being couldn’t go that fast. (There are lots of practical reasons, but I’ve never let that stop me.) In fact, there’s no theoretical reason a land vehicle couldn’t go much faster. Technically speaking, if we ignore aerodynamic effects (which we theoretical types always do, which is why there are engineers to explain to us that astronauts don’t like burning up in the atmosphere), the fastest a land vehicle could ever go is 7.91 kilometers per second. That’s orbital speed at sea level. It’s Mach 23. This is the speed at which the centrifugal acceleration from traveling around the circular earth exactly balances the acceleration due to gravity. To put it another way, this is the speed where your vehicle becomes weightless, and if you go any faster, you’re going to leave the ground.

7.91 km/s is fast. Here’s a good way to understand just how fast it is. Say you’ve got a really good reaction time (around 100 milliseconds; let’s say you’ve had a lot of coffee). If you were trying to time this ultimate land-speeder on a 1,000-kilometer track (about 10 football fields end-to-end) with a stopwatch, the speedy bugger would have traveled from the beginning to the end of the track by the time your brain noticed that it had entered the track, processed the fact, and sent the signal to your finger to press the button on the stopwatch. It wouldn’t matter, of course, because you’d be obliterated by a superheated shockwave a moment later.

But even 7.91 kilometers per second isn’t the ultimate limit on land speed. As a matter of fact, if you have a vehicle that can reach that speed anyway, it’s going to have to have some aerodynamic surfaces on it to keep it from lifting off the ground and turning into the world’s fastest plane. But, while we’re adding downward thrust (in the form of aerodynamic lift, or perhaps I should say anti-lift), why not go all the way? Why not put some rockets on this thing and make it stay on the ground?

The fastest a human being could reasonably expect to travel across flat ground and survive is 23.7 kilometers per second. Before I get into explaining just how horrifically fast that is, and why you can’t go faster than that without killing the pilot, I want to paint a picture of the vehicle we’re talking about.

In all likelihood, it looks more like a plane than a land vehicle. It’s got some sort of massive engine on the back that burns sand to glass behind it. It’s got enormous wings to keep it from bounding into the stratosphere. It’s got rocket motors mounted on the tops of those wings. And we’re not talking wimpy JATO motors. We’re talking ballistic-missile-grade motors. Motors powerful enough that, if you just strapped a human to them, the human would have a hard time staying conscious through the acceleration.

The cockpit’s weird, too. It’s a sort of pendulum, with a reclined seat aligned along the axis of rotation. Because of the pendulum arrangement, the seat rotates so that the occupant always feels the acceleration as vertical. You could be forgiven for thinking this is some kind of Edgar Allan Poe torture device.

I’ll explain all that in a minute. But for right now, I want to convey to you how fast 23.7 km/s is. It’s the speed of extinction-triggering asteroids. It’s Mach freakin’ 71. It’s twice as fast as the crew of Apollo 10 (the holders of the ultimate human speed record) were moving on their way back to Earth. It’s faster than both the Voyager probes and New Horizons. Matter of fact, there are only two human-constructed objects that have ever gone faster than this: the amazing Galileo atmospheric probe, which dropped into Jupiter’s atmosphere so fast that all the speeding bullets in the world momentarily blushed (47.8 km/s, for those who don’t like overwrought metaphors), and the equally amazing Helios 2 probe, which holds both the record for the fastest human-built object and the human object that’s gotten closest to the sun (at perihelion, it was moving at 70.2 km/s; hopefully, NASA won’t can Solar Probe Plus and we can break that record).

23.7 km/s is one of those speeds that just doesn’t fit very well into the human mind, unless it’s the kind of human mind that’s accustomed to particle accelerators or railguns, and frankly, those minds are a little scary. At this speed, our peculiar death-trap vehicle could circumnavigate the Earth in 28 minutes and 9 seconds. It could travel from New York to Los Angeles in 2 minutes and 47 seconds.

“But hell,” I can hear you saying, “we’ve already got a ridiculous impractical land-speed vehicle. Why not crank it up all the way? Why not go as fast as Helios 2? Or faster!” The problem is that I specified a vehicle being driven (or at least occupied) by a human being. Before I explain, here’s a video of a person making a very funny face.

That’s a pilot in training being subjected to 9 gees in a centrifuge. You’ll noticed that he briefly aged about 60 years and then passed out. But he was being trained for practical stuff (that is, not blacking out when making a high-speed turn in an airplane). That’s boring. And, more relevant to our speed record, he was almost certainly experiencing gees from head-to-foot. Humans don’t tolerate that very well. The problem is that human beings have blood. (Isn’t it always?) When gee forces get very high, it takes a lot of pressure to pump blood to levels above the heart. Unfortunately, when you’re dealing with vertical gees, the brain is well above the heart, and all the blood essentially falls out of the brain and into the legs. (There are some ways to compensate for that, like with the weird breathing technique the trainee was doing and the pressure-compensating suits most high-gee pilots wear, but there are limits).

But even if the gees were from back to front (that is, you’re accelerating in the direction of your nose), 9 gees would probably still be the upper limit. Because, even lying down, that acceleration is going to make the blood want to pool below the heart. It’s going to flood into places where you don’t really need it like your buttocks, your calves, and the back of your head. In fact, at 9 gees, you run a pretty good risk of rupturing blood vessels in the back of your brain from the pressure. But human beings can tolerate 9 forward gees for a few seconds, so we’ll pretend they can tolerate it for the 2 minutes and 47 seconds it takes to blaze from New York to LA.

And that’s why we’ve got the weird pendulum recliner in our hypothetical ultra-hypersonic land vehicle: at 23.7 kilometers per second, the vehicle’s going to have to accelerate towards the ground at 9 gees just to keep from flying off into space. The pilot’s seat will be upside-down, relative to the ground, with the pilot all smashed down and funny-looking for the duration of the flight. If we try to go any faster, our pilot isn’t going to be able to survive the acceleration for more than a few seconds at a time. According to this nifty graph

(Source.)

whose source material I unfortunately couldn’t verify, a human being can’t tolerate 10 gees for more than 10 seconds. A human can tolerate 20 gees for 1 second (this I know to be true, because lunatic rocket-sled pilot John Stapp did it; actually, he pulled 25 gees for a full second, and in spite of all his insane rocket-sled stunts, lived to be 89). And human beings have been known to survive 30 gees or more (up to about 100 gees) for very brief periods in car crashes.

But trust me, the weird French organization that certifies land speed records (and air speed records, and altitude records) probably isn’t going to be very impressed by your traveling 50 km/s for a tenth of a second. If you want to go that fast long enough to actually get anywhere, you’re limited to 8 or 9 gees, and even then, you’d damn well better make sure your life insurance is up to date.

So, unless you use weird technologies like liquid respiration (in which you breathe oxygenated liquid fluorocarbons instead of air, and which is a real thing that actually exists and is sometimes used for hospital patients with burned lungs) and those creepy full-body gee-tanks from Event Horizon, the 23.7 km/s land speed record can never be broken. Partly because of the gee-forces involved, but mainly because trying to go that fast on land is absolutely, certifiably insane.

Tune in next time, where I get all gory and try to imagine what would happen to a human body exerted to much larger gee forces.

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