Tag Archives: g

Uncategorized

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.

Standard
Uncategorized

Centrifuging Fruit

In my last post, I detailed some of the very gory things that would happen to a human being in a high-gee centrifuge. Then I remembered that I have access to a high-gee centrifuge. Sort of. You see, I’ve got one of those fancy front-loading washing machines. It saves time on drying by spinning your clothes at a ridiculous speed at the end of the wash cycle. And when I say “ridiculous speed”, I’m talking 1,100 RPM (at least, according to the manufacturer). That’s 18 revolutions per second! I measured the drum’s diameter at 55 centimeters. If you do the math, it tells you that the acceleration on the inner surface of the drum, when the thing’s running full pelt, is 372 gees. Okay, so it’s not ultracentrifuge material, but that’s still a lot of acceleration.

And I thought, you know what? We’ve got some fruit in the refrigerator that would be just as tasty pulped as it would be whole. Let’s see what 372 gees does to it! (Sometimes, I worry about how close I came to growing up to be a serial killer…)

I’ve tried this experiment once before (for another blog, which is why this one might look a bit familiar). Let’s do it again, but this time, with our gory, scary centrifugal thought experiment in mind. Here are our astronauts:

1 - The Astronauts

That’s a plum and a lime. The plum was pretty soft. We had a firmer one, but it wouldn’t fit in the container, and, crazy as I am, I didn’t want to risk splattering the inside of my washing machine with plum pulp. The lime, on the other hand, was so hard it could probably cut glass. Either way, these are our volunteers (it was a pain in the bum getting them to sign the release forms, let me tell you…) Let’s seal them in their space capsule.

2 - The Capsule

I must say, they look pretty brave, as far as produce goes. Note the extra precautions: each fruit sealed in an individual bag, and packing tape to seal up the container. I didn’t want it flipping over during spin-up and seeping stuff everywhere. But enough talk! Let’s get ’em in the centrifuge!

3 - In Position

There they are, their capsule strapped into place. Can you tell how worried I was I’d end up painting the inside of my washing machine with fruit?

4 - Spin

I could’ve sworn I heard a high-pitched shriek when the washer reached maximum spin. Then again, I’ve been hearing a high-pitched shriek ever since the Exploding Kikkoman Bottle Incident, so perhaps it’s just me.

5 - Max G

This is what the picture above would have looked like if I’d remembered to turn the flash on. Believe it or not, the drum is actually spinning here. Sometimes, I’m impressed by what my cheap little point-and-shoot camera can do. And then I remember that it’s got no time-lapse or long-exposure settings, and I stop being impressed. Either way, in this picture, the top of the container is experiencing about 237 gees (2,322 m/s^2). The bottom is experiencing 372 gees (3,649 m/s^2). The difference is because the top of the container is significantly closer to the axis of rotation than the bottom, and the acceleration is the distance from the axis times the square of the angular velocity. I’m surprised how well the space capsule tolerated the gees. I shouldn’t be surprised. After all, lives are at stake here. The capsule was engineered to survive all conditions. Still, considering how many times that capsule has been through the dishwasher, I’m impressed that it didn’t collapse.

Other things, however, did collapse…

6 - There Can Be Only One

This is almost exactly how our juicy astronauts were when I pulled them out of the centrifuge. I moved them around for photographic purposes, but that’s it, and even I’m not clumsy enough to completely obliterate a plum just by touching it. At least not when I’ve had my coffee.

The lime did remarkably well. It was noticeably flattened on the bottom, but it was very much intact. Now, under 1 gee (earth surface gravity), my scale says that a similar lime (someone ate my surviving astronaut; the nerve!) weighed around 100 grams. Under 372 gees, that lime weighed the equivalent of 37 kilograms. That’s 82 pounds. That’s the size of the dumbbells those really gigantic scary guys with the tattoos are always curling at the gym. It’s heavier than a gold bar. But the lime had little trouble. It’s the toughest substance known to man. I feel sorry for whoever ate it.

The plum, as you can see, didn’t fare so well. Here’s a gory close-up:

7 - The Aftermath

(Just an aside: I wonder if there’s anybody who’s genuinely upset by the sight of squashed fruit. Not in a “that’s a waste of food” sense, but in a visceral sense, the way some people can’t stand the sight of blood. If that’s you, I apologize. And you might want to consider some counseling. I’d give you the number of my therapist, but she lives on Jupiter.)

That plum is flattened. It looks like it was squashed under a very heavy weight. Which is exactly what happened. I don’t have a similarly-sized plum for comparison, but I’d say it’s reasonable to assume that, without all that weird white pithy stuff to decrease the density, the plum was at least twice as heavy as the lime, meaning, at maximum acceleration, it weighed almost 80 kilograms (176 pounds). That’s as much as my cousin. (I would invite her over for a comparison test, but even I recognize that “Will you come to my house and stand on a plum for me?” is a pretty weird request.)

But here you have an excellent practical demonstration of what I talked about in the last article. Under high acceleration, the weight of the plum exceeded its structural strength, and it split and oozed horribly all across the bottom of its bag. If the pit had been denser, it might very well have squelched down through the pulp and ended up on the bottom, but even my terrifying washing machine has its limits.

Oh, and before anybody complains that I’m wasting food on silly experiments… First of all, NYEH. Second of all, I didn’t waste it. I ate the plum. Somebody else ate the lime (for some reason). And you know what? That plum was one of the most delicious things I’ve ever eaten. I’m serious. It was all squishy and ripe. I used it because I thought it had gone over the edge already. But no. It was perfect. So not only did I get to centrifuge something, but I got some lovely fruit, too! I might have to try these practical experiments more often…

Or perhaps not. I must remember the Exploding Kikkoman Bottle Incident…

Standard
Uncategorized

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.

Standard