A Toyota in Space

I talk all the time about the weird nerdy epiphanies I had as a kid. One of those epiphanies involved driving a car around on the outside of a space station. I realized that the car would have to bring along its own air supply, because an internal combustion engine can’t run on vacuum. I know that sounds obvious, but when you consider I was like nine years old at the time, it’s almost impressive that I figured it out. Almost.

Now that I’m older, I realized “Hey! I can actually figure out how much air I’d need to bring with me!” Conveniently, the worldwide craze for automobiles (some say they’ll replace the horse and buggy. I think that’s a pretty audacious claim, sir.) means that all sorts of vital statistics about gasoline engines are known. For instance: the air-fuel ratio. It’s as simple as it sounds. It’s the mass of air you need to burn 1 mass unit of fuel. The “ideal” ratio is 15:1: combustion requires 15 grams of air for every gram of fuel burned. Of course, if you’ve watched Mythbusters, you’ll know that stoichiometric (ideal) mixtures of air and fuel detonate, often violently. You don’t actually want that happening in a cylinder. You want subsonic combustion: deflagration, which is rapid burning, not an actual explosion. Supersonic combustion (detonation) produces much higher temperatures and pressures. At best, it’s really rough on the. At worst, it makes the engine stop being an engine and start being shrapnel. So, in practice, mixtures like 14:1 and 13:1 are more common. I’ll go with 14:1, although I freely admit I don’t know much about engines, and might be talking out my butt. No change there.

Either way, we now know how many mass units of air the engine will consume. Now, we need to know how many mass units of fuel the engine will consume. There are lots of numbers that tell you this, but for reasons of precision, I’m using one commonly used in airplanes: specific fuel consumption (technically, brake specific fuel consumption). The Cessna 172 is probably the most common airplane in the world. It has a four-cylinder engine, just like my car, though it produces 80% more horsepower. Its specific fuel consumption, according to this document, is 0.435 pounds per horsepower per hour. The Cessna engine produces 180 horsepower, and my car produces 100, so, conveniently, I can just multiply 0.435 by 100/180 to get 0.242 pounds per horsepower per hour. Assuming I’m using 50% power the whole way (I’m probably not, but that’s a good upper limit), that’s 50 horsepower * 0.242, or 12.1 pounds of gasoline per hour.

So, we know we need 12.1 pounds of gasoline per hour, and from the air-fuel ratio, we know we need 169.4 pounds of air per hour. That’s all fine and dandy, but I’m not sure how much room 169.4 pounds of air takes up. Welders to the rescue! According to the product catalog from welding-gas supplier Airgas, a large (size 300) cylinder of semiconductor-grade air has a volume of 49 liters, and the air is stored in that bottle at about 2,500 PSI. (I don’t know what you actually do with semiconductor-grade air, but it’s got the same ratio of gases as ordinary air, so it’ll do.) At room temperature, the bottled air is actually a supercritical fluid with a density 1/5th that of water. Therefore, each cylinder contains about 10 kilograms (22 pounds) of air. Much to my surprise, even when it’s connected to an air-hungry device like an internal combustion engine, a single size-300 cylinder could power my car for over seven and a half hours.

But you guys know me by now. You know much I like to over-think. And I’m gonna do it again, because there are a lot of things you have to consider when driving a car in a vacuum that don’t come up when you’re driving around in air.

Thing 1: Waste heat. This is a major issue for spacecraft, which live in a vacuum (unless you’ve really screwed up). The problem is that there’s only one good way to expel waste heat in a vacuum: radiation. Luckily, the majority of automobile engines are already radiator-cooled. Normally, they depend on heat flowing from the engine to the cooling water, into the metal fins of a radiator, and into the atmosphere. In vacuum, the cooling will run engine-water-radiator-vacuum. The engine produces 100 horsepower at maximum, which is about 75 kilowatts. A radiator operating at the boiling temperature of water radiates about 1,100 watts per square meter, for  a total area of 68 square meters, which means a square 27 feet (8.2 meters) on a side. You could play tennis on that. Luckily, the radiator is two-sided, which cuts the radiator down to a square 19 feet (5.8 meters) on a side. It’s still going to be larger than my car, but if I divide it into ten fins, it would only be absolutely ridiculous, rather than impractically ridiculous. That’s already my comfort zone anyway.

Thing 2: Materials behave differently in a vacuum. Everything behaves differently under vacuum. Water boils away at room temperature. Some of the compounds in oil evaporate, and the oil stops acting like oil. Humans suffocate and die. To prevent that last one, I’m going to have to beef up my car’s cabin into a pressure vessel. And since I’m doing that, I’ll go ahead and do the same to the engine bay, so that I don’t have to re-design the whole engine to work in hard vaucuum. I’ll make the two pressure vessels separate compartments, because carbon monoxide in a closed environment is bad and sometimes engines leak.

I’ll also have to put a one-way valve on the exhaust pipe, because my engine is designed to work against an atmospheric pressure of 1 atmosphere, and I feel like working against no pressure at all would cause trouble. I’m also going to have to change the end of my exhaust pipe. I’ll seal it off at the end and drill lots of small holes down the sides, to keep the exhaust from acting like a thruster and making my car spin all over the place.

Thing 3: Lubrication. A car’s drivetrain and suspension contain a lot of bearings. There are bearings for the wheels, the wheel axles, the steering linkages, the universal joints in the axles, the front and rear A-arms… it just goes on and on. Those bearings need lubrication, or they’ll seize up and pieces will break off, which you very rarely want in engineering. Worse, in vacuum, metal parts can vacuum-weld together if they’re not properly protected. We can’t enclose and pressurize every bearing and joint. That would make my car too bulky, for one. For two, there would still have to be bearings where the axles came out of the pressurized section, so I’ve gotta deal with the problem sooner or later. Luckily, high-vacuum grease is already a thing. It maintains its lubricating properties under very high vacuum and a wide range of pressures, without breaking down or gumming up or evaporating. We’ll need built-in heaters to keep the grease warm enough to stay greasy, but that’s not too big a hurdle.

Thing 4: Tires. My car’s owner’s manual specifies that I should inflate my tires to 35 psi (gauge). I’ll have to inflate them to a higher gauge pressure in vacuum, since they’ll have almost no pressure working against them. If I don’t, they’ll be under-inflated, and that’ll make them heat up, and in vacuum, that goes from a minor problem to a potentially fatal tire-melting and tire-bursting disaster. Actually, I think I’ll eliminate that risk altogether. I’ll do what most rovers do: I’m getting rid of pneumatic tires altogether. Because my car’s going to be fast, heavy and have a human passenger, I can’t do what most rovers have done and just make my wheels metal shells. I need some cushioning to stop from rattling myself and my car to pieces.

That’s Gene Cernan driving the Lunar Roving Vehicle (the moon buggy). It’s about five times lighter than my car, but it proves that airless tires can work at moderate speed. Michelin is also trying to design airless rubber tires for military Humvees, and while they don’t absorb shocks quite as well as pneumatic tires, they can’t puncture and explode like pneumatic tires. So I’m going with some sort of springy metal tire, possibly just composed of spring-steel hoops or something like that.

Thing 4: Fuel. If I was sensible, I’d have chucked the whole idea of powering a vacuum-roving Toyota with a gasoline engine. (Actually, I’d have chucked the whole idea of a vacuum-roving Toyota and started from scratch…) We know I’m not sensible, so I’m going to demand that my Lunar Toyota run on gasoline. 10,000 liters of gasoline (I like to mix units, like an idiot) will let me drive 42,500 kilometers. Enough to go around the Moon’s equator three (almost four) times. You might think that carrying a small tanker’s worth of gasoline to the Moon is an impossible feat, but when you consider that the mass of my car (about 1,000 kilograms) plus the mass of all that gasoline (7,300 kilograms) plus tankage is less than the weight of the Apollo Command-Service Module and the Lunar Module, not only does the Apollo program seem that much more audacious and impressive, but it becomes possible to talk sensibly (sort of…) about putting my car, my air tanks, and a lifetime supply of gasoline on the Moon. That also takes care of…

…Thing 5: Getting my car on the Moon. We can just use a Saturn V, or wait for the engineers to finish building the Falcon Heavy or Space Launch System. Lucky for me, the rocket scientists have already solved the problem of landing a heavy vehicle, too: the ballsy sky-crane landing used during the Curiosity rover’s descent would almost certainly work just fine for my car, since it’s only 200 kilograms heavier than Curiosity. The fuel and air can just be landed under rocket power, or by expendable airbags.

So it wasn’t all that insane for my nine-year-old self to imagine driving an ordinary street car around on the Moon. That is, from the point of view of fueling and aspirating (ventilating? aerating? Providing air to, is what I mean…) the engine and the passenger. But the physics of driving around in vacuum and/or under low gravity pose another challenge, and that challenge is interesting enough to get a post of its own. Watch this space!

Addendum: A City On Wheels

While I was proofreading my City on Wheels post, I realized that I’d missed a golden opportunity to estimate just how heavy a whole city would be. When I was writing that post, I wanted to use the Empire State Building’s weight as an upper limit, because I was pretty sure that would be enough space for a whole self-sufficient community. Trouble is, the weight of buildings isn’t usually known. The Empire State Building’s weight is cited here and there, but never with a very convincing source. I couldn’t figure out a way to estimate its weight that didn’t feel like nonsense guesswork. That’s why I used the Titanic’s displacement as my baseline.

The reason estimating the mass of a building was so tricky is that, generally, buildings are far form standardized. Yeah, a lot of houses are built in similar or identical styles, but even if you know their exact dimensions, converting that into a reasonably accurate weight turns into pure guesswork, because you don’t know what kind of wood was used in the frame, how much moisture the wood contained, how many total nails were used, et cetera. But, just now, I realized something. There is a standardized object that represents the shape, size, and weight of a dwelling pretty well: the humble shipping container.

You may notice that that’s not a shipping container. It’s a bunch of shipping containers put together to make a rather stylish (if slightly industrial-looking) house. Building homes out of shipping containers is a big movement in the United States right now. They’re cheaper than a lot of alternatives, and they’re tough: shipping containers are built to be stacked high, even while carrying full loads. For example:

The things are sturdy enough that they far exceed most building codes, when properly anchored. Their low price, their strength, and the fact that they’re easily combined and modified, has made them popular as alternative houses.

Because different shipping containers from different manufacturers and different countries often end up stacked together, they all have to be built to the same standard. Their dimensions, therefore, are standardized, which is good news for us. I re-imagined the rolling city as a stack of shipping containers approximately the size of the Titanic, with their long axes perpendicular to the ship’s long axis. You could fit two across the Titanic‘s deck this way, and 110 along the deck, and if you stacked them 20 high, you’d approximate the Titanic’s shape and volume. To account for the fact that the people living in these containers are going to have furniture, pets, physical bodies, and other inconvenient stuff, I’ll assume that each container would have twelve pieces of the heaviest furniture I could think of: the refrigerator.

Amazon is a great thing for this kind of estimation, because from it, I learned that an ordinary Frigidaire is about 300 pounds. Multiply that by twelve, add the mass of the container itself (3.8 metric tons each), round up (to keep estimates pessimistic), and you get 6 metric tons per container. Considering that a standard 40-foot intermodal container (which is the standard I worked with) can handle a gross weight (container + cargo) of over 28 metric tons, we’re nowhere near the load limit for the containers. There are 4,400 containers in all, for a total mass of 26,400 metric tons. Increase the mass by 25% to account for the weight of the nuclear reactor, chassis, and suspension, and we get 33,000 metric tons. That’s still a hell of a lot, but it’s only just over half of the 50,000 tonnes we were working with before.

As you might remember, I wrote off the Titanic-based city on wheels as probably feasible, but requiring a heroic effort and investment. But using the shipping container mass, which is 1.5-fold smaller, I think it moves into the “impressive but almost sensible mega-project” category, along with the Golden Gate Bridge, the Burj Khalifa, the Great Pyramid of Giza, and Infinite Jest.

Another note: There’s one heavy, mobile object whose weight I didn’t mention in the City on Wheels post: the Saturn V rocket. I did mention the Crawler-Transporter that moved the Saturn V from the Vehicle Assembly Building to the launchpad, however. And the weight of the fully-loaded Saturn V gives us an idea of how massive an object a self-propelled machine can move: 3,000 tonnes. Because, to nobody’s surprise, NASA knows the weight of every Apollo rocket at liftoff. Because it’s mildly (massively) important to know the mass of the rocket you’re launching, because that can make the difference between “rocket in a low orbit” and “really dangerous and expensive airplane flying really high until it explodes with three astronauts inside.”

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:

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.)

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.