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.)

Why the hell am I talking about mining equipment, you ask? Let me distract you from that question with another picture.

crawler-transporter

That is one of NASA’s Crawler-Transporters. There are two of them (nicknamed Hans and Franz, which makes a nice change). They were the workhorses of NASA’s crewed spaceflight program from 1965 onward. Hans and Franz moved every Saturn V and every Space Shuttle from the Vehicle Assembly Building to the launchpad. (That sounds like the start of a really weird German children’s story…) Funnily enough, the Crawler-Transporter, like the Liebherr, is a diesel-electric machine. It’s got two Alco locomotive diesels to power its sixteen traction motors, and two more Cummins diesels to run the hydraulic leveling system and everything else. One more cool thing: even though they first become operational way back in 1966, they’re not scheduled to be retired anytime soon: they’re slated, with modifications, to carry the Space Launch System, whenever NASA gets that up and running.

One more detour, and then I promise I’ll start talking about rolling cities. Meet my friend Otto.

alma_en_route_to_chajnantor_28scale29

Okay, he’s not actually my friend. On account of he’s a truck and don’t got no emotions. But that’d make for a cool cartoon, wouldn’t it? Either way, Otto is responsible for transporting the radio antennas that make up the Atacama Large Millimeter Array (ALMA). Otto’s job is anything but easy. He has to work in one of the driest, harshest places on Earth: Chile’s Atacama Desert. He spends his life hauling antennas as heavy as 115 metric tons at high altitudes, where the air is thin. He has to navigate unpaved roads, and then he has to set the antennas on their concrete pads with literal millimeter precision.

I mention Otto because he’s a good example of another class of heavy machinery: the awesome self-propelled modular transporter (SPMT).One more picture.

dsc04658

That terrifying spectacle is an SPMT (which is just the wheels and the red platform at the bottom) moving a record-breaking 13,191-tonne offshore oil platform. And when I say record-breaking, I mean Guinness-certified. Although it’s not the fastest thing in the world (1 mph is fast for a SPMT), a fleet of SPMTs can transport just about anything. If you Google SPMT, you’ll see pictures of them transporting oil platforms, ships, gigantic pressure vessels, massive stacks of steel plates, huge blades for wind turbines, gigantic transformers (electrical, not cartoon), pieces of bridges… Basically, if you’ve gotta move an enormous thing, an SPMT is a good way to do it.

But the real reason I bring SPMTs up is their unique drivetrain. I refer you to the picture above. That oil platform is being supported by 512 axles. The axles join close-set pairs of wheels, and each pair can steer independently of the others and provide power independent of the others. You know how there are 4×4 offroad trucks and 8×8 military trucks? Hah! Try 512×512. When I first heard about SPMTs, I couldn’t wrap my head around how they got power to the wheels. I knew they weren’t electric. I knew they couldn’t be traditional driveshaft-type wheels. Try to figure out how to arrange a branching tree of driveshafts, transfer cases, and differentials for 512 wheels, and you’ll be in a madhouse faster than John Trent.

No. SPMTs have a much more elegant solution. They use their diesel-engine modules (referred to as “power packs”, which amuses me for some reason) to drive hydraulic pumps. Hydraulic cylinders act as the SPMT’s suspension. And nifty devices called hydraulic motors act as the motors.

So here’s what we know: transporting loads in excess of 10,000 tonnes is entirely feasible, but it’s gonna take a lot of wheels. I’m imagining a sort of hundred-axled SPMT, but instead of those little truck-type wheels, it has four-meter-wide Liebherr wheels. But I’m getting ahead of myself. Let’s do some math and see if that’s feasible, or if we really are gonna need ten thousand wheels.

The Load

Here’s a picture of the only ship I’ve ever been on.

OLYMPUS DIGITAL CAMERA

That is the Norwegian Star, on which I sailed to Alaska. Why the hell am I showing you pictures of cruise ships? I’m glad you asked, hypothetical person. The reason is that, according to my guesswork, a cruise ship is a good middle-of-the-road benchmark for a mobile community that can sustain itself for long periods, if not indefinitely. After all, ships of similar size make trans-Atlantic and trans-Pacific voyages all the time, relying on nothing but their own cargo of consumables and fuel.

A cruise ship is a handy benchmark for a bunch of other reasons: it packs both necessities and luxuries into a reasonably small space. It’s more horizontal than vertical, which makes tipping over less of a problem. (In some of the preliminary calculations, I imagined putting a vertical skyscraper on wheels. Balance was a big problem.) And, unlike a skyscraper, its mass is well-known.

I’m going to assume that a self-sufficient community will mass around 50,000 tonnes (the displacement of the Titanic, which is similar to that of modern cruise ships). Since we don’t have to deal with water and therefore don’t need a bulky hull, I could probably shave a few thousand tonnes off that figure, but as you know, I prefer a pessimistic estimate to an optimistic one.

Our community, therefore, is a refurbished cruise ship. Saw the keel off. Strip the top deck down to the boards and cover it with hydroponic farms, pens for livestock, and biodiesel fermenters. Drop it onto a suitable chassis. Put that chassis on wheels. Bam! Rolling town!

Well, actually, the rolling part is where it gets tricky…

The Hard Part

The formula for rolling resistance (the force needed to drag a given load on wheels) is beautifully simple: it’s a dimensionless coefficient that tells you what percentage of the load’s weight gets converted into opposing force. If you can’t overcome the rolling resistance, then your load’s not going anywhere. The best-case scenario for rolling resistance is a fairly hard wheel on a fairly hard, flat surface. For steel train wheels on steel rails, the coefficient can be 0.001 or less. For a truck tire on a hard surface, the coefficient is something like 0.005. Among the worst-case scenarios is a car tire on sand: the rolling resistance is 0.3. I’m going to experiment with coefficients of rolling resistance between 0.005 and 0.5, to test the feasibility of driving around in a cruise ship. I’ll be honest, though: 0.005 is probably way too optimistic. As you’ve probably noticed if you’ve ever lost a boot in mud, nature is not a big fan of hard surfaces. And unless I come up with some alternate universe where highways are 200 meters across (which would be awesome, Department of Transportation. Just saying), the City on Wheels probably isn’t going to spend much time on roads. But 0.005 is still at least within the realm of sensibility.

Either way, the City on Wheels masses 55,000 tonnes, figuring 5,000 extra tonnes for the chassis, wheels, drivetrain, and engine. That means it weighs 539 meganewtons. In Europe, tractor-trailers are very rarely allowed more than 10 tonnes per axle. That means 5,500 axles or 11,000 wheels. Not good.

But then again, what are the Polizei gonna do? Pull my rolling cruise ship over! Hah! Sie können ünter ein Rasenmäher schlafe! We can go above 10 tonnes per axle!

SPMTs are more forgiving: 40 tonnes per axle line (which is what you call a pair of wheels either side of your machine when there’s no physical axle joining them, I think). That cuts our number down to 1,375 axles, or 2,750 wheels. I have an issue with this: every wheel we add comes with a certain level of inefficiency. Good engineering can make that very small, but can’t make it zero. So, the fewer wheels, the better. Well, BelAZ to the rescue! Their 75170 dump truck (not to be confused with the more massive 75710; alphabet soup strikes again) can carry something like 140 tonnes per axle. The actual 75710 can do 400 tonnes per axle. So, for haul trucks, 100 tonnes per axle is not unreasonable. That means 550 axles, or 1,100 wheels. A few more than were used to haul that oil platform from before, but still within reason. Well, more or less…

But the real question remains: is there any engine that can actually overcome the rolling resistance of those 1,100 wheels. In the best-case scenario (a rolling resistance of 0.005), we need 2.7 meganewtons of tractive force (which is just a fancy way of saying force applied by the wheels). If we assume wheels 2 meters in diameter (which is almost reasonable), a maximum speed of 10 mph (4.47 m/s), and 100 tonnes per axle, we’re going to need 29.35 horsepower per axle. How did I get that number? Well, I know the torque per axle: it’s got to be at least equal to the rolling resistance (force) times the radius of the wheel (length). And I know the angular velocity of the wheel, since I know its radius and its overland speed (4.47 m/s). From torque and angular velocity, you can get power required. In total, we need, at absolute minimum, 16,200 horsepower. That’s a hell of a lot, but entirely doable. I’ve already shown you one engine that can deliver that much power. Here it is again, for the sheer spectacle:

t4axht8

That’s the Finnish-made Wärtsilä-Sulzer RTA96-C (I’m calling it Gustav, because I’m tired of alphabet soup). It can deliver over 40,000 horsepower. I’ve just noticed something a little scary. Look at the top-right of the engine. There’s a toroidal gray object. You know what that is? That’s a fucking turbocharger. A turbocharger big enough to suck you up and grind you to a pulp like a jet engine. I wonder if the engineers on ships that use the Gustav spend a lot of time worrying about that.

But that’s only in the most optimistic scenario. If we assume a much more realistic rolling-resistance coefficient of 0.1, then we need 588 horsepower per wheel. To give you some perspective, even the Dodge Viper’s engine, with its 8.3 liter (506 cubic inch) V10, can’t quite turn a single wheel.  You’d need six of my car’s engines to do it. The total is a horrifying 323,400 horsepower. Or, to put it in nuclear terms, 241 megawatts. Why am I putting it in nuclear terms? Because I think nuclear power is probably our best option, once we need this much power in a (relatively) small space. A lot of long-haul ships use nuclear reactors anyway. I always assumed nuclear power was only for military vessels like aircraft carriers and submarines, but as it turns out, the American merchant ship NS Savannah had a nuclear reactor, and the still-operational Russian icebreaker and container ship Sevmorput has one. Russia also has a couple dozen dedicated nuclear icebreakers. And we might need to turn to Russia to power our rolling city, because Russian engineers are working on the VBER-300, a 1,300-ton pressurized water reactor meant for desalination, running ships, and powering and heating remote cities (which Russia has a lot of). The VBER-300 can produce, like the name hints, over 300 megawatts of electrical power, and it’s small enough to fit on our rolling city without breaking our weight budget. Here’s how I imagine the rolling city: an engineering section at the back with plenty of security and shielding. The VBER-300 (or multiples thereof) runs steam turbines that produce electricity. The electricity is used to power lighting, heating, and other necessities, but mostly to run 550 gigantic traction motors.

The reason I say we might need more than one VBER-300 is that I haven’t done the math for the worst-case scenario yet: a rolling resistance coefficient of 0.5. Unsurprisingly, since the rolling-resistance coefficient is five times larger than in the previous case, each axle needs five times the horsepower: 2,940 horsepower per axle. That’s six Dodge Viper engines per axle, or three Bugatti Veyron engines. I have a bad feeling about our power requirements…

Well, it just so happens that we need Christopher Lloyd’s DeLorean, because we need just under 1.21 gigawatts. 1.2056 gigawatts, to be exact. I couldn’t come up with a more perfect Back to the Future reference if I tried. I think we’ll ditch the VBER-300. We’ll need five of them to get the power we need, and that’s a lot of extra weight. Better to combine the reactors into one common plant that only needs one set of shielding and one set of turbines. Let’s use a CANDU reactor. One of those could probably be beefed up to give us over 1.21 gigawatts. The individual reactors at Ontario’s Darlington Nuclear Generating Station already produce almost a gigawatt each.

Of course, a nuclear reactor this size is a meltdown risk, it needs a lot of cooling water and machinery, and it requires pretty hefty shielding. In other words, weight limits and safety concerns push the rolling city right to the bleeding edge of feasibility. It’s the kind of thing that would take the commitment of a large industrial nation (or a Bond villain) to build. But it could probably be done. Here’s what it might look like:

And once it was done, you’d have the ultimate doom fortress: an all-terrain city for housing and training your minions, completely self-sufficient (well, for as long as your fuel rods last, but that can be a very long time if you reprocess them yourself) and unstoppable by anything smaller than a tactical nuke or a really huge patch of airport tire-spikes.

Either way, I’ve finally answered the question to my own satisfaction. Can you drive around in a mobile fortress the size of a cruise ship? Probably, although it’s not exactly going to be easy to pull off, and a major failure in the suspension (say, from an army jet angry that you just steamrolled its base) will bring it to a grinding halt. Hell, a rolling fortress could be defeated by a nice deep bulldozer trench. Maybe that’s why flying fortresses and sea fortresses and space fortresses are so much more popular. But they’re not nearly as intimidating as seeing this rolling your way:

Rolling_Titanic_Better.png

But hey…flying fortresses. Look for that in an upcoming post!

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One thought on “A City on Wheels

  1. Pingback: Addendum: A City On Wheels | Sublime Curiosity

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