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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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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