.. of alcohol and math.
Ever argue a point with somebody? Ever do it when the other person doesn’t know math? What’s this supposed to mean? Well, somebody didn’t understand why the mileage on the car can be off if your tyres aren’t the standard size. I mean, the odometer knows about speed variations, so you can’t argue that. But it’s off quite a bit if it comes to checking it against some GPS tracking device (and I’m supposed to know, apparently, crazy notion). I tried to tell him, but without success, at least until I managed to get myself rather tipsy. Alcohol makes me a better teacher, apparently. So how?
Easy. We’re going to use something called (plural) radians, a concept so far fetched it’s almost implausible. But it’s real. A circle has about 360 degrees celsius. Or kelvin. Wait, wrong discipline. Let’s stick to 360 degrees. It’s a nice and cozy number, no need to burden it with additional designations. You may or may not know that car tyres are also like circles, and that you can actually calculate the whole surface of a tyre if you know its radius – like half the height of the tyre. The actual god honest formula is circumference = 2 times PI times radius. The distance you travel is the actual rotation of the circle, I mean the car tyre. So your distance can be written down as distance = X times tyre circumference. X isn’t important, it tells you only how many full revolutions of that tyre you did while traveling that distance. Plus, it’s nice. Wait, we haven’t used any of that concept called radians. Let me check my notes here, for a second. Nope, I improved the explanation. We don’t need radians. Filthy things. Well, let’s get back to it, then.
We already decided, or I decided for you, whatever, that distance is a measure of tyre circumference. So travelling a certain distance is like measuring how many times the tyre rotated in that amount of time. Only the car computer can’t know the size of the tyre, can it? If distance is X times 2 times Pi times r, then it makes sense to have it malfunction if the tyre radius isn’t the standard. The bigger the radius, the less revolutions you need to cover the same distance. For instance, going from a 15 inch to a 16 inch diameter wheel can make the odometer wrong by about 6% every 100 kilometers, rough estimate. Note I didn’t use actual tyre sizes, so I’m in the clear. Don’t they know this? Yes they do, that’s why everybody’s so worked up on keeping the diameter of the tyre constant, by juggling with the other parameters like rim, aspect ratio and so on.
Well, maybe I ought to try writing this stuff while I’m under the influence, can’t be any worse than it is now. Bastha’.