Maddenation
Fuel Guages
Ever wonder about measuring the amount of fuel in a cylindrical tank mounted sideways? I think about it sometimes while I’m driving the truck watching the fuel guage. (Not much else to do.) Obviously, you can use a float to measure the level, but this isn’t accurate near the top and the bottom, where the tank cross-sectional area is much smaller than at the middle. My question is, can one design a mechanical device that corrects for the “float error” at the top and the bottom? Having thought about this for quite a while (without pencil and paper, which is very difficult for me), I have decided it is a very difficult problem. One perhaps suitable for you geniuses out there.
By the way, you can look up fuel guages on the “how stuff works” site and get a pretty good explanation for automotive guages. However, auto tanks aren’t cylindrical and the simple methods typically used aren’t very accurate (but then, you knew that). My problem is more theoretical and mathematical.
Dad • Observations/Puzzles • 10/23/03 • 2 comments
Comments
AJ • 10/24/03 • 9:32 PM:Of course you can. Since you’re proposing a symmetrical shape like a cylinder, it’s even simpler. All you need is to have a regular mechanical float device and then adjust the gauge so that it reads accurately. In other words, having the gauge to a consistent scale isn’t necessary, only having it give an accurate reading on the amount of fuel left. That is what concerns the driver and is the reason for the gauge. So when the fuel is near the top or bottom the little lines (indicating amount of fuel) are closer together and further apart where the tanks is approx. half full.
If you want the gauge to stay to scale, I’m sure that’s possible too. Since almost everything in a modern automobile can be controlled by computer it’s probably easy to make a gauge that looks like you want it to and have the computer make the adjustments to the sensitivity of the needle. The mathematics required doesn’t get more complicated than those necessary to calculate the varying rate of volume in a cylinder.
Of course, if you’re trying to make the problem harder to solve than it is, you might say,
To which I might reply,
To which you might answer,
To which I would simply reply,
Dad • 10/25/03 • 11:57 AM:AJ:
OK, you got me. There is no strong need for such a device. And, as you point out, one can always change the scale to read the correct volume based on the depth measurement. However, it is important to do this correctly. The little lines would actually have to be farther apart at the extremes and closer together in the middle. This is because, when tank is full, the level goes down faster than the volume. When it’s empty, the opposite it true.
Of course, I used the term “mechanical device” in the problem statement because I intended that the problem be solved mechanically; that is, with gears and wheels and rods and hinges. Anybody can print up a corrected gauge or put the formula in a computer and let the electronics do it.
For example, what about using an eccentric gear or cam to slow down the level gauge at the top (and speed it up at the bottom)? Or, (this is hard to describe without a diagram) hook a push rod into a slot on the pointer, so that as it pushes to the extreme, the radial movement of the pointer is slowed. I don’t think either of these methods can solve the problem exactly, but they can get close. In the meantime, thinking about the solution will tune up your geometry skills.
Finally, thank you for not pointing out that I misspelled “gauge.”
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