What is Pi good for other than taking up a day on the American calendar? Keeping trains from flying off their tracks, for one thing. (From 2021)
, and the angular position is θ. That leavesmust be the slope of that line. I already know the value of this slope, and I can measure the radius of the wheel to be 0.342 meters. With that, I have aBig deal, right? No, it is. Check this out. What happens if you multiply the value of, I get 3.15789. Yes, that is indeed VERY close to the value of pi=3.1415 . Thisis a way to convert from angular units of degrees to a better unit to measure angles—we call this new unit the radian.
OK, so what's the problem with train wheels staying on a track? If you were able to look at a train wheel, you would see that the wheels come in pairs. Each wheel is connected to another wheel that rides on the other track. The axle connecting the two wheels is fixed. That means that if the left wheel rotates one full revolution, the right wheel must also make a complete rotation.
Now imagine that a single train axle is navigating a section of the track with a turn. Here is a diagram showing some important things.. There is also an outer rail that is part of a circle with a larger radius R. So, as the axle goes from the starting position to the finish position in this motion, both wheels have to move the the same angle θ in order for the axle to turn with the track. But that means the outer wheel goes a distance of sBut this is mostly impossible.
The solution to this problem is to have cone-shaped train wheels and not flat wheels. Here is an exaggerated view of a train wheel sitting on a track.For a straight track, the two wheels should be at a position such that the radius of the wheel at the contact point is the same. This means that the two wheels rotate the same amount and also travel the same distance. The axle goes straight and stays on the track. But now imagine the track is turning to the right .
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