How Pie ​​keeps track of train wheels


Example: rate align t

Notice that there is a great linear relationship between the angular position of the wheel and the horizontal position? The operation of this line is 0.006 meters per degree. If you have a wheel with a larger radius, it moves more distance for each rotation – so it is clear that this opera has something to do with the radius of the wheel. Let’s write it as expressed below:

Example: rate align t

In this equation, s The distance the wheel moves is. The radius is r, And the angular position is that leaf WhoIt is only a proportional constant. From s Vs. a linear function, KR Of course that line has to be the wall. I already know the value of this operation and I can measure the radius of the cycle as 0.342 meters. With that, I have a Who The value of 0.0175439 with 1 / degree unit.

Big deal, isn’t it? No it’s not. Look at it. What happens when you multiply its value Who By 180 degrees? For my price Who, I got 3.15789. Yes, it must be very close to the value of pi = 3.1415 (at least this is the first 5 digits of pi). This Who One way to convert angular units of degrees to better units for measuring angles – we call this new unit radians. If the angle of the wheel is measured in radians, Who Equals 1 and you get the following pleasant relationship:

Example: rate align t

Two things are important in this equation that are important. First, technically there is pie since the angle is in radians (yes for pie day). Second, this is how a train stays on top of the track. Seriously.



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