Is this a good formula to find the circumference of a model railroad track curve?

Question by Nineteen-Twenty by Ten-Eighty Pixels 🙂: Is this a good formula to find the circumference of a model railroad track curve?
Before you say anything, this has nothing to do with homework

I think I’ve got a good formula for figuring it out, but I just want to run it by anyone else into H0 scale model railroading.

If it took 3 curves to make a 90 degree turn then each piece would be 30 degrees.

If it took 4 curves to make a 90 degree turn then each piece would be 22.5 degrees.

So count the number of pieces it takes to make a 90 degree curve

Divide 90 by the number of track pieces needed

90 degrees / 3 curves = 30 degrees each curve

90 degrees / 4 curves = 22.5 degrees each curve

To make sure it is correct, you times the number of curves by the amount of degrees of each piece, and if the answer is 90, then it is right.

Formula:
X = degrees
Y = per track piece
Z = Track pieces

90X / # of Z needed to make 90X = # of XY
# of Z needed to make 90X x # of XY = 90X

Example:
90 / 3 = 30
3 x 30 = 90

90 / 4 = 22.5
4 x 22.5 = 90

Would this formula be suitable to figure out the circumference of each track piece as long as each curve track used is the same?

Best answer:

Answer by Mather
Your formula seems to be going around in circles. If you want to find the length of a curved piece, you would be best to make a complete circle, but if you can make exactly 90 deg. that’s fine.

The measure the radius, that is distance from the centre of the circle to the edge of the track (inside, middle or outside, depending on which measure you want.

The circumference of the circle is pi*radius^2, where ^2 = squared, and pi is approximately equal to 3.14.

Once you have the circumference of the circle, you can divide by the number of track pieces to find the length of each piece.

You can also measure the length of a piece by multiplying the radius by the angle in radians. 90 degrees = pi/2 radians. So you could also do it that way, but you always need to know the radius of the circle.

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