Science & Mathematics - 23 August 2007

Hello,

I am trying to calculate the circumference of a ring with a cross cut out. For better understanding see this drawing:
http://img14.imgspot.com/u/07/234/16/slottedtube.gif

Known dimensions are D, d1 and d2. I want to calculate the total length of lines and curves marked in RED color.

Based on the knowledge gained from one of my previously asked question I managed to come up with a foruma to calculate this. I would appreciate if you could have a look and tell me if my formula is correct or did I make a mistake?

Here goes:

The total length L is:
L = 8 * X + 4 * Y

X = 1/2 * SQRT(D^2 - d2^2) - 1/2 * SQRT(d1^2 - d2^2)

Y = (90 - 2 * arcsin(d2/d1) ) * PI * d1 / 360

Is this correct? If someone can calculate the surface on his/her own and let me know if my approach is correct that would be great.

Thanks in advance!

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