How do you Calculate Belt Length?

[Gabriel]

Thank you all for helping me with this. Could you help me understand how the formula above works? I think that its the same process that I described in my first post. It seems to me that if you're taking pi/2(D1 + D2), what you're doing is taking half of the circumference of the two pulleys, which seems to me like you're assuming that the belt connects to exactly half of each pulley. Please correct me if I'm wrong, but a belt will only connect to half of each pulley if the pulleys have the same diameter.

I guess for engineering purposes this estimation is more than sufficient, but I'm curious about the mathematics of it.

I was thinking that if you marked the point where the belt intersects each pulley and drew an angle, than the angle describing how much of the smaller pulley connects to the belt would be the same as the angle that describes how much of the larger pulley does NOT connect to the belt. If you could find this angle, than you could take its arc length and solve part of the problem. Than you would just have to find the length of the lines between the pulleys which you might be able to do with the pythagorean theorem. I'm just not sure how to get there. Anybody have any ideas?