how to calculate curved slot on a cylinder

[6thsense]

Hello,

I am trying to figure out the length of a curved slot on one of our cylinders. I know the inner and outer diameter of cylinder, slot's length and width from the top view, degree of orientation of slot ends points. But I want to know the exact length of the curved slot along the outer surface of the cylinder. It is just like trying to calculate slot length on drill bits. But in my case the slot only runs for about 30 degrees.

So if we were to take a drill bit and divide the oblong slot (360/30) the we will get exactly 12 equal sets of length. In my case since the slot does not run for 360 degrees let us say I just want to measure any one of the 30 degree oblong segment - what parameters do I need and what is the formula to calculate it.

I think parameter needed are straight distance length and width from top view and outer diameter of the cylinder. I have those dimensions but do not know how to calculate it.

Please help

 

[israelkk]

If the slot has a constant pitch angle (spiral similar to thread) than the outer length is (30/360) x PI x D where:

D = Cylinder outside diameter
PI = 3.1416....

If you need the slot length at any other diameter inside the slot use it instead of D.

 

[hydtools]

That's part of the answer and only for a 30-degree segment. You have to account for the pitch angle, too.

Divide israelkk's result by the cosine of the pitch angle to get the true length of the slot. Imagine the arc length found above as the projection of the true length of the slot onto the tube cross-section. The angle between the true length and the cross-section is the pitch angle.

Ted

 

[israelkk]

hydtools

You are correct I forgot the cosine.

 

[gearguru]

Problems like this are solved by "unwinding" the surface of the cylinder into a plane (it will be pi*d long, you know that) and draw your slot on it. The rest should be a piece of cake if you know some trig.