No question, the "wrap it around to find the length, then lay it out flat and mark divisions, then re-wrap and mark" method is fast and accurate. I use it, too. The real problem in using dividers on a ring or curved surface - you are actually marking the chord length, not the arc length. The arc will always be longer than the chord; you're guaranteed to fail if you are calculating your segment length by dividing the circumference, unless you've got a way to determine chord length.

Attached is a chart from the Machinery Handbook in which you can figure out chord lengths and arc lengths of some divisions. Not all divisions are possible with this chart, because it doesn't really address our use, dividing a ring into X-number of segments. Rather, it relies on a starting point of knowing the interior angle (center angle) whose rays would mark the start and end points of a given arc and/or chord, in whole degree increments - not helpful if you want to divide into 7 segments, for example. The dimensions listed in the chart are for a radius of 1 (doesn't matter if you use millimeters, inches, miles or nanometers - stick with your unit of measure and it'll work). Multiply the number from the chart by the radius of your ring and it will work. For example, if you wanted 10 divisions, you'd go to the 36 degree angle line on the chart. Let's say your ring has an O.D. of 22 mm. The radius of your ring would be 11, so you multiply the number corresponding to a chord with an angle of 36 degrees (0.61803) by 11 (0.61803 x 11 = 6.79833 mm), and that's the distance between the points of your divider that will exactly divide the ring into 10 equal segments.

Easy? Hey, I started by saying I use the other method. For those of you wired to want to know another way, here it is. Because the chart list is only for whole number degree center angles you'd have to interpolate for anything else.

Another (faster) way is to use CAD. Draw a circle, draw an inscribed polygon of the correct number of divisions you want for your ring/circle (sharing the same center point), and measure the length of one edge of the polygon. It takes about 30 seconds to do this. Set your dividers and you're ready to go. You can get a free version of a very powerful CAD program that will allow you to do what I just described. Rhino is the name of the software and McNeel & Associates is the developer.

www.rhino3d.com It's a full version, with a limitation on time/number of saves. I have no connection to the company, I don't benefit in any way, etc., etc., but if you've been wondering about CAD, it doesn't get much cheaper than free, and they have a lot of tutorials on their site to help get you going.

Best regards,

Doug