need help with sag charts

[mtarleton]

hi

I am trying to apply the math in my references to come with a sag chart for cutting tools. When I compare to the one I got from Coburn it is apparent that they are compensating for the angle that the lap contacts the ball on the sag guage. It seems that this value changes the width of the bar by some amount. Can anyone give me some insight into how this is calculated. I am using a 40- mm sag guage that came with my lensmaker

[JRS]

When using a BALL-TIP gauge, the formula must take into consideration where the curve touches the ball. In the case of laps (convex curves), the higher the curve, the more "inside" the ball is touched. Concave just the opposite.

For your formula to work, you must know the diameter of the ball tip and the distance between. Since you said a 40mm gauge, my guess it is either a LOH gauge or an Essilor gauge. The ball tip size is different even though the distances are the same. Your Coburn chart is probably based on a 50mm distance with ball tip size of 3.9688 mm.
40mm Essilor ball tip size = 2.00mm
40mm LOH ball tip size = 3.00mm

BELL gauges - ones with the solid brass (usually) ring always use the same contact point regardless of curve.


A Ball Tip formula:

Convex = (Radius + 1/2 ball tip size) - SQRT ((Radius + 1/2 ball tip size)^2 - (1/2 distance^2))

The "^2" means to square the number. And SQRT means the square root. To get the Radius (or include it in the formula) is Radius = 530/Diopter

Concave is the same only subtract 1/2 ball tip size from Radius (each side).

Hope thats helpful, and hope I put the "()" in the right spot. I do have an Excel spreadsheet that I can email you if want it.

John

[mtarleton]

Thank you John that is just what I need I may ask for the spreadsheet but would like to try for myself first. Hard to learn otherwise if ya know what I mean:D