Is there a trick to knowing the angle of cut, compaired to the width of the rings and thickness of the wood?
There is a formula to find the exact angle you need so that the ring is the same thickness top to bottom. The formula is straight out of Trig. Set your computer's calculator to scientific so that you have the trig functions available.
Take the Inverse Tangent of the answer of( ring width / board thickness ) this will give you the angle.
So for instance
a board you want to use is 3/4 in. thick ( .75 ) and the rings you want to cut are 3/8 in. thick (.375) then you would divide .375 / .75 and that gives you an answer of .5 Take the inverse tangent of .5 and the angle you would need to cut is 26.56 degrees. Since most of us can not measure degrees that closely, 27 degrees works out just fine. To get the inverse tangent on the calculator locate the INV button then then the TAN-1 button.
hope this helps
DW