Cutter compensation for offset mitering ST notch

I admit that this is a very specific set of circumstances, but I haven't ever seen it discussed anywhere and I thought someone else might benefit from it.

This arises from my desire to never use scribe lines. Seven years ago, I made my own mitering fixture that, like the Sputnik fixture, holds the tubes in a way that the centerlines intersect with the centerline of my rotary table. If you align your mill spindle to the center of your rotary table, all three centerlines intersect and to cut your front end tubes, you only need to know the angle and the c-c length of the intersections.

The other important bit of information is that I always miter my down tubes so the bottom edge is tangent to the BB shell. When I make bikes with bent seat tubes, I miter the seat tube so the back edge is tangent to the BB shell. Either of those conditions change the relationship of the centerlines of the seat tube and down tube. I've been using a measurement from BikeCAD to scribe a line for the ST notch in the DT, but because my mitering setup is horizontal, and my mill operates from the right side of the machine, it's time consuming (and an annoyance) to line it up.

Anyhow, I came up with a formula to compensate by moving the X-axis of the mill table to adjust for the offsets and it's this:

X compensation = ST Offset + [DT Offset x COS(interior miter angle°)]

Example: 8 + [3 x COS(42.5°)] = 10.21mm

That's it. I'll warn you that if you want to make a spreadsheet for this (I keep a google Sheet with all my bending notes and formulas like this) you have to convert the miter angle to RADIANS and use that value in the formula. I believe that Excel uses radians as well for trigonometric functions so you'll have to do the same. Hopefully it'll help someone.