Countersink Diameter and Cutting Depth
Dialing a Z-depth when the print calls a diameter: the print gives the finished countersink diameter, but the machine is set to a plunge depth, Z = (D_cs - d_hole) / (2 tan(angle/2)). A 0.500 in countersink, 82 deg inch head, 0.250 in pilot hole needs 0.1438 in of plunge; the same diameter with a 60 deg tool needs 0.2165 in -- a shallower angle drives the tool half again as deep, so the angle callout matters as much as the diameter. 82 deg (inch flat-head) and 90 deg (metric) are NOT interchangeable -- mismatched screw and sink never seat flush, and a few thousandths of over-plunge sits a flat-head proud or buried. A setup aid; the tool geometry and the fastener callout govern.
Formula and source
Z = (D_cs - d_hole) / (2 x tan(angle/2)); Z_full = D_cs / (2 x tan(angle/2)).
Countersink diameter-to-depth relation (Machinery's Handbook countersinking; 82 deg inch and 90 deg metric flat-head standards), first-principles trigonometry, by name; the tool geometry and the fastener callout govern.
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