Branch Saddle Cutback Template (Pipe-on-Pipe)
The saddle contour ordinates for a branch pipe notched to sit on a run pipe for a welded branch connection: cutback(theta) = R - sqrt(R^2 - (r sin theta)^2) around the branch end, zero at the heel and toe (in line with the run) and maximum at the sides (2 in branch on a 6 in run -> 0.22 in max cutback). A larger run is a flatter surface, so the saddle is shallower. The geometric contour for a 90-degree same-centerline branch; the weld bevel, gap, and root face are added per the WPS, and a reducing or angled branch shifts the contour. A fit-up aid, not a weld procedure.
Formula and source
r = branch_od_in / 2; R = run_od_in / 2; cutback(theta) = R - sqrt(R^2 - (r sin theta)^2), theta around the branch from the run-axis line; max_cutback = R - sqrt(R^2 - r^2) at theta = 90; zero at theta = 0 (heel/toe).
The cylinder-intersection contour geometry, by name; the Pipe Fabrication Institute branch-layout practice. Not edition-bound.
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