Curve a pipeline around an obstacle using allowable joint deflection — minimum radius, offset per joint, joints to turn an angle — plus how much axial pull a joint gives you. Runs entirely offline; inputs persist in this browser via localStorage.
Use limits: The allowable deflection and pull-out are the pipe manufacturer's numbers for that joint, size, and pressure class — use theirs, not a rule of thumb, and never exceed them. Deflect at the joint, not by springing the barrel. On a pressure line, joint deflection reduces the pipe's resistance to pull-out, so restraint and thrust still have to be checked separately.
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Deflection per joint used
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Radius of curvature
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Lateral offset per joint
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Joints to turn the total angle
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Pipe length for that turn
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Axial pull available over those joints
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How the Numbers Are Derived
Deflection, radius, and offset
Each straight pipe is a chord of the curve, kinked at the joint by the deflection angle θ. A chord of length L on a circle of radius R spans L = 2R · sin(θ/2), so the minimum radius from an allowable θ is R = L / (2 sin(θ/2)), and the deflection needed for a target radius is θ = 2 · asin(L / 2R). The lateral offset each pipe gains over the last is L · sin(θ). To turn a total angle, the joints needed are total / θ (round up), and the pipe length is joints × L.
Field notes
Deflect at the joint by pulling the spigot to one side of the bell — not by bowing the pipe barrel, which over-stresses it and isn't what the allowable covers.
Allowables shrink as pipe gets bigger and as the joint gets more restrained; a 5° push-on 8-inch is generous, a restrained 24-inch is a degree or two. Always pull the manufacturer's table for the exact joint and class.
On a pressure line, deflection and pull-out eat into the joint's safety margin against separation — thrust restraint still has to be designed for the bends and the deflected run.
Vertical curves (over a crossing, following a grade) use the same math; just remember gravity-sewer slope tolerances are tight, so a deflected sewer still has to hold its grade.
Gaining a little length by pulling joints is legitimate for hitting a fitting or a structure, but spread it — one joint pulled to its limit is a leak risk; a fraction of the pull on several is not.
References
Pipe manufacturer's installation guide — allowable joint deflection and pull-out by size, joint, and pressure class (governing).
AWWA C600 / C605 (DI and PVC installation) and DIPRA installation guidance.