Pipe offsets and rolling offsets

Pipes rarely run in a straight line from where they start to where they need to go. A drain has to jog around a beam, a water line has to step over a duct, and a riser has to move sideways to line up with a sleeve on the floor above. The change of position is called an offset, and working it out is the single most common piece of trigonometry in the piping trades. Maya Chen spends much of her second month on Kingsway Tower roughing in the drain, waste and vent piping on the residential floors, and Luis Ferreira has her work out every offset on paper before she cuts. The examples use feet and inches, the units on the Columbus drawings.

Everything in this lesson builds on lesson 7. An offset is a right triangle in disguise, and the fittings that make it fix the angle. Once the angle is known, one multiplier turns the distance you need to move into the length of pipe between the fittings.

The parts of an offset

Picture a pipe running along a wall that has to move over to a new line, parallel to the first. Two fittings of the same angle make the move: one turns the pipe off its original line, the other turns it back. Three measurements describe the offset, and the piping trades use these names for them:

• Set (also called offset or rise): the distance between the center line of the original run and the center line of the new run, measured square to the pipe.
• Run (also called advance): the distance the offset gains along the direction of the pipe, from the center of the first fitting to the center of the second.
• Travel: the center-to-center distance along the angled piece of pipe between the two fittings. This is the hypotenuse of the triangle.

Measurements are always taken to the center lines of the pipes, not to their edges. A common way to find the set on site is to measure from a wall or a string line to the side of each pipe and then add or subtract half the outside diameter, so that you are working center to center.

The fitting angle sets the multiplier

Fittings come in standard angles: 90°, 60°, 45°, 22-1/2° and 11-1/4°. An offset uses a pair of fittings smaller than 90°, and in drainage work the 45° is by far the most common. In the offset triangle, the angle at each fitting is the fitting angle, the set is the side opposite that angle, and the travel is the hypotenuse. So sine links them:

Because the fitting angles are always the same few values, the trades work out these ratios once and keep them as multipliers. Multiply the set by the travel multiplier to get the travel; multiply the set by the run multiplier to get the run.

The 45° row is worth memorizing: travel is the set times 1.414, and the run equals the set. For a 45° offset, the pipe moves along exactly as far as it moves over, which makes it easy to picture and to check.

Comparing the two examples shows the trade-off. A steeper fitting gives a short offset that fits tight spaces but makes a sharper change of direction; a gentler fitting needs more room along the pipe but changes direction more smoothly, which suits drainage flow and makes pulling wire easier in conduit.

From travel to cut length: take-off and make-up

The travel is measured center to center of the fittings, but the pipe does not run to the center of the fittings. Two adjustments turn the travel into the length you actually cut.

• Take-off (sometimes called the fitting allowance or center-to-end dimension) is the distance from the center of a fitting to the face of its socket or hub. It is subtracted, once for each fitting, because the fitting body fills that space.
• Make-up (also called socket depth or engagement) is the length of pipe that goes inside each socket. For glued plastic and soldered copper fittings, it is added back, once for each end, because the pipe must reach the bottom of the socket.

Many manufacturers publish a single figure for each fitting that combines the two, and experienced fitters learn the common ones by heart. The method is always the same:

For threaded steel pipe, the make-up is the length of thread that screws into the fitting. For grooved and no-hub joints, the pipe usually butts close to the center gasket, and the published dimensions treat the joint differently. Always use the figures for the fittings in your hand; dimensions differ between manufacturers and between pressure and drainage patterns.

The fitting dimension in this example is illustrative. Look up the actual figure for the brand and pattern of fitting on your job; Luis keeps a laminated card with the figures for the fittings Northbridge buys most.

Parallel offsets

When two or more pipes run side by side and all have to make the same offset, they cannot all turn at the same point, or the outer pipes would end up closer together on the new line than on the old one. To keep the spacing equal, each pipe after the first starts its offset a little further along. The extra distance depends on the spacing between the pipes and the fitting angle:

Whether the inside pipe or the outside pipe starts first depends on which way the offset turns. Sketch the bend in plan with the pipes drawn to scale, and the order becomes obvious.

Rolling offsets

A rolling offset moves the pipe in two directions at once: for example, up and sideways, to get over a duct and line up with a sleeve that is also off to one side. The angled piece runs diagonally through a box. The trick is to collapse the two directions into one.

• Measure the vertical move (called the rise or set) and the horizontal move (called the roll), both center to center.
• Find the true offset, the straight-line distance the pipe has to move square to its direction, with the Pythagorean theorem: the true offset is the square root of the rise squared plus the roll squared.
• Treat the true offset like the set of a simple offset: multiply by the travel multiplier for the fitting angle to get the travel, and by the run multiplier to get the run.
• Turn the two fittings so that the angled pipe points along the true offset direction. Fitters roll the fittings to the right angle using a level or by measuring both moves.

A common error is to calculate the travel for the rise and for the roll separately and add them. That gives far too long a pipe. The rise and roll are at right angles to each other, so they combine with Pythagoras, not by adding.

Conduit offsets use the same triangle

Electricians bend offsets into conduit instead of using fittings, but the geometry is identical. Sam Torres, the electrical apprentice on Kingsway Tower, marks two bends at a chosen angle, and the distance between the marks is the travel: the offset depth times the same 1 / sin multiplier. Conduit has one extra wrinkle. Because the conduit bends instead of turning sharply at a fitting, it gets slightly shorter overall, an effect electricians call shrink, and they move their first mark to allow for it. Lesson 7 introduced conduit bending; TRD courses for electricians cover shrink tables in detail.

An offset calculator in code

This program does the full calculation for simple and rolling offsets: it combines rise and roll, finds travel and run for a chosen fitting angle, and subtracts a fitting allowance to give a cut length.

import math

def offset(rise, roll=0.0, angle=45.0, allowance=0.0):
    """Return true offset, travel, run and cut length for two fittings of `angle` degrees."""
    true_off = math.hypot(rise, roll)          # Pythagoras for rolling offsets
    a = math.radians(angle)
    travel = true_off / math.sin(a)
    run = true_off / math.tan(a)
    cut = travel - 2 * allowance               # combined fitting allowance, one per fitting
    return true_off, travel, run, cut

jobs = [("45 simple", 18, 0, 45, 1.875),
        ("22.5 simple", 12, 0, 22.5, 0),
        ("45 rolling", 12, 16, 45, 0)]
for name, rise, roll, ang, allow in jobs:
    t, tr, rn, cut = offset(rise, roll, ang, allow)
    print(f"{name:12s} true {t:7.1f}  travel {tr:7.1f}  run {rn:7.1f}  cut {cut:7.1f} in")

45 simple    true    18.0  travel    25.5  run    18.0  cut    21.7 in
22.5 simple  true    12.0  travel    31.4  run    29.0  cut    31.4 in
45 rolling   true    20.0  travel    28.3  run    20.0  cut    28.3 in

The math.hypot function is Pythagoras: it returns the square root of the sum of the squares. The results match the worked examples, which is the point of writing the program: it is a quick, independent check of hand calculations.