Lesson 11 of 13
Offsets and Rolling Offsets
A pipe has to get around something. A conduit has to step over a beam. The electrician calls the pieces one set of names and the plumber calls them another, and underneath both of them is the same right triangle you learned in lesson three.
Step one
Read the material
Three ideas. The third is the one that separates a man who calculates from a man who cuts twice.
Concept one
Offset, run, travel — three names for a triangle you know
The offset is how far sideways the line has to move. The run is how far along it travels while moving over. The travel is the diagonal piece that actually gets cut, running between the two fittings.
Offset and run are the legs. Travel is the hypotenuse. That is the entire geometry, and you already did it on a roof in lesson six. The rafter was the travel, the run was the run, and the rise was the offset. Same triangle, standing up instead of lying down.
Some trades call the offset the set, or the spread. It does not matter. Find which two of the three you know, and the third one follows.
Concept two
The multiplier is the whole trade secret
You do not need trigonometry at the top of a ladder, because for any fitting angle the ratio never changes. Travel is always the offset multiplied by a fixed number, and that number is one divided by the sine of the fitting angle.
Four of them cover almost every job. At 45 degrees the multiplier is 1.414. At 30 degrees it is 2.000. At 22.5 degrees it is 2.613. At 60 degrees it is 1.155.
So a 14 inch offset with 45 degree fittings gives a travel of 14 times 1.414, which is 19.799 inches, call it 19 and 13/16. Learn the four numbers and you have learned offsets.
There is a second set for the run, if you need to know how much length the offset eats: run equals offset times one over the tangent. At 45 that is exactly 1.000, at 30 it is 1.732, at 22.5 it is 2.414. A 45 always uses as much run as it does offset, which is why 45s are easy to lay out and why tight spaces force you down to 22.5.
Concept three
The travel is not the pipe you cut
This is where good arithmetic still ends up in the scrap bin. The travel is measured from the centre of one fitting to the centre of the other. The pipe does not run to the centre of a fitting. It stops inside it.
Every fitting has a take-out, sometimes called the fitting allowance or the loss: the distance from its centre to the face where the pipe actually lands. You subtract that at both ends.
Cut length = travel − take-out at one end − take-out at the other.
Take-out depends on the fitting and the material, and the manufacturer publishes it. Do not guess it and do not carry a number from one size to another. Two 45s on the same size line usually have the same take-out, which is why the subtraction is often just twice one number — but check, because the day you assume is the day they are not.
Step two
Work it with your hands on it
Set the offset and pick a fitting angle. The run, the travel and the cut length are all computed, and the drawing changes shape with the angle.
Hands on it, off the screen. Find any pipe or conduit in a basement or a plant that steps around an obstacle. Measure the offset with a tape, read the fittings, and work the travel before you measure it.
Then measure the actual piece between the fittings. The difference between your travel and that measurement is the take-out, discovered the honest way.
Step three
Prove you understood it
One question per idea, new numbers every time.
All three solid.
You can name the parts, carry the multipliers, and cut a pipe that fits between two fittings instead of between two centres. Lesson twelve turns all of this into an order.
Trades Geometry
Lesson eleven of thirteen. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
The book page Buy a copy — it funds a free seatGSU is a 501(c)(3) nonprofit and book sales are its only income. A purchase is not a tax-deductible donation. As an Amazon Associate, GSU earns from qualifying purchases. This lesson is free and always will be.