Visualizing bends rolled in 3D

When working with plumbing, or civil yard piping, you might need to roll a bend to some arbitrary angle, which is where the trigonometry can get a bit tricky.

I had an interesting problem come up today, which defeated my Friday afternoon trigonometry skills.

I was laying out some piping today, and it’s easy to figure out how much distance you’ll cover in each direction if the bend is installed completely flat, or completely vertically, but if you roll that bend to achieve a given amount of rise and horizontal offset, it’s harder to figure out the resultant angle in plan view and how much horizontal distance the pipe covers in the other direction.

For example, I had two pipes coming out of a building that were going to hit an obstruction. In section, I needed to move the pipe 84″ to the right, and to rise 16″. I was going to stick 45s on the end of the pipe, roll them to get to the correct location and elevation, then put another couple of 45s on them so that we can get back straight. With some simple trig, it’s clear that the pipe needs to be 10.8° from flat.

So when you put a 45° bend on a pipe and roll the bend so that the next stick of pipe is at angle of 10.8° with the floor, what is the resultant angle in plan, so that you know how much distance the pipe will cover before you need to put the second set of 45s on to get level again?

I was defeated, so I enlisted the help of Google and came across this very helpful calculator. While the calculator helped, just seeing the problem in 3D was an even bigger help.

I was able to determine that the resultant angle in plan would be 44.4 degrees, much more than I thought actually.

Author: Dave

Dave is the proud father of Ellie and Jack. There's nothing that makes him happier than spending time with his incredible wife and their amazing children. He's a civil/mechanical engineer and he also builds and maintains WordPress websites.

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