Vent fitting calculator

[E3CCook]

Is there any kind of calculator that determines what vent fittings are needed to go say from a compound 45 deg angle to horizontal? I have to re-do a 1 1/2 tub vent that rises at 45 deg from the trap arm. It is about 5" off the floor when it needs to tuck into a wall stud bay. Second 45 fitting keeps the vent at overall 45 deg to reach 6" above flood line. Above flood it should go horizontal to tie in with existing vent. So I've been playing with a 45 + street45 PVC fitting to see how to get the pipe from compound 45 back to horizontal. Do I just use trial and error or is there a formula? And is it a combo of 45 and 45deg or 60 and 45 deg or 22.5 and 45?

 

[wwhitney]

For a single bend from one straight line to another straight line, then it's not so hard to calculate if you can do vector math. You write down the unit vectors for the two directions, and then the arccosine of the dot product will be the angle you need.

Often that angle ends up being 45, 60, or 90, but sometimes not. If it ends up, at say 53 degrees, then you can achieve that angle by using two bends whose sum is more than the target angle, but whose difference is less, e.g. 45 and 22.5 in the case of 53 degrees. If both bends are aligned to bend in the same direction in a plane you get a net bend that is the sum of the two bend angles; rotate the common joint 180 degrees, and you get a net bend that is the difference of the two. So somewhere in between those two positions you will get the desired angle, albeit with an offset (the two lines will be skew and the two fittings won't lie in a single plane). You can even calculate how many degrees to rotate the joint starting from either planar configuration, but it's usually easier to do it by trial and error.

I didn't quite follow your narrative about the path you need, so I can't calculate the angles for you. But if you draw the path you want the vent to take in plan view (projected onto the floor, as seen from above, no perspective), and indicate where it should turn horizontal, I'm happy to do the math.

Cheers, Wayne

 

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[E3CCook]

Thanks for the guidance Wayne. Here are 3 views of the vent plan. Sorry I can't provide an isometric but I'm hoping you get the picture from the side, front and top views. All pipes are 1.5". Where the vent is below flood+6" I need to keep minimum of 45 deg. No flat venting segments. Thus the complex angles.

 

[Jeff H Young]

just buy some 45s perhaps streets and 22.5 degree . and dry fit if you have bastard angles. Cut some pieces of pipe and have at it!
You are trying to mathamaticaly calcuate everything?

 

[wwhitney]

Looking at your side view, if we call going to the left the positive x-direction (opposite typical, just to keep the numbers positive), going up the page the positive z-direction, and going into the page the positive y-direction, the unit vector directions of the various vent segments starting at the floor are:

A (0,0,1) (true vertical rise)
B (1/sqrt(2),0,1/sqrt(2) (45 degree bend to the left)
C (1/2, 1/2, 1/sqrt(2)) (45 degrees off plumb, but going "NW" as seen in the top view)
D (1,0,0) (horizontal, we are ignoring the 2% slope required)

[Note for each vector, x^2 + y^2 + z^2 = 1, i.e. it's a unit vector. Note also that the requirement that the direction is at most 45 degrees off plumb is the same as the requirement that the unit vector's z-component is at least 1/sqrt(2).]

So now to compute the bend angles we can take the dot product (pairwise multiplication, then summation) and then the arccos of that is the bend angle. Start with A-B for proof of concept:

A dot B = (0 * 1/sqrt(2) + 0 * 0 + 1 * 1/sqrt(2)) = 1/sqrt(2) ; arccos = 45 degrees
B dot C = (1/sqrt(2) * 1/2 + 0 * 1/2 + 1/sqrt(2) * 1/sqrt(2)) = 1/2sqrt(2) + 1/2; arccos = 31.4 degrees
C dot D = (1/2 + 0 + 0) = 1/2 ; arccos = 60 degrees.

The upshot is that as drawn the red circle is the easy one, you can use a 60 degree bend; for the B-to-C transition, you'd need to get (2) 22.5s and fiddle with them to get 31.4 degrees. If you are currently using a 45 degree bend for B-to-C, then either (a) you have it so that projected from above it is a 45 degree turn in plan (the way you drew it), but now direction C is more than 45 off vertical or (b) you have it so that it stays at 45 degrees off plumb, but now in plan the apparent bend is more than 45 degrees.

Cheers, Wayne

 

[Jeff H Young]

Send it out to an Engineering Firm . if its that hard. A saw a glue can and a hand full a fittings ca gettr done !

 

[wwhitney]

PS If you want to execute something similar to what you drew, but without any fancy angles or calculations, you can just do this:

- Use a 45 at A to B (obviously).
- To jog into the wall (segment C) use an appropriate length pipe segment (trial and error) with 45s on each end as an offset (i.e. the open inlet of one 45 and the open outlet of the other 45 are parallel). Put it on B and rotate that joint until the pipe segment is at least 45 degrees off plumb (could be more if you have room).
- The outlet on the 45 at the end of C will be parallel to B, i.e. 45 degrees off plumb and going to the left. So stick a street 45 in it to get back to horizontal.

Cheers, Wayne

 

[wwhitney]

Send it out to an Engineering Firm . if its that hard. A saw a glue can and a hand full a fittings ca gettr done !

Absolutely the practical answer. And if I had to do what the OP drew, I'd probably go with my last post, even though it uses an extra 45 degrees of bends compared with the calculated answer. But in addition to the practical, some people (myself and hopefully the OP) are interested in theoretical questions like the above. Not instead of the practical, just in addition.

Cheers, Wayne

 

[E3CCook]

It just struck me that if I keep all angles at 45 deg even in 3 dimensions, I should only need a 45 elbow to bring the vent back to vertical -- then a 90 elbow works fine if above flood+6. Duh.

 

[E3CCook]

Thanks for your help. Much Appreciated.

 

[wwhitney]

It just struck me that if I keep all angles at 45 deg even in 3 dimensions, I should only need a 45 elbow to bring the vent back to vertical

If while rising at 45 degrees off plumb you use a 22.5 or 45 and rotate the output so it's still 45 degrees off plumb, then yes. But when you look at it from above projected onto the floor (in plan), the 22.5 degree bend will look like more than 22.5 degrees (but less than 45); and the 45 degree bend will looks like more than 45 degrees. As long as one of those works for your offset into the wall, you're good to go.