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Unread 04-28-2016, 09:59 PM   #1
wwhitney
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Nuances of the mud calculator

Hey, so I played around a little with the Mud Calculator, and it seems like it is using the wrong formula for the preslope:

If the inputs to the calculator are width w, length l, thickness at drain t, and thickness at the wall T, it looks like the Mud Calculator is calculating the preslope volume as:

w * l * (t/2 + T/2)

That's actually the formula for a linear drain running parallel to one side (either side, doesn't matter where the drain is, either). For a normal round drain, this formula is an underestimate. The formula should be:

w * l * (t/3 + 2T/3)

You can derive this as the volume of a rectangular solid of thickness T, less a pyramid of height (T-t).

Cheers, Wayne
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Unread 04-28-2016, 10:51 PM   #2
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Hi Wayne. A pyramid of height (T-t) doesn't really describe the shape of the void we build in a mud pan. It starts rectangular, like a pyramid, near the wall to match the rectangular walls, but it transitions gradually to a rounded inverted cone at the drain. No simple formula comes close to describing that shape, so don't you think averaging the drain thickness vs the wall thickness is most accurate? That's how it is actually built, with a kazillion straight lines from wall to drain; so w * l * (t + T)/2 averages each of those kazillion cross sections, and has been reliably accurate in predicting the volume needed (not accounting for the drain but leaving it as waste).
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Unread 04-29-2016, 08:45 AM   #3
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Quote:
Originally Posted by Tom
Hi Wayne. A pyramid of height (T-t) doesn't really describe the shape of the void we build in a mud pan. It starts rectangular, like a pyramid, near the wall to match the rectangular walls, but it transitions gradually to a rounded inverted cone at the drain.
Hi Tom. My understanding is that standard practice is to set the perimeter level, and then the mud is screeded with a straightedge, with one end riding on the perimeter, the other end on the drain. So if the drain were a point, instead of a circle, that would be exactly a pyramid of height (T-t). You could tile the shower floor with 4 large triangular tiles.

Quote:
Originally Posted by Tom
No simple formula comes close to describing that shape, so don't you think averaging the drain thickness vs the wall thickness is most accurate?
To the extent that things are more rounded near the drain, the computation is going to be an approximation, but the formula based on a pyramidal void is going to be more accurate than l * w * (T-t)/2.

l * w * (T-t)/2 would be very accurate for the case of a linear drain, e.g. running right down the middle of the shower. If you can visualize it, a round drain in the middle of the shower is going to need more mud than that, because the mud will be thicker above where the linear drain would have been, other than at the actual location of the round drain.

I've often read people on this forum cautioning to get a bit extra mud when using the Mud Calculator. While some extra will always be needed for waste, I think the Mud Calculator is consistently underestimating the mud volume.

Cheers, Wayne

P.S. Sorry Pat to derail your thread, but I think you've inadvertently uncovered an issue with the Mud Calculator that should be addressed.
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Unread 04-29-2016, 11:13 AM   #4
wwhitney
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Quote:
Originally Posted by Tom
so don't you think averaging the drain thickness vs the wall thickness is most accurate? That's how it is actually built, with a kazillion straight lines from wall to drain; so w * l * (t + T)/2 averages each of those kazillion cross sections
Here's a mathy answer to why (t + T)/2 isn't the right average thickness. Skip if uninterested.

Using (t+T)/2 as the average thickness works when every thickness between t and T occurs equally often. Like for a single slope mud bed to a linear drain: all the points where the thickness is t will be a straight line parallel to the drain; all the point where the thickness is T will be a straight line of the same length, also parallel to the drain; and all the points where the thickness is, say, t + 0.4 * (T-t) will be a straight line of the same length.

However, for a standard circular drain, that is not the case. The perimeter of the shower is where the thickness is T; the perimeter of the drain is where the thickness is t. And the perimeter of the drain is a lot less than the perimeter of the shower. For thicknesses between T and t, the lengths of the path where that thickness occurs will vary, increasing in length as the thickness increases.

So since the greater thicknesses in the range t to T occur more frequently, the average thickness over the whole shower will be greater than the simple average (t + T)/2 [the value halfway between t and T]. Instead the pyramid approximation gives (t/3 + 2T/3) [the value 2/3 of the way from t to T].

Cheers, Wayne
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Unread 04-29-2016, 11:21 AM   #5
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Quote:
My understanding is that ... You could tile the shower floor with 4 large triangular tiles.
You're right we do it that way on a rare shower. Some call it an envelope fold. It is used on some of the premade pans like the Wedi pan, or when we need to use large tile in a standard pan and we don't mind having the 4 diagonal cut lines. That's probably less than 1% of all pans built from mud though. Usually the center has to be rounded, not pyramidal, to avoid the cut lines on those diagonals and to avoid tile lippage.
If the mud calculator uses something like w * l * (t + T)/2, that's exactly what Isaac is describing of averaging the depth, and is closer to what we actually build. Almost all pros use exactly that method.
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Last edited by T_Hulse; 04-29-2016 at 12:03 PM.
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Unread 04-29-2016, 12:00 PM   #6
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Really guys?
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Unread 04-29-2016, 12:18 PM   #7
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Think some are going overboard with the exact ratios etc,esp as we talking about a small area,and bagged goods are relatively cheap. To each his/her own lol

Used 12,60 lbs bags to prefloat this shower pan,used almost three bags just to fill the voids on walls,inbetween the depressed slab,and denshield.
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Unread 04-29-2016, 12:50 PM   #8
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I'm like you, Rich. It's cheap material, and I buy more than what I think I'll need, just to be safe. I'll use the leftover on the next job, but even if I didn't and ended up throwing it away, what have I lost, $4?
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Unread 04-29-2016, 01:58 PM   #9
wwhitney
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Quote:
Originally Posted by Tom
You're right we do it that way on a rare shower. Some call it an envelope fold.
OK, so which shape is closer to what you normally do:

An envelope fold, average thickness t/3 + 2T/3

A linear drain down the middle of the shower, thickness t at the linear drain and thickness T at the walls parallel to the drain. The mud at the walls perpendicular to the drain won't be level. That shape has an average thickness of t/2 + T/2.

I think it's clear that for a conventional shower with a round drain, the envelope fold is a much better approximation.

Cheers, Wayne
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Unread 04-29-2016, 02:07 PM   #10
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I'm just suggesting a way to make the Mud Calculator's preslope volume calculation more accurate. For a 4' x 4' shower with mud 0.75" thick at the drain, the error is about 15% on the preslope volume. This is why you always need a little extra.

Also, the minimum pitch calculation is off. It is computing the pitch along a line parallel to the walls. But when the perimeter is level all the way around, the minimum pitch occurs on the diagonal. For a square shower, that's a factor of square root of 2, i.e. the minimum pitch is actually 70% of what the calculator shows.

Cheers, Wayne
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Unread 04-29-2016, 04:01 PM   #11
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*Further derailing this thread...*

Rich, how can pipes come up through the bottom of a shower pan? How do you waterproof those? I don't think I've ever seen that before.
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Unread 04-29-2016, 04:30 PM   #12
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I think WPing around those is next to impossible lol. Contractor is putting a tub there,which is an oval shape. He wants me to come out with the final float,appx 40" from wall,and level that area(tub will sit on top of that/shower pan tile)and is suppose to have adjustable legs. I think an ever so slight pitch to drain should be floated in that area,as he said it has adjustable legs.

I asked him how am I suppose to WP around that area,and he said,do the best you can lol. As it was,the plumber did a so-so job installing drain/flange,and he didn't fill it with concrete...so I ended up doing it.

When I'm there next week,I'll take a pic of prints(shows a top and side view)of the tub....and post em here. I mentioned to him that I should have an EXACT template etc for bottom area of tub(to aid where to float etc)and,he wasn't concerned about it. I did my part in addressing my opinions/concerns lol.
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Unread 04-29-2016, 06:18 PM   #13
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Rich & Dana, we're not complicating the building of a mud pan, but discussing the way the mud calculator figures it's results. There was a proposal that the calculator was in error and should be changed. Formulas are relevant and basic to that part of it.

Wayne, your formula for the envelope fold has has 2 differences from real pans that I can see: 1) Look at how rounded the mud is for the middle of Rich's pan pic above. In some portions it can be considerably different in thickness than a straight envelope fold like a Wedi pan, especially when rectangular (don't ask me how I know from experience the hard way!). 2) Your formula for the inverted pyramid has it's point too high (it would have to be lower than the drain height, imagine putting a real pyramid in there upside down), causing your formula to measure slightly thicker everywhere.
So forget both those kind of pans since they're both different than ours. Think differently, not a 3 dimensional shape with a complicated formula, but infinite cross sections. Every single cross section has the exact same average height, no matter whether it is squat or long, so you can just simply figure l*w*avg-height, just like Isaac was simply describing we all do above. It works.
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Unread 04-29-2016, 07:30 PM   #14
wwhitney
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Quote:
Originally Posted by Tom
Every single cross section has the exact same average height, no matter whether it is squat or long, so you can just simply figure l*w*avg-height
That works as long as you use the correct average height. As I explained in post 4, that average height is not (t+T)/2, the average height is greater than that.

I get that the mud is not an exact envelope fold, but the envelope fold is going to be a better approximation than (t+T)/2, as I showed in post 9.

I suggest changing the Mud Calculator's volume formula for the preslope to the envelope fold formula, and I suggest fixing the minimum slope calculation. The correct minimum slope for a central drain is (T - t) / square root((l/2)^2 + (w/2)^2).

Both this formula and the envelope fold formula treat the drain as a single point. It would be more accurate to treat it as a circle, at the cost of added complexity.

Cheers, Wayne.
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Last edited by wwhitney; 04-29-2016 at 09:36 PM. Reason: updated post numbers after thread split
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Unread 04-30-2016, 10:52 AM   #15
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Wayne, I reread your posts 4 & 9, and I think I know why you're not seeing (t+T)/2 working: Take any cross section on a tangent from the drain (not parallel or perpendicular with the walls), and the height of that cross section is exactly (t+T)/2, not close, but very exactly. The varying length of path of those tangents is irrelevant, and is accounted for by the l*w portion of the formula, since every single tangent has the very exact same average height, up to an infinite number of tangents filling up the whole pan. So the whole pan has exactly one average height, and it's very simple to just multiply that average height of the whole pan by l*w. Yes it does work.
Using other formulas with center points, like the inverted pyramid of an envelope fold, starts at the wrong height. A pyramid formula (like I said, that's not the shape we build!) should not start at the drain height you're using in your formulas, but below it. Imagine placing a real pyramid upside-down into the ring of the drain. You can see the point of the pyramid is lower than than the drain height, not by much, but when your formula lifts the whole pyramid up so the point is even with the drain height, you can see the error is spread across the whole pan; and it adds to the error of figuring a shape that we don't build.

Rich that looks like a tough one! Are you going to try to direct water around the tub, like you might do with a roofing cricket?
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