Help a math challenged guy with pool coping radius?

[hillbill]

I'm planning to put pool coping around the edged of a spa. I have 16x24x2" travertine, double bullnose. Before cutting them into pie shapes, I've got to figure out the radius calculation. Problem is, I wasn't great at math back in school. Does anyone have any tips or what math calculation I should be using to cut/calculate the inside/outside radius of the travertine cut pieces?

The outside spa diameter is 129-129.5" (due to concrete being slightly irregular)
The inside spa diameter is 103.5-104"
The travertine is 16"x24"

Two variables I'm uncertain about:
1. I think there would be some overhang (for the travertine) on the inside diameter of the spa. But I'm not sure what the standard overhang would normally be (since that is where peoples' heads would lay against when sitting in the spa)? The excess outside overhang of the travertine can be less precise, as there will be ledgestone on the outside wall.
2. The widths of the pie shapes for the travertine. I'd prefer the finished appearance to look as seamless and rounded as possible, but again, perhaps someone could recommend a standard size cut that would give an overall rounded/seamless appearance?

I've included a couple of photos to help illustrate better. Any advice would be greatly appreciated. Thanks so much in advance!

 

[JamesW]

Outside diameter = 134” for a 2.25” to 2.5” overhang outside.

Inner Diameter = 102” for a 0.75” to 1” overhang inside.

Outside Circumference = 134 π inches ≈ 420.973 inches

If you use 18 stones and you want a 1/2” grout joint, you will have 18 grout lines, which is 9” for the grout lines and that leaves 411.973”/18 = 22.8874” for the outside cut.

If the inside diameter is 102”, that is a circumference of 320.442 inches - 9” for grout leaves 311.442” for the stones/18 = 17.302” on the inside cut.

Note: The picture has 16 stones, but the calculation is for 18 stones.

 

[JamesW]

Note: This is probably close, but the exact numbers are difficult, so verify for yourself before cutting.

The stones have flat edges on the front and back so you have to decide if you want to cut the radius or leave the flat sides.

If you cut the front and back sides, then that will eliminate the bullnose unless you reshape the bullnose.

Below is a diagram with 18 stones and the inside overlap is about 2" at the center of the stone to about 1" at the side of the stone.

This will allow you to cut the radius if you want.

The stone is pushed in by 1", so the outside diameter is 132" for an outside overhang of 1.25" to 1.5".

The angle of the cut is 10 degrees.

Circle with a diameter of 132”

Circumference = 414.69

Grout = (18 x 0.5") = 9”

Total = 405.69/18 = 22.54 (22.642”).

Circle with a diameter of 102”

Circumference = 102 π inches ≈ 320.442 inches

Grout = 9”

Total = 311.442/18 = 17.302 (17”).

 

[JamesW]

If you want to move the stone back one inch, then I would do 22.8874” and 17.245”.

That would give you about 1" overlap on the inside at the center of the stone but close to zero at the edges of the stone.

So, it depends on if you want to cut the radius and how much overlap you want.

 

[JamesW]

22.8874" coping + 0.5" (for grout) = 23.3874" edge length.

Outside height = 132.637".

Inside height = 102.637".

Inside diagonal = 104.222 (No overlap).

Inside Edge = 18.098 inches - 0.5” for grout = 17.6”

18 sided polygon side height = 102.637" - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

18 sided polygon side length = 23.3874 - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

18 sided polygon side edge = 18.098 - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

 

[JamesW]

An inside edge of 17.63” - 0.5” (grout) = 17.13” coping inside length.

Inside height = 100” and an overlap of 1.75” to 2” at the center of the stone.

Inside diagonal = 101.527” for an overlap of 0.9865” to 1.2365” at the edges of the stone.

Outside height = 132” and an overlap of 1.25” to 1.5” at the center of the stone.

Outside diagonal = 134.037”

Overlap at the edge of the stone = 2.2685” to 2.5185”.

Outside edge length = 23.2752” - 0.5” grout = 22.775” coping outside edge.

18 sided polygon edge length = 23.2752 - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

 

[hillbill]

James, first I'd like to thank you for taking the time to write out such a detailed and well-thought out response. Greatly appreciate it. I'm going to need to take a bit of time studying each reply, but before I do so, I'd like to answer a couple of your key points.

1. For grout lines, I guess for some reason I always had it in my mind to have no/very little grout lines at all. Maybe that's not practical, but as a novice with no prior experience at this, it was preferred, if possible. I've attached another photo below showing double bullnose rounded travertine pieces. I can't tell for certain, but I initially thought this photo had no grout lines. Perhaps with your expertise you can tell whether that's the case or not?
2. I hadn't anticipated the squared nature of the pie shape wedges, and so your advice about the inside overhang being 1" at the middle and near zero at the outside edges was an education. So thanks for that. Again, using the photo below, what is your impression of the overhang shown below? And would that be a practical amount of overhang for a spa?

I'll spend some time going over your above responses now. Again, thank you for generously offering your time and advice on this.

 

[Toxophilite]

I watched my tile guy do it on freeform of pool and spa. No math, he used a method not unlike this, he actually laid them all out first:

 

[JamesW]

When stones are mortared down, it’s common to use grout lines between the stones.

In both pictures, I can see grout lines.

Typical lines are 1/4” to 1/2”.

With the correct grout the lines look good.

The second picture is not very clear, so it’s hard to see the grout lines.

If you are using coping stones with a straight front and back edge, you won’t get two concentric circles; you get two concentric 18 sided polygons.

You can round the stones with the correct interior and exterior radius, but that would mess up the bullnose and you would have to reshape the bullnose if you wanted the bullnose vs. a flat front and back edge.

The interior and exterior overhangs are a personal preference.

If the stones are straight on the front and back, then the overhang will not be equal from the center of the stone to the edge of the stone.

The overhang in both pictures looks pretty good.

I think that my last post #6 is the most accurate.

 

[Toxophilite]

If you are using coping stones with a straight front and back edge, you won’t get two concentric circles; you get two concentric 18 sided polygons.

You can round the stones with the correct interior and exterior radius, but that would mess up the bullnose and you would have to reshape the bullnose if you wanted the bullnose vs. a flat front and back edge.

Mine came out exactly like the pic. After using straight cut travertine, no bullnose, it does not look good at all left that way. Then, a skilled guy with a bullnose grinder dressed both inside and out. Acid washed the fresh grind, and after a few month of weathering, you can't tell it was ground.

 

[JamesW]

If you want to plan it out to see how it will look, you can cut the pieces out of plywood and then put them in place to see how it all fits.

The pieces will be trapezoids.

It's important to make the trapezoids exactly symmetrical.

The cuts need to be exactly 10 degrees.

If you cut without the grout lines, the pieces should fit exactly.

Inside edge = 17.625”

Inside height = 99.9563”

Inside Diagonal = 101.498”

Inside overlap = (103.5 - 101.498)/2 = 1.001” at diagonal (edge of stone)

Inside overlap = (103.5” - 99.9563”)/2 = 1.777185” at the center of the stone (Height).

Outside Edge = 23.26746”

Outside Height = 131.956”

Outside Diagonal = 133.992”

Outside Overlap = (131.956 - 129.5)/2 = 1.228” at the center of the stone (height).

Outside Overlap = (133.992 - 129.5)/2 = 2.246” at the edge of the stone (Diagonal).

If you place these pieces in a circle, they should fit together with no gaps and then you can draw the inside radius and outside radius.

Inside Radius = 101.498/2 = 50.749”

Outside Radius = 131.956/2 = 65.978”

You can cut the plywood templates on the radius lines and then they should form a circle.

You can then use the templates to cut the stones.

For the grout lines, subtract the grout line width from the stone size.

For example, if you want a 3/8” grout line, subtract 0.375” from the stone size.

Subtract 0.1875” from each side of the stone.

 

[hillbill]

Toxophilite, thanks for the video. Seeing the actual bullnose being cut in action makes the process feel a little less intimidating. I couldn't find a video like that on YouTube to save my life, so that's really helpful.

James, I like your suggestion about cutting plywood ahead of time to dry fit the pieces. Better to make any mistakes on a sheet of plywood first!

Taking the most recent measurements of 23.26746" x 17.625", I guess it would be logical to assume that cutting the pieces by half (11.63373" x 8.8125") would yield a better radius curve appearance (less polygon appearance). I see from the YouTube video above, the pieces used looked to be maybe 8" in width to start. Does that sound like a pretty standard size used in the pool tiling business?

 

[JamesW]

36 sided polygon inside edge length = 8.8465”

Height 101.116

Diagonal = 101.502

Minimum Inside Overlap = (103.5 - 101.5”)/2 = 1”.

Maximum Inside Overlap = (104 - 101.116)/2 = 1.442”

36 sided polygon outside edge length = 11.6461372328”

Height = 133.1159”

Diagonal = 133.6244”.

Minimum Outside overlap = (133.1159 - 129.5)/2 = 1.80795”

Maximum Outside Overlap = (133.6244 - 129)/2 = 2.3122”.

Note that this is without grout lines.

You have to add the grout lines by subtracting the grout line width from the stone sizes.

If you want a 3/8” grout line, then subtract 0.375” from each stone.

The angle for each cut would be 5 degrees.

 

[JamesW]

You can cut the templates out of maybe cardboard or thick poster paper or plywood; just something you can use to set in place to see how it looks and fits.

You can cut it with no grout lines for a tight fit or with grout lines to see how that looks.

Or, you can cut the stones and hope there are no unexpected surprises.

You also have to figure out how you want to work around the skimmer.

 

[Newdude]

James, first I'd like to thank you for taking the time to write out such a detailed and well-thought out response. Greatly appreciate it. I'm going to need to take a bit of time studying each reply,

He types them faster than I can read them. I need a couple of DAYS to fully understand them.

 

[hillbill]

Ok, I'm going to cut test pieces from plywood/cardboard this weekend. Before I begin, since your geometry is light years better than mine, I thought I'd ask one last favor. Would you be able to calculate the width of each piece, halved again. So I guess a 72 sided polygon with no grout lines? I ask since that looks quite a bit like the approximate paver width shown in the video above, and maybe that will achieve the best overall curved appearance that I'm looking for. So very appreciative for your assistance James!

p.s. For the skimmer, it's a 10.5" x 10.5" square (although I believe it could be trimmed a bit if needed). I think my intention would be to have 2 paver pieces (of the 72 sided polygon) that would cover the skimmer. Maybe grind down the underside of the 2 pieces so they create a pocket that lays neatly over the skimmer, or glue the skimmer lid to the underside of the travertine pieces, so it could be lifted off as a single piece. Not really sure, just thinking aloud.

 

[JamesW]

72 sided polygon inside edge = 4.4274".

Inside Diameter = 101.501”.

Inside Height = 101.404

72 sided polygon outside edge = 5.82455017307".

Outside Height = 133.4041315".

Outside Diameter = 133.5312”.

 

[hillbill]

Thank you!

 

[rcerf]

When I cut the limestone capping for these walls I used half inch foam insulation board to make my templates. It’s easy to cut , it maintains its shape, and it’s inexpensive.

 

[JamesW]

Make sure that the stones are exactly 16" wide as that will affect the calculations.

If they are slightly smaller, then you have to recalculate.