Need help with a circle layout...

[Jeremy]

Here is the layout. The circle is 20' diameter, outside edge to outside edge. It is to be made from 12"x12" cut into quarters. The circle will be three tile wide. A straight lay pattern will be inside the circle using 12x12 tile. Outside the circle will be a broken joint pattern (brick) using the same 12x12's. Total area of tile is 20'x28', the circle will extend out of the rectangle by a few feet on one side. Here are my questions:

Will the quartered tiles need to be cut at an angle in order to keep them from "running wide"? The grout joint will be 1/8" throughout.

How do you figure the area of a circle? Is it Radius+Radiusx 3.14?

How do you figure the total length of the circle? I have not a clue.

Give me some ideas as to how you would bid this one??

Thanks for the lessons, and add any tips that make layout easier if you wish...

[Great British Tiler]

Hi,

in a bit of a rush but.........

area is:

3.142 x radius squared.

& circumference (which is what i think you mean by length) of a circle is:

diameter (i.e. radius x 2) x 3.142

Hope that helps a little

Ainsley

[Scooter]

Any circle layout will have a lot of cuts. Each tile will be cut on each side.

I did a circular hot tub once, and it had me scratching my head. I can not recall exactly how I figured it out, but there was a mathematical answer to it.

Each "row" of tiles is in a circle, and each side is angled down. The top of the tile row has a set circumfrances, which when calculated with grout lines, we kept dividing the circumfrances until we reached the number of tile we needed, with grout lines.

The cut and the width of the bottom of the tile will depend on the circumfrance at that point, and again, you know the circumfrance, and the width of the bottom course is figured out by division.

And so on for each course. The tile gets narrower and narrower for each course until they are little slivers at the center.

I'd invest in a Construction Master 5, and watch the DVD to help you on this. It is pretty good on circles. I know I was helpless without mine, although mine was "4". I think Construction Master know is up to No. 5.

Good luck, and I don't envy you. I would probably bid this very very high, like $30 plus per square foot. If the customer has an architect, then the architect will have design drawings for you, with all the layout pre-done. Indeed I am sure there is a CAD program out there that will design this circle for whatever tile size you have. I don't have a CAD program, only some straight edges, some lasers, some chaulk boxes, and some sharpies, and you can leave the squares and straight edges at home on this job. You will probably need some trammel points, though.

[Jeremy]

Thanks guys for the advice so far. I am still wondering how to come up with the angle needed on each cut in the circle in order to end up with a 20' diameter circle with 1/8" grout joints? I know someone has the answer. Keep em coming guys, I really need the help on this one.

[michaelhazuka]

Jeremy,

I'll give my 2 cents on the exterior circle and its installation....

When I have radius borders I set one side of the border by extending my field tile about 2-3 inches past the desired radius line. The following day after the thinset has dried you can re-mark your radius line on the set tile. All you need to do is run a grinder with masonry blade on top of the radius line. You can then take a scraper and cold chisel to remove the unwanted scraps of tile that you intentionally ran past the radius mark.

Cutting the interior circle is going to be a little more challenging, but if you set the exterior circle on day 1, and used a grinder on day 2 to remove the deliberate excess of the exterior circle, You should be able to start to set the interior circle on day 2, and if anything you can leave out the cut pieces and continue them on day 3(cause it will take you all day to cut the remaining radius pieces).

That's how I would do it. I would center the entire installation(i.e. interior circle, exterior circle) on the exact center of the circle...just to keep everything symmetrical.

[T_Hulse]

Michael I think he means that each individual tile is going to be installed perpendicular to the exterior circumference of the circle. So each tile would have pie cuts on 2 sides going all the way around the circle. Kinda like when you would set vcap around a tight circle with pie cuts.

Jeremy I can show you how to do it with math but it's a pretty involved process. We'll need some geometry & trig. Are you sure you want the long version before I type a book?

[Dimension tile]

You need to have the outside circumfrance which is PIxD so in your case 3.14x20= 62.8 then I beleive you would reduce your diameter by 2 because you'll have 12 inches less on both sides so 3.14x18=56.52. change those into inches so...C1= 753.6inches and C2= 678.24 inches (inches because tile is in inches) Then I think you divide the width of you tile with joints by the linear inches you have to cover ie 11 7/8 (11.875) divided by 753.6 = 0.01575 which translates to slightly more than an 1/8 that must be cut. C2 = 11 7/8 divide 678.24 = .0175 which is .005 from 3/16. You'll more than likely have to divide what needs to be cut overall off the tile by two so that equal amounts can be taken off both sides. I might be wrong on the less 2 feet for the C2 but I think this will get ya close. At least it sounds confusing Oh yeah area = 3.14(r sqaured)

[Tool Guy - Kg]

1) Grab a 12' 1x8 from the garage.
2) Lay it onna floor.
3) Pound a nail in the center of its width, towards one end of the length.
4) Measure exactly 10' away from center of nail to the other side of the board and put a tick mark in the middle of the board.
5) Use a speed square to make a perpendicular line across the width of the board at this 10' mark.
6) Lay 3 tiles down, 1/8" apart, starting from this perpendicular mark. Each tile after getting closer to the nail onna other side.
7) Use sharpie on furthest tile and write “TOP”on it. Write “CENTER” on the center tile. And write “INNER” on tile closest to the nail.
8) Hook chaulk line onna nail and stretch it to the upper right corner of the furthest tile. Snap the line.
9) Pivot chalk line to the upper left corner of the same furthest tile. Snap.

You now have three patterns. Cut em out as perfectly as humanly possible. The “TOP” tile is the pattern for all the tiles in the outer row. The “MIDDLE” tile is the pattern for all the tiles in the middle row. And the “BOTTOM” tile is the pattern for all the tiles in the inner row.

You have to remember that as you get closer to the middle of the circle, the circumference is smaller. This means you can’t make all the tiles exactly the same, unless you cheat a little with each tile and the grout lines continuously shift around the circle from row to row. This may be fine for you. But if you use the method above, all 3 rows will have 124 tiles in them. By the way the angle is something like 1.4516129 degrees. I didn't mention this earlier because how are you going to set an angle this precise? A lot easier to just snap the lines to make the patterns. Then rig up something on the wetsaw to reproduce 124 of each of the 3 patterns.

You have to make sure to lay enough of them dry as you get close to completing the circle, or you are going to wind up with a partial tile. Again, this may be fine with you to have a partial tile (and it sure will make it less intense), but I’m assuming not and warning you ahead of time.

[T_Hulse]

Jay the circumference will give you a measurment of basically a long arc, not a straight line. The tops of the 6" tiles will each be a straight measurement (even if you cut it curved later; then the top will be longer than 6" if measured along a curve). You cannot just divide up the curved circumference & expect it to be anywhere close the sum of all those little straight sides. You won't even get in the ballpark that way. The little straight segments will theoretically touch the circumference only at tiny points. These 6" segments in effect take a bunch of little "short cuts" around the circle that prevent you from directly comparing them to the circumference.

Kurt that's an excellent method but like you mentioned it gets pretty dicey when you try to complete the circle & join them up. If you're unlucky, (plan on it) you'll end up with a 3" gap to fill up at the end. With only 1/8" grout lines you really can't eat that up by dry-laying a portion of it. 3/16" joints for only a part of a 1/8" job is too big. I think the most you could add is 1/32" per grout line. That would take about a hundred tile to eat it up. Maybe he can accept a wedged dutchman at the end, I know I couldn't. I think you also made Jay's mistake of dividing a curved circumference measurment into to a bunch of straight segments. The 124 tile figure isn't right.

Jeremy whatever you charge, it's not enough.

[Tool Guy - Kg]

I dunno Tom, this is what I think. See if I'm wayward:
The 20' circle has a curcumference of 753.98224". If chopped into 124 pieces, each would occupy 2.9032258 degrees of the circle. And each arc would measure 6.08050" along the curve. This curve is indeed longer than the distance between the 2 points on either end (or straight segment, as we are referring to it). The straight segment measurement between the two can be figured out mathematically. Each pie piece is an equallateral triangle with 5 of 6 known figures. The 2 equal lengths of the triangle measure 120.00000 inches. The little inside angle is 2.9032258 degrees, and the remaining 2 equal inside angles are both 88.533875 degrees each (180 degrees - 2.9032258; then divide that by 2). This math equates to the straight segment as 6.07984 inches, or .00066 shorter than the arc measurement.

Ok, let's flip to the tile for a second. It is 12" long. As close as I can measure the kerf of the blade, it's .0875". Subtract that from 12" and split it in half and you are left with square tiles that are 5.95625". This represents the maximum length of any tile that can exist on the floor. In our case, this would be the longest side of the tiles on the outer ring being laid.

Ok, back to the straight segment length of 6.07984 that is needed on the outside of the circle to get 124 equal pieces. A 5.95625" long tile with a 1/8" grout line added to it equals a total of 6.08125". This is .00141" longer than it needs to be. Since less than 2 thousands of an inch is less than the thickness of ordinary paper, we are good to go. There is little we could do to set up a jig for cutting tile that would be less than 1/100th of an inch in its consistancy, rather than 2/1000ths of an inch measurement that I'm within.

I would agree that a 3" gap upon completing the cirlce would be a pain. Dry laying 100 tiles is too much to make a crap load of corrections. But rather than stretch the grout joint 1/32" for the last 100 tiles (agree that it would be kinda crazy), cut a bit less than 1/8" off the last 25 tiles to get another tile in there and keep the grout lines the same. Nobody will pick up on the tiles that are cut less than 1/8" shorter to make up the distance. If you were to lay out the circle with a trammel point and use dividers to mark off 124 segments, you will have a visual to keep yourself on-track the whole time you tile and you would avoid the problem altogether.

[T_Hulse]

Darn you Kurt! You just had to make me me actually do the math. I thought maybe I could talk Jeremy out of it & I'd get off without homework.
That's a pretty nice job you did there. I'll agree now you could almost do it with 124 tiles theoretically. There was only 1 small error. You grouped the 1/8" grout line with the straight segment length (that puts it at an angle to the line of the radius which is the true grout line) instead of with the arced segment. This changes the tile to each being .006 short instead of .0006 long, not really critical.
In real life though I think you need a lot more cutting room for a few reasons. First it's really tough to make hundreds of repetetive cuts where you're shaving angles down with no waste at all. Most blades will bend out & give you unwanted curves (BTW, Green Hornet reinforced 10" blade at Master Wholesale is my new favorite for that). Also it's nice if you can stay away from the rounded or pillowed or rough edges on some tile if everywhere else doesn't have it. Also very few 12" tile are coming 12" anymore.
Hey why don't you show him the trig to convert the arc to the straight side.

Jeremey you also asked if the sides need to be angled. I show the sides at around 1/4" to 5/16" different from the inside to outside of the inner row of tile. I definately think you need to angle them.

[Tool Guy - Kg]

You want me to show the steeeenking math Cripes, I got 3 pages of scribbles and circles & triangles that I can barely decipher! Ain't no way I'm typing that!

First of all, you got me on grouping the 1/8" grout line like you said. But....and here's the but...I got a present for you for you in return....the straight line segments would remain the same length with 124 pie pieces as before. The 1/8" that I had continued straight, instead of angled, is running to the outside of the circle and results in the distance between tiles as being slightly less than the required 1/8" grout line on my drawing. And if my groutline is too small, enlarging it to 1/8" means I have slightly too much tile.......and could do it with the 124 tiles.

(Oh please don't let this late night logic backfire on me or I'll never hear the end of it. It's 4:48am for cryin out loud!)

You have a great point on the issue of deflection as the blade tries shaving tiny amounts off the sides at the start of each cut. I think if this was my job, I'd do it with more tiles around the circle to shorten up the width of each tile. This would allow the blade to enter more "meat" of the tile to help eliminate the problem. The suggestion on the Green Hornet blade is something new for me. Kewl! I had one other thought that I didn't say before. If you tried to enter the blade from the side like we are talking about several hundred times throughout the course of this job, I think you can kiss a couple a blades goodbye. You'd wear away too much cutting surface off the sides of the blade...then it wouldn't cut a kerf big enough for the body of the blade to pass through. The blade would get stuck in it's own path. I'd put a few bucks in the bid for blades.

[Davestone]

Stop, guys he already did the Damn thing with the nail and board,while you two braniacs were triggin. Now can ya help me figger a 2 ft.rhomboid inside a four ft. oval medalion

[muskymike]

Yeah you're making my head hurt.

[Jeremy]

WOW!! I never dreamed things could get so tricky. I am coming close to grasping these lessons, so please keep them coming. I would like some more advice in the way of pricing this one too. Im sure that I wont make what one should make by the time its all said and done, but I want to be fair for both sides with my figure. I am leaning towards $12 per foot for the entire job. Which would put the bid at $6720 for the entire floor. Sound reasonable? Again, THANKS for the advice!