Need help with a circle layout...

[Tool Guy - Kg]

John,
There must be something with that software. Starting at top, you are off...not by a lot, but by the time you make it to the bottom, you are off by 1/16". Maybe the resolution is a bit low? And the 3/1000 of an inch difference between the bottom of one tile to the top of the next is correct, but it only accounts for one side of the tile. With both sides, the difference is a little over 6/1000 of an inch.

Here are the actual tile sizes with the angle of the grout line taken into consideration:
First row: 5.9548113 top, 5.6529391 bottom.
2nd row: 5.6466039 top, 5.3447317 bottom
3rd row: 5.3383965 top, 5.0365243 bottom
Tom offered to explain how to compensate for the angle of the grout line for a case of beer, or a chocolate cake....I'll do it for a 1/2 case....provided its Corona.

Certainly these measurements are far more precise than we can measure to cut tile. When all is said and done, I'd do the following to guide the layout and cutting of the tiles on the job. (For the sake of discussion, the fact that Jeremy's circle will fall outside the tiled area is being ignored.) First, do the math that we described above to come up with the number of segments (tiles) and the straight line segment length (width of tile & grout line)....this will give you a great starting point to "space apart" a pair of dividers. Then layout the outer circle on the floor with a trammel point. After the circle is down, arbitrarily mark a starting point somewhere on the circle. Grab your dividers and "walk out" the perimeter of the circle with 124 lengths of the divider....when you finally make it around the whole circle back to the starting point, you will likely not end exactly on the starting point. Take that measurement that you are off and estimate 1/124th of that distance. Do your best to enlarge or reduce the distance between the caliper points and then walk out the circle once again. (You absolutely need the type of dividers with a screw adjusting wheel.) It will take multiple tries, but when you get the dividers correctly spaced, walk it out one last time; making tick marks along the perimeter of the circle as you go so that you have a reference for each grout line for the whole circle. Now its time to make 3 “Master Tiles”…..arbitrarily select 2 tick marks next to each other and connect them with a straight line. Lay 3 tiles down on the floor (like I described with the board and string method), only do it right on the floor using the straight line you just drew as your starting line for the "outer tile". (Don’t forget to space the tiles 1/8” apart.) Measure inwards 1/16" from the tick marks on the floor (this accounts for the 1/8" grout line) and put a pencil mark directly on the tile. Now snap a line from the trammel point to each of these 2 pencil marks to layout your 3 "Master Tiles". Cut them out as perfect as possible. Reproduce 124 of each tile and you are ready to install them. Using the tick marks on the floor, the layout will work perfectly by keeping you directly on target. You will end your last tile precisely 1/8" from the first. No guesswork.

[Steven Hauser]

Yes, Everything said is quite good.

Now, what I'd like to say is this, in order to do the circle more simply, A master template of the area would be taken. We'd get about 130 tiles and lay them inside and outside the circle.

We'd mark them, cut them and lay them.

We'd charge a flat radius fee + footage. We'd know that it would look good because we template things every day.

I'd wish that my people could do the calcs, run a software program, or explore the proofs like I did and discovered that everyone is right depending on the kerf allowance and grout spacing. It doesn't matter though because we'd eyeball the grout and order extra tile in reality.

[Stoneguy]

Great discussion gentlemen!

[John K]

Steven,

Your way sounds alot easier. What material would you use to template a 20 ft circle?


Blackberry,

Would a guy have to physically measure on site or could the measurements be taken off a set of plans? ( for layout in Corel Draw)

[Steven Hauser]

John K,

Either vinyl laid upside down, brown paper, cardboard sheets, etc. Whatever it took to do.

The last one was drawn with the paper and transferred to cardboard.

You could scale it from the plans or scan it in to the computer as well.

[T_Hulse]

I know it may seem like we're being overly picky or showing off when we use all those long decimal points, but it actually is good to get more accurate than the nearest 1/32nd. If for instance you want to lay out your circle in sections of 10 tile at a time, and you're 1/64th off per tile when calculating this, then you would be off by more than 1/8th of an inch for each 10 tile section, and an accumulation of about 2" when your done.

Stephen, so you would just accept a dutchman on a job like this?

I've followed this with interest because I've gotten the chance to dust off some math skills and do some calculations.

If it hasn't already been said, then I would add the observation that I think the way to approach the installation would be to end up with a number of tiles that are multiples of 8 (120, 128, etc) so that the 20' diameter circle can be divided into 8 equal arcs. Each arc will be just under a very manageable 8', and once all the tiles are cut, with a template or jig to ensure consistency, then each arcuate section can be set with the assurance that no dutchman will be needed.

Jeremy doesn't need the tiles to be as close as possible to 6", only that 12" tiles can be cut into quarters. Whether each tile ends up being 5 7/8", or 5 3/4", or something else that is close, I don't think is important as long as the dimensions work out for an even number of tiles in the concentric circles.

Neat project, I would like to do one sometime.

[Stoneguy]

Originally Posted by Rob Zschoche

I've followed this with interest because I've gotten the chance to dust off some math skills and do some calculations.

If it hasn't already been said, then I would add the observation that I think the way to approach the installation would be to end up with a number of tiles that are multiples of 8 (120, 128, etc) so that the 20' diameter circle can be divided into 8 equal arcs. Each arc will be just under a very manageable 8', and once all the tiles are cut, with a template or jig to ensure consistency, then each arcuate section can be set with the assurance that no dutchman will be needed.
.

Good point.
What I will add.
I hate breaking up a circle or arc into sections that are some odd number of degrees. If possible I'd like to do this particular layout in 120 pcs of 3 degree section. This could be done with the 12 x 12 tiles **IF** the tiles were ripped once into 5 31/32" x 12" strips, assuming 1/16" blade kerf.
The second cut would be the slighty diagonal cut, done exactly centered on the 12" length. It would be pretty simple to set up a jig to ensure all the cuts were done the same. You would then have peices that had 2 90 degree corners, and the length of the longer (top) side would now be slightly over 6", allowing you to have the (insert exact dimension here)" size required to do the complete circle in 120 pcs.
This also substantially reduces the number of saw cuts required to complete the job. (I'm all about doing lesser numbers of cuts)

David
????Did that make any sense???

[Steven Hauser]

Yeah David it makes sense,

In fact that's pretty much what we do once we loose lay the tiles on the template. We create a jig for that job.

I wouldn't of ended up with a two inch dutchman. I would have spaced the grout joints appropriatley to close the 2" over 20' off, or else close them up enough to make a wider dutchman.


That's what grouts for isn't it?

Now, seriously, if we do slabs and we do them, and we do columns radius tubs, circle floors circles within circles, once we get strted in even increments as David stated, we'd get it even more precise.

Sometimes we use the Cad programs to get us started, but always end up doing the dry mock up before we set it.

It works even with 1/32" grout joints. I'd take pictures but (well y'all know I'm camera top website challenged)

[Stoneguy]

Well i just realized the method I suggested above won't work. By my calculation, each tile needs to be 6.157516" across the top, & 5.843391" across the bottom, so the 12" tile would have to start out at 12.000907" wide, PLUS the thickness of the blade, in order to cut as I described. This is assuming the joint is 1/8" wide for it's full length, and not on a tangent to the perimeter.

Are we having fun yet?

[geniescience]

Originally Posted by Stoneguy

Well i just realized the method I suggested above won't work. By my calculation, each tile needs to be 6.157516" across the top, & 5.843391" across the bottom, so the 12" tile would have to start out at 12.000907" wide, PLUS the thickness of the blade, in order to cut as I described. This is assuming the joint is 1/8" wide for it's full length, and not on a tangent to the perimeter.

Are we having fun yet?

Actually David, don't give up; your idea can be salvaged. If I were there and part of the process, (dream on! ) I would negotiate with the architect to have permission to make the circle approximately 20' in diameter, and then I could do what you have shown above knowing that I could squeeze the tiles together all round and end up with a circle that may be 20'1" (or 19'11") in outside diameter. That way the grout line can be adjusted to suit whoever's perference who happens to be in charge that day and they sign off and it is done. This assumes the 3-rowed circle is the first batch of tiles laid, and the rest is filled in around them. ((But I'm a DIYer so go easy on me if I'm dreaming in technicolor)).

In your previous post you mentioned making fewer cuts, ending up with tiles that have two 90-degree angles. In that case the 1/8th" 'error' gets carried over onto the outside side of the tile, it does not disappear or get reduced, and it creates a 'problem' or a 'pattern' or a 'feature' in the way it shrinks the grout line between the next row. Each of the rows has a little zigzag flow in it. This is most problematic in the inner two rows. The outside row will meet tiles cut to fit, but the 1/8" jaggedness is still there. One way around this is to cut a little off on one half only so you end up with a 1/16th" 'peak'. This could be a feature, unique and highly prized.

If this idea is valid, I'd like to extrapolate right now. You mentioned wanting to get exactly 120 pieces and also wanting to minimize cutting. Suppose that minimizing cutting is more important. Then think about this: when the 12"x12" tiles get cut down to make four pieces, you could plan to do a batch that produces two 'large' ones for the outer row and and two 'small' one for the inner row. Then exactly half that batch size is needed to cut four pieces all the same size for the middle row. Then your "slighty diagonal cut, done exactly centered on the 12" length" is only the way you do the half-batch. Your non-symmetrical full batch is cut NOT on the center. Will calculate this later if people confirm that the odd shape is OK with the grout line-width variation.

One more point: when the number of sides in an almost-circle is far more than just ten or twelve sides, the closeness of fit gets better and better, so approximating a flat-sided tile to a rounded arc is closer and closer to a perfect fit. Other factors become far more significant ('kerf' cut loss, grout width and probably the actual tile's edges too). And if you are able to do the circle to a spec of e.g. 20 feet "more or less one inch" than you don't need to calculate too precisely until the other issues get sorted out. My opinion. If I were a tile layer I would minimize cuts and get a shape that is going to look good. Would the 'peak'ed' square tile look good?

Hope this helps. And thank you all for letting a DIYer post on the Professionals' Forum.

[Stoneguy]

[Blackberry]

So, lots of ways to do this. In the end it's only important that the grout lines look even to the eye and there is a minimum of lipping.

I will say that for even more complicated layouts I have printed a full size piece from my drawing, pasted it to a tile and cut around the lines to arrive at a piece that looks and works just the way it should.

Tom, good luck converting all this into a lesson on trigonometry. I'm looking forward to your explanation of trigonometric ratios and how to use them. Actually there is a good math series - Geometry the Easy Way, Algebra the Easy Way, etc. My brother and I have used it for years to try and keep up with our bright young engineers. (We have found that it's way easier and cheaper in the end to hire someone to do this stuff).

Meantime if anyone wants help with Corel or a CAD app, drop me a line.I've been doing this since the dark days of DOS 2.0

[Steven Hauser]

Help!!

[Stoneguy]

John,

Funny that you mention DOS 2.0. I still use an old DOS based CAD program, circa 1980-something, to figure out stuff like this. I think I was using something like DOS 3.2 or 3.5 when I bought the software. It's Generic Cadd 6.0, by Autodesk. Very simple to use, & can give you accuracies to many decimal points if desire. I usually only use 3 decimal points, but for the sake of this discussion I changed to 6 for fun. It makes & reads .dxf files. It kinda sucks trying to configure printers, pointers, & display adapters when using on a modern computer, but I can still run the program OK on new Gateway XP Pro systems, as long as I fool it into thinking I'm using an old HP4 laser or old Okidata 5** series dot matrix printer.