Need to calculate angles to cut capstone for a circle

lonestarmojoMay 26, 2012

I am building a 36" diameter circle shaped flowerbed for my wife. I'm building it from 4"High x 8"Wide x 5"Deep retaining wall blocks, is 3 courses high and I need to calculate the angled cuts needed for the sides of the capstones. The capstones I have are 2"High x 9"Wide x 6"Deep. Is there a formula for this calculation? Or is this gonna have to be trial and error?

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You don't any calculation.A "S" fluid curve bed nice.formal circle is hard.

    Bookmark   May 26, 2012 at 2:29AM
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This is one of those simple problems that could become complicated depending on the details... and you don't give enough information. Does the 36" dia. represent the inside planting area, or the outside perimeter of the block border? I take it that the blocks will not be cut except for the capstone? And you'll want to set the capstone outward so that it hangs over the perimeter of the "wall" blocks by 1"...? Is there a mortar joint involved or is this all dry stack? There are a lot of variables!

If there is no cutting of "wall" blocks, I'm guessing that by the time you create a circle of them, it will not come out to exactly 36". So a calculation based on that will be in error. Better to lay out an actual circle of them and see how the dimensions fall.

It would probably be a lot easier to take 20 sheets of copy paper in a stack and with a utility knife and straight edge, cut them into the exact dimensions of the capstone... 9" x 6". Draw out the right size capstone circle on the garage floor or plywood. Lay out the paper "blocks" so that their outside edge fit's within the circle. See illustration. If arranged with the minimum angled overlap, then--depending on the actual circle size-- there'll probably be a partial block left over. If you want ONLY whole blocks, you'll need to Re-divide the perimeter by the number of whole blocks required to make it. Re-cut the paper to this revised (slightly shortened) block length in order to create the cap of a uniform number and size of whole blocks that will fit the circumference perfectly. The steps are summed up as follows:

dia. x pi = perimeter circumference

perimeter circumference divided by block length = number of blocks needed

round up to nearest whole number

re-divide perimeter circumference by rounded up whole number of blocks to calculate revised (shortened) individual block length.

Cut paper blocks to that length and arrange within drawn circumference. The overlapped portion is the angle of end cut.

For the sake of example let's theorize that after you lay them out, the planting diameter is 36" and the outer diameter of the block wall surround is 10" greater (adding on 2 x the 5" block "depth".) We calculate the outer perimeter of the wall, then, at 46" (36" + 10".) A one-inch cap overhang will add another 2" to the diameter so now we're at 48". The perimeter of that (48" x Pi) = 150.78". Dividing that by 9" (the length of each capstone block... unless a mortar joint must be calculated in) comes to 16.75... the number of blocks needed to complete the circle. Round up to 17 blocks. Re-dividing the circumference by 17 blocks indicates that each will need to be shortened to 8.87" length in order to make the cap come out to a uniform number and size of blocks. Since each end of the block will be angle-cut, 17 blocks will require 34 end cuts. The end cut angle will be determined by dividing the whole number of degrees of the circle (360) by 34. The angle of each end cut will be 10.58* This answer must be recalculated, plugging in the correct numbers, for different size diameters of a circle.

    Bookmark   May 26, 2012 at 11:27AM
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A formula for this calculation:
Cut block capstone part wide = block capstone part wide -
inside circle diameter/outside circle diameter x bloc wide

But I prefer a visual feeling,a iron wire to make a fluid curve bed shape than a calculation.

    Bookmark   May 30, 2012 at 9:19AM
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