Hi fellow woodies,
My latest project involves the planning and construction, of an octagonal (8
sided) summerhouse/workshop on a base measuring 4.5 metres square, with a
floor capacity of 4 metres² - 43.056 feet² - 6200.12 inches², and a wall
height of (2.14 metres - 7 feet and 0.25 inch - 84.25inches). Try as hard
as I can, I've been unable to get my head around the calculations necessary
to work out how wide each of the individual 8 sides should be. I visited a
book called 'The Woodworker's Complete Shop Reference' by J Churchill.
However, my insufficient brain capacity cannot cope with the math, which
seems to read as :- Radius=(Length / 2)² /
height² / 2 x Height ( /
divided by). I've most likely misinterpreted the math calculation, as this
is a weak point with me.
Simple checks using a graphics program seem to suggest a length in the
region of 1.57 metres, however, I'm not sure if the prog has also measured
the effects of certain viual effects used to make the plans look good when
printed (thick outer lines of 5 points and rendering/bevelling and shading
The answer is 1.657 m per side for a perfect octagon. Given that the angled
sides are at 45 degrees, and a side is x, that means that a 4 m edge will
"see" x + .707x + .707x. So that means 4m = 2.414x, or x = 1.657
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