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Posted: Fri Feb 17, 2006 12:01 am
by jones2004
If you have a square cobble, just say 120mm x 120mm and you want to build a circle with no cuts how do you determine how big a circle can be with just the dimension of the cobble and the width of the tapered gap between each one.
Hopes this makes sense? but you must be able to find out the diameter of the circle with just the dimensions of the cobble and width of the tapered gap.
Posted: Fri Feb 17, 2006 12:40 am
by IanO
(Mr) Jones2004
I know about as much about block paving as ..er, I do about - concrete mixing (see my posting). However, your question is much more akin to my real job - at a desk.
The answer depends on how much the taper, ie gap on the outside edge, is acceptable.
Assume you create a 1 metre diameter inner circle (your 120mm blocks laid on the outside edge of this). You would use 26 blocks and the outer gap would be 29mm.
A 2 metre diameter inner circle would require 52 blocks (on the outer ring) and the outer gap would be 14.5mm.
The maths are: Circumference = Pi (3.142) x 1000mm = 3142mm. Now divide this by the block size (120mm) and the result is 26. However, this is the inner circle - blocks touching each other. The diameter of the outside edge is two blocks wider (1000mm + 120mm + 120mm), so back to the first formula - Circumference = Pi(3.142) x 1240 = 3896mm.
Take the inner circumference from the outer circumference and divide by the number of blocks (3896mm-3142mm = 754mm now divide by number of blocks (754mm / 26) = gap of 29mm per block. etc.
It is easy to do this calculation in an Excel spreadsheet, if you could make use of it let me know and I'll somehow post it up.
Regards
Ian.
Posted: Tue Feb 21, 2006 10:00 pm
by Tony McC
I have such a spreadsheet gizmo already. I toyed with the idea of posting it online but never got around to it, as I thought I might like the challenge of writing summat in javascript to match the other claculators on the site. Never got around to that, either!
Although everything Ian has said is spot on, I wonder whether the OP is questioning the minimum diameter of a circle that can be created with a block of dimensions a X b, with no cutting, and a joint width not exceeding the recommended maximum? I have a spreadsheet for that, too!
We just need jonesy to define what is meant by "tapered gap"! 