Yes, there is a mathematical approach. If you know the length and height of the arc, it is easy to calculate but Rump is quite correct in stating that it will be less than perfect. In my experience when trying to fit anything to an existing architectural element, throw out the calculator and do it manually, it will fit better.
Excuse me Rumpy, I forgot the "y". Wasn't trying to be a smart **s.
While I agree that, with the problem as originally posted, a perfect arc will probably not fit into most work done by a mason, I'll have to disagree with your statement above. With the with design and manufacturing techniques used today there are a lot of instances where the mathematical solution will yield very good results when trying to work with existing architectural elements. I was part of the earlier discussion about finding a radius for a window while knowing just the cord length and height of the arc. I can testify that not only did the formulas work great but the resulting jam extensions and trim pieces were very accurate. The time savings involved in not making a template (or using trial and error to find the radius) makes it well worth keeping a few formulas in the notebook along with the calculator.
Mike O.
Rumpy is actually the name of one of our cats. We call him Rump all of the time, so it's not offensive. ;-)
You have to be a pretty good guy, you have cats. I've got five.
Only five, don't you like them :-). We now have only eight, all registered PixieBobs. We did have nine. I hope you do not know what FIP is and I hope you never find out.
This is the Cattery all of our blood lines are from, (not our site):
You are correct. There has to be an element of both; practical and theory for the best advantage. Been there, done that in the steel business. In particular I assisted my brother [structural steel] by doing calculations on an arch for the recovery after the 911 disaster. His practical knowledge far exceeded [he's now passed on] mine, but he said I saved him many hours of work. On another occasion he couldn't get the CAD dawings to give him what he expected. I saw the flaw through calculation that the had been given two sets of unmatching detail on two different drawings. Both are necessary for a better job: practical experience and base theory. He knew there had to be a mistake, and I found it. It's not enough to use a sledgehammer to get the motor started. You have to know where to hit it.
So CW, Do you know of a formula?
Yes, posted to A.B.P.W.
See if DJ's site will help.
Radius = R, center height = h, full chord length = C.
Pythagoras: (R - h)^2 + (C/2)^2 = R^2
Simplify: R^2 - 2Rh + h^2 + C^2 / 4= R^2
2Rh = h^2 + C^2 / 4R = (h^2)/(2h) + (C^2 / 4)/(2h)
This can be combined into one fraction, but why bother ...just stick the numbers in the above.
So with h = 3" and C = 36", you'd have
R = 3/2 + (36 x 36)/(8 x 3) = 55 1/2"
Also easily checked with a CAD program.
Thank you, I very appreciate it.
They sell caulk by the truckload. Rabbit
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