It’s been a while since I’ve logged onto the forums, but I find that I need to calculate the radius of a circle from the length of a chord, and am looking for some help.
I obviously know the length of the chord (22″), and the length of the section of the radius from the center of the chord to the edge of the circle (9″). I need to be able to lay out the arc or calculate the radius from these two numbers.
I did pretty well in plane geometry , but I’ve checked a couple of web sites – one of which said, “this can be solved by a simple equation” – which proceded to lay out a about a six-step formula, each of which was pretty damn complicated. More than I want to go through, if possible.
I know, that given the way framers lay out the radius for an arched window top, there should be some easy way to lay this out without 30 minutes of calculations.
Any advice?
The person who says it can’t be done should not interrupt the person doing it. – CHINESE PROVERB
Replies
The quick and dirty way for me is to draw it in SketchUp. The radius is 11 7/32.....
I know it's cheating.....
View Image
r = (d^2+h^2)/2h
Edited 10/1/2009 10:13 pm ET by DaveRichards
Dave, what does the symbol ^ stand for? I didn't do any math past high school algebra and geometry (in the 60's) and don't remember that symbol.forestgirl -- you can take the girl out of the forest, but you can't take the forest out of the girl ;-)
Hi there Forestgirl. That's the method for indicating that the next number is a power when you can't use superscript. h^2 would be h squared.
Ahhhhh, thank you Dave. When I was using a chisel on stone in class, that wasn't an issue. ROFL!forestgirl -- you can take the girl out of the forest, but you can't take the forest out of the girl ;-)
Ha! I'd have pegged you for no older than chalk on a piece of slate but I'm not a good judge of age. ;)My apologies to anyone who was confused by the formula as I wrote it out.
I had a prehistoric teacher. ;-)forestgirl -- you can take the girl out of the forest, but you can't take the forest out of the girl ;-)
Thanks for all your help and replies, guys. I'm going to try these methods this afternoon.
The person who says it
can't be done should not interrupt the person doing it. - CHINESE
PROVERB
Try this site.
http://www.1728.com/circsect.htm
Often in error but NEVER in doubt!
Easy one for me to remember and real easy to figure is; 1/2 chord squared plus rise squared divided by 2 times the rise = radius.
This would be, chord is 22 so 1/2 the chord is 11.
11 times 11 = 121
rise is 9 so 9 times 9 = 81
121 plus 81 = 202
202 divided by 18 (2 x rise) =11.222 or 11-7/32
All simple multiplication and division that can easily be done with a pencil on a scrap of wood. This is the same one DaveRichards posted.
Rich
The Professional Termite
Edited 10/2/2009 9:14 am ET by trialnut
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