View Full Version : Trig Question
Michael O'Sullivan
02-09-2009, 1:33 PM
I am tryng to figure out the radius of a circle from the portion that is contained in a slight arch.
So if you have the length of a chord (L), and the distance (H) from the center of L to the top of the arch (which should by definition be perpendicular), is there a simple trig fromula to determine the radius (R) of the entire circle?
I was really good at this in the 11th grade, but now ... not so much.
Alex Shanku
02-09-2009, 1:37 PM
r = (m² + ¼c²)/2m
I think.
Alex Shanku
02-09-2009, 1:37 PM
m = height and c = chord
Chris Padilla
02-09-2009, 2:18 PM
I'll help you derive it because I rarely remember the formula.
Referring to the attached pic, we have:
H = height of the arch
L = length of the arch
R = Radius (what you want)
x = R - H (a convenient variable)
Using Pythagorean:
x^2 + (L/2)^2 = R^2, now expand that since you know x = R - H -->
(R - H)^2 + (L/2)^2 = R^2 - 2RH + H^2 + (L/2)^2 = R^2
Now we have:
-2RH + H^2 + (L/2)^2 = 0, solve for R -->
R = [H^2 + (L/2)^2]/2H, which agrees with Alex's Formula Q*E*D !!
Michael O'Sullivan
02-09-2009, 2:29 PM
thanks, guys
J.R. Rutter
02-10-2009, 10:03 AM
I've been using this excel sheet for a couple of years:
http://www.woodweb.com/knowledge_base/_Spreadsheet_Calculation_Program.html
Anthony Whitesell
02-10-2009, 10:18 AM
I've encountered this a few times in the last few years (wanting to find R having H and L). The piece I was missing to find the solution was that R=x+H.
Thanks Chris.
Chris Padilla
02-10-2009, 11:00 AM
Anthony,
I had one of those "eureka!" moments as I sat down one day several years ago to try and figure this problem out when I, too, realized that R = x + H...suddenly everything worked out. Pretty cool!
Joel Blauvelt
02-10-2009, 9:55 PM
I used the link below when I needed to calculate the radius of a circle when you only know the chord and segment height.
http://www.1728.com/circsect.htm
Joe Chritz
02-10-2009, 10:44 PM
You have the answer but interestingly enough this is a calculation we use to determine speed in accident investigations under some conditions. The radius is the dimension needed but we are only able to measure a portion of the radius and a chord.
Who said math wouldn't be important in 20 years?
Joe
Leigh Betsch
02-10-2009, 11:05 PM
Kock this stuff off, woodworking is supposed to be fun.
Karl Brogger
02-11-2009, 10:20 AM
Here's how I do it. Simple formula that I was given by a co-worker years ago. All you need is the Height (H) and the lenght (L) to figure the radius. Its so much easier to explain in MS Paint.
Chris Padilla
02-11-2009, 11:23 AM
Kock this stuff off, woodworking is supposed to be fun.
Math is half the fun in woodworking!! ;)
:D
...for me! :cool:
Chris Padilla
02-11-2009, 11:26 AM
Here's how I do it. Simple formula that I was given by a co-worker years ago. All you need is the Height (H) and the lenght (L) to figure the radius. Its so much easier to explain in MS Paint.
Cool...we have 3 agreements! :) My issue is that I NEVER remember the formula but I know how to derive it....
Karl Brogger
02-11-2009, 12:11 PM
Cool...we have 3 agreements! :) My issue is that I NEVER remember the formula but I know how to derive it....
Double click the image, and save it. I've got it written on the wall in my shop.
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