Trig Question

[Michael O'Sullivan]

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]

r = (m² + ¼c²)/2m

I think.

[Alex Shanku]

m = height and c = chord

[Chris Padilla]

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]

thanks, guys

[J.R. Rutter]

I've been using this excel sheet for a couple of years:
http://www.woodweb.com/knowledge_base/_Spreadsheet_Calculation_Program.html

[Anthony Whitesell]

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]

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]

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]

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]

Kock this stuff off, woodworking is supposed to be fun.

[Karl Brogger]

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]

Kock this stuff off, woodworking is supposed to be fun.

Math is half the fun in woodworking!! ;)

:D










...for me! :cool:

[Chris Padilla]

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]

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.