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Calculating Radians/ChordsQuestion
Forum Responses
To find the radius of a curve segment, use the following: 2 x A x R = A squared + B squared For example:
Work that down to:
Reduce that by dividing the left and right sides both by 22, and you get:
A whole lot harder to type than it is to do. Write up a sample with the numbers all plugged in and it's easy to use. Turn it around to work backwards - say if you have the radius and height, need to know the length.
From the original questioner: Sweet. Sweet. Sweet. If I am right, the tan(theta)=B/(R-A) [that is the tan of the interior angle (really 1/2 of the angle formed by the two radii at the ends of the chord)] giving radians, multiplied by R gives the length of the curve! Yahooooo. Radius of an arc knowing the chord length and arc height (same formula as above, just reduced differently): R= (((A/2)^2) + (B^2)) / 2B
I say this as:
********************************* Arc length when you know the chord length and the radius: Angle in Radians = 2 * ASIN((Chord Length) / (2 * Arc Radius)) Arc Length = Arc Radius * Angle in Radians Said as:
The angle in radians equals 2 times ASIN of the chord length divided by 2 times the arc radius. ********************************* Arc height when you know the chord length and radius: B = R - sqrt( R^2 - (A/2)^2 )
Said as:
I have on the shelf here by the computer the CRC Standard Mathematical Tables (14th edition, 1965) that my brother gave me when I graduated from high school. Besides all those useful logarithm, trig, exponential, hyperbolic trig, ... tables are sections on geometry, trig, etc. formulas that I need when designing and building new pieces. No joke. I even use my slide rule in the shop so I don't have to worry about keeping batteries in a calculator.
From the original questioner: Thanks ever so much to all. Makes a big difference. Now I don't have to guess that a 4x8 will do the job or not... I've had a spreadsheet with many formulas available for download on this website for almost two years now: Spreadsheet Calculation Program The Excel file has a whole lot more formulas and drawings than the original works spreadsheet. I wanted a quick, accurate way to calculate arcs for work I did. And I expanded on those ideas and made other useful formulas for woodworking. Best of all this is a free download for everyone. Would you like to add information to this article? Interested in writing or submitting an article? Have a question about this article? Have you reviewed the related Knowledge Base areas below? 
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