[sawdustfactory]

Any math whizzes out there? I'm trying to remember how to calculate the radius or diameter of a circle when I have a known arc (?) I'm trying to make a permanent template for the rockers on a rocker board
http://www.ebay.com/itm/Rocker-Boar...ors-rehabilitation-and-athletes-/251263785366

The length of the straight edge is 15" and the "height" at the center of the rocker is 3.5" It's been a long time since trig so any help is appreciated.

 

[johnmark]

could you set up the problem?

What is the "straight edge"? what is the "height"?

circumference= πd

or 2πr

my guess is that the line from one side of the rocker to the other is 15 and the distance at that midpoint is 3.5. is this correct?

 

[Dave Paine]

Formulae are available, but you may prefer a web site to enter the data.

http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry

 

[johnmark]

if you had a sewing tape measure, this would be a lot easier.

 

[mics_54]

r = (m² + ¼c²)/2m

where m is the "height" and C is the cord length

I get 9.78 radius or.. approx 9 25/32

 

[johnmark]

Formulae are available, but you may prefer a web site to enter the data.

http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry

that's awesome. now i want to know how it's done.

9.78571?

 

[woodnthings]

will this help?

http://mathforum.org/library/drmath/view/55037.html

 

[sawdustfactory]

Thanks guys! I knew I could count on y'all ;-)

 

[4DThinker]

I get a diameter of 19.6406" using my CAD software. Drew the arc as described, then a straight line from the center of the arc to each end. Found the center of those line segments and drew a line 90 degrees from their centers until they crossed. That intersection was the arc center.

 

[woodnthings]

the online calculator posted above says...

http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry

The Complete Circular Arc Calculator
Color Code Entered Values Calculated Values

17.09083 15 3.5

If it were me and I didn't know math or have the online calculator I would .... draw the 15" line, bisect it to get 7.5". draw a vertical line at the 7.5" extending it. measure down 3.5". Using a beam compass on the vertical, which will become the radius, strike arcs until the compass passed through the three end points of the lines.

 

[GeorgeC]

Any math whizzes out there? I'm trying to remember how to calculate the radius or diameter of a circle when I have a known arc (?) I'm trying to make a permanent template for the rockers on a rocker board
http://www.ebay.com/itm/Rocker-Boar...ors-rehabilitation-and-athletes-/251263785366

The length of the straight edge is 15" and the "height" at the center of the rocker is 3.5" It's been a long time since trig so any help is appreciated.

The problem is that you are trying to use trig and it is a geometry problem.

G

 

[cabinetman]

Another method for arriving at the arc would be to use the string and nails technique used for drawing ellipses. With a few test positions for the nails, you can strike the arc you want on the length of the straightedge. That could qualify for your template.

http://www.waterfront-woods.com/Articles/Ellipse/stringellipse.htm

http://www.mathopenref.com/constellipse1.html

http://www.thisiscarpentry.com/2013/09/06/drawing-an-ellipse-the-string-method/

.

 

[Dave Paine]

that's awesome. now i want to know how it's done.

9.78571?

I get the same answer with the link and confirm with separate calculation.

This can be solved by trig or geometry.

Geometry solution

The property of chords in a circle state
"Where two chords intersect, the product of the segment lengths of one chord must equal the product of the segment lengths of the other chord"

A chord is any line drawn within a circle. In this case the chord will intersect at 90 deg.

One chord in this puzzle is 15 in long. The other chord would bisect this, so each segment is 7.5in long.

The other chord is ( 3.5in + a in) long which is the diameter.

Hence (7.5 * 7.5) = ( 3.5 x a).

Hence a = (7.5 * 7.5) / 3.5 = 16.0714 in

So diameter = 3.5 + 16.0714 = 19.5714 in

Radius = 19.5714 / 2 = 9.785714 in

Trig method is to use right angle triangles. I am not going to attempt to draw this one out.