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Create the curve

Total Topics: 22
Total Posts: 158
Folks. Recently I started my LMI kit and wanted to work out how to make a 15 and 30 foot radius curve in order to make sanding boards for radiusing and shaping braces. Simple - I thought.

I searched over here for answers but found that stretching wire with a pencil attached was difficult. Our friend, BillM saved the day and gave me a quick algebra refresher and the numbers required. Below is the message BillM sent me…

Formula for a circle is X^2 + Y^2 = R^2

Solved for Y: Y = sqrt(R^2-X^2)

Say your "slice" is 24" long, we'll center it on the X axis so it runs from -12" to 12", or -1' to 1'.

Take 15' radius. For the peak (X=0), Y equals 14.96'. So there is a difference of .033'. So you would cut the peak of your arch to .033', or .4” (roughly 26/64").

Going inch by inch, your curve should look like the following. Mark these distances and make the cut:

X Y (R=15') Y (R=30')
0” .400” .200"
+/-1” .398” .199"
+/-2” .389” .195"
+/-3” .375” .188"
+/-4” .356” .178"
+/-5” .331” .165"
+/-6” .300” .150"
+/-7” .264” .132"
+/-8” .222” .111"
+/-9” .175” .088"
+/-10” .122” .061"
+/-11” .064” .032"
+/-12” 0” 0"

And then, for us convicts and the like, I converted it to metric

0 10.16mm 5.08 mm
+/-25.4 mm 10.10 mm 5.05 mm
+/-50.8 mm 9.88 mm 4.95 mm
+/-76.2 mm 9.52 mm 4.77 mm
+/-101.6 mm 9.04 mm 4.52 mm
+/-127 mm 8.40 mm 4.19 mm
+/-152.4 mm 7.62 mm 3.81 mm
+/-177.8 mm 6.70 mm 3.35 mm
+/-203.2 mm 5.63 mm 2.81 mm
+/-228.6 mm 4.44 mm 2.23 mm
+/-254mm 3.09 mm 1.54 mm
+/-279.4 mm 1.62 mm 0.81 mm
+/-304.8mm 0 mm 0 mm

Simply plot the dots and then take your long metal ruler and bend it so it touches all the dots along the curve and have your friendly third hand trace the line onto your board.

Jan 01, 07 | 3:57 pm
Ken Hundley

Total Topics: 40
Total Posts: 2169
Might be easier to put a finishing nail in each end point, lay the metal ruler against them, and with one hand, push the ruler to meet the curve. Still have hand # 2 to do the drawing, but thanks for posting this info, will be very helpful!

Jan 03, 07 | 5:19 pm

Total Topics: 32
Total Posts: 145
Hi guys -

I spent some time today making up 15' and 30' templates in Powerpoint to these measurements.

Now - obviously, Powerpoint is not a CAD tool (and I found it doesn't keep shapes exactly accurate as you move them around), and printers are going to have some variation too. But - I've got it tweaked to my setup, so I can print them and cut them out whenever I need for a template.

If anyone wants a copy, I can email it - it's yours for the asking. May take some tweaking for it to be exactly accurate for your computer / printer, but wouldn't be too much effort. - BillM

Jan 06, 07 | 1:23 pm

Total Topics: 32
Total Posts: 145
Took this to the next level and made a radius dish -

Calculated the numbers for the 30' circle in half-inch increments. Cut out a disk of plywood, drew concentric circles in half-inch increments. Routed it out according to the calculations, sanded it smooth. Voila! 30' radius dish.

Prior to this, had radiused a single brace, tested it out - fit right in the dish, perfect match.

Jan 17, 07 | 7:09 pm

Total Topics: 22
Total Posts: 158
Bill, I must admit that I had to google 'concentic circle' but now I understand what you have done. Do you have any picutres?

I personally like the look of the way that David made his dish. Check out his blog for January 12, 2007

Jan 18, 07 | 5:44 am

Total Topics: 32
Total Posts: 145
Yeah, I saw that, looked pretty cool. Actually began to try out his method, but wasn't well set-up to make it work. Could have done it with some work, but decided on my routing method as more straightforward.

Didn't take pictures, but I can recreate it when I get some time. Actually going to be out of town for a week starting Saturday, so may or may not be able to get to it before then (busy couple of days). Will see what I can do -

Jan 18, 07 | 6:48 am

Total Topics: 32
Total Posts: 145
OK Ted - here's my mock-up of what I did. I have no expertise here, just what I came up with.

First, I cut out my plywood circle:

Next, I put a nail in the center and used a square as a guide to draw concentric circles of incrementing radii of half an inch. Basicly held the pencil in position and swung the square around.

OK - this picture isn't as clear as I'd hoped - but trying to show that my router is marked in main increments of 1/32nd of an inch...

So I calculated the numbers for 1/2 inch increments - show in inches, then 32nds of inches

For each ring, I set the router to the calculated setting, and routed out everthing from the inside of that line. Started in the middle and worked out.

Did it outside and made a big mess. (This is a day later after a windy day)

Sanded it smooth (or nearly smooth)

And here's a picture of my brace (which I had already radiused) sitting it the dish. Pretty good match...

Jan 18, 07 | 7:34 pm

Total Topics: 34
Total Posts: 567
I almost went with billm's method but decided that my hand would not be steady enough to do it correctly. I figured that making the jig once is worth it because I can make as many dishes as I want easily and quickly. Of course, it is quite messy too!


Jan 22, 07 | 8:30 am

Total Topics: 9
Total Posts: 7
Ok, ive been sitting around today pondering on this situation, this may be dumb but I think that it would probably work and be less work than the router route. John at Blues Creek told me that in order to get the radius needed, take a top or back brace, whichever radius you are trying to recreate, turn it on its side and then trace the radius to the block that will be used for lets just say the sanding bar.

Well this got me to thinking, why couldnt you use the offcut of this sanding bar (if you had a radius dish already made, the offcut would sit down in it just like one of the braces would.) to make yourself a jig for a drill? Slap some high grit sand paper on the curved edge, find the center of this jig and put some sort of bit into the drill that would spin the entire jig rather than just drilling a hole in the jig. Then start sanding with this jig on top of the plywood that will be used for the radius dish. Would this work?

Jan 30, 07 | 12:40 pm

Total Topics: 19
Total Posts: 244
That'd be a LOT of sanding! I think rough cutting it first is the best solution. If you had a fly cutter and a milling machine you could make that work! I'm afraid your shape would have to be I-beam strong to hold the shape as you sanded. Good idea though.

Feb 12, 07 | 1:52 pm

Total Topics: 2
Total Posts: 61
At the bottom of this post is the layout measurements for several Radii. They are in PDF form so you will need Adobe Acrobat to view them.

Mar 28, 07 | 9:40 pm
Gary Palmer of Palmer's Stringed Instruments

Total Topics: 0
Total Posts: 65
Working out the curve for a blind radius - an arc where both tangents and the apex of the curve are known, but the striking point is not - is really simple. Especially if you know the degree of offset between guitar rim and the apex/highest point in the soundboard or backplate.


Take a square, place it against the guitar side (with the rule/straight edge resting upon the back plate) and measure the offset distance between rim and arc apex. Eg 1" (A quick example). Then measure the span between the widest points of the lower bouts (Eg. 16").

Measure body length eg. 20"

Apex (X) = 1"
Span (A-B) = 16"
Length = 20"

Take a straight section of 3"x1.5" dressed timber/ply/mdf measuring 24" in length or an inch or so longer than the desired body length. Mark the centre line on the 3" face side. Make two further marks 8" from the centre (These will become the tangents/springing points of the arc) which equate to the span of the lower bout being replicated or measured.

Locate both tangents (A & B) on the timber batten at 1" from the face edge.

Draw a line between both tangents (A & B). Bisect this line and measure the degree of desired arc offset (1") perpendicular to the centre point. We now have the apex of the curve and can now begin plotting/drawing the arc.

Draw a line between tangent A and apex X. Bisect it and measure half the offset (Points A-B offset is 1") perpendicular to the line. This is 0.5". Mark this point.

Draw a line between point A and the new mark. Bisect it and measure half of the previous offset. (0.25"). Repeat the process 4 times using point A as one tangent, before plotting points between X and the original 0.5" offset point. You now have half of the curve plotted and can draw the curve by linking each offset point or joining the dots.

Repeat for the other side/between X and B.

I typically measure in millimetres on work of this size and the entire process takes a matter of minutes using pencil and rule/tape measure.

If you wish to use an arc as a routing guide, simply halve it along it's length and use both sections as rails on which you mount the router. Mount the sanding disc/dish blank on a central pivot (Resting at the extreme end of the midway point) and rotate the blank whilst routing.

May 09, 09 | 9:13 pm

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