This one was suppose to be easier. Although I am finding the step of brace construction and radiusing the sides quite difficult. am struggling.
During my planning phase, I settled on simply making a “slice” of a sanding dish, as used by Bill Corey, instead of buying a couple of sanding dishes ($US 150.00 + postage). I have tried using wire (metal memory-curled up), extension cord (too heavy), fishing line and string (stretched) all in failed efforts to trace a 30 foot and 15 foot radius to a length of pine.
One of my first efforts seemed to be working out okay – When I finished I had two curves which were basically the same and uneven.
I pulled out the dreadnought cross brace that was included in my Stewmac OOO kit and traced that onto the board and I and happy to use that curve for the top. That leaves just the 15 foot radius.
Anyone got ideas? Any mathematical wizards out there that can work this out? Any one know where I could download a template?
Time taken : a few hours
Tools used : items mentioned above, jigsaw, sand paper, wood file, scraper.
AU$'s spent : $6.00 for the pine
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7 comments:
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"
- BillM
Wow Bill! Don't tell me that you just scribled that out on the spot. I've been trying to wade through the haze that was my high school memories, trying to remember algebra. Thanks very much.
My pleasure Ted!
Plugged it into a spreadsheet to quickly hash out the numbers. :)
Bill, Would I be correct in saying that this was the conversion to millimetres?
0 10.16 5.08
+/-1" 10.10 5.05
+/-2" 9.88 4.95
+/-3" 9.52 4.77
+/-4" 9.04 4.52
+/-5" 8.40 4.19
+/-6" 7.62 3.81
+/-7" 6.70 3.35
+/-8" 5.63 2.81
+/-9" 4.44 2.23
+/-10" 3.09 1.54
+/-11" 1.62 0.81
+/-12" 0 0
Yep, I come up with the same figures (assuming 25.4 mm per inch)
I might be a little dense about this (after all, it has been a loooong time since high school math!) but am I to understand that these are points on a curve. Say for the 15' radius I would start in the center of the 24" board mark .4" up. Go 1" either side and mark .398". Go another 1" either side and mark .389 etc.. Then it is a "connect the dots" thing, and cut the curve? If so, thanks a ton for this. I would have been out there all day with a piece of wood, 15 and 30' strings, and a pencil trying to do this lol!
Yep David, that is exactly what it means. I spent hours trying to make this curve and then Bill came up with the answer for us. If also been tipped into some advice for when you go to draw the line. Use a long metal ruler and hammer in a nail at the first and last point, that way you can push the ruler to the curve with one hand and draw with the other
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