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Calculating an arc

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Forum topic by revanson11 posted 01-28-2012 05:14 AM 1350 views 0 times favorited 13 replies Add to Favorites Watch
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revanson11

70 posts in 1077 days


01-28-2012 05:14 AM

I wonder if anyone can give me some ideas for figuring the radius of a circle that I would need for cutting an arc for a headboard. the headboard is 60” long and is 7” in the middle and 5” on the ends. So, basically the arc drops 2” in 30” of run. How long of a radius would I need to lay out to make that arc. Anyone with a mathematical background that can help me out. TIA

-- Randy, Central MN


13 replies so far

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Lifesaver2000

524 posts in 1856 days


#1 posted 01-28-2012 05:36 AM

I found this site:

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

and if I understood correctly, your radius would be 226 inches.

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Danpaddles

540 posts in 1056 days


#2 posted 01-28-2012 05:45 AM

you don’t need to know that.

http://gicl.cs.drexel.edu/people/sevy/luthierie/compass/Long_compass.html

does that help?

I think there are ways to do it with string too. Or you can get a very nice even curve by ripping a 60 inch long board with even grain, thin, about 1/8 inch. set posts at the ends, push the middle to where it needs to be. If that doesn’t make a radius, it will make something that looks about right anyway.

-- Dan V. in Indy

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RandyM68

693 posts in 1062 days


#3 posted 01-28-2012 06:03 AM

The radius is 226” I checked it on my cam software. You’ll need a 18.83 foot beam on your circle jig. You can also use a flexible strip of wood. Put nails on each side of the headboard where you want the curve to end, and push the middle up to where you want it. Mark along the edge of the stick and cut it with a jigsaw. Cut outside the line and you can sand it to where it looks good.

-- I can explain it to you, but I can't understand it for you. I'm sorry,thanks.

View kiefer's profile

kiefer

3354 posts in 1411 days


#4 posted 01-28-2012 06:26 AM

http://lumberjocks.com/projects/49135
Try this it may work for you .

Kiefer

-- Kiefer 松

View kizerpea's profile

kizerpea

746 posts in 1111 days


#5 posted 01-28-2012 04:31 PM

I used a old plastic flat molding 1/8 thick 1in wide. the only thing about wood is the grain will efect the bend. thats the trouble i had.

-- IF YOUR NOT MAKING DUST...YOU ARE COLLECTING IT! SOUTH CAROLINA.

View richgreer's profile

richgreer

4525 posts in 1818 days


#6 posted 01-28-2012 05:02 PM

Forget all the computer based tools – - this is your chance to actually use what you learned in your trigonometry class. Enjoy the experience.

FYI – I have an advanced math degree and spent my entire career as a quasi-mathematician (actuary).

-- Rich, Cedar Rapids, IA - I'm a woodworker. I don't create beauty, I reveal it.

View CharlieM1958's profile

CharlieM1958

15777 posts in 2962 days


#7 posted 01-28-2012 06:20 PM

Forget all the computer based tools – – this is your chance to actually use what you learned in your trigonometry class. Enjoy the experience.

Rich, you’re assuming I actually learned anything in my trig class. :-)

-- Charlie M. "Woodworking - patience = firewood"

View revanson11's profile

revanson11

70 posts in 1077 days


#8 posted 01-28-2012 07:04 PM

Kiefer, I loved your solution to this challenge. How simple yet so effective. Thanks to all of you that responded.

-- Randy, Central MN

View Jorge G.'s profile

Jorge G.

1526 posts in 1219 days


#9 posted 01-28-2012 07:08 PM

Jeezzz…This is one of those cases where you need to keep it simple. From the back of the head board nail a penny nail in the middle of the board at the top of the arc (make sure it sticks out about an inch), on the two ends nail another 2 penny nails one on each side. Cut a thin strip of wood larger than your head board length, run the thin strip of wood from the ends through the middle on to the other end. You should get a perfect curve. Hold the ends with clothes pins and draw the curve.

I am remodeling a house where I have 6 windows with arches, this is one of the methods I use, there are more but for your situation this is the simplest one.

-- To surrender a dream leaves life as it is — and not as it could be.

View KnickKnack's profile

KnickKnack

993 posts in 2310 days


#10 posted 01-28-2012 08:17 PM

Typing into a web page is no fun, besides, who can believe what’s on the web…?

-- "Do not speak – unless it improves on silence." --- "Following the rules and protecting the regulations is binding oneself without rope."

View 404 - Not Found's profile

404 - Not Found

2544 posts in 1713 days


#11 posted 01-29-2012 03:05 AM

I deal with all my curved work by drawing shapes on the computer, printing page ‘tiles’, and gluing them down on a piece of 6mm mdf with spray adhesive. Cut out with jigsaw/clean up with block plane/sander to make a template, and shaping with shank mounted bearing guided cutter.
Sounds more involved than it is but results are perfect every time.

View devann's profile

devann

1735 posts in 1436 days


#12 posted 01-31-2012 06:48 AM

Will this help?

-- Darrell, making more sawdust than I know what to do with

View ajosephg's profile

ajosephg

1860 posts in 2305 days


#13 posted 01-31-2012 04:11 PM

While the idea of using a thin strip of wood and three nails will give you a good looking arc, it is not a segment of a circle, i.e. the radius will not be the same at the ends and the middle.

If my memory serves me, this approximates a catenary curve. I think in the application you are considering a catenary is aesthetically more pleasing than the segment of a circle.

-- Joe

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