Calculating an arc

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Forum topic by revanson11 posted 01-28-2012 05:14 AM 1795 views 0 times favorited 13 replies Add to Favorites Watch
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105 posts in 2327 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

View Lifesaver2000's profile


551 posts in 3106 days

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

I found this site:

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

View Danpaddles's profile


573 posts in 2305 days

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

you don’t need to know that.

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

View RandyM68's profile


693 posts in 2311 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


5619 posts in 2660 days

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

View kizerpea's profile


774 posts in 2361 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.


View richgreer's profile


4541 posts in 3068 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


16274 posts in 4212 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


105 posts in 2327 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.

1537 posts in 2469 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


1088 posts in 3560 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 2963 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


2246 posts in 2686 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


1880 posts in 3554 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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