How do I draw an arc that is 39 1/4 long,8" high in the center & 5" high at the ends?

[dennis thompson]

I am building a twin bed.
The headboard top rail will be 41 1/4 inches long, this includes 1" at each end for a tenon. The exposed part of this rail will be 8" high at the center & 5" high at the ends & 39 1/4 long(allowing 1" at each end for the tenons).
How do I draw the arc that goes from 8" at the center to 5" at each end?
Thanks
Dennis

[Wayne Morley]

You can use this to draw a circular arc through any three points.


Layout the points that you want the curve to pass through A, B, and C
lay out the two straight edges as shown and tape or glue them together
Put pins or brads at points A and B
Holding the point of your Pencil at Point "C" , slowly move the straight edge assembly, keeping it touching points "A" and "B".

200113

[Gary Curtis]

Usually people make a 'bow' out of a long thin slat of wood. Fashion the arc shape by pulling the ends together with a length of string. Make sure you can tie/untie the string to adjust properly. You trace a pencil along the edge of the arc to transfer the shape.

I've also seen a tutorial in which the bow string slides over a fixed pivot, such as a pencil, for form complicated arcs.

[scott vroom]

I am building a twin bed.
The headboard top rail will be 41 1/4 inches long, this includes 1" at each end for a tenon. The exposed part of this rail will be 8" high at the center & 5" high at the ends & 39 1/4 long(allowing 1" at each end for the tenons).
How do I draw the arc that goes from 8" at the center to 5" at each end?
Thanks
Dennis

Dennis, it sounds like you're trying to draw an arc that has a height of 3" (8" high at the center; 5" high at the ends) and a width of 39.25". Is this correct? If so, then use this calculator:
http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry Enter width as 39.25" and height as 3". Hit calculate; it returns a radius of 5.47'. Use string and a pencil to trace the arc.

Or do it as Prashun suggests...probably easier/quicker :)

[Prashun Patel]

I would cut a piece of 1/4" hardboard that is 44" long. Put brads or screws in at the endpoints on a large piece of plywood. Then put the hardboard below the screws and push up to the apex and trace out the curve.

[Alan Schaffter]

Do you speak SketchUp? That is the easiest and quickest way.

If you want a true arc, a segment of a circle, then:

1. Divide the headboard in half with a long vertical centerline
2. Draw a diagonal line from the intersection of the centerline and the 8" line to the point where arc will meet the tenon (5" high line, 1" from the end)
3. Draw a line that is perpendicular to and bisects that diagonal.
4. The point where the bisector meets the original vertical centerline will be the center of the circle for that arc that includes the 8" point and two 5" high points.

200119
It will likely look better with an elliptical shape rather than a true arc however. I recommend you use SketchUp or a batten to draw the curve.

[Kent A Bathurst]

I would cut a piece of 1/4" hardboard that is 44" long. Put brads or screws in at the endpoints on a large piece of plywood. Then put the hardboard below the screws and push up to the apex and trace out the curve.


+1 - the gentleman from New Jersey nailed it.

[Jim O'Dell]

When I was setting up track for my HO train set at the other house, I used Prashun's method to create an "ease" into the curves, marked it and attached flex track to the mark.
On furniture, I would use the same method to lay the arc out on MDF to make a pattern, then a pattern bit in a router to cut the actual wood to match, after taking off the majority of the waste at the BS or with a jig saw if the BS wasn't available. Jim.

[Chris Fournier]

This is simple geometry (thank goodness, even I can do it). I'd use a beam compass and use the three layout points to generate the centre point of the arc and away you go. Just google your question and use the beam compass for the ultimate in accuracy in this situation.

[Alan Schaffter]

This is simple geometry (thank goodness, even I can do it). I'd use a beam compass and use the three layout points to generate the centre point of the arc and away you go. Just google your question and use the beam compass for the ultimate in accuracy in this situation.

I assume you are using the three layout points to define two equal chords so you can draw perpendicular bisectors to them which will intersect at the center of the circle. With just a beam compass, you must do trial and error to find the radius.

All that aside, I don't think a circular arc is the best shape. An ellipse or shape draw with a batten will look the better.

[Peter Quinn]

To me the answer depends on what you want to take from this exercise, and how much time you want to spend doing so. If fast and dirty is required, the "bend something thin" method works well enough assuming your something thin bends in a more or less consistent manor. If you want to work towards an accurate method that can accomplish more complex tasks, you may want to get some trammel points or make a quick beam compass, and follow the link below to understand how to use them. For an arc that size it helps to have a sheet of something 4X8 as a layout aid, even a piece of cardboard will do though 1/8" masonite or similar may work better. Suppose you were making a frame and panel head board, and you needed to make two different arcs with parallel radii come together in a predictable manner. The "bend something thin" method will not likely be accurate enough for that. So its good to have a few different tricks in your bag, and this may be a good chance to practice accurately and predictably laying out curved work for future projects.


http://www.newwoodworker.com/layoutarc.html

[Alan Schaffter]

Looks like Tom Hintz used my perpendicular bisector method, ;) except he used one minor chord and one major chord instead of the two minor chords- sounds like music class! :D

[Mike OMelia]

In addition to sketchup, that fellow at woodgears.ca has a program that will convert a jpeg into a full scale pattern. It's called bigprint, I think. I used that for my toybox. Sketchup produces the jpeg, and bigprint makes the pattern out of as many pages as are needed. Just glue to wood and head for the bandsaw!!!

Mike

[Chris Fournier]

I assume you are using the three layout points to define two equal chords so you can draw perpendicular bisectors to them which will intersect at the center of the circle. With just a beam compass, you must do trial and error to find the radius.

All that aside, I don't think a circular arc is the best shape. An ellipse or shape draw with a batten will look the better.


That is the technique that I have used for years. I looked it up in an applied mathematics book published in the forties and bought for 25 cents in a used book shop. A wealth of shop knowledge. I agree that the ellipse and batten generated forms are very pleasing shapes but they're not what our OP asked for, he needs a "bullseye" solution - arc through three specified points.

[Bob Wingard]

Make a trammel jig for your router that is 65 11/16" from the pivot point to the edge of the bit. I use a few aluminum extrusions that I can extend out over 20' if necessary, but you can make a quickie out of scraps.

[dennis thompson]

I would cut a piece of 1/4" hardboard that is 44" long. Put brads or screws in at the endpoints on a large piece of plywood. Then put the hardboard below the screws and push up to the apex and trace out the curve.
I decided to try Prashun's method. Instead of a 1/4" piece of hardboard I bought a 1/8" thick piece of aluminum stock that is 48" long & 3/4" wide & used that.( I thought I might have other uses for the aluminum & it would last longer.) Anyway It worked great .
Thanks for all the help
Dennis

[Jim Neeley]

With a beam compass and the link on Scott's message (#4), the radius is 5.47' (mightly close to) 5.5' = 66".

Set your beam compass to 66" and get a helper to move the center point until you get the end points from the same center point. Then mark the arc... schwiiing!!

Even easier would be to mount a router to a 1"x8"x6' with a screw driven through 66" from the far side of the router bit. Then you wouldn't just mark the arc, you'd cut it in one fell swoop!

[Jeff Duncan]

I use the router myself. The other methods work, but then you just have a line marked, still have to remove the material somehow.
I have several router circle jigs I've made up over the years with radius' up to 12'. Set it up and cut it all at once and be done with it. Or alternatively set it up and route a piece of 1/2" mdf and use that as a template to mark your workpiece. Trim oversize on the bandsaw and use a pattern bit on the router with the mdf guide.

good luck,
JeffD

[Mike Cutler]

Dennis

Glad you found a solution that worked for you.
One tip for the future, that I use, is an the Archimedes Trammel, or the Kentucky Do Nothing.
Make one stout enough and you can hook it up with your router. Wikipedia is your friend.