Help Drawing An Arc

Re: Help Drawing An Arc

Clint Searl

The pattern for the piece is two concentric arcs of unequal radii. Top more than the bottom.

Re: Help Drawing An Arc

Sgian Dubh

You simply need to use the same centre point for each concentric arc. I can't imagine how you could possibly get a variation in the distance between the arcs if you're using the same centre point.

A nail driven through a thin stick of wood into your centre near one end, and two tight holes 3-1/2" apart at your desired radii, into which you can push a pencil should do it ... assuming you don't possess an adjustable trammel which does make life relatively simple for such marking out.

Assuming you work this way, your arcs will be the same distance apart as measured along any radial line you choose, but the distance at B in your photograph is a tangent line, so this measurement between each arc cannot match the radial length between each arc. How much it differs from a radially measured length between the arcs depends upon how far around the arcs you choose to put a line (gate stile) parallel to the vertical radius at the centre point of your gate. Slainte.

Re: Help Drawing An Arc

Lee Schierer in McKean, PA

What I have done is locate a thin strip of wood that is wide enough to drill a hole in about 1" from the end. This hole should be a tight fit for a pencil. Determine the radius of one of the curves and place a nail through the thin strip at that point on your thin piece of wood. Tap the nail into your workbench and draw that arc. Move the nail exactly 3-1/2" shorter or longer on your strip of wood and draw the second arc. Put the nail in the same center hole where it was for the first arc.

Lee

Re: Help Drawing An Arc

Hank Knight

Concentric arcs of unequal radii will not yield an arch of consistent width. The top of the arch will be thinner than the ends because the bottom arc with the shorter radius will yield a tighter circle than the top arc.

Re: Help Drawing An Arc

Ellis Walentine

Use a trammel and set it for two different radii 3 1/2" apart. The only thing you have to worry about is where to put the pivot point of the trammel. This will depend on how high you want the top of the arc to be relative to the stiles of the gate.

Ellis

I think we have a failure to communicate...

Barry Irby

The OP seems to be talking about a spline Curve where you use a thin flexible strip and bend it to the curve you want. Everybody else is talking about a curve drawn with a trammel.

A spline curve is not necessarily a section of a circle and is likely a section of an ellipse. Also, the spline does not bend consistently. The first several inches are likely to be straight or nearly straight. It would take an excellent spline to bend to two different radii and have them be perfectly concentric.

To the OP, look up how to use a trammel on YouTube. It's just a stick with two holes, one for the pivot and the other for a pencil or even the router.

Re: Help Drawing An Arc

houblon

B is necessarily larger than 3.5 because you are not cutting the arch orthogonally. Its the same as if you cut a 2x4 at an angle - the cut will be wider than the width.

Re: Help Drawing An Arc

Brian from monument colorado

It appears that the pix of the gate is taken not perpendicular to the gate. The arc viewed in the pix is NOT a part of a circle. Thus the gate pix is not best evidence. But in general should it be desired to make the top part of the gate a part of a circle, the trammel points will draw circles.

Use the same center point for the sides of the arc but different radii.

Re: Help Drawing An Arc

Clint Searl

Concentric circular arcs will be equally wide by definition. The parallel vertical boundaries will be greater.

Re: I think we have a failure to communicate...

John McGaw

Splines are great for experimenting with curves to achieve pleasing-to-the-eye results but, as you say, they are not precise and coming close to a true arc would be something close to a miracle. A simple string, tack, and pencil will do the job here to draw it out or if the arc is to be cut in one step with a router or jigsaw a trammel will do the job perfectly. Probably the hardest thing with these methods comes if the radii are really long making the process unwieldy, especially in a small shop like mine.

Better yet

Ellis Walentine

Make a router trammel and just cut out the top rail.

Ellis

Re: Help Drawing An Arc

Hank Knight

The more I think about this, the more I think you are correct and my view is wrong.

Alternative

Gary Smyth

I'm lucky enough to have a set of drafting radius curves (also known as railroad curves). Each curve varies from very tight to a long sweep. There are 52 in the set.

If you can get access to a set I would lay out the stiles with the correct spacing and determine the center of the height of the arc. Using cardboard as a template between the stiles trace a fair line from the top edge of the arc you want to the entrance you want in the one stile. Repeat on the other side. Then using dividers set at the desired 3 1/2" follow the line you just drew on the top edge of the arc down to the stile. That is the curve with a consistent width dimension. You may need a 2x10 to fit the curve for that top rail if in one piece. Once you have the curve make sure to allow additional wood for the tenons to enter the stile.

If you lay out the gate and plot a fair curve by eye then only dividers will be necessary for the inside radius.

Re: Help Drawing An Arc

Walter Ahlgrim

To my eye often a segment of a circle is not the shape I want it is boring and lifeless.

I think you should use a metal yard stick and form your curve drive a nail at the 2 end points and move the center of the yard stick until you find the right curve. I use a compass and draw 3.5 inch arcs and connect the points to make the parallel line.

When I look at the side rails they seem to be thinner than the top rail. If you make them the same the gate will not look as elegant.

I also try to avoid leaving anything at the 2x4 dimensions people recognize 3.5 inch part is a common 2x4 and it makes things look cheap.

Walta

Re: Help Drawing An Arc

KenK

Thanks everyone for weighing in. That was way more response than I expected and much appreciated.

I ended up using this technique -> https://www.mathopenref.com/printellipse1.html to draw a section of an ellipse that seemed close to what I wanted.

I think part of the problem with my initial post was calling the structure I wanted to produce an arc. I'm not especially well versed in math/geometry but I believe an arc represents part of a circle. I think an ellipse more accurately describes what I was looking for.

I'll post pictures of the final product when assemble and finish it.

Re: Help Drawing An Arc

Paul in NJ

Use a spline to create a pleasing top shape whether it is an arc or eclipse. Then scribe the second shape using a compass set to 3.5". Alternately you can cut out a circle 7" in diameter with a small hole in the center for a pencil and use it to trace the second shape by rolling it against the spline.

Regards,

Paul Dzioba

Look up a Trammel of Archimedes

Barry Irby

I have made and modified several and you can use it to draw an ellipse and you and set one up with a router and cut the shape. By playing with the setup you can get an almost unlimited set of arcs.

Re: Help Drawing An Arc

Sgian Dubh

I think it's interesting that you've been persuaded, or perhaps convinced, to move on to creating an ellipse rather than an arc. There's nothing wrong with using an ellipse if you find it pleasing, but an arc would, I believe have been just as effective, and I suspect that's what is illustrated in your original post.

Just to give some calculations regarding a possible arc for your gate, if your gate is 30" wide and the stiles are ~3-1/2" this leaves ~23" between the inside edge of the stiles. Visually, to me, the rise of the arc from the points where the arc intersects the inside edge of the two stiles appears to be roughly 2".

So running some relatively simple arc radius calculations, or just drafting it out by hand (or using a CAD programme) you end up with a radius for the lower arc of approximately 34-1/16", therefore the longer radius would be +3-1/12" or ~39-9/16".

Of course, I converted and calculated in my habitual metric, and then had to convert back again into those clunky feet, inches and fraction things so beloved of many, not all, on the western side of the Atlantic, so there could be an error or two that has crept in, ha, ha. Slainte.

39 9/16"?????

Barry Irby

therefore the longer radius would be +3-1/12" or ~39-9/16"

That's way too close to a meter and we will be having none of that on this side of the pond!

Trickery I tell you....

Re: 39 9/16"?????

Sgian Dubh

Ah, you're right, close to a metre: no sacrilege, surely?. But I notice, because of your response I appear to have incorrectly tapped in 39-1/12 instead of 39-1/2. Maybe I can get away with claiming it was the result of 'fat finger syndrome' ... or maybe not, ha, ha. Slainte.