How do you draw an arc?

[dennis thompson]

I need to draw two arcs, one is 13 inches wide & one is 15 inches wide, they are both 3 inches high at their highest point. Does anyone have any idea how to do this?
Thanks
Dennis

[Rod Sheridan]

Put three push pins at the three points of the arc. (Both ends and the middle).

Bend a ruler against the three pins and trace it..........Rod.

[Bob Riefer]

If you put a thin finish nail at the starting and ending points, and at the highest point of your arc, you can bend a thin piece of stock between the nails (think of a very thin yard stick.. just make a cut off from some scrap.. wood strip will be on inside of starting and ending nail, and on the outside of the apex nail) and it will hold a nice shape while you trace it with your pencil. Trace on the outside of the thin piece so that when you make your cut on the line, it'll remove the small nail holes.

edit: or what Rod said in many less words than I did :)

[Logan William]

I cheat :) Autocad then plot out and cut on the line, trace and done!

[Karl Brogger]

http://sawmillcreek.org/attachment.php?attachmentid=109709&d=1234365637

[Mike Davis NC]

No math, just a compass and straight edge.



http://www.ncwoodworker.net/pp/data/791/Creat_an_Arc.jpg

[John Coloccia]

I need to draw two arcs, one is 13 inches wide & one is 15 inches wide, they are both 3 inches high at their highest point. Does anyone have any idea how to do this?
Thanks
Dennis

Do you want pretty arcs or actual, accurate sections of circles? If you want accurate circles, let me know and I'll point you towards the "long compass" technique. For pretty arcs, I usually sketch a simple 1/2 arc freehand on a piece of construction paper, and then use that to make draw the arc on the wood, thus insuring a symmetrical arc.

[Van Huskey]

After doing them for years by trial and error and dealing with stock that bent differently based on grain etc I bought the Lee Valley ones, they have a symmetrical and an asymmetrical version. Not cheap but work very well, I wouldn't consider them for a one off arc but if you plan to use them a decent amount they are worth a look.

[Erik Christensen]

What Van said - they work SLICK

[Wes Grass]

Bending something is fine if you want a catenary curve. If you need a true radius, however, you've got to use a compass of some sort.

[mickey cassiba]

http://sawmillcreek.org/attachment.php?attachmentid=109709&d=1234365637

You go Karl!

[steven c newman]

can be made with either a TRAMMEL point set-up, or a bent piece of thin stock. Even a thin piece of plexiglass will work. I used the three pin trick on some aprons for a couple of tables I made a while back. A couple pictures:

[Mark Dorman]

No math, just a compass and straight edge.



http://www.ncwoodworker.net/pp/data/791/Creat_an_Arc.jpg

Mike that is an awseome example how arcs can help problem solve.
I use them even with my autocad.

[Dave Zellers]

Mike that is an awseome example how arcs can help problem solve.
I use them even with my autocad.

I agree- that is fabulous. I use my CAD program for this stuff too (PowerCadd on a Mac) to find the radius, but Mike's drawing shows the power of just staying in the shop and using a compass.

Awesome.

[Chris Kennedy]

http://sawmillcreek.org/attachment.php?attachmentid=109709&d=1234365637


No math, just a compass and straight edge.



http://www.ncwoodworker.net/pp/data/791/Creat_an_Arc.jpg

Umm, yeah, there isn't any math in that. Euclidean geometry, use of bisectors . . . nope, not math. Using some of the oldest mathematics known to mankind . . . don't worry, it isn't actual math.

Sorry, but as a mathematician, I can't let this one go. Karl Brogger's solution is perfectly good, as is the ruler/compass construction, both of which are mathematics AND they are equivalent in a somewhat metrisable space (i.e. one where you have a ruler, not just a straightedge).

And as Wes Grass pointed out -- this is assuming your arc is the section of a circle. Given three points, there are a mess of arcs that pass through them.

Cheers,

Chris

[Dave Zellers]

I thought that an arc is, by definition, a segment of a circle.

[John Coloccia]

I thought that an arc is, by definition, a segment of a circle.

As a mathematical term, you're correct, but most people refer to curves as arcs and they usually don't want a circular curve.

[Dave Zellers]

...but most people refer to curves as arcs and they usually don't want a circular curve.
Well then, that's just weird.

I'm pretty sure the OP wanted an arc.

Or two.

[John Coloccia]

Well then, that's just weird.

I'm pretty sure the OP wanted an arc.

Or two.

In that case, the simplest method I know, that doesn't require strings, trammels or anything else, is the long compass, which works like this:

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

It takes me just a minute to set it all up.

[Dave MacArthur]

Ok, I have to say Karl Brogger and Mike Davis get my awards for best posts of the night. I was like, "YEAH Karl! Straight jump from a "modern tools are all crap" bender to some respectable math!" Ok, then I thought "uuuuunnnabomber..." ;)

And that geometry is just sweet too.

By the way, John C is right, when people freehand in "pleasing curves" they are much more likely to draw a catenary than a true section of a circle. Catenary is a curve created when there is tension along the line, but a constant force acting at angles to the chord. Ermm, like the sag of a power line between poles or bridge suspension lines. Or a strip of wood or metal with the ends brought towards each other to make a curve. They look more natural and smooth at the ends.

[Kent A Bathurst]

.......... Euclidean geometry.........

heh-heh-heh.

Hosted a dinner party a while back, one down-the-street neighbor is a retired math professor from Ga Tech.

Good news-bad news: Good news: I finally got a captive audience to explain non-Euclidian geometry to me [how can parallell lines meet? that's impossible? had a mountain of math at Va Tech engine school, but still....]. Bad news - asked while on the 3d glass of wine. I was lost by the second sentence of the answer. :p I guess I'll never know.

[JohnT Fitzgerald]

don't worry, it isn't actual math

My wife looks at me funny when I say "that's arithmetic, not math".

"A mathematician is a machine for converting coffee into theorems. "

[John Coloccia]

heh-heh-heh.

Hosted a dinner party a while back, one down-the-street neighbor is a retired math professor from Ga Tech.

Good news-bad news: Good news: I finally got a captive audience to explain non-Euclidian geometry to me [how can parallell lines meet? that's impossible? had a mountain of math at Va Tech engine school, but still....]. Bad news - asked while on the 3d glass of wine. I was lost by the second sentence of the answer. :p I guess I'll never know.

It's easy. Take a dowel. Grab a pencil and draw a ring around the circumference. You've just drawn a straight line that intersects itself. Now, take a sphere, like the earth. All "straight lines" (by the definition of shortest distance or where something goes when you don't apply any forces to it) are great circles, like the equator. They're called geodesics if you're interested. A geodesic on the Euclidean geometry is a straight line. On the cylinder from before, I would guess it's an ellipse. On a circle, it's a great circle. ALL great circles intersect each other so believe it it or, it's impossible to draw parallel lines on a sphere. Think about the lines of longitude. No matter how you arrange the lines, they will all meet at the north and south poles. Now think about any other line you can draw. It will either meet at the north and south pole like the other longitudinal line, or it will cross it somewhere in the middle. There is no parallel line.

And it didn't even cost you a bottle of wine this time :)

edit: by the way, you can get non-euclidean parallel lines that intersect at infinity, but nowhere else, just like functions can approach 0 at infinity, but never get there.... 1/x for example....make x as large as you want. It will get closer to 0 but will never be 0. It's 0 at the limit of infinity, which is just another way of saying it gets closer and closer to 0 but will never be 0.

[John Coloccia]

My wife looks at me funny when I say "that's arithmetic, not math".

"A mathematician is a machine for converting coffee into theorems. "

That was Erdos, wasn't it? He's a Hungarian, just like Frank Klausz. Clearly there's SOMETHING in their coffee given all the craftsman and mathematicians that have come out of Hungary.

[Chris Kennedy]

That was Erdos, wasn't it? He's a Hungarian, just like Frank Klausz. Clearly there's SOMETHING in their coffee given all the craftsman and mathematicians that have come out of Hungary.

Pal Erdos often used that quote and made it famous, but he wasn't the author. I think it was Alfre Renyi (?), who was another Hungarian mathematician.

Geodesics are not necessarily going to provide the shortest distance. For example, you can take a sphere where the great circles are the geodesics (and do give the shortest distance), and remove a small disc. If you take two opposing points on the border of the hole, the geodesic between them goes the "long way" around the back of the sphere, while simply going around the hole is shorter, but no longer geodesic.

Now, it is often the case that a geodesic will give you the shortest distance. If I remember correctly, geodesics are basically defined by the appropriate second derivative vanishing on the manifold.

Cheers,

Chris

[John Coloccia]

Pal Erdos often used that quote and made it famous, but he wasn't the author. I think it was Alfre Renyi (?), who was another Hungarian mathematician.

Geodesics are not necessarily going to provide the shortest distance. For example, you can take a sphere where the great circles are the geodesics (and do give the shortest distance), and remove a small disc. If you take two opposing points on the border of the hole, the geodesic between them goes the "long way" around the back of the sphere, while simply going around the hole is shorter, but no longer geodesic.

Now, it is often the case that a geodesic will give you the shortest distance. If I remember correctly, geodesics are basically defined by the appropriate second derivative vanishing on the manifold.

Cheers,

Chris

Commonly the geodesic is defined as the path particle takes when no external force is applied to it, which is equivalent to what you stated, i.e. there's no acceleration.

[Marty Paulus]

No math, just a compass and straight edge.



http://www.ncwoodworker.net/pp/data/791/Creat_an_Arc.jpg

you have a couple of extra lines in here (no need to connect the dots with a straight line ;)) but this is how I learned how to draw a circle through three points. Way back when, before CAD, a pencil, compass, two triangles and a french curve were all you needed to design most anything. I still have all my manual tools in a brief case in the basement. Every once in a while they come in handy for something...of course that was before I discovered Sketch up.

[Mike Davis NC]

Sorry Chris,

Don't mean to step on your mathematician's toes.

Obviously, what I meant to say is no mathematical formula is needed for drawing a simple arc (segment of a circle). I learned most of the common constructions in high school drafting. That skill/knowledge has served me well through the years.

Most wood workers have a compass and a straight edge or should have. Even just a string and anything that will make a mark can be used.

Like you said these are some of the oldest principles known to man. They didn't have calculators or computers when the built the pyramids, just sticks and strings.




Umm, yeah, there isn't any math in that. Euclidean geometry, use of bisectors . . . nope, not math. Using some of the oldest mathematics known to mankind . . . don't worry, it isn't actual math.

Sorry, but as a mathematician, I can't let this one go. Karl Brogger's solution is perfectly good, as is the ruler/compass construction, both of which are mathematics AND they are equivalent in a somewhat metrisable space (i.e. one where you have a ruler, not just a straightedge).

And as Wes Grass pointed out -- this is assuming your arc is the section of a circle. Given three points, there are a mess of arcs that pass through them.

Cheers,

Chris

[Wes Grass]

" I still have all my manual tools in a brief case in the basement. Every once in a while they come in handy for something...of course that was before I discovered Sketch up."

Of course, if you want a real curve, you still need them ;-)

[Dave Rathert]

I use the bent wood/three pin trick with a bit of a twist. I’ll actually glue the curved wood to a piece of scrap or 1/4” MDF. Cut off most of the side of the curve that I don’t want and flush trim to the bent wood on the router table. Now I have a template that I can flush trim to (after getting close on the band saw) as opposed to free handing a cut on the Band Saw right down the line. It’s a little extra work but it comes in very handy for making identical curves/arcs in multiple work pieces. It should be noted that I’m not very good with my cheap ol’ band saw and this is my way of getting around my inaccuracies.
-D

[Kent A Bathurst]

It's easy........... There is no parallel line....

Alright, John - a few observations:

1. Just one more example of the multitude of people that are smarter than me.
2. Short essay, but I gotta spend some time [later] thinking through what you wrote. There's a lot packed into that one. Thanks.
3. No, it's not easy. See #1 above. I had calculus stacked on top of calculus, and did fine in those classes, but they weren't easy either. Not as tough as raising a number to a negative fractional power using a Post Versalog, though :eek:
4. I already knew there are no parallel lines - routinely produce examples of that when building repro furniture. :D

[John Coloccia]

4. I already knew there are no parallel lines - routinely produce examples of that when building repro furniture. :D

ROFL. Yeah, my shop doesn't exist in euclidean space either at times it would seem :)

[Joe Kieve]

What Mike Davis has shown is classic textbook mechanical drawing..."how to draw an arc or a circle through any 3 points not in a straight line". Just connect the points, bisect the lines and where they cross will be the center of the arc or circle.
Thanks for showing this Mike!

[John Coloccia]

The thing is that with a long compass, you can draw practically any arc of any diameter without actually needing something the length of the radius. For example, you can easily make a 100' radius arc (for example), 1 foot long with nothing but a couple of nails and two sticks that are 1' long each joined at the appropriate angle. It's really slick for accurately make sections of very large circles. I think the problem is typically along the lines of "I have a board, 5 inches wide and 2' long that I want to make an arc on", and how do you do it when you want a 25' diameter arc in a shop that's only 20' wide?

I'm really surprised that someplace like Lee Valley doesn't make a "long compass stick" with a little knob you turn to fix the angle with a little pencil holder in the corner, a couple of push pins, and a few lines of instructions how to use it. No need to thank me for the idea, Rob. Free shipping every now and then is thanks enough :D

[Jack Camillo]

No math, just a compass and straight edge.



http://www.ncwoodworker.net/pp/data/791/Creat_an_Arc.jpg

now that's awesome, thanks for posting

[Troy Turner]

Google Fairing stick. Pretty simple to make and easy to use and yields great results. That's the thin piece of wood and string Steven has.

[dennis thompson]

Thanks for all the replies, I cut my arcs, using all your advice & they came out very nice.
Thanks again
Dennis

[Jaze Derr]

wow, this thread made my head hurt...
My method? Search around the house for something that has the curve I want, then trace it :)

[Mike Davis NC]

Not going to tell which method you used, huh?

[Dave MacArthur]

Ok John C, I'm not following you on the two stick /angle doofer to simulate a long radius. But it sounds interesting...
You're going to have to draw something, 'cuz your paragraph describing it sounds elegant already, and I didn't get it. But all the rest on non-euclidean geo, very nice ;)

[Kevin Stockwell]

http://www.shop.osbornemfg.com/product.sc?productId=19&categoryId=5

How about that device?

[John Coloccia]

Ok John C, I'm not following you on the two stick /angle doofer to simulate a long radius. But it sounds interesting...
You're going to have to draw something, 'cuz your paragraph describing it sounds elegant already, and I didn't get it. But all the rest on non-euclidean geo, very nice ;)

I usually post this link since it's about the clearest explanation out there.

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

The basic idea is:

1) mark the endpoints of your arc...stick two nails in there
2) mark a 3rd point on your arc. You can either do this by eye or calculate it. I usually mark the midpoint, calculate the sagitta of the arc I want, and then measure up and mark that point
3) take two sticks and glue them at such as angle that when they're riding on the two nails, the corner is over the midpoint
4) stick a pencil in the midpoint and move the two stick to trace the arc.

This comes up a lot with luthiers because we routinely deal with 15' to 30' radiuses. It's very convenient to be able to accurately draw such a thing without needing a trammel at the end of a 30' stick, but it's also particularly convenient if you just need an arc that's approximately close. Drive the nails, eyeball the height, glue your sticks and draw. I usually just superglue a couple of scrap pieces of plywood. It's very easy to make a perfectly centered arc with about a minute of setup time.