Workshop Geometry - Arcs & Radii Question

[Todd Burch]

I've attached an image of an arc (in yellow). I need to know the radius of the circle in order to lay out this arc. Anyone know the formula, given the length of the chord(?) of 20½" and rise of 1 3/8"?

The application is an arched panel in a set of doors I'm making. I have other doors to arch as well, so a formula would be better than the answer.

Thanks! Todd.

[Jim Earls]

I've attached an image of an arc (in yellow). I need to know the radius of the circle in order to lay out this arc. Anyone know the formula, given the length of the chord(?) of 20½" and rise of 1 3/8"?

The application is an arched panel in a set of doors I'm making. I have other doors to arch as well, so a formula would be better than the answer.

Thanks! Todd.

Lessee now, IIRC, that would be 1/2 the length of the chord squared plus the rise squared, all divided by twice the rise, or about 38.89" (if my math is ok).

[Noah Alkinburgh]

I think this will give you exactly what you are looking for.


http://www.visualstatement.com/ezine/11152002MeasuringArcs.aspx

[Chris DiCiaccio]

Lessee now, IIRC, that would be 1/2 the length of the chord squared plus the rise squared, all divided by twice the rise, or about 39.89" (if my math is ok).

I'm not sure, but my little arc program says 38.89. Not sure which is correct but an inch will make a lot of difference.

[Todd Burch]

Thanks everyone! I'll call it 39" and let my precision incra rasp take care of the rest.... :D

Todd.

[Kirk (KC) Constable]

Thanks everyone! I'll call it 39" and let my precision incra rasp take care of the rest.... :D

Todd.

Autocad says it's 38-7/8 with tolerance set at 1/16"...

[Jim Earls]

I'm not sure, but my little arc program says 38.89. Not sure which is correct but an inch will make a lot of difference.


Oops! Must have been that cheap calculator I was using. :o Anywho, 39 inches should get you right close.

Jim

[Bruce Page]

Just for giggles, the actual diminsion is R38.8290

Life is too short for traffic. -- Dan Bellack

[Paul D. May]

I've attached an image of an arc (in yellow). I need to know the radius of the circle in order to lay out this arc. Anyone know the formula, given the length of the chord(?) of 20½" and rise of 1 3/8"?

The application is an arched panel in a set of doors I'm making. I have other doors to arch as well, so a formula would be better than the answer.

Thanks! Todd.



Todd,

Why don't you just use a scrap piece of wood and bow it at the center to scribe your arc? By eye-balling it you would be very close anyway.

Just wondering....


Paul

[Todd Burch]

Hi Paul.

I did consider bending a piece of wood into an arc, but didn't do it for two reasons: (OK, 3)

1) I've yet to find (or produce) a thin strip of wood that will bend into a perfect arc. If you find one, let me know.

2) I needed the repeatability of a jig. Keeping track of a small stick of wood in my shop, would be, well, let's just leave it at "impossible."

3) I didn't need to draw a line. I needed to route an arc to produce the jig.

Anyway, as for the rest of the story, the doors are made and the arched top rails and raised arched panels came out perfect! Thanks again to everyone for the formula.

Todd.

[Chris Padilla]

This new feature of related articles in the bottom of a window is kinda cool...it can resurrect old posts.

Anyway, Todd, I noticed only a "word" formula so:

let L be the length of the chord
let h be the heigh of the maximum point of the arc relative to the chord
let r be the radius of the arc

r = (L^2 + 4*h^2)/(8*h) or as Jim gave it: ((L/2)^2 + h^2)/(2h)

If you want to know how I derived it, drop me an email. Basic geometry really.

I get 38.892045.....

[Rob Littleton]

This new feature of related articles in the bottom of a window is kinda cool...it can resurrect old posts.

Anyway, Todd, I noticed only a "word" formula so:

let L be the length of the chord
let h be the heigh of the maximum point of the arc relative to the chord
let r be the radius of the arc

r = (L^2 + 4*h^2)/(8*h) or as Jim gave it: ((L/2)^2 + h^2)/(2h)

If you want to know how I derived it, drop me an email. Basic geometry really.

I get 38.892045.....

The sprinklers have gone to your head..............

[Chris Padilla]

Oh, you don't know, my friend, you don't know!!! :(

[Jason Roehl]

The sprinklers have gone to your head..............
Geez, are you saying Chris is all wet?? :D :D :cool:

[Dean Baumgartner]

Hi Paul.

I did consider bending a piece of wood into an arc, but didn't do it for two reasons: (OK, 3)

1) I've yet to find (or produce) a thin strip of wood that will bend into a perfect arc. If you find one, let me know.



Todd.

Todd if you want to try the bend something method I agree that with differences in wood you probably won't find one that bends uniformly. Go to a welder's supply and get a small diameter 0.030" stainless welding rod. It'll bend into a nice smooth arc.

Dean

[Alan Turner]

Todd if you want to try the bend something method I agree that with differences in wood you probably won't find one that bends uniformly. Go to a welder's supply and get a small diameter 0.030" stainless welding rod. It'll bend into a nice smooth arc.

Dean
Or, shop at Lee Valley for a drawing bow, which is a 4' fiberglass strip, with eyes at each end connected by a cord whihc is adjustable. So, set the arc, and draw from it. I use it when designing, esp. with a client present, since you can lay out an arc, and adjust it to their taste, and then just put it aside, and still have the correct arc.
By the away, thanks to all for the formula!
Alan