For you math wizards

[Richard]

An 18 foot radius template?

[Gramp's shop]

I need to draw an arc for a piece of trim. The end points of the arc are 5 feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

There ought to be an equation for this that would be far superior to trial and error, oui?

Larry

[Just Wondering]

feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

error, oui?

[Just Wondering]

feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

error, oui?

[Leon]

feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

error, oui?

R=226" according to Sketchup.

[-MIKE-]

According to those cool calculators, 18'10".

[Gramp's shop]

feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

error, oui?

[Larry Blanchard]

Bend a piece of thin cutoff around the points?

[Lew Hodgett]

-------------------------------------------------------------- Find a copy of Fred Bingham's book, "Practical Yacht Joinery" at the library.

A very easy graphical solution is shown.

I laid out all the deck cambers for my boat using it.

Lew

[Leon]

radius :-) I have a couple of ideas and will post pix of the process.

feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

and error, oui?

!8' string with a pencil died around one end. Nail in the ground on the other end.

Or use sketchup to print out a template.

[Greg Guarino]

Trigonometry concurs. :)

Thanks to the O.P. for a pleasant lunchtime puzzle.

[Greg Guarino]

My sense of the physics involved tells me that that method will not produce an arc of a circle. Will it matter? Might the resultant curve be subtly nicer than a circular arc? That's up to the designer.

[Greg Guarino]

It was more fun to try to work it out for myself, but I just looked it up and there is (of course) a more direct way to find it.

Radius = H/2 + W^2/8H

Where H = the height of the arc (2") and W= the width of the base (60")

In our example that's:

2/2 + 60^2/8(2)= 1 + 3600/16 = 1 + 225 = 226

[Doug Miller]

"Gramp's shop" wrote in news:384921f5-292d-40cc-9e3e- [e-mail]:

feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

224 inches

error, oui?

There is.

radius squared = (radius minus height) squared + (half the distance between endpoints) squared

In this case:

r^2 = (r - 2)^2 + 30^2 r^2 = r^2 -4r +4 + 900

4r = 904 r = 226

[practice]

news:384921f5-292d-40cc-9e3e-

feet apart and the

and error, oui?

Now we know how long a piece of string is!

[Gramp's shop]

My plan exactly, Larry. I'm going to start with drilling screws into the waste side of the end points and the top of the arc, attach a thin strip of one-by with spring clamps and then add a couple of screws/clamps along the arc.

The other Larry

[Greg Guarino]

news:384921f5-292d-40cc-9e3e-

feet apart and the

and error, oui?

I just drew that out. Clever. It's much more elegant solution than the one I posted. Good work.

[Bill]

Greg, We both drew the same picture. How much math background do you have (if you don't mind me asking)?

Bill

[Bill]

feet apart and the depth of the arc at the center point is 2 inches. What is the radius of the circle?

error, oui?

Pythagorean Theorem: 30^2 + (r-2)^2 = r^2. Solution is 226" exactly, which is 18' 10", as hasalready been disclosed,I believe. Didn't even need trig. (which surprised me).

[Greg Guarino]

Nothing too advanced. Algebra, geometry and trig in high school, a little calculus in college. That would all have been in the '70s.