# For you math wizards

On 4/15/2013 10:10 AM, Gramp's shop wrote:

Two lengths of PVC pipe. Drill a hole in one end, attach a pencil to the other at 18'. Draw the arc on the ground, spiking the pivot end in the ground and putting the wood at the pencil end.
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Gramp's shop wrote:

========================================="Just Wondering" wrote:

========================================You've obviously never done this.
Lew
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Lew Hodgett wrote:

I couple of "trammel points" on a piece of steel pipe, along with two humans, may work. What is your solution?
Bill (who just happens to have 40 feet of Schedule 40 black pipe)

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On 4/16/2013 5:19 PM, Bill wrote:

I gotta ask Bill why pipe instead of string? and for that matter I have drilled a hole in a 25' tape measure and anchored a screw through that hole and held a pencil at the distance desired.
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Leon wrote:

I thought of drilling a hole in a tape measure too! String or even wire is probably too elastic. I don't thing 3/4" steel pipe is too elastic. I've got ten 4' sections of pipe, along with 10 connectors--for emergencies! So far, I've only used them pair-wise (in my pipe clamps). Evidently you were successful at 25' with your tape measure.
Bill
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On 4/16/13 8:17 PM, Bill wrote:

Many tape measures already have a hole for a finish nail exactly on the 1' mark.
--

-MIKE-

"Playing is not something I do at night, it's my function in life"
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Pipe don't stretch. String do.
I found out just how much string stretches last summer when laying out a curved sidewalk. Next time I do a project like that, I'm using something rigid to mark my arcs: board, angle iron, steel rod, something like that -- but *not* string.
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You do have a point there.
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Doug Miller wrote:

--------------------------------------------- Which is why full size arcs by swinging a radius SUCKS.
There is an easier way to run the railroad.
See Fig 5-42 over on APBW.
Lew
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Gramp's shop wrote:

-----------------------------------------------------------------

----------------------------------------------------------------- Lew Hodgett wrote:
From a previous post.
-------------------------------------------------------------- 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
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"Gramp's shop" wrote:

-------------------------------------------------------------- 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
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depth of the arc at the center point is 2 inches. What is the radius of the circle?
224 inches

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
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On 04/15/2013 01:47 PM, Doug Miller wrote:

Now we know how long a piece of string is!
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On 4/15/2013 2:47 PM, Doug Miller wrote:

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

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

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).
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Gramp's shop wrote:

Trial and error isn't needed, neither is knowing the radius of the arc's circle.
Put two nails 5' apart in a piece of ply. Put another nail 2" above the line formed by the first two. Take a batten, bend it between the nails and draw the arc.
--

____________________________
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On 4/15/13 4:32 PM, dadiOH wrote:

The potential flaws I see in that method are... ...you might get a peak/angle in the curve at the center nail ...you can't always count on getting equal bending at every point along the length of a piece of wood.
I know it's a standard method to use a long, flexible piece and something to mark out a curve so I'm certain it works. I would just want to double check and practice a few times to make sure the bendable thing was bending equally.
--

-MIKE-

"Playing is not something I do at night, it's my function in life"
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Perhaps the curve could be checked by flipping the layout stick end for end?
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On 4/15/13 7:01 PM, Phil Kangas wrote:

--

-MIKE-

"Playing is not something I do at night, it's my function in life"
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Gramp's shop wrote:

------------------------------------------------

--------------------------------------------------------------- Nice try but no cigar.
The end result needed is a cambered beam shape which requires more than the three points you suggest.
Bingham outlines the method that works in his book.
Have used the method to define the deck cambers which varied from 10' to 16' in length for the boat I built.
BTW, a batten is needed, I used a 3/4" x 3/4" x 1/16" x 96" aluminum angle which provides a knife edge for fairing out the profile with a fairing board.
Lew
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