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Crazy geometry problem...

Started by Paschale, September 22, 2010, 10:37:46 PM

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Paschale

So I was peeling some paint off an old beautiful wooden pillar I've got on my 1928 house.  It's made of Douglas fir, and it'll be a shame to cover it with paint again, but that's off topic.  Anyway, as I was peeling the paint, I saw an odd line in the paint, and so started digging around.  Turns out a previous owner decided when the pillar got some dry rot in it that he would just cover the thing up with some thin sheet metal, and call it good.  Sealed with a couple of coats of paint, it's actually done just fine, but now it's time to properly fix it.  I'm going to cut out the punky stuff, and want to replace it.  I'm thinking I'll cut some pieces with the radius of the  circle somehow, so I can sort of cooper together a patch that will fit.  I'll use the band saw to cut off the square joints, to help round it out, and then get it rounded the old fashioned way, with a lot of elbow grease and a sander.  (I suppose I could figure out a jig with a router too...).  Anyway, the question I have really is a math question.  How would one move from the diameter of a circle, to find the correct angle to cut square pieces of wood to match the arc of the circle.  I like these sorts of challenges, honestly, but right now, I need to do some studying up, or learning from someone who's figured such things out.  ???

Anyone have some suggestions on calculating this thing out?
Y'all can pronounce it "puh-SKOLLY"

pigman

Now you are making it too hard. Forget all that math stuff and do a little trial and error and be done in two minutes. In other words, I don't have a clue on how to do the math. ;D
Things turn out best for people who make the best of how things turn out.

Tom

Pretend that you aren't working with a circle.  When you cut the punky stuff out, make the hole square and plug it with a timber.  Then shape the outside of the timber to a circular shape.   Plastic wood works too.  :D

woodbowl

Quote from: Paschale on September 22, 2010, 10:37:46 PM
How would one move from the diameter of a circle, to find the correct angle to cut square pieces of wood to match the arc of the circle.

The first thing I'd do is find the diameter. Either bend a stiff piece of wire to make callipers, then measure the two contact points or measure the circumference and divide by pie, 3.1415 to find the dia. Use a compass to draw a circle on the wood you want to use for the patch and cut out what you need on a bandsaw. Shape the insert like a pumpkin wedge untill it fits snug, then glue it.
Full time custom sawing at the customers site since 1995.  WoodMizer LT40 Super Hyd.

metalspinner

A square hole in a piece of plywood and a plunge router will make quick and precise work of that project, paschale.  Then, as Tom mentioned, plug it with a square board.
I do what the little voices in my wife's head tell me to do.

Paschale

More brains are better than one!   ;D

I like that idea of using the square hole with the plunge router, and viewing this as a square timber, and then using the band saw to make it curved after the fact.

Thanks guys!   8)
Y'all can pronounce it "puh-SKOLLY"

terrifictimbersllc

All the above are excellent and practical.   But unless you change your question you don't have your answer yet.   :(   One way to get this is with a drawing program that lets you draw the circle, make the lines you want then measure distances and angles on it.  You can do that on paper if you've got compass, ruler and protractor, it's easy to make a full scale drawing here.  The program I've taken to for this is Google Sketchup, it's free.  It's a 3D program but you can do the 2d you need probably with just a little fooling around. But this isn't for everyone, it can be really annoying.
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Gary_C

There is a quick and dirty way to get your angles. A circle has 360 degrees and to convert that to a flat sided circle you just need to know the number of sides. For example a square has four 90 degree sides, an octagon has eight 45 degree sides, etc.
Never take life seriously. Nobody gets out alive anyway.

neilg

Assuming that you know the diameter, radius = diameter / 2. Cutting square notches makes the problem easier because you have 90 degree corners. If you cut to the middle of the circle you can use a square block where each side equals the radius. Draw an arc between the corners if you want to bandaw the curve before sanding.

But I would do it differently since I wouldn't assume that the circle is perfectly round. Cut your notch in the circle and cut a block of wood to fit it. The block can be square or rectangle. Put it in the notch and just trace the curves onto it and cut them on a bandsaw. Leave a little extra wood on the arcs so that you can sand them down to match after. Way easier (less chance for errors) and no figuring involved.
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Jim_Rogers

To begin to try and figure the size of a board needed to fill the gap created by the rot, if I understand the question correctly, which I may not, but anyhow; you need to start with a line.

I have drawn a line and to use as an example, I made my line 12" long.

You can draw a straight line with a pencil and a ruler and then divide the line in half; so that you have a center point.

Using the center point you set your compass to the center and one end of the line and draw a circle:



Now you have some place to start.

Next draw another circle the same size but use the end point of the line for the center and draw the second circle:



The straight line you first drew is the diameter of the circle.
If you draw a straight line from the circle's center point to the point where the two circles intersect this line would be the radius, in this case 6".

And if you draw a line from this point to the center of the second circle you form a triangle and this second line is also the same length as the radius, again 6".



This second straight line is also the chord of the arc that goes from one point where the two circles meet to the center of the second circle.

If you offset that line by say 1" the standard thickness of a rough sawn board, you'd see that the arc can be cut in the board to place the rotten section of the post, if of course the post is 12" in diameter:



Whatever you do, have fun doing it!
Woodmizer 1994 LT30HDG24 with 6' Bed Extension

logwalker

The room just got real quiet. I hate smart kids.   ;)

Joe
Let's all be careful out there tomorrow. Lt40hd, 22' Kenworth Flatbed rollback dump, MM45B Mitsubishi trackhoe, Clark5000lb Forklift, Kubota L2850 tractor

Paschale

Yeah, thanks Jim!  There's no question who's got the brains in the operation!   :P   8)
Y'all can pronounce it "puh-SKOLLY"

isawlogs


Nice layout Jim ,  :P  Your the man.

Me , well I would of cut a rectangle out of the post glued in a board and drawknifed it to the post contour.
I aint real good wiff math formulations   :-\
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SwampDonkey

What about shrinkage? Ok I'll  :-X :-X :-X


:D :D
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Jim_Rogers

The shrinkage would be something to consider, so I'd try and use the driest piece of wood I could find so that it will be a small amount....

And I just recently learned about all the geometry stuff.... it looks like it would work to me, but I never tried it....

In high school, I took geometry but it was the first class right after lunch and I think I spent more time napping than paying attention......

QuoteI would cut a rectangle out of the post; glue in a board and drawknifed it to the post contour

That's is what I would do, but you should/could figure out what size board to use, doing it my way, and there is no math there just making lines and circles.....

To make it accurate you'd need to know the diameter of the post to start with, and make that the line you draw your circle(s) on......
Whatever you do, have fun doing it!
Woodmizer 1994 LT30HDG24 with 6' Bed Extension

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