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Geometry on cutting timber

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Geometry on cutting timber
Posted by rolfjoy on Monday, June 11, 2018 11:54 PM

Clearly most wood doesnt bend. Be great if it would. Pardon the pun.
Out of a piece of wood which is perhaps 120mm wide and length is irrelevant, but say 400mm long, at which angles would we need to cut to obtain 12 pieces to make a semi-circle?
I say 15 degrees. The old man says 7.5 degrees with 24 cuts.

Anyone here who is  maths wizzard?

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Posted by Tinplate Toddler on Tuesday, June 12, 2018 10:59 AM

Neither of you is correct, but your old man knows his math a little better!

A semi circle has a curvature of 180 degrees, for 12 pieces of timber that makes 15 degrees for each piece, but 7.5 degrees on each end! This makes 24 cuts, but as you want to form a semi circle, you can omit the cuts at each end. That makes it 7.5 degrees and 22 cuts!

Cheers,

Ulrich

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Posted by j. c. on Tuesday, June 12, 2018 11:22 AM
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Posted by 7j43k on Tuesday, June 12, 2018 2:27 PM

Since the length has been stated to be irrelevant, I will assume all the needed pieces can be cut from a single piece.

It will take 13 cuts.  You will then have 12 pieces, each having ends angled at 7.5 degrees.

 

Ed

 

Who has spent a lot of paid time using a miter saw.

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Posted by 7j43k on Tuesday, June 12, 2018 2:36 PM

Tinplate Toddler

...as you want to form a semi circle, you can omit the cuts at each end.

 

 

No, you can't.

 

Ed

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Posted by ROBERT PETRICK on Tuesday, June 12, 2018 2:45 PM

Doesn't say how thick the 'timber' is, but assuming the boards are fairly thin (maybe 1/2" or 3/4" or so),  then several layers can be cut at once.

Figuring six layers at 1/2" each (3" total, well within my chop saw capacity), you could do this in three cuts. Ignoring the square ends.

But who counts such stuff?

Robert 

LINK to SNSR Blog


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Posted by 7j43k on Tuesday, June 12, 2018 2:58 PM

3 cuts it is, sir.  I like it!!

But if you ignore the square ends, you only get 165 degrees of turn.

I do suspect that cutting the pieces "in the flat" (13 cuts) will be faster than stacking the pieces.  I am wary of dealing with the three pieces "meandering" while I cut.

 

Ed

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Posted by bogp40 on Tuesday, June 12, 2018 5:33 PM

7j43k

3 cuts it is, sir.  I like it!!

But if you ignore the square ends, you only get 165 degrees of turn.

I do suspect that cutting the pieces "in the flat" (13 cuts) will be faster than stacking the pieces.  I am wary of dealing with the three pieces "meandering" while I cut.

 

Ed

 

That's what the supplied clamp is for with most chop saws or sliding compound miter saws. But the time to line up and set clamp I can duplicate the other 2 to 3 pieces. You may do just as I do, the info is for ones that want to make multiple cuts.

Modeling B&O- Chessie  Bob K.  www.ssmrc.org

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Posted by rrinker on Tuesday, June 12, 2018 6:07 PM

7j43k

 

 
Tinplate Toddler

...as you want to form a semi circle, you can omit the cuts at each end.

 

 

 

 

No, you can't.

 

Ed

 

13 pieces of wood, 2 of them with a 7.5 degree angle cut on one end and flat on the other, and the other 11 with a 7.5 degreen angle cut on both ends is 22 angles of 7.5 degrees, which is 180 degrees. With the two flat ends, perfect to attach to a rectangular bench to add a curved end.

                                            --Randy

 


Modeling the Reading Railroad in the 1950's

 

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Posted by 7j43k on Tuesday, June 12, 2018 6:31 PM

rrinker

13 pieces of wood, 2 of them with a 7.5 degree angle cut on one end and flat on the other, and the other 11 with a 7.5 degreen angle cut on both ends is 22 angles of 7.5 degrees, which is 180 degrees. With the two flat ends, perfect to attach to a rectangular bench to add a curved end.

                                            --Randy

 

 

 

Who said 13?

We all said 12.  

 

I did say 13 CUTS of one "plank" to get 12 pieces with 7.5 degree ends.

 

 

Each piece of the 12 subtends 2 x 7.5 degrees = 15 degrees

12 pieces x 15 degrees = 180 degrees.

So this design will mate perfectly with an edge of a straight table.

 

 

I do agree you can make a 180 degree turn with 13 pieces, the way you describe.  And it will probably work.  But it's not the "official" way--it is inaccurate.  But probably accurate enough for model railroad benchwork.

You've also got to design the two "custom" ends.  They're different than the other 11--they have different dimensions.  

With the "12" method, all pieces are the same.  Plus it's easy to dimension the pieces--check out J. C.'s link, above.

 

 

Ed

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Posted by hon30critter on Wednesday, June 13, 2018 12:13 AM

Hi rolfjoy!

Welcome to the forums!!      Welcome

Interesting question. Could you provide a little more information in terms of what the semi-circle will be used for?

Cheers!!

Dave

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Posted by bogp40 on Wednesday, June 13, 2018 4:52 PM

hon30critter

Hi rolfjoy!

Welcome to the forums!!      Welcome

Interesting question. Could you provide a little more information in terms of what the semi-circle will be used for?

Cheers!!

Dave

 

After all the disussion of cutting and math, I too was wondering the use of the semi-circle. figured at first it is roadbed for a turn, but why cut so short. normally cookie cutter , you can just draw the radius on plywood to cut out the arcs. These pieces and cuts are more what you would do for a helix, but with numerous pieces for the spiral.

Modeling B&O- Chessie  Bob K.  www.ssmrc.org

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Posted by rrinker on Thursday, June 14, 2018 7:32 AM

 Also true, unless you are building cabinet-grade benchwork and want it to be as round as possible for some aesthetic reason. I don't like perfectly square ends, the 90 degree angle ends up punching people in the gut (or even more painful areas depending on their height and the height of the benchwork) so splitting it out into a few pieces is probably preferable to making it square. 

                               --Randy


Modeling the Reading Railroad in the 1950's

 

Visit my web site at www.readingeastpenn.com for construction updates, DCC Info, and more.

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Posted by dknelson on Friday, June 15, 2018 10:33 AM

rolfjoy
Clearly most wood doesnt bend. Be great if it would. Pardon the pun.

Heh - have you checked out the 2x2s that Loewe's sells?  Most if them look like bacon.  I bought one strictly for use as a prop in my benchwork clinic to get a laugh (I use 2x2s for legs).  I say it may not be much as a benchwork leg but it makes a great template for easement curves.

Dave Nelson

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Posted by gregc on Friday, June 15, 2018 10:42 AM

rolfjoy
Clearly most wood doesnt bend.

has anyone built a helix using splines?

greg - Philadelphia & Reading / Reading

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Posted by Track fiddler on Saturday, June 16, 2018 8:49 PM

I built a clock once in my buddy Rod's cabinet shop while he was making bird houses. I remember we both had to think kind of hard about it.

There are 12 sides 360 divided by 12 is 30

But there are two ends to every board 360 divided by 24 is 15

If you're going to make a semicircle 12-sided. I would figure you just divide what I did above in half.

12 boards with 2 angled ends is

24x7.5=180

P.S. Ed said it..... I've just been there done it a time or twoBig Smile

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