framing square and chõ gen

For those wishing to discuss the material found in The Art of Japanese Carpentry Drawing essay series.
craigak
Hopper I
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framing square and chõ gen

Mon Jul 25, 2011 9:54 pm

In vol.2, p.109, Chris uses the square to layout the miter cut. I am using my new inch base-10 square.
So the run is 10 and this is the value on the long arm. Chõ gen is 9.28 and this is the value on the short arm. The resulting line produces an angle closer to 48˚. Working with TAN produces a chõ gen angle of 42.8736˚. Any see what mistake I am making?
Thanks,
Craig
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Chris Hall
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Re: framing square and chõ gen

Mon Jul 25, 2011 11:30 pm

Yikes! You're not making any mistake Craig. The drawing in the text is absolutely correct when it comes to laying out the chōgen slope - the mark is made along the short arm of the square, which is at the value for chōgen (9.28 in the case of a 10/4 -sloped hopper). The developed drawing on page 110 showing how the chōgen slope triangle can be developed directly from the unit triangle is also correct.

My mistake comes on page 111 where I show the calculation - I've reversed the 'opposite' and 'adjacent'. Since the miter line is made along the short arm of the square, the cut angle is also produced there, which means that the angle in question actually has opposite/adjacent of 10/9.28, which indeed works out to 47.1240...˚.

i feel bad at such a simple goof up, but hey, nobody's perfect and I'm glad to have the chance to correct the error in the text.

Here's the chōgen triangle on the edge of the board:
CSG Hopper 2 chogen explained correctly.jpg
CSG Hopper 2 chogen explained correctly.jpg (94.21 KiB) Viewed 5816 times
And here's the framing square with the same measures on the edge of the board:
CSG Hopper 2 chogen on hopper.jpg
CSG Hopper 2 chogen on hopper.jpg (78.13 KiB) Viewed 5816 times
Yep, revision 5 will have to come down the pike soon enough. I'm astonished that one got missed, so good on you Craig for finding it! I hope you find more (sorta :oops: )
craigak
Hopper I
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Re: framing square and chõ gen

Tue Jul 26, 2011 11:00 am

Chris,
It is gratifying to make some sense of this stuff. I am astonished by your knowledge of this material and the way you present it. It has been a slog for me but I keep at it.
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Chris Hall
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Re: framing square and chõ gen

Tue Jul 26, 2011 11:24 am

Like all of you, I'm learning as I go.

Craig, glad it's making more sense to you now. I know how easy it is to get hung up on and bogged down by a particular detail - you're doing well to forge ahead.
craigak
Hopper I
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Joined: Fri Jul 15, 2011 6:27 pm

Re: framing square and chõ gen

Thu Jul 28, 2011 10:18 am

Ok, so where would the angle 47.1240˚ be in the 4/10 triangle shown on pg.110?
Craig
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Chris Hall
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Re: framing square and chõ gen

Thu Jul 28, 2011 5:57 pm

Consider that opposite over adjacent was used to solve...

"the angle in question actually has opposite/adjacent of 10/9.28, which indeed works out to 47.1240...˚"

What angle is opposite the length of 10?

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