weird sashigane

Straightedges, rules, squares, sumitsubo, sashigane - those items we employ when 'putting the lines on the wood'
MBarnes
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weird sashigane

Fri Jan 20, 2017 4:26 pm

I just received two sashigane from Japan. One each of shaku and cm scales.

the root 2 side of the shaku sashigane isnt quite what I expected. The long arm is correct, but the short arm appears to be the same on both sides.
Note how the first scale marks do not form a square as would be expected if they were the same scale. Shouldn't both arms be root two larger?
IMG_20170119_1601274 small.jpg
IMG_20170119_1601274 small.jpg (841.31 KiB) Viewed 8134 times
the metric scale on the short arm of the shaku shashigane is also incorrect. compare the 5cm mark on the metric square to the 5cm mark on the shaku square. its about 1.3mm short over 5cm. Is there a reason why this would be correct?
IMG_20170119_1601179 small.jpg
IMG_20170119_1601179 small.jpg (859.96 KiB) Viewed 8134 times
is the shaku sashigane just messed up?
sorry for the size of the pictures, I will make adjustments in the future.
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Chris Hall
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Re: weird sashigane

Fri Jan 20, 2017 6:48 pm

Shouldn't both arms be root two larger?
No, only the ura side of the long arm will have the √2 scale markings. If both short and long arms had √2 markings, you would not be able to use the sashigane to lay out regular hip rafter slope lines; i.e., if the common slope were 5/10, then the hip slope would be 5/(10√2). After all, the hip rafter triangle has the same rise as the common.
The metric scale on the short arm of the shaku shashigane is also incorrect. compare the 5cm mark on the metric square to the 5cm mark on the shaku square. its about 1.3mm short over 5cm. Is there a reason why this would be correct?
The lower scale on the backside of the short arms of the shaku-measure sashigane looks to have a maru-me scale, which tells you the circumference of an object by measuring its diameter. The shaku-measure sashigane does not have any metric markings on it.

To explain the maru-me scale a little more using the comparison of the two framing squares, I attach the following annotated close-up:
IMG_20170119_1601179 small.jpg
IMG_20170119_1601179 small.jpg (326.85 KiB) Viewed 8129 times
Notice that the mark of '5' on the upper sashigane corresponds to a measure on the lower framing square of a bit more than 4.8 - - actually it is exactly 4.8223 cm (I can calculate that value by working backwards - it's not a guess on my part).

To obtain a circumference, we multiply diameter by π. So, take 4.8223cm * π = 15.15cm.

Now, in the Japanese traditional system, 1-sun is equal to 3.03cm, so if we divide the above 15.15cm by 3.03, we obtain a value of, drum roll please, 5-sun. That's why 4.8223cm on the metric square would correspond to a mark of 5-sun on the maru-me scale on the traditional measure square.

Hope that makes good sense.
MBarnes
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Re: weird sashigane

Sat Jan 21, 2017 5:14 pm

Thanks for clearing that up Chris. I have never had a root 2 scale available before.

Next question: The short arm of the ura side only goes to to 7.5 sun. Should I use 5 sun and 1/2 the common slope?
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Chris Hall
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Re: weird sashigane

Sat Jan 21, 2017 9:06 pm

Next question: The short arm of the ura side only goes to to 7.5 sun. Should I use 5 sun and 1/2 the common slope?
You can, but why?

Look on the front side of the long arm and stick your thumbnail on the 10 mark. With your nail in the same position, turn the leg of the square over to the √2 scale side. You should find an arrow marked there at the mark of your nail, at a value of 10/√2, or 7.071. You can therefore use the the long arm of the square on the ura side, at that mark, to lay out conventional slopes, using the short arm for the rise of the triangle in question.

Similarly, if you note the mark of 10 on the √2 scale side, and turn the square over to the omote, or front face, you will find a corresponding arrow marked, and it will be located at a length equal to 10√2, or 14.1421.... on that front face. Thus you can use the sashigane with the front face showing, using at marked spot, to lay out slopes with 10√2 as the run, and taking the rise on the short arm as usual.
MBarnes
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Re: weird sashigane

Sun Jan 22, 2017 9:56 am

Thanks Chris,

I was sick yesterday and my brain was foggy. I mean to ask about the hip slope. The short arm is only 7.5 sun so I cannot use the square as you show in TAJCD Vol4 pp28. I thought about it some more and I can flip the square and put the run on the long arm but use the 5sun measure from the ura side (using the mark you referred to) and the common rise on the short arm. Is there a better way?
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Chris Hall
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Re: weird sashigane

Sun Jan 22, 2017 9:58 am

If the square's markings do not go up to a large enough number for your needs, then you will have to divide, just as you are suggesting.

~C
MBarnes
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Re: weird sashigane

Sun Jan 22, 2017 10:03 am

Thanks Chris.

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