5 Cut Method Math

Ok. I am trying to wrap my head around the accumulated error associated with the 5-cut method. I read somewhere that the accumulated error increases by a factor of 5 or was it 4? Anyway, I think both are wrong. I drew up a mock 5-cut in CAD and used an angle error of 5 degrees. The box is 4" by 4".
Cut1=red line Cut2=green line Cut3=orange line Cut4=yellow line Cut5=grey line
Cut one:
http://www.garagewoodworks.com/5cut/cut1.jpg
Cut two: Rotate clockwise and cut. Red line is now against the fence. The distance at the top goes from 0.35 to 0.6440 - Not double, but close.
http://www.garagewoodworks.com/5cut/cut12.jpg
Cut three: Again rotate clockwise and put the green line against the fence.
http://www.garagewoodworks.com/5cut/cut123.jpg
Cut four: Rotate and put the orange line against the fence.
http://www.garagewoodworks.com/5cut/cut1234.jpg
Cut five: Rotate and put the yellow line against the fence.
We went from the original 0.35" to the accumulated 1.0". That's an increase of 2.86".
Not four or five. Am I missing something?
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On Mar 8, 11:56 am, snipped-for-privacy@garagewoodworks.com wrote:

Cut 5
http://www.garagewoodworks.com/5cut/cut12345.jpg
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Two observations/questions...
I thought the accumulated error warning was in terms of angular measures, not distance measures. For example, being off by a degree on cutting a miter would yield a 2 degree gap.
Secondly, I'd think you would see a different distance result if you kept the side length 4" in your example instead of starting with a 4" square and making cuts. If you measure the lengths of your final sides in the graphic they aren't 4". For example, make the first cut, mark off 4" and make a second cut, mark off 4" and make a third cut, etc. Can you easily mock that up? I'd be curious to see the difference.
John

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On Mar 8, 12:25 pm, "John Grossbohlin"

How does one calculate the accuracy level in degrees that the method will get you? Obviously it depends on the length of the sides and the delta distance you accept in your fifth cut from front to back.
How close to 90 degrees will I get if I use a 18" square board and accept a delta of 0.004" on the fifth cut?
(snip)
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snipped-for-privacy@garagewoodworks.com wrote in wrote:

89 degrees 59 minutes 50.8 seconds, or 89.9975 degrees.
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wrote:

Hey cool. I'd appreciate it if you could show the equation(s) you used. (degrees only) Thanks.
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snipped-for-privacy@garagewoodworks.com wrote in

Sure thing, Brian, here you go:
Accumulated error of 0.004" in five cuts = 0.004 / 5 = error of 0.0008" per cut.
Error of 0.0008" at a distance of 18" gives the tangent of the angle at 0.0008 / 18 = 0.000044444444....
Inverse tangent of 0.0000444... (that is, the angle whose tangent is 0.0000444...) = 0.002546 degrees.
0.0025 degrees deviation from a 90-degree angle 90 +/- 0.0025 89.9975 or 90.0025 degrees.
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wrote:

Thanks Doug. That's actually what I had originally, but I started to second guess myself. I appreciate your help.
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wrote:

Seems close enough to 90 to not worry about it... ;~)
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We do something like that I guess when we tune our sliding table saws. We take about a 48" square and spin it 4 times and then measure the thickness of a thin ripping at the front and the back and see if they're the same. If they are, we've got a nice square cut. If not, we scientifically calculate the difference and use a calibrated striking mallet to bump it into square. ish. Works great! JP
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I absolutely need one of those calibrated striking mallets!!! It must be a home-built as I can't find one at the hardware store.
Ralph
We do something like that I guess when we tune our sliding table saws. We take about a 48" square and spin it 4 times and then measure the thickness of a thin ripping at the front and the back and see if they're the same. If they are, we've got a nice square cut. If not, we scientifically calculate the difference and use a calibrated striking mallet to bump it into square. ish. Works great! JP