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5 cut method Math

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Forum topic by Panthers65 posted 12-17-2017 09:22 PM 1418 views 1 time favorited 14 replies Add to Favorites Watch
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Panthers65

12 posts in 339 days


12-17-2017 09:22 PM

After going through the 5 cut method on my new sled, I decided to do it again to see how close I was.

A/Top = .458
B/Bottom = .442
difference = .016
.016/4 = .004
Length of Cut = 21-1/16

Using the last two above, .004/21.0625 = Margin or Error of 1.8991E-4
so my 90 cut is actually (1-1.8991E4)90 = 89.983?

With a 27-7/16” pivot point, I’d have to move the end of my fence back .00521”

Is the above right. I’m prety sure I can live being off by .017th of a degree.


14 replies so far

View jmos's profile

jmos

839 posts in 2397 days


#1 posted 12-17-2017 10:43 PM

The math is a bit more complicated than that. William Ng has a good video. But you have to divide the error by 4, since you are compounding the error by cutting 5 times, and then use the length of the cut, and the length of the fence to determine how much you would need to move the fence to get it perfect.

If I were you I’d do a single test cut a board that’s a typical width for you and put an accurate square on the end and see how it looks. Edit – I misread, thought the 0.04” was the cut error – yeah, at 0.016” you may want to adjust the fence and try again.

-- John

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Carloz

1147 posts in 619 days


#2 posted 12-17-2017 10:52 PM

0.016” on four cuts is pretty bad. If for example You make a 2×2’ frame it will not glue in on the last corner. You should aim at 0.007” or so.
And forget about degrees.as no one cares about them.

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clin

853 posts in 1024 days


#3 posted 12-18-2017 12:29 AM

0.004” over a 21 1/16” cut is pretty darn good. I come up 0.043 deg error. 21” is a pretty long cut, so this must be a pretty big sled you’ve made.

I’d leave it alone. You could cut a piece of wood perfect, and check it a few hours later and it could easily have moved on it’s own that much.


0.016” on four cuts is pretty bad. If for example You make a 2×2 frame it will not glue in on the last corner. You should aim at 0.007” or so.
And forget about degrees.as no one cares about them.

- Carloz

While for the same degree error, a longer cut will be more absolute error. The longer the cut the more flex you have with the piece and can usually squeeze parts together easily. So in many ways, degrees is more representative of the size of the problem you are dealing with.

And your example doesn’t apply. The length of the frame doesn’t matter. It’s the width of the frame that matters. If it were a 3” wide frame, the error over that length is just 0.6/1000”.

That’s pretty darn small.

-- Clin

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Carloz

1147 posts in 619 days


#4 posted 12-18-2017 01:05 AM

Gclin, you got all wrong’. Imagine that tou have an incredible long frame, like 100’. At that length the error will be very significant, like half of foot or so. Nobody makes such long frames, so the error is much smaller but the fact is, the longer the board, the bigger is the deviation on the same non square cut. The width of the board does not matter.
I just happened to attempt glue together a beveled door yesterday and it would not. I checked my incra miter gauge and it was off almost the same exact amount as in OP. Forcing things with clamps might work, but that is something what distinguishes good work from sloppy work.

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clin

853 posts in 1024 days


#5 posted 12-18-2017 01:48 AM


Gclin, you got all wrong . Imagine that tou have an incredible long frame, like 100 . At that length the error will be very significant, like half of foot or so. Nobody makes such long frames, so the error is much smaller but the fact is, the longer the board, the bigger is the deviation on the same non square cut. The width of the board does not matter.
I just happened to attempt glue together a beveled door yesterday and it would not. I checked my incra miter gauge and it was off almost the same exact amount as in OP. Forcing things with clamps might work, but that is something what distinguishes good work from sloppy work.

- Carloz

I understand that the small angle error would translate to the frame itself being out off alignment by that amount. But even if you glued it up with 3 of four butt joints having that error AND you made all the cuts in the worst possible orientation (after all you could do it where they cancel). After 100 feet you’d have the end of that frame being 3×0.004”/21” x 100 ft = 0.686”. Seems like a lot. But over a 100 ft length, a butterfly could flex that frame into position, and you’d still have only a gap of 4×0.004/21” x 3” = 2.3/1000” for a 3” wide frame.

Here’s an image so we can make sure we’re talking about the same thing.

Over your initial 2 ’ (24”) frame you used as an example, that worst case, alignment error of the frame (not the gap in the joint) would be just 0.014” = 3×0.004/21×24”, off of perfect. That’s extremely small. Again, this isn’t the gap in the joint, this is how much you’d have to flex the frame to align it. Unless this frame is made of steel, that’s trivial to do. And once done, the bending force needed would spread to all 4 frame members. And I’d hazard a guess that this stress would be less than the wood might experience during normal temperature and humidity cycles in it’s life time.

Furthermore, if all your cuts had the same angle error, your frame would in fact still align just fine, it would just be ever so slightly trapezoid in shape. Obviously, how this comes out depends on how you orient the wood when making the cross cuts of each member.

I really don’t think you realize that the OP is talking 0.004” (4 thousandths of an inch) over a 21” long cut. That’s an error of 0.02%. I’d bet 99.999% of all woodworking ever done had larger errors than that.

Could he make it better, maybe. But this error is not one of those, “it’s wood good enough.” It’s very much less than that. And heck, even if he got the sled perfect, how long is a wood sled going to stay perfect? Shop temp or humidity change will affect the sled also. There comes a point that you are just chasing ghosts.

-- Clin

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Panthers65

12 posts in 339 days


#6 posted 12-18-2017 02:13 AM



The math is a bit more complicated than that. William Ng has a good video. But you have to divide the error by 4, since you are compounding the error by cutting 5 times, and then use the length of the cut, and the length of the fence to determine how much you would need to move the fence to get it perfect.

If I were you I d do a single test cut a board that s a typical width for you and put an accurate square on the end and see how it looks. Edit – I misread, thought the 0.04” was the cut error – yeah, at 0.016” you may want to adjust the fence and try again.

- jmos

I had William’s video up when I did the math, that is what I did (a-b)/4 /Length of Cut * pivot point to reference point.

View Panthers65's profile

Panthers65

12 posts in 339 days


#7 posted 12-18-2017 02:20 AM

Gclin, you got all wrong . Imagine that tou have an incredible long frame, like 100 . At that length the error will be very significant, like half of foot or so. Nobody makes such long frames, so the error is much smaller but the fact is, the longer the board, the bigger is the deviation on the same non square cut. The width of the board does not matter.
I just happened to attempt glue together a beveled door yesterday and it would not. I checked my incra miter gauge and it was off almost the same exact amount as in OP. Forcing things with clamps might work, but that is something what distinguishes good work from sloppy work.

- Carloz

I understand that the small angle error would translate to the frame itself being out off alignment by that amount. But even if you glued it up with 3 of four butt joints having that error AND you made all the cuts in the worst possible orientation (after all you could do it where they cancel). After 100 feet you d have the end of that frame being 3×0.004”/21” x 100 ft = 0.686”. Seems like a lot. But over a 100 ft length, a butterfly could flex that frame into position, and you d still have only a gap of 4×0.004/21” x 3” = 2.3/1000” for a 3” wide frame.

Here s an image so we can make sure we re talking about the same thing.

Over your initial 2 (24”) frame you used as an example, that worst case, alignment error of the frame (not the gap in the joint) would be just 0.014” = 3×0.004/21×24”, off of perfect. That s extremely small. Again, this isn t the gap in the joint, this is how much you d have to flex the frame to align it. Unless this frame is made of steel, that s trivial to do. And once done, the bending force needed would spread to all 4 frame members. And I d hazard a guess that this stress would be less than the wood might experience during normal temperature and humidity cycles in it s life time.

Furthermore, if all your cuts had the same angle error, your frame would in fact still align just fine, it would just be ever so slightly trapezoid in shape. Obviously, how this comes out depends on how you orient the wood when making the cross cuts of each member.

I really don t think you realize that the OP is talking 0.004” (4 thousandths of an inch) over a 21” long cut. That s an error of 0.02%. I d bet 99.999% of all woodworking ever done had larger errors than that.

Could he make it better, maybe. But this error is not one of those, “it s wood good enough.” It s very much less than that. And heck, even if he got the sled perfect, how long is a wood sled going to stay perfect? Shop temp or humidity change will affect the sled also. There comes a point that you are just chasing ghosts.

- clin

This sounds more rational to me. The length of the frame doesn’t matter, the length of the cut is what matters. a picture frame that is 100’ tall or 1’ tall would have the same size gap at the corners if both frames were 3” wide.

If I’m .004” over at a 21” long cut, then at 6” wide cut (a pretty thick picture frame) i would have .00114” gap on the inside corner of the frame at a perfect 90* angle.

View Panthers65's profile

Panthers65

12 posts in 339 days


#8 posted 12-18-2017 02:29 AM



0.004” over a 21 1/16” cut is pretty darn good. I come up 0.043 deg error. 21” is a pretty long cut, so this must be a pretty big sled you ve made.

I d leave it alone. You could cut a piece of wood perfect, and check it a few hours later and it could easily have moved on it s own that much.

0.016” on four cuts is pretty bad. If for example You make a 2×2 frame it will not glue in on the last corner. You should aim at 0.007” or so.
And forget about degrees.as no one cares about them.

- Carloz

While for the same degree error, a longer cut will be more absolute error. The longer the cut the more flex you have with the piece and can usually squeeze parts together easily. So in many ways, degrees is more representative of the size of the problem you are dealing with.

And your example doesn t apply. The length of the frame doesn t matter. It s the width of the frame that matters. If it were a 3” wide frame, the error over that length is just 0.6/1000”.

That s pretty darn small.

- clin

Sled is 2’X3’ (or pretty close to it). I copied William Ng’s video as I was building it, just didn’t make it look as pretty as he did.

View ArtMann's profile

ArtMann

952 posts in 844 days


#9 posted 12-18-2017 03:35 AM

I think Carloz needs to review his trigonometry notes from high school days. 0.004 error over 21 inches is about as good as you are going to get with woodworking equipment.

View Rich's profile

Rich

3017 posts in 617 days


#10 posted 12-18-2017 05:17 AM


After going through the 5 cut method on my new sled, I decided to do it again to see how close I was.

A/Top = .458
B/Bottom = .442
difference = .016
.016/4 = .004
Length of Cut = 21-1/16

Using the last two above, .004/21.0625 = Margin or Error of 1.8991E-4
so my 90 cut is actually (1-1.8991E4)90 = 89.983?

With a 27-7/16” pivot point, I d have to move the end of my fence back .00521”

Is the above right. I m prety sure I can live being off by .017th of a degree.

- Panthers65

Yes, you got it right. An error of ~1.9E-4 per inch is plenty good.

-- Half of what we read or hear about finishing is right. We just don’t know which half! — Bob Flexner

View jmos's profile

jmos

839 posts in 2397 days


#11 posted 12-18-2017 12:56 PM

All math aside, I would still suggest making a cut and putting a square to it, that’s really the test. If you crosscut a board and can see gaps under the square, you probably want to keep working at it. If you can’t, you’re probably fine.

Alternately, if you have a shooting board, you can just plan on shooting any critical cut perfectly square.

-- John

View TheFridge's profile

TheFridge

9608 posts in 1514 days


#12 posted 12-18-2017 02:16 PM

I rebuilt my sled last night.

To make the math easier. Add up each side individually. Mine was .009 difference over 75”.

.009 divided by 75” is .00012 per inch out.

Mine had 16” pivot point and needed .00192 (or .002 which is close enough) to bring it to square.

I moved the fence and now it has a .001 difference over 74”. Close enough for me.

If the 5th cut bottom measurement is smaller then you angle is small than 90. If it’s the bigger of the 2 then it’s bigger than 90.

-- Shooting down the walls of heartache. Bang bang. I am. The warrior.

View Panthers65's profile

Panthers65

12 posts in 339 days


#13 posted 12-18-2017 02:26 PM



I rebuilt my sled last night.

To make the math easier. Add up each side individually. Mine was .009 difference over 75”.

.009 divided by 75” is .00012 per inch out.

Mine had 16” pivot point and needed .00192 (or .002 which is close enough) to bring it to square.

I moved the fence and now it has a .001 difference over 74”. Close enough for me.

If the 5th cut bottom measurement is smaller then you angle is small than 90. If it’s the bigger of the 2 then it’s bigger than 90.

- TheFridge

So after your 5th cut you measured the top and bottom and only had a .001 difference between the two? That’s awesome. I planned my fence down after I glued it together and I don’t even think its flat enough to get that small of an error.

on another note, how accurate would the miter gauge and fence be compared to the crosscut sled? I can’t imagine any fence could be moved multiple times and keep a margin or error in the thousands of an inch.

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TheFridge

9608 posts in 1514 days


#14 posted 12-18-2017 05:35 PM

yeah no lie. I jointed the face to be as flat as a straightedge would get it.

Depends on the gauge. I trust the incra 1000hd I have. It’s indexable for every degree. It’s it’s set it’s dead nuts. Until I drop it.

-- Shooting down the walls of heartache. Bang bang. I am. The warrior.

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