Five cut method on MFT3 explained

[paulhtremblay]

I've written a document outlining the method for doing a five cut test with the MFT3 table.

Could someone please review this for accuracy and clarity?

I made the document into a PDF so I could make changes and arrange the pictures in the right order. You can't do this easily with just a posting.

Thanks!

 

[bertv]

Hi Paul, in a reaction in this thread
http://festoolownersgroup.com/festool-how-to/mft3-34937/
I wrote a description of my take on the Five cut method on a MFT3. This also includes a description of how to fix the eventual error & is (I think) less complicated than yours.
Feel free to use that information for version 2 of your pdf!

 

[Rick Christopherson]

Your mathematics are incorrect because you based them on what Evenfall wrote. Unfortunately, many internet versions of the calibration copied Evenfall and they all repeat this same mistake. This is the reason why the Kapex manual presents the information with a built-in angular calculator so people aren't tempted to make this mistake.

The resulting error on the final offcut piece to be measured is completely independent of the lengths of the previous cuts. So you should not be adding up the lengths of the previous cuts in order to determine the "offset per length" value. The resulting error is simply the difference in the widths of the last piece divided by 4 (because it is compounded 4 times) and divided by the length of only the very last cut.

I have extracted the appropriate pages out of the Kapex manual as a stand-alone document for the 4/5 cut method. That PDF is located here:
4-Cut Calibration

 

[Rick Christopherson]

By the way, the other reason for calculating the angle instead of leaving the result as a linear error is to make it universal for all lengths of fences. The angular error will be correct regardless whether you are performing this for Kapex or the MFT.

If you want to know how far to move the MFT fence sideways, then simply take the sin of the result in my formula and multiply by the length of the MFT fence. (Or if you are calculating by hand, just don't take the arcsin in the formula). The result without arcsin is your linear error per unit length (either metric or imperial) as "error per inch" or "error per mm". Then multiply this number by the length of the MFT fence between the pivot point and the stop. (I don't have my MFT fence set up, so I don't have this number for you, but I think it is somewhere around 830mm.)

Oh, another P.S.: The only reason for the 5th cut is to ensure the 1st edge of the board is straight. Because this calibration gets repeated several times to tweak the result, each successive attempt only requires 4 cuts, not 5 cuts. This is why 5-cut is a misnomer.

 

[paulhtremblay]

Your mathematics are incorrect because you based them on what Evenfall wrote.

I have extracted the appropriate pages out of the Kapex manual as a stand-alone document for the 4/5 cut method. That PDF is located here:
4-Cut Calibration

Yes, that must be correct. I just came back from the coffee shop where I tried to work one out, knowing the two conflicting versions of the method I had already come across, and knowing this point would come up. I got as far as calculating that, if your alignment was off by 1 degree, by the fourth cut your board would have 3 angles of 89 degrees and one angle of 93 degrees.

Your link calculates the angles for the offcut, the correct way. If I calculate the angles for each offcut, here's what I get. I list the angles starting at the upper left and going clockwise:

Cut 1: 91, 90, 90, 89.

Cut 2: 91, 91, 90, 88.

Cut 3: 91, 92, 90, 87.

Cut 4: 91, 93, 89, 87.

Cut 5- infinity: 91, 93, 89, 87 (Same as cut 4).

The last offcut pieces do not form a right triangle. You have to form two right triangles, one with a measure of 1 degree, and one with a measure of 3 degrees. I would like to seem something more explicit as far as using arcsine. We are not measuring hypotenuse and sides of a right triangle, but the sides of a quadrilateral, none of the angles of which are 90 degrees--unless I made a mistake in my calculations, which could very well have happened. 

 

[paulhtremblay]

By the way, the other reason for calculating the angle instead of leaving the result as a linear error is to make it universal for all lengths of fences. The angular error will be correct regardless whether you are performing this for Kapex or the MFT.

It is probably simpler to use a proportion. That is the way it is usually explained, and the way most people can grasp it. If your cut is off by .5 mm over 1000 mm, and the distance between your pivot points on your fence is 500 mm, adjust your fence .5mm /2.

In addition, degrees can be pretty meaningless in woodworking. My example yields .01 degrees. That doesn't mean much. Knowing your side will be .1 mm wider at the bottom (or whatever the case) is more useful.

 

[paulhtremblay]

Hi Paul, in a reaction in this thread
http://festoolownersgroup.com/festool-how-to/mft3-34937/
I wrote a description of my take on the Five cut method on a MFT3. This also includes a description of how to fix the eventual error & is (I think) less complicated than yours.
Feel free to use that information for version 2 of your pdf!

Thanks. I saw this post and had been meaning to post a detailed description with pictures so members could follow the method.

 

[Rick Christopherson]

If I calculate the angles for each offcut, here's what I get. I list the angles starting at the upper left and going clockwise:

Cut 1: 91, 90, 90, 89.
Cut 2: 91, 91, 90, 88.
Cut 3: 91, 92, 90, 87.
Cut 4: 91, 93, 89, 87.
Cut 5- infinity: 91, 93, 89, 87 (Same as cut 4).

You're over-thinking the offcuts. They also will not have the angles you listed above unless the original scrap of wood was perfectly square to begin with, which the 4th offcut is completely immune to. That is the core basis for the method, and why the first 3 offcuts are discarded without examination. To better understand this, repeat your mathematics, but start out using a non-square trapezoid (or even a semi-circle, as long as it has 1 straight edge).

It is probably simpler to use a proportion. That is the way it is usually explained, and the way most people can grasp it. If your cut is off by .5 mm over 1000 mm, and the distance between your pivot points on your fence is 500 mm, adjust your fence .5mm /2.

You are in effect using the angle, but it is just not obvious because you bypass the arcsin/sin function when normalizing to one unit. And while that is easier on the calculator, it is harder to explain to the reader.

Your example of dividing by 2 is correct only if you have pre-planned your previous cut in order to make your 4th cut be exactly half of your fence length. That is easy to say in words, but far more difficult to do in real life.

 

[paulhtremblay]

You're over-thinking the offcuts. They also will not have the angles you listed above unless the original scrap of wood was perfectly square to begin with, which the 4th offcut is completely immune to. That is the core basis for the method, and why the first 3 offcuts are discarded without examination. To better understand this, repeat your mathematics, but start out using a non-square trapezoid (or even a semi-circle, as long as it has 1 straight edge).

Yes, of course. I was thinking of applying a specific case and then generalizing it. None-the-less, the fifth cut will always have the measurements I listed. And that gets me no closer as far being able to use an arcsine function to a trapezoid. I guess I will just work this out.

You are in effect using the angle, but it is just not obvious because you bypass the arcsin/sin function when normalizing to one unit. And while that is easier on the calculator, it is harder to explain to the reader.

Your example of dividing by 2 is correct only if you have pre-planned your previous cut in order to make your 4th cut be exactly half of your fence length. That is easy to say in words, but far more difficult to do in real life.

I have not seen an explanation that uses angles, and it is not hard to explain to the reader. I believe the originator is William Ng, and I believe he explained it as I did. I have taught a lot of math, and most people are not comfortable with sin functions, let alone arcsin functions.

 

[Rick Christopherson]

I think you may be confusing 2 different topics here. One is subjective opinion, but the other is a mathematical error.

How you present the final answer, whether it be in angular form or a linear ratio, is entirely subjective opinion and your choice to make. Both are correct and both are nearly identical in function.

However, back in your original posting you asked for your document to be reviewed for errors. You have a mathematical error that is completely independent of whether you provide an angle or a linear ratio.  William Ng's video does not contain this error. It is a mathematical error that you acquired either from Evenfall's article or an article based on his writeup.

The error I speak of is adding up the lengths of the previous offcuts and using that to derive your linear ratio. All but the last offcut should be discarded as meaningless to the final results. Note that I did not say "4th" or "5th" offcut, because this error is also unrelated to which offcut you choose to use. It doesn't matter whether you use the 4th, 5th, 6th or 100th offcut; your error ratio (or angle) is based on 1/4 the length of only that last offcut. Every cut that came before the last one is completely meaningless scrap wood.

 

[Administrator_JSVN]

I wonder if a video wouldn't be a better medium for teaching the method and how to adjust accordingly.  [wink]

Volunteers?

 

[Rick Christopherson]

William Ng already has a video showing the procedure. It's good and has been around for quite a few years.

 

[Administrator_JSVN]

William Ng already has a video showing the procedure. It's good and has been around for quite a few years.

Then maybe a linky or embed it in the thread.  [smile]

 

[paulhtremblay]

I think you may be confusing 2 different topics here. One is subjective opinion, but the other is a mathematical error.

However, back in your original posting you asked for your document to be reviewed for errors. You have a mathematical error that is completely independent of whether you provide an angle or a linear ratio.  William Ng's video does not contain this error. It is a mathematical error that you acquired either from Evenfall's article or an article based on his writeup.

Yes, completely agree. Sorry if I didn't make that clear that I agree with you. Thanks for pointing that out. I will definitely change my document.

But I would like a formal proof for your link. I am working on one right now. As I said in my last post, the offcut will always result in a trapezoid like figure, with the top having two angles either both less than or greater than 90 degrees. In our example, one angle is 91 and the other 93. One angle will always be equal to the angle of the error, and the other, 3 times that, and when added together, you will have an error or 4 times the real error.

But I would like to work out the exact relationship using trigonometry. I am looking at the law of tangents right now.

 

[paulhtremblay]

Then maybe a linky or embed it in the thread.  [smile]

It's a good video. I thought a clear document on how to do it on the MFT3 would be a good addition. Maybe not!

One issue that hasn't been addressed is whether you actually try to adjust the rail or fence to correct for your error, as is done in the video. As I said in my document, I am unsure, since you may not be able to get the same accuracy as on a table saw (within thousandths of an inch), and unlike a sled, you change the fence configuration on an MFT3.

 

[Rick Christopherson]

But I would like a formal proof for your link.

With all due respect, you asked that your article be reviewed for accuracy. I did that, but I can't force you to accept it. That is something you will have to decide for yourself as the author. I am happy to guide you, though.

 

[paulhtremblay]

With all due respect, you asked that your article be reviewed for accuracy. I did that, but I can't force you to accept it. That is something you will have to decide for yourself as the author. I am happy to guide you, though.

I agree with you as I have stated that numerous times. You are right; I was wrong. You did me a great service to point out my error.

For my own elucidation, as well as my being able to understand the problem better, I would like a formal proof of the link to Kapex. Do you have that? If so, I would be grateful. If not, I will work it out on my own. I am getting closer.

 

[Rick Christopherson]

Yes, I did go through a graphical proof 6 years ago when I wrote the Kapex manual, but it isn't anything I saved, as it was just for my own benefit. If you want to go through a proof for yourself, here are a couple of tips:

• Take a look at the lead graphic in the Kapex manual. That graphic is the final outcome of my graphical proof, which is why I used it in the manual. You'll also notice that William Ng drew something very similar in his video, except he mistakenly didn't realize the 4th and 5th offcuts were the same.
• Focus on the angles of the main workpiece, not the angles of the offcuts. The only time you should focus on the offcut is for the very last one to prove that it carried the original error compounded 4-times.
• For your proof you need to work with angles, not the error ratio. Your final error ratio you present to the reader is mathematically derived from the angle. Your error ratio is nothing more than the sine of your error angle. This will be much clearer as you proceed through your proof.

 

[Michael Kellough]

As Rick's graphic shows all the off cuts are trapazoids until you achieve 90 degrees.

On am MFT it's best to adjust the fence so the kerf in the surface stays narrow as the blade. Moving the fence I've managed to get the error down to .001 degrees more than once.

 

[paulhtremblay]

I think I have the proof.

The problem is, that the Kapex manual made some simplistic assumptions. Technically speaking, the formula is not correct. I will have to draw pictures tomorrow, but here is what I have.

The final offcut is a trapezoid like figure (but not a trapezoid!). For simplicity's sake, let's use Kapex's example of each cut being off 1 degree. Also, assume the final length is 500 mm. If you start on the upper left and move clockwise, you get angles of 91, 93, 89, and 87. You have no right triangles, and no equal sides. Strictly speaking, you can't use trigonometry to solve the problem at all.

But if you make some simplistic assumptions, you can. First, we can make two right triangles form the trapezoid like figure. On triangle will angles of 1, 89, and 90 degrees. The second one will have angles measuring 3, 87, and 90 degrees. The sum of the bases of the triangles will give the error. But we have to make some assumptions.

Assumptions 1: assume the hypotenuse of each triangle is equal. In our example one hypotenuse was .6 mm different. That is a small amount, especially considering it is unlikely you will have a measure off by a full degree.

Assumption 2: assume sin(e) + sin(3e) = sin(4e), where e is the error of the cut, in our case 1 degree. Strictly speaking, this math is wrong, and you can't do this. But for small angles, it will work out okay.

So the real formula is: [WidthLeft - WidthRight/Length] = sin(e) + sin(3e)

If you assume sin(e) + sin(3e) = sin(4e) you can solve for e:

[WidthLeft - WidthRight/Length] = sin(4e)
arcsin[widthLeft - WidthRight/Length] = 4e
1/4 arcsin[widthLeft - WidthRight/Length] = e

Two disclaimers here. First, I could have easily made a mistake. If so, I am open to corrections. I only posted this because I have worked and re-worked the problem, and I believe I have it right.

Second, I am not implying in any way that the Kapex manual made a blunder. It is a perfectly acceptable strategy to make the simplistic assumptions the manual made in order to solve a real world problem. I am thinking back to calculus when I had to differentiate a problem that would not solvable, until you realized the number e became insignificant as you approached a limit. The course was pure math, and if that strategy was applicable there, it is certainly applicable here.

This was a tough problem because, given Kapex's formula, I assumed there was a simple solution, or at least one that didn't involve bending some rules.

To be clear, my document as it stands is in error. You should not add up the sides. The final piece gives you all the dimensions you need. I will update my document tomorrow and include a section at the end explaining the math. I couldn't find any real math explanations on the web.