Old vs New Formula Difference...

[cbwx34]

A couple of people have asked about the difference between the "old" and "new" formulas... here's my take on it...

In the original book Dutchman (Ton) produced, he measured the Projection Distance to a point above the USB...



... and made his calculations from it, although the actual location was slightly different..



This, (as pointed out here by Jan), resulted in a slight difference (often less than 1°).  As Dutchman stated, the intent of his original book was "not an academic item, but a proposal to simplify the jig-setting", and served that purpose well, even beyond its original intent.

However, this difference did make a difference in the "4 Stop Collar" (4SC) setup I used...



... which is what I asked Ton's help with.

So, basically, the "new" formula" in two steps "mathematically moves" the reference point to the center of the USB...



... making it more accurate to deal with.  Since this update applies not only to the 4SC setup, but also the original jig setup, those formula(s) can be modified to eliminate the slight difference.

That's my take!

[cbwx34]

This part may only matter to a couple of people, but I'll stick it here anyway.

Dutchman and Jan have a slightly different approach to this.  Dutchman uses what I call the "Right Triangle" approach...



... where he first solves for a right triangle, then solves the Cosine Formula.

Jan uses what I call the "Double Cosine" approach...



... where he uses two Cosine Formulas to solve the problem.

But overlay the two...



and the answer comes out the same!

[cbwx34]

I did a few CADD drawings to see how things were comparing...
(CADD drawings are done independent of the formula, then compared)









...vs. the Formulas
                                        Top of USB to Casing                                    Top of USB to Wheel
Data                         Old Formula     New Formula     Cadd              Old Formula     New Formula     Cadd

T8D250PD139A15     169.54             168.46              168.37           79.74              78.88                78.81

T8D250PD139A20     176.39             175.75              175.67           86.39               85.95               85.88

T4D200PD139A20     165.17             165.36              165.25           91.80               92.20               92.12

T8217PD139A15        156.56             156.03             155.89           83.67               83.38               83.24

Seems to be working...   
(Will add more as time permits).

[RickKrung]

Nice work, CB.  I for one, appreciate the work you've done and how you have come a long way with your CADD work.  I enjoy CADD and use it for nearly all of my projects.  The consistency of your new formulas and the CADD means your are either, 1) doing things well, or 2) you are very consistent with your errors across different media 

Rick

[cbwx34]

Nice work, CB.  I for one, appreciate the work you've done and how you have come a long way with your CADD work.  I enjoy CADD and use it for nearly all of my projects.  The consistency of your new formulas and the CADD means your are either, 1) doing things well, or 2) you are very consistent with your errors across different media 

Rick

Haha... can't disagree... it's why I put it out for others to take a look at.

Do try to look at each part independently though... so that it (hopefully) double checks the process.

[Jan]

CB, really very nice work! Congrats! I have enjoyed your comparison between my and the new Dutchman's approach. CAD drawings are very important, because they provide independent verification of formulas and calculations. 

I have checked your "New formula" calculations of the "Top USB to Wheel" and can confirm that your results are correct. (The difference between your and my results is less than 0.02 mm.)

I would be glad to see the "New formula" embodied in all applets, programs and scripts. 

Jan

[cbwx34]

CB, really very nice work! Congrats! I have enjoyed your comparison between my and the new Dutchman's approach. CAD drawings are very important, because they provide independent verification of formulas and calculations. 

I have checked your "New formula" calculations of the "Top USB to Wheel" and can confirm that your results are correct. (The difference between your and my results is less than 0.02 mm.)

I would be glad to see the "New formula" embodied in all applets, programs and scripts. 

Jan

Thanks.  I figured you might be the only one to appreciate the comparison.  You're right about the CADD drawings... been very helpful.

The calculator options I posted have a "new formula" version now... users can pick what works best for them.

[Jan]

CB, your mastering both approaches, Dutchman's "Right Triangle" and my "Double Cosine", gives you the opportunity to design similar calculator also for the Tormek Square edge jig in the future. 

I think Ken will be happy with such a calculator.

Jan

[RickKrung]

...snip...
I figured you might be the only one to appreciate the comparison. 
...snip...

Hey!  I take a little bit of issue with that statement...   

Rick

[Jan]

Rick, this is really a serious omission!  I am sorry that CB forgot to mention you.

Jan

[cbwx34]

CB, your mastering both approaches, Dutchman's "Right Triangle" and my "Double Cosine", gives you the opportunity to design similar calculator also for the Tormek Square edge jig in the future. 

I think Ken will be happy with such a calculator.

Jan

I don't think we can pry the Kenjig from his cold... chiseled fingers. 

...snip...
I figured you might be the only one to appreciate the comparison. 
...snip...

Hey!  I take a little bit of issue with that statement...   

Rick

Didn't know you were a "double cosine" fan. 

[Ken S]

CB, your mastering both approaches, Dutchman's "Right Triangle" and my "Double Cosine", gives you the opportunity to design similar calculator also for the Tormek Square edge jig in the future. 

I think Ken will be happy with such a calculator.

Jan

l

I don't think we can pry the Kenjig from his cold... chiseled fingers.




Speaking as Ken, I make no apology for liking chisels. A chisel provides a very simple working platform. One straight bevel large enough to easily see.

Like Ton (Dutchman), I was looking for a way to simplify setting up knife bevels. I had worked out a reasonably good method by trial and error. Ton's tables have been a giant step forward for me. Whether or not they are the ultimate step, they have been very beneficial. They are the basis of the kenjig. Set up is definitely simpler. If an angle is not exactly 15°, it is close and consistent.

I am all for any change which moves us forward. I feel the knife set up process has passed the sharpening stage. Our improvements are definitely procedure honing measures. If we ever get a self centering jig, our set up procedure will be ready for it.

Ken

[Dutchman]

I get the impression that the "simple adjustment ..." is now hijacked with all possible means that the internet and smart phones offer.
For the ordinary user, however, setting with the kenjig will be most obvious with a table as a good second.
The tests that "cbwx34" performed show that the accuracy of this simple approach is not a matter of debate.

[cbwx34]

I get the impression that the "simple adjustment ..." is now hijacked with all possible means that the internet and smart phones offer.
For the ordinary user, however, setting with the kenjig will be most obvious with a table as a good second.
The tests that "cbwx34" performed show that the accuracy of this simple approach is not a matter of debate.

I don't consider it "hijacked"... I consider it an alternative.   Even for the "ordinary user" it's an alternative way for setting the USB... not really a better or worse one (nor any harder).

[cbwx34]

I don't think we can pry the Kenjig from his cold... chiseled fingers. 

Speaking as Ken, I make no apology for liking chisels. A chisel provides a very simple working platform. One straight bevel large enough to easily see.

Like Ton (Dutchman), I was looking for a way to simplify setting up knife bevels. I had worked out a reasonably good method by trial and error. Ton's tables have been a giant step forward for me. Whether or not they are the ultimate step, they have been very beneficial. They are the basis of the kenjig. Set up is definitely simpler. If an angle is not exactly 15°, it is close and consistent.

I am all for any change which moves us forward. I feel the knife set up process has passed the sharpening stage. Our improvements are definitely procedure honing measures. If we ever get a self centering jig, our set up procedure will be ready for it.

Ken

I think the (attempted) humor of my statement was lost in the coldness of a forum post.