Calculate Compound Miter Joints

JPG · Post by **JPG** » Mon May 18, 2009 3:50 pm

dusty wrote:Angles expressed to the hundredth of a degree? How am I going to measure that?

How indeed!

He does make the point regarding the universal utility of a 'program' as opposed to a 'chart'. This is exactly the point I was making(chart unseen[could NOT find it in online PTWFE]). One one hundredth of a degree IS (IMHO) over kill though!

JPG · Post by **JPG** » Mon May 18, 2009 4:39 pm

dusty wrote:This is doable!

I just came back from a trial test to determine what .001 degree adjustment would be.

Five full revolutions of the thumbscrew changes the tilt 1.4 degrees as indicated on the wixey. Therefore, .001 degree equals .00028 revolutions of the thumb screw.

Establishing a ratio to calculate the unknown:

1.4/5 = x/.001

therefore

5x= 1.4x times .001

therefore

x = (1.4x times .001)/5 equals .00028 revolutions per 1/100 degree.

I just gotta get a large, finely calibrated dial to measure rotation of the thumb screw. I might need new glasses, too.

Oops. That is 1/1000 of a degree.

Corrected answer is .0028 revolutions per 1/100 degree. That'll make that calibrated dial a lot easier to make and to read.

BTW - it is easy to find someone who will tell you "you got it wrong"!

According to my calculation, the following result!

5T = 1.4° table tilt
5T = 5 x 360° knob rotation

1.4° tilt = 1800° rotation

1° tilt = 1800° / 1.4 = 1286° rotation

.001° tilt 1.286° dial rotation.

This IS readable, BUT all this has a problem!

The sine of an angle is NOT linear. You are providing the length of a side opposite to the angle(roughly at a right angle). The result above is accurate ONLY for a narrow range of angles near to that when you measured.

At 45° tilt, a larger number of turns is required per degree than at 5°.

All that being said, WE are all nuts discussing this. NO one has a need to adjust his saw table to .01° let alone .001°!

Cowboy+ was making the point that it IS possible with a 'program' to include all possible needs of a future user, whereas a 'chart' is limited to its present contents. This .001° silliness is absurd! I plead guilty(also)!

JPG · Post by **JPG** » Mon May 18, 2009 4:40 pm

dusty wrote:This is doable!

I just came back from a trial test to determine what .001 degree adjustment would be.

Five full revolutions of the thumbscrew changes the tilt 1.4 degrees as indicated on the wixey. Therefore, .001 degree equals .00028 revolutions of the thumb screw.

Establishing a ratio to calculate the unknown:

1.4/5 = x/.001

therefore

5x= 1.4x times .001

therefore

x = (1.4x times .001)/5 equals .00028 revolutions per 1/100 degree.

I just gotta get a large, finely calibrated dial to measure rotation of the thumb screw. I might need new glasses, too.

Oops. That is 1/1000 of a degree.

Corrected answer is .0028 revolutions per 1/100 degree. That'll make that calibrated dial a lot easier to make and to read.

BTW - it is easy to find someone who will tell you "you got it wrong"!

According to my calculation, the following result!

5T = 1.4° table tilt
5T = 5 x 360° knob rotation

1.4° tilt = 1800° rotation

1° tilt = 1800° / 1.4 = 1286° rotation

.001° tilt 1.286° dial rotation.

This IS readable, BUT all this has a problem!

The sine of an angle is NOT linear. You are providing the length of a side opposite to the angle(roughly at a right angle). The result above is accurate ONLY for a narrow range of angles near to that when you measured.

At 45° tilt, a larger number of turns is required per degree than at 5°.

All that being said, WE are all nuts discussing this. NO one has a need to adjust his saw table to .01° let alone .001°!

Cowboy+ was making the point that it IS possible with a 'program' to include all possible needs of a future user, wherever a 'chart' is limited to its present contents. This .001° silliness is absurd! I plead guilty(also)!

dusty · Post by **dusty** » Mon May 18, 2009 7:59 pm

You see, cowboy, how easy that was.

dusty · Post by **dusty** » Tue May 19, 2009 11:40 am

[quote="JPG40504"]According to my calculation, the following result!

5T = 1.4&#176]
Momentarily it was my intention to just let this lay and rest but....I could not. That is not my nature.

You say that the sine of an angle is not linear and imply that therefore this can't work. Well, I am not attempting to prove that the sine of an angle is linear but I am convinced that the threaded rod approach works and works very well.

With the table sitting at 0 degrees, using the threaded rod, I adjusted the table down to 20 degrees and then back up to 0 degrees in equal increments recording the results at every position.

The increment used was one full revolution of the knurled knob on the threaded rod.

The final conclusion is that one turn of the knurled knob will result in a change of .2941 degrees per change on the average. I have not calculated the standard deviation factor but I have the data if you want to do that. Looking at the numbers and acknowledging that all of this is for use in a woodworking environment where "close is good enough" I have concluded that the threaded rod is an excellent way to adjust the table tilt in mighty small increments.

Mathematically - 1/4 turn of the knurled knob produces a change of .0735 degrees of tilt. I don't think I need to get closer. If I did need to get closer, I would have to find a finer threaded rod. If it is not linear, I don't care.

This number has been empirically verified through four excursions between 0 degrees and 20 degrees in one revolution increments and calculated for changes in 1/4 revolution increments.

yep, you are right though - "All that being said, WE are all nuts discussing this. NO one has a need to adjust his saw table to .01° let alone .001°!" Maybe, just maybe this is why the Wixey is accurate to ONLY .1 degrees.

BTW - if you check with some avid segmented turnersyou may find that they disagree.

JPG · Post by **JPG** » Tue May 19, 2009 12:53 pm

I see you point re segments(if you are making a LOT of them for ONE project)!:)

Not to nit pick, but your need to 'Average' the numbers implies non-linearity.

No doubt the adjustment method IS useful and reasonably predictable over a small(20° near zero) range. The larger angles incur larger adjustments/°.

As an example of the non-linearity of which I speak:

Degrees------Sin-------difference/° Average/°
1°-----------.01745
2°-----------.03489-----.01744----.01744
3°-----------.05233-----.01744----.01744
4°-----------.06975-----.01742----.01743
5°-----------.08715-----.01739----.01741

15°----------.25881-----.01689----.01714

20°----------.34202-----.01645----.01667

30°----------.50000-----.01519----.01582

40°----------.64278-----.01346----.01432

45°----------.70710-----.01244----.01295

Nuf Said!;)

derk · Post by **derk** » Tue May 19, 2009 1:24 pm

Check out Beall Woodworking Tools for their Woodworking Chart. Lots of info on multi-sided projects, on the wall, at a glance for those of use that are mathematicaly challenged. see http://www.bealltool.com/products/other/wallchart.php

dusty · Post by **dusty** » Tue May 19, 2009 2:24 pm

[quote="JPG40504"]I see you point re segments(if you are making a LOT of them for ONE project)!:)

Not to nit pick, but your need to 'Average' the numbers implies non-linearity.

No doubt the adjustment method IS useful and reasonably predictable over a small(20&#176]
Not to nitpick but actually my need to average the numbers does not indicate non linearity. If non linearity was the issue, each and every reading taken would be off by some amount always in the same direction. Your input shows that. As you progress from 0 degrees to 45 degrees the sine increases from .01795 to .70710; it never jumps backward.

Now you did not see my actual numbers so I know you were not made aware that the numbers were inconsistent but you did jump to your conclusion without checking.

Now, having said all of that - when I noticed that the numbers were inconsistent, I made some modifications to my collection methods. I increased the size of the adjustment know and created a rudimentary scale that better allows me to turn the knob in more consistent increments.

With the modified knob, 1 revolution of the knob results in a .1 degree change in table tilt with only occasional deviation. I contribute that deviation to the Wixey - remembering that the Wixey is accurate to .1 degree. I have retested this from 0 degrees to 35 degrees. I am satisfied that this works sufficiently well for all of my tilting table needs. Enough is enough.

[ATTACH]4574[/ATTACH][ATTACH]4575[/ATTACH]

reible · Post by **reible** » Tue May 19, 2009 3:49 pm

Hi,

In our reading through the PTWFE study information I've added the missing table 3-1 and dug up an old table I had made and posted a few years back that expands that information.

That post is at:
http://www.shopsmith.net/forums/showthr ... 049&page=4

Look for post #40

The table (3-1) is at:
http://www.shopsmith.net/forums/attachm ... 1242758749

The supplemental table is at:
http://www.shopsmith.net/forums/attachm ... 1190651857

Ed

mickyd · Post by **mickyd** » Tue May 19, 2009 4:04 pm

JPG40504 wrote:According to my calculation, the following result!..................................

All that being said, WE are all nuts discussing this. NO one has a need to adjust his saw table to .01° let alone .001°! ...................... This .001° silliness is absurd! I plead guilty(also)!

I KNOW you guys know that sometimes we do things just because we can. It's fun, it's challenging, and it is what keeps the brain cells from turning into mush. I think it's great to see these posts. It's good to learn / reinforce skills with every opportunity. Good job dusty, good counters jpg. You guys are obviously THINKING!!