Obtaining Unusual Angles with Precision

[smorgasbord]

From the TLL-90S specs:
1) High accuracy ± 0.005° and 0.001° high resolution;

That is how a proper metrological spec should look. This one seem to be the real deal.

Depending on which model/age of Wixey he's testing, the current unit's spec is:

Specifications
Range: +/- 180 degrees
Resolution: 0.1 degrees
Accuracy: +/- 0.2 degrees
Repeatability : +/- 0.1 degrees

http://www.wixey.com/anglegauge/index.html#wr300type2

So that would seem to conform to your expectations.

Unfortunately those "tests" are just random chance. Claiming a digital scale with a 0.1° resolution to be "spot on" down to 0.1° accuracy is just amateurish at best, misleading at worst. What they actually checked is the Wixie one is indeed within the +/- 0.2° range that it can display. And that even ignores if they used a calibrated reference (most likely not ..).

Wixey itself only claims +/-0.2º accuracy, so his tests, while not against traceable units, does seem to confirm that. I would expect that most surface plates, sine bars, and gage blocks, if not the cheapest junk available and properly cared for, would be far more accurate than the Wixey unit being tested, and so would give a reasonable estimate of its accuracy, or lack thereof.

The $45 unit I just purchased, which hasn't arrived yet, is specced at an accuracy of +/-0.05º and resolution of +/-0.01º. I don't understand how it could be different enough to be 4X more accurate than the $20 cheapies at double the price, but for this money I'm interested in it just for the convenience for non-super-critical blade angle and jointer fence settings as well an curiosity.

 

[smorgasbord]

From the TLL-90S specs:
1) High accuracy ± 0.005° and 0.001° high resolution;

That is how a proper metrological spec should look. This one seem to be the real deal.

Depending on which model/age of Wixey he's testing, the current unit's spec is:

Specifications
Range: +/- 180 degrees
Resolution: 0.1 degrees
Accuracy: +/- 0.2 degrees
Repeatability : +/- 0.1 degrees

http://www.wixey.com/anglegauge/index.html#wr300type2

So that would seem to conform to your expectations.

Unfortunately those "tests" are just random chance. Claiming a digital scale with a 0.1° resolution to be "spot on" down to 0.1° accuracy is just amateurish at best, misleading at worst. What they actually checked is the Wixie one is indeed within the +/- 0.2° range that it can display. And that even ignores if they used a calibrated reference (most likely not ..).

Wixey itself only claims +/-0.2º accuracy, so his tests, while not against traceable units, does seem to confirm that. I would expect that most surface plates, sine bars, and gage blocks, if not the cheapest junk available and properly cared for, would be far more accurate than the Wixey unit being tested, and so would give a reasonable estimate of its accuracy, or lack thereof.

The $45 unit I just purchased, which hasn't arrived yet, is specced at an accuracy of +/-0.05º and resolution of +/-0.01º. I don't understand how it could be different enough to be 4X more accurate than the $20 cheapies at double the price, but for this money I'm interested in it just for the convenience for non-super-critical blade angle and jointer fence settings as well an curiosity.

One thing I haven't seen discussed is the compounding of errors using a sine bar:
1) You have the error in the surface plate.
2) You have the error in the sine bar.
3) You have the error in each gage block that is stacked.

My basic QA analysis is that the errors have to summed. Let's take a greatly simplified, not realistic, caseL

A) Surface plate accurate to +/-0.0001" per inch
B) Sine bar accurate to +/-0.001" over its 5" length
C) Each gage block accurate to +/-0.0001", and there are 4 of them stacked.

Thus the error sum would be:
A) 0.0001*5  = 0.0005
B) 0.001 as specified
C) 0.0001*4
A+B+C = 0.0019

So, the accuracy of the sine bar setup is +/-0.0019" and with a 5" hypotenuse, that would be an angle accuracy of about +/-0.02º

The compounding of errors is why thinking in 1/32" or mm or half degrees isn't sufficient even  for some woodworking tasks.

 

[smorgasbord]

Just received a DXL360S Digital Angle Inclinometer. Not in my shop, so have limited tools available for testing. Unit was not calibrated well when I received it, so I went through the procedure (6 sides to set).

I do have a cheap gage block from Banggood (claims to be accurate to 0.005mm), so my idea was to use the base magnet to hold the finder unit on one side, zero it, then move the finder to the other side. The results were pretty impressive:
[attachimg=1]
[attachimg=2]

Now, the finder does fluxuate by 0.01 º or 0.02º, but that's within the +/-0.05º claimed accuracy, and apparently such fluxuations are common due to earth's magnetic field variations.
[attachimg=3]

With the finder zeroed horizontally on the gage block, inserting a Chinese DIN 875-2 45º triangle under reads 45.01º-45.03º one direction and 44.97º-44.98º the other direction (pivoting the 45º triangle on the fixed gage block with finder fixed to triangle via its magnets).
[attachimg=4]

With the unit zeroed on the gage block, a 0.10mm feeler gage slipped about 2mm in under the gage block (to clear the beveled corners) registers 0.09º-0.10º of difference. I think that math is 0.1/75.0 (25-50-75 block) *180/Pi to get degrees = 0.08º, so very close - and note that these measurements are pretty darn finicky. The worst thing is that you have to hold the unit while pressing the Zero button and it takes more pressure on the buttons than I would like so you end up being firm holding the unit while pressing, but that changes the orientation slightly when you let go.

The thing also has a bubble level mode:
[attachimg=5]

So, for $74 on Amazon, so far this looks pretty decent for things like tablesaw blade angle. I'll try it out on my tablesaw, etc. in a few weeks when I'm back in the shop. For the miter gauge/sled/saw, I still want to play around with the Shinwa gauge geometry and a digital caliper.

 

[Crazyraceguy]

How do people set their saws to cut these super accurate angles?

Regards
Bob

It kind of depends on what you call "super accurate". Making 45 degree miters on both ends of 4 pieces to make a picture frame takes more precision than most people would assume. The more sides you get involved, exponentially increases the difficulty. Even the best of set-ups should still be tested on scrap first, but it is in your best interest to test on similar material.

 

[smorgasbord]

As a side note, here's a pretty short (I watched at 1.5X speed) and interesting video on how NIST tests tape measures:

A 1930's promotional tape is checked and found to be within 0.022" at the four foot mark. Pretty darn good for free back then.

BTW, there's a shot near the end of the video of NIST traceable tape measures you can buy. That's from the McMaster Catalog:https://www.mcmaster.com/products/t...ficate/?s=tape-measures-with-nist-certificate

And for metric rules:https://www.mcmaster.com/products/rulers/certificate-type~calibration-certificate-traceable-to-nist/certified-corrosion-resistant-stainless-steel-rulers/system-of-measurement~metric/

 

[mino]

As a side note, here's a pretty short (I watched at 1.5X speed) and interesting video on how NIST tests tape measures:
...

A 1930's promotional tape is checked and found to be within 0.022" at the four foot mark. Pretty darn good for free back then.

BTW, there's a shot near the end of the video of NIST traceable tape measures you can buy. That's from the McMaster Catalog:https://www.mcmaster.com/products/t...ficate/?s=tape-measures-with-nist-certificate

And for metric rules:https://www.mcmaster.com/products/rulers/certificate-type~calibration-certificate-traceable-to-nist/certified-corrosion-resistant-stainless-steel-rulers/system-of-measurement~metric/

Well, ehm, that about as bad as it gets. But a nice video indeed.
European "Class I" standard requires that at 20 feet the deviation is no less than 0.6 mm and respectively less across the length.

Me got lucky - my class I was within 0.3 mm across the length per the calibration report.

The bigger problem for tape measures or long rulers is the temperature expansion - wood expands differently to metal so if measuring at 35C in a hot summer or at 5C in winter cold shop, one will be easily 1mm off over a couple meters distance.

 

[smorgasbord]

iGaging has a digital miter gauge out. The usual +/- 0.2º accuracy:https://www.chipsfly.com/EZ-Digital-Miter-Gauge_p_272.html

Stumpy Nubs, whom I generally like, doesn't understand:=bf3QS1-3e4Kec8wu&t=357

But for the money it does seem pretty decent for where that accuracy is good enough.

 

[rst]

As a commercial glazier I run into many unusual situations requiring accurate angle.  I have various different tools.  I keep a Bosch electronic folding level in my van as well as a can't think of the British made, small protractor.  I have the I gaging cube for my table saws.

 

[smorgasbord]

Peter Parf has a new "Parf Protractor" for cutting integer and half degree angles accurately on a track saw cutting station. Here's the video:


It appears to use the same principles as the Shinwa gauge discussed up thread. But, unfortunately requires drilling new holes in your table for every angle you decide to cut. My thought would be that a better product would be one where the guides for drilling the holes are actually a fence you clamp to the table and place the stock against that to cut. But, I'm not an MFT user, so maybe I'm missing something.

Separately, I recently acquired a Bridge City Angle Master 6i (not the Pro unfortunately). I'm playing around with it when I have some spare time (which I really don't have given I'm still trying to finish my Murphy bed project).

But, I'll spend some more time looking over the Parf Protractor and how that works to see if I can design something on my own that becomes its own miter sled fence or track saw cutting station fence.

 

[Crazyraceguy]

I was just about to say the same thing.....smorgasbord beat me to it.

 

[Lbob131]

How do people set their saws to cut these super accurate angles?

Regards
Bob

On an european  slider  the  outrigger  table  has  very  accurate  angle  settings.
Thats  how  I set  mine.

 

[Mini Me]

I have a question, how do tool rooms such as Suburban Tooling measure angles as they are certified to some level of manufacturing.

https://www.subtool.com/

 

[mino]

I have a question, how do tool rooms such as Suburban Tooling measure angles as they are certified to some level of manufacturing.

https://www.subtool.com/

This is what basic trigonometry is for. You measure sides of a triangle that gives you the exact angle. Conversely, you sine/cosine the angle you want and use it to mark it.

"Transforming" angles to distances and vice versa. Then, for efficiency, use metrological standards made/purchased to use as a direct reference.

This is why one of the key tools in a /non-digital/ machine shop are (big) compasses for distance transfer .. and angle marking.

---
Unfortunately, with the ubiquity of digital aids, there is now almost a generation out there to whom sine/cosine are seen as something belonging to "advanced math" ..

 

[Mini Me]

My maths skills stop at the basic four functions due to poor education and I wouldn't know what a Cosine was if it bit me so there are good reasons for some of us to use whatever aids are available.

 

[ChuckM]

When I studied Accounting, everything was done on paper. To produce something with a computer, I punched cards and handed them to a computer operator to " run" them. Today, none of that exists anymore. So going digital is the only option.

But trigonometry (most of which I've forgotten) is at your finger tips...and its digital name is Google! Recently, I was able to complete a triangular unit by using this online calculator:https://www.calculator.net/triangle...=&va=45&vz=870&vb=45&angleunits=d&x=Calculate

I wouldn't go and buy a new tool or gadget just because I have a single project involving odd angles to do. I'd most likely be able to find a solution online.

 

[Mini Me]

Thanks Chuck but in the end it comes down to taking the number and cutting to that number accurately as pointed out earlier in the thread. Digital measurement has a tolerance and mechanical measurement has its own issues so how does a certified service such as Suburban Tooling get that number onto a piece of metal accurately. As you point out angle templates can be bought on Ebay so how accurate are they and do we blindly just believe they are accurate to the number. It is something I think about fairly often I must admit.

 

[mino]

Thanks Chuck but in the end it comes down to taking the number and cutting to that number accurately as pointed out earlier in the thread. Digital measurement has a tolerance and mechanical measurement has its own issues so how does a certified service such as Suburban Tooling get that number onto a piece of metal accurately. As you point out angle templates can be bought on Ebay so how accurate are they and do we blindly just believe they are accurate to the number. It is something I think about fairly often I must admit.

Example:

Say I want an angle of 21°57'23", just for the sake of it. I want it with an accuracy of within 0,001".

For easier calculation, we first convert 21°57'23" to degrees (21.95639°) and radians (0.383211).
Most calculators support all three, so this is just for visibility: (1"(angle second) = 1/60' ; 1'(minute) = 1/60° ; 1°(degree) = pi/180 rad(radians) )

Option one: using square + ruler
needs: accurate square + accurate ruler, is a simpler process, but more-demanding on expensive kit and a good marking technique

tan (21°57'23") = a/b = 0.403140... = a/10" = 4.03140" / 10"

0) the edge of the material is the adjacent side of the triangle
a) mark a point where we want the cut/angle to start and measure 10" (b) distance from there, mark it
b) take a square and make a squared (to the adjacent edge) line at the mark, that will be the opposite side line
c) take a ruler and mark 4.03140" (a) distance of the opposite side on the squared line
Done. Your starting point and the new "X" point now form a 21°57'23" angle with the edge. The inaccuracy is about as much as your square + your ruler inaccuracies combined.

Option two: using straight edge + compass + ruler
needs: straight edge, shop compass (10" or bigger) + (not-so)accurate ruler, may seem a bit harder process, but gets by with just a good straight edge

View attachment 1

reference: https://en.wikipedia.org/wiki/Sine_and_cosine#Elementary_descriptions

 

[Packard]

In my experience, most angles can be transferred rather than measured—the actual measured angle be damned. 

Aside from that, a mathematical scaled angle will be most accurate in my opinion as you can scale the measurements to size.  A 6” protractor to measure the angle of a wall?  No.  You need something larger.
 

You can fashion your own.  Two straight edges and a decent locking mechanism.

Trig-Jig makes a fairly elaborate version for about $80.00.  I have not used it, but it looks impressive.  They make 4 sizes.  And they have a lot of YouTube videos, but annoyingly they focus on how they are made rather than how they are used.  So I have not linked any of their videos.  But they do make a big deal over the fact that they are made in England.
https://trigjig.us/products/trigjig-af6-mkii-angle-finder

 

[rst]

I bought the smallest thing one for tight spaces, I have the Bosch electronic that will lock for use as a level.  The angle function was great when we needed to determine angles for glass panels in staircases.

 

[Packard]

In the early 1970s, I was working for a company that produced large weldments.

We were to build a table from 3” x 4” heavy wall steel tubing that was about 8’ wide and 20 feet lone.  It was an open table, just the framework.  It was to hold mirrors and a laser for testing at Brookhaven National Laboratories on Long Island. 

The kicker was that there was to be a vertical steel plate at each end of the table and they had to be parallel with 0.005”. 

We had a magnetically attached surface grinder, so doing the machining after assembly was not an issue.  What was at issue was how to measure the parallelism. 

I was not in attendance during the process, but it involved a surveyor and a transit and “a lot of math”.

It cost $20,000.00 to produce, with a big chunk of that money going into the process of attaining parallelism, and making accommodation to make the shipment without damage. 

The irony to this was that when I inspected the table all set up, I saw that the laser had about a 1/4” of fore and aft adjustment as did the mirror assembly. 

I asked, “Why the 0.005” tolerance on the parallelism?”

And the reply:  “Well, we had to put a tolerance on the print.”

And that was the point in my life where acknowledged that “sometimes math matters.”