Woodpeckers Protractor (ruler)
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PaulMarcel
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smorgasbord said:
I nearly ordered the Shinwa after this discussion because I could see it being very useful for the extended range. Just requires calculating the angle-caliper relation.
As for the table saw fence, it's something I wanted to build also based on the DRO design mentioned. Maybe this discussion will get the idea moving again...
smorgasbord
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Packard said:
Sort of, if you're comfortable with math. Here are close-ups of the 44º, 45º, and 46º settings:
[attachimg=1]
[attachimg=2]
[attachimg=3]
44º is close to 15.2cm. Maybe 15.21
45º is close to 15.9cm. Probably 15.88
46º is over to 16.5cm. Probably 16.53
That makes 6.7mm from 44º to 45º, and 6.5mm from 45º to 46º, if my eye-balling of sub-millimeters is correct. So, yeah, assuming [member=3513]PaulMarcel[/member] 's observation on the BCTW AMPv2 that linear interpolation between integral degrees also applies to the Shinwa (they have different geometries since the AMPv2 has legs that are the same length [or about], while the Shinwa's fixed legs are not the same lengths as each other so maybe that affects interpolation accuracy), then yeah that could be done.
More potentially exciting is that this means instead of actually trying to figure out how to install a DRO on the Shinwa, or building my own Shinwa design with a DRO, I could use a long digital caliper's depth rod to make a very accurate setting. I bought a 12" (300mm) digital caliper at Taylor Toolworks recently since it was on overstock sale at a price too good to pass up, and could use that to set the Shinwa up to about 65º - maybe higher angles if I add a fixed length rod extension or try to measure from the depth stop rod end to the fixed jaw to double the capacity. Hmm. I'll see if I can try that out in the next couple days (I'll be back in my shop Tuesday morning). Maybe this is a reason to get the medium size Shinwa instead of the big one I got?
I'll have to see what measurements I can pull off the Shinwa itself for the triangle legs length (pivot to pivot) but my observation is that the spacing between degree is very non-linear. Even with them being closer at 20º and 100º than at 50º, the amount of closeness is still different between 90º and 100º than between 20º and 30º. So, I'll have to do the math, but yeah, I should be able to use my long digital caliper on the Shinwa to set pretty accurate non-integer angles.
[member=3513]PaulMarcel[/member] , if you do get a Shinwa I'd be interested in a comparison of accuracy at the integer marks compared to your BCTW AMPv2.
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PaulMarcel
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Just ordered the Shinwa; will be here Wednesday.
As for the AMPv2, you can linearly interpolate between printed angle settings and be really close. It clearly is still not linear; the error would depend on the angle you are looking at as the integral steps on the caliper map to different size angle ranges. Since I have the function, I may write up a script tomorrow to see how far off linear interpolation between the printed settings will be. It will actually be interesting.
As for the AMPv2, you can linearly interpolate between printed angle settings and be really close. It clearly is still not linear; the error would depend on the angle you are looking at as the integral steps on the caliper map to different size angle ranges. Since I have the function, I may write up a script tomorrow to see how far off linear interpolation between the printed settings will be. It will actually be interesting.
I meant, for example, you want 45.3 degrees.
So you set it at 45 degrees, then count the number of hash marks on the mm scale when you shift to 46 degrees. So let’s say there were 6 hash marks between 45 ans 46 degrees on the mm scale.
So 45.33 degrees would be 45 degrees plus two hash marks on the mm scale. So to get 45.3 degrees I would set it at 45 degrees plus two hash marks (scant).
It would be more accurate than just eyeballing the degree setting.
Not really math, more like counting (the hash marks).
Why am I calling these “hash marks” and not “millimeters? So as not to confuse what is really being measured.
Borrowing the mm hash marks seems like an easy way to up the accuracy of your interpretations.
So you set it at 45 degrees, then count the number of hash marks on the mm scale when you shift to 46 degrees. So let’s say there were 6 hash marks between 45 ans 46 degrees on the mm scale.
So 45.33 degrees would be 45 degrees plus two hash marks on the mm scale. So to get 45.3 degrees I would set it at 45 degrees plus two hash marks (scant).
It would be more accurate than just eyeballing the degree setting.
Not really math, more like counting (the hash marks).
Why am I calling these “hash marks” and not “millimeters? So as not to confuse what is really being measured.
Borrowing the mm hash marks seems like an easy way to up the accuracy of your interpretations.
Packard said:For this demonstration, I used 3/4” plywood about 6” x 12”.
The first step was to set the saw angle using a 30/60/90 triangle that is part of a $4.00 set. It’s intended audience is high school students studying geometry.
The first photo shows the board with the opposite ends cut on the angle.
I next sliced the board into 6 equal sized pieces.
I taped it up into a hex. I am confident that with proper clamping all the miters will close up. It might close up if I used packing tape instead of masking tape. If it did not close up, I would tweak the angles until it did, or I would burnish the joints to close up any outside gap.
I re-taped the hexagon with a strong packing tape. It tightened up the joints to what I would call “ideal”.
The photo hosting site I use (IMGUR) is “over capacity”. I will try posting the image a little later.
Addendum: IMGUR got its act together. Here is the hexagon assembled with stronger packing tape. You can enlarge the image to better see the joints.
The set up triangle was part of this Staedtler “math” set, which was $3.79 at staples. It included a protractor, 30/60/90 triangle,, 45/90/45 triangle, 6” ruler.
These are all small items and perfect for my table saw.
https://www.staples.ca/products/455884-en-staedtler-4-piece-math-set-instruments
Since I had already cut and taped the pieces, I figured I might as well glue them up and see what I could learn from that.
So I applied glue (Woodworkers’ 3) to all 12 surfaces and then taped it closed to allow the glue to dry.
I came back two hours later expecting to find a nice little hexagon. That was not the case. The twelve surfaces that were coated with glue expanded as they absorbed the water content. The result: The joint nearest to the ends of the tape popped open. I added more glue and closed the gap by applying pressure across the hexagon from the opened joint to the one across from it.
Below is thr final result. I might one day make a pedestal for a small sculpture or something similar. I will remember to either add strap clamps or a couple extra wraps of tape.
I would note:
1. I did not tweak the initial set up, and the initial setup would be close enough for the type of work I do.
2. I could close any minimal gap on the outside of the hexagon by burnishing it closed with a smooth round rod (chrome plated rods work best, and some of my screwdrivers have chrome shafts).
3. You can enlarge the imag on-screen to check if these joints are tight enough for your work.
4. I still think making a test is going to get the closest result.
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smorgasbord said:
I don't have the mental acuity right now (or maybe just the patience) to determine whether it would be the sine or cosine, but yes, the distance between the degree markings should be variable.
Packard said:
See above. It's not an evenly-divisible relationship, it's either the sine or cosine, so they're closer or further depending on where you are on the scale.
smorgasbord
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Packard said:
I included close up photos so we could do an actual example, because your idea requires splitting mm's AND some math.
First, where is the 45º mark on the mm scale? 158.8? 158.9? Or, call it 158.85?
Now we have to look at the 46º mark, where's that? 165.3? 165.4? or, call it 165.35?
So, what's the span difference? Anywhere from 6.4mm to 6.6mm, or something else depending on what you eyeballed above?
Then you can do 0.3 times 6.4 or 6.6 or somewhere in between to get between 1.92mm or 1.98mm
Thus, the answer range is somewhere between 158.8+1.92 and 158.9+1.98, or between 160.7 and 160.9 , depending on how you split the mms on the whole integral degrees. Note that this is somewhat easier here with these large close up photos - real life is actually a bit harder, but I guess one could build a table of whole integer to mm values once and print it out.
So, your process might help since splitting closer hash marks is easier than splitting further hash marks, and we've got the answer down to a 1/10 of a mm. If you're willing to go through all that math - it's not just counting. I think using the digital caliper depth rod on the index mark would be more accurate, and even easier. I'll play with this tomorrow.
One more note: While Shinwa's rules have nice etched markings into which you can rest a pencil or even (gently) a knife, this triangle protractor thingie has only ink markings. They're good ink markings, high contrast and pretty thin, but not as good as etched would be.
[member=3513]PaulMarcel[/member], note that the math on the Shinwa will be slightly harder than on the AMPv2 since Shinwa (and caliper registration) will be from the free end, not between the two leg pivots. Once we measure the lengths we can do the appropriate subtractions to get values to plug into the Law of Cosines equation. Should still be an easy program to write, perhaps even just do it as an Excel spreadsheet that can be easily shared.
smorgasbord said:
On the middle image above, If I draw a line straight up from the 44 degree mark, I see 7 hash marks separating the 44 degree mark and the 45 degree mark, so each hash mark is equal to .143 degrees.
Yes, you would need a calculator, but a simple way to make interpolation more accurate. Certainly more accurate than the oldtimers’ R.C.H. (Red hair) increment of old.
smorgasbord
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Packard said:
You see 7 hash marks, I see between 6.4 and 6.6.
And then there's where you start counting from - just where is that 44 degree hash mark on the mm scale?
Finally, note I can get 0.1 degrees, maybe 0.083 degrees accuracy from my AngleWright without interpolation, between 45 and 90. But, as noted above, there are situations where that isn't really good enough.
This all seems more like machine shop tolerances than woodworking tolerances. It would not affect me or how I work. I get as close as I can in the initial set up and then make a test. I add or subtract a hair and then either test again or proceed.
smorgasbord
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Packard said:
Check out Paul's Angle Madness Blog and Videos
It's a few 8-sided (non-uniform length) tapered boxes, so all the angles are compound. There's a point in one of the videos where he does a test fit and the domino was milled slightly off and it affects the tightness of the joint. Luckily, that was in the MDF prototype. At any rate, his need for angular accuracy was very real in that woodworking project.
BTW, Paul, if I were doing your project today, I'd consider using my small CNC to cut the triangles you used on your table saw crosscut sled to set the miter angles. And then for the blade bevel angles, I'd cut another set of triangles, which would include a blade teeth clearance notch. I haven't done an accuracy test on my CNC, but it should be pretty darn accurate.
Injection molded draftsmen’s triangles from a major supplier of drafting equipment are exceptionally accurate.
When you think on it, if you are going to pop $75,000 to $200,000 for a mold, you are going to carefully check accuracy before signing the acceptance letter.
If you are looking for a 30,45,60 or 90 degree angle, you would be hard put to come up with something more accurate than a draftsman’s triangle.
A cnc might (might) match it, but it had better be machined from a very stable material. No wood product would be up to snuff.
When you think on it, if you are going to pop $75,000 to $200,000 for a mold, you are going to carefully check accuracy before signing the acceptance letter.
If you are looking for a 30,45,60 or 90 degree angle, you would be hard put to come up with something more accurate than a draftsman’s triangle.
A cnc might (might) match it, but it had better be machined from a very stable material. No wood product would be up to snuff.
Packard said:
I suspect that most people won't believe that something so simple and cheap can be as accurate as they are. I have always thought doing mechanical drawing needs a high degree of accuracy and it is not surprising that these simple tools are so well made.
smorgasbord
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Packard said:
We're not. Again, check out Paul's Angle Madness Blog and Videos (see up thread for link). I could post my newel toppers yet again if you really want....
smorgasbord said:
I was thinking of Pijol’s original post where he complained about the failure to get repeatable results with the Woodpeckers unit.
I would say that 90% or more of the angles used in woodworking are 22.5, 30, 45, 60, and 90 degrees. Triangles will yield perfectly repeatable results for those angles and using a protractor to achieve those angles seems silly to me.
How often are other angles called out? And where. I’m sure we all have at least one project where a custom angle is required. But a custom angle for 25, 50, or 100 projects? I would be greatly surprised.
I have a sliding table miter saw that is set at the factory to precisely 45 degrees. It gets almost all of my miter cuts up to it’s maximum depth of cut (about 3”—I will measure that when I get home).
Other angles do come up, but 45 and 90 degree angles make up almost all of the angle cuts I make in the shop (cabinets, and cabinets masquerading as furniture).
smorgasbord
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Packard said:
The one-hit wonder who didn't say what angles he was trying to get?
Packard said:
Often enough that I think many of us benefit from having a thread discussing how to achieve accurate and repeatable angles.
Projects using something other than 22.5, 30, 45, 60, 90 degree angles:
1) This Home Depot tapered planter box:
[attachimg=1]
2) [member=3513]PaulMarcel[/member] 's "Diamond" (aka "Angle Madness") cabinet and "Tim Burton" wall table.http://www.halfinchshy.com/2012/04/angle-madness-product-design.html andhttp://www.halfinchshy.com/2013/02/no-comment-2-full-build.html
3) My own staircase newell toppers:
[attachimg=2]
4) This Halloween prop:
[attachimg=3]
5) This old-fashioned bird house:
[attachimg=4]
6) This cool stool:
[attachimg=5]
I could go on and on. If you want, I'll start a whole new thread and call it "Unusual Angles" so 90% of the time 90% of the people don't have to pay attention to it.
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I cut edge miters the way it was described in an article in Fine Woodworking.
I first cut the pieces to the exact size.
I put a sacrificial fence on my regular fence. I cut a generous relieve (about 1/8” wide and 5/8” high).
I tilt my saw over to 45 degrees and bury the blade into the sacrificial fence.
I then feed each sheet into the saw taking a tiny triangle off the edge.
The worry would be that the drop off would kick back. But the generous relief means that the drop off just rattles around a bit. (However, I still stand off to the side.)
I’ve been doing this for years, as did the author of the article. I never had a kick back. I do keep that possibility in mind however.
So regardless of the shape of the sheet, the miters are all the same for the top to the sides to the bottoms.
I first cut the pieces to the exact size.
I put a sacrificial fence on my regular fence. I cut a generous relieve (about 1/8” wide and 5/8” high).
I tilt my saw over to 45 degrees and bury the blade into the sacrificial fence.
I then feed each sheet into the saw taking a tiny triangle off the edge.
The worry would be that the drop off would kick back. But the generous relief means that the drop off just rattles around a bit. (However, I still stand off to the side.)
I’ve been doing this for years, as did the author of the article. I never had a kick back. I do keep that possibility in mind however.
So regardless of the shape of the sheet, the miters are all the same for the top to the sides to the bottoms.
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