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Digital Angle Guage Accuracy

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Blog entry by DennisC posted 2330 days ago 3145 reads 0 times favorited 12 comments Add to Favorites Watch

I have a Wixey angle guage and a Craftsman 12” digital level. I decided to discover just how accurate 0.1 degree is. I put the Wixey on top of the Craftsman and zeroed both while sitting on my table saw. By inserting a feeler guage under one end of the Craftsman level I could determine how many thousandths of an inch it takes to go from 0.0 to 0.1 degrees. My finding; 0.010”. At 0.011” both guages changed from 0.0 to 0.1 degrees.
0.010” per foot

This can be further proven mathematically.
((12 X 3.14159265)/360)/10= 0.0104719755 or rounded to 0.010
For those that might be confused I’ll explain the formula.
12 is the number of inches in one foot
3.14159265 is the ratio of any circle’s circumference to its diameter
360 is the number of degrees in a circle
10 is to divide each of those degrees by ten to get 0.1 degrree.

The question then, for each of us Lumberjocks, is, ” Is ten thousandths of an inch in a foot close enough?”

For me it is.

-- Gen 8:22 While the earth remaineth, seedtime and harvest, and cold and heat, and summer and winter, and day and night shall not cease.



12 comments so far

View brunob's profile

brunob

2275 posts in 2795 days


#1 posted 2330 days ago

Close enough for me too. Love my Wixey guage.

-- Bruce from Central New York...now, if you'll pardon me, I have some sawdust to make.

View Scott Bryan's profile

Scott Bryan

27251 posts in 2447 days


#2 posted 2330 days ago

Me too. I like mine as well and use it to check bevel cuts and 90s. I especially like it for the digital readout.

But to tell the truth I still pull out my engineer’s square to check the fence/table alignment at 90 degrees. I guess there is too much old school in me (I also would rather use my stick rule).

Thanks for the post.

-- Challenges are what make life interesting; overcoming them is what makes life meaningful- Joshua Marine

View motthunter's profile

motthunter

2141 posts in 2424 days


#3 posted 2330 days ago

I love to see metalworkers learn to do woodworking. They want things to the thousandth.. Wood is dynamic and grows and shrinks. If you get it to the thousandth today, the only lesson you will learn is that tomorrow it no longer meets spec. You need to be precise.. but you have to decide what that means to you.

End game is a fantastic looking project.

-- making sawdust....

View Tom Adamski's profile

Tom Adamski

306 posts in 2396 days


#4 posted 2330 days ago

Dennis,
Thanks for the post. I think Wixey makes a great product. I’m already into them for the angle gauge, the calipers and the tablesaw fence readout. Not a dud in the bunch.

Tom

-- Anybody can become a woodworker, but only a Craftsman can hide his mistakes.

View GaryK's profile

GaryK

10262 posts in 2614 days


#5 posted 2330 days ago

I use my Wixey all the time. I use thousands of an inch when i measure things, but I don’t get anal about it.
.010 a foot is fantastic as far as I’m concerned. 1/16” at 10 feet is great for wood.

-- Gary - Never pass up the opportunity to make a mistake look like you planned it that way - Tyler, TX

View rikkor's profile

rikkor

11295 posts in 2500 days


#6 posted 2330 days ago

Close enough. I love my Wixey, too.

View Sawdust2's profile

Sawdust2

1467 posts in 2713 days


#7 posted 2330 days ago

We used the Wixey Wed nite to set the angel on the table saw. Digital readout wandered all over the place.

The solution we used was to take the battery out, clean it off, put it back. Digital readout was fine.

My question is: How long should the battery last?

Lee

-- No piece is cut too short. It was meant for a smaller project.

View Sandy's profile

Sandy

137 posts in 2550 days


#8 posted 2330 days ago

Dennis, I’m sorry to be picky, but the presentation of a “mathematical” formula requires something more than merely taking some numbers and going through some operation. In fact, from my understanding of your experiment, you took a Craftsman digital level (“the Craftsman”), having a known 12 inch length, and based on both the Craftsman and the Wixey gauge (NOT “guage”) confirming that your table top was absolutely level (with the Craftsman) you set the Wixey to “0.0”. You then raised one end of the Craftsman, with the Wixey on top of it, until they both read “0.1”. So far, so good.

What you now have is a right triangle with the thickness of the feeler gauges determining one of the legs, and the length (12”) of the Craftsman level being the hypotenuse. As the sin of the angle by which the Craftsman has been raised from the “level” table by the feeler gauge is the ratio of the thickness of the feeler gauge divided by the length of the hypotenuse (12”), you can now mathematically determine the angle. Alternatively, you can raise the end of the Craftsman by inserting feeler gauges until you see a change of “0.1” degree. In that (latter) instance the angle is known, so you can confirm the accuracy of the Wixey gauge, which is what I think you are trying to do.

Based on your numbers and description, it appears that you raised the end of the Craftsman until it and the Wixey went from 0.0 to 0.1. Now, you must realize that the accuracy of all “digital” devices is constrained to show a discrete number. Had you continued to raise the end of the Craftsman until the Wixey read 0.2, you could have then approximated the thickness of the feeler gauges needed for the “true” 0.2 degree reading, as being approximately .010 minus one-half the difference between the thickness of the feeler gauges when the reading changed from 0.1 to 0.2 (Remember, that the accuracy of any scientific reading cannot exceed the number of decimal places available from the actual items used. Therefore, carrying the value of pi out to 100 digits does not improve your accuracy if you only know that your Craftsman is 12.0” long and your Wixey can only measure degrees to the tenth of a degree.). In any case, let’s assume that when you initially zeroed the Wixey it automatically “centered” the “0.0” mid-range (i.e., if you raised the Craftsman in the opposite direction, it would have also taken 11/1000’s to have the Wixey read -0.1). This means that your Wixey reading would not read 0.2 until you got to approximately .031 using feeler gauges, rather than .021, as might be expected. Based on these admitted assumptions, your data appears to indicate that a change of 20 thousandths of an inch in height (.020) would result in a 0.1 degree change over 12 inches.

Now, for the real math. “Wixey” corresponds to the angle displayed, and Feeler is the thickness of the feeler gauges:

sin(Wixey) = Feeler / hypotenuse
sin(0.1 degrees) = Feeler / 12
Feeler = 12 x sin(0.1 degrees)

While we can look up the sin(0.1 degrees) in a trig table, for very small angles the sin of the angle is very close to the size of the angle in radians, a radian being 180/pi degrees, e.g., there are 2 pi radians in 360 degrees, so:

Feeler ~ 12 x (0.1 x pi/180)
Feeler ~ 12 x .314/180
Feeler ~ .0209, or about 21 thousandths per foot (at 0.1 degrees of inclination)

How about doing the experiment again and reporting back both the thickness where the Wixey went to 0.1 from 0.0 and the thickness where it went from 0.1 to 0.2?

Now, as far as the Wixey goes… I love it…

View Betsy's profile

Betsy

2913 posts in 2521 days


#9 posted 2329 days ago

WOW – all this math and figuring going on. I like my Wixie also, but not enough to spin around all those numbers!

Lee – can’t say how long the battery will last – but my Wixie came with two batteries. I’ve not used the second one yet, but getting two gives me an idea that they are not going to last a long time.

-- Like a bad penny, I keep coming back!

View naomi's profile

naomi

5 posts in 1507 days


#10 posted 1507 days ago

Accroding to the user manual, battery life can last for more than 3,000 hours in continuous using.

How about thinking from other sides, like: It’s very thoughtful of the manufacturer to offer bonus battery. Or save me the trouble to buy another battery, etc…

-- Advanced Angle Accuracy----CE, ROHS,PAHS----www.gemred.com

View naomi's profile

naomi

5 posts in 1507 days


#11 posted 1507 days ago

and Dennis, I have to say you are really good at math, and I like you professional !

-- Advanced Angle Accuracy----CE, ROHS,PAHS----www.gemred.com

View Jim Jakosh's profile

Jim Jakosh

11285 posts in 1731 days


#12 posted 855 days ago

.010 is too much if you are fitting tapers, then you want to be in the ten thousandts. But for woodworking, no one will ever see .010 . The wixie is invaluable in the wood shop or in the milling machine for setting up angles accurately.

-- Jim Jakosh.....Practical Wood Products...........Learn something new every day!! Variety is the Spice of Life!!

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