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Setting precision angles #3: The framing square

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Blog entry by Boatman53 posted 12-21-2012 05:05 AM 5311 reads 9 times favorited 8 comments Add to Favorites Watch
« Part 2: The Sine Bar Part 3 of Setting precision angles series no next part

The framing square

The bevel board and the sine bar, as good as they are, have one drawback, lack of portability. One was big and the other is a bit awkward to set a bevel gauge. Enter these little tools.

I used them for many years they are good, two of them being Starretts,but they are too small to offer any real accuracy. The scale is only two inches from the pivot and the width of the index lines is almost equal to 1/4 degree. The late Dan Sutherland, a boatbuilder, produced a stainless steel “bevel board”. It is still available from some tool dealers but at the moment I can’t remember which. On gnarlyeriks post he had a link to print a paper one which could be handy. But I was still on the hunt.
This summer I purchased a stainless steel framing square from this company 

http://chappellsquare.com/

I was impressed with the quality and since it is guaranteed square I bought one. Stainless it wouldn’t rust and more durable than the two aluminum ones I used up. I don’t do any framing so all those fancy tables are wasted on me. Plus the size I got was smaller and more handy for me, 12”x18”. The one thing different than any other framing square is the scales are laid out in 20 parts to the inch. No 8’s, 16’s or 32’s. I figured I could get used to it, besides I was going to use it as a big accurate square and some layout, but that was about it. For the record I have no affiliation with that company but I do recommend them.
I knew they could be used to layout angles, framers do it all the time, I just couldn’t figure out a simple way to do it. Thinking of angles in rise over run didn’t work for me when I wanted to find say 26 degrees. My 1923 copy of Audel’s Carpenters and Builders Guide had a chart that listed all the angles from 1 through 45 and the corresponding numbers on the blade and tongue to lay it out. Beautiful I thought but there was no commonality to the numbers. As an example, a 10 degree angle is 3.47” on the tongue and 19.7” on the blade, a 26 degree angle is 8.77” on the tongue and 17.98” on the blade. Nice, but at the time I had a square that had fractional divisions not decimals, there was no rhyme or reason to the list and I wasn’t going to carry that old book around. Then ShopNotes in vol. 19 issue 114 did an article on using a square as a layout tool. This too had a chart with the same confusing layout of numbers but at least these were in fractions, but again I wasn’t interested in carrying around a chart to layout angles.
Then I “found” in one of my book shelves and old 1949 instruction booklet from Stanley for the framing square. As I was looking throughout it on almost the last page I found this.

It is a layout guide for polygon miters. Eureka it was organized and and I saw my original bevel board in the same picture. All angles started at the 12” mark.
Back to my new square and here comes the math. I wanted something I could do easily and now I knew it would be accurate. The sine bar works with a fixed hypotenuse, but this was going to work with a fixed base. So instead of using the sine function I would need the tangent function. Again it is a constant, you do not need to calculate it just look it up in a book or on a calculator, it is the button labeled “tan”. This is where this works great with my new square. The inner scale on the tongue is 10” long, perfect all I need to do is shift the decimal one place. It works nice using the end of the tongue because it is self indexing and I only need to look at one number to set an angle. So this is using this info to set a miter gauge. Only the number on the right requires my attention.

Using 26 degrees again, enter 26 in the calculator then press the “tan” button, and 0.4877 should appear. The base distance is ten inches so I just shift the decimal one place to the right and I get this 4.877”. That is the number I need to index on the blade. Remember I said I wasn’t happy about the scales divided in 20 parts to the inch? Wrong I love it. As it turns out one twentieth of an inch is in fact .05” per division. That means it is now possible to estimate to one or two hundredths. Over ten inches that is a very accurate angle.
If you want to set a bevel square this setup gives options no other method does. One setting, in this case 10 degrees, you get 10, 80, and 100 degrees.

!

This photo shows this method for setting an angle on a table saw sled. There is no back fence on this sled. If there was a fence then the sine bar would be better.

I’m using the long body as the base so the tangent is multiplied by 16.5”. The aluminum angle on the left is not attached and is just used to keep that corner aligned with the edge.

This photo shows the number to layout on the right side for 10 degrees.

Here is the math for the photos above. 
The tangent for ten degrees is .17632 and on and on.
Multiply that number by the length of the base in this case 16.5 and the answer is 2.90939 and more. Round that to hundredths and the answer is 2.91 and that is the number I’m showing.

In this photo I’m setting the miter gauge to 45 degrees. The leg at the top is 14” and stops the straight edge. The right side lined up to 14”. The miter head is loose and just slid up to the straight edge and locked down.

If you have a standard framing square with fractional markings you will have to convert the decimals. Plus keep in mind that if your square isn’t square everything will be off. So either true it up or buy a new one, you can’t lay out accurate angles with a square that isn’t square.

You can also use your calipers to set out the distance.

Sorry this got a bit long winded but it did take me 30 years to get here. So if you want to do something just keep at it and don’t give up. This framing square is the most versatile of the three methods but the bevel board and sine bar both still have a place in my shop. Good luck and I hope this opens up new possibilities for projects with angles.
Happy holidays to everyone.
Jim

-- Jim, Long Island, NY Ancorayachtservice.com home of the chain leg vise



8 comments so far

View ksSlim's profile

ksSlim

999 posts in 1612 days


#1 posted 12-21-2012 08:29 AM

Excellent presentation!
I taught technical math and it took some students quite a while to grasp trig principals.
Ratios are easy, many technical fields use radians instead of degrees. Just another math conversion.
Again, one nice job.

-- Sawdust and shavings are therapeutic

View macatlin1's profile

macatlin1

58 posts in 1665 days


#2 posted 12-21-2012 10:07 AM

Great article ! I printed it out and placed a copy with my table saw. Perfect way of setting the miter gauge.

View jap's profile

jap

1237 posts in 776 days


#3 posted 12-21-2012 04:57 PM

awesome idea

-- Joel

View Sylvain's profile

Sylvain

574 posts in 1222 days


#4 posted 12-21-2012 07:53 PM

Boatman53,
I really like to see the diversity in the way to perform a similar function.
I have myself salvaged trigonometric tables from the bin. So I am able to use the method without batteries/electricity.

Slightly off topic.
I guess as a former surveyor and maybe now a yachtman, you might be interested about :
http://www.tecepe.com.br/nav/cdsextantproject.htm

It shows the use of a vernier to enhance accuracy.
It might be used on the bevel board wih the vernier in a circular groove.
The print out of the scales might be used in the shop.
The web site of this Guy, Omar F. Reis, merits a visit.

-- Sylvain, Brussels, Belgium, Europe - The more I learn, the more there is to learn

View Dan Krager's profile

Dan Krager

1687 posts in 956 days


#5 posted 12-22-2012 04:01 PM

Nice tip! I’ve been intrigued with how many uses there are for the humble and underused carpenters square. I’m about to build a fully housed staircase, so will get a chance to put some of this to use. Thanks.

And Merry Christmas!
DanK

-- Dan Krager, Olney IL http://www.kragerwoodworking.weebly.com

View Ralph's profile

Ralph

164 posts in 855 days


#6 posted 12-22-2012 11:40 PM

Sweet.
If I may add…
Since you are using a calculator, you can use it to easily convert decimals to fractions.
In your 10 degree example, you get 2.90939…
If you subtract the integer, 2 in this case, you are left with the decimal 0.90939…
Just multiply it by, say, 64 and you get 58.2… which is the number of 64ths in 0.90939 inches.
Hope I am not way of and that it helps.

-- The greatest risk is not taking one...

View Boatman53's profile

Boatman53

848 posts in 919 days


#7 posted 12-23-2012 04:53 AM

Thanks Sylvain, Ralph and others for your input. I actually had not thought much about converting to fractions so thank you. I loved the link to the sextant project. I do own one as well as a surveyors transit but I always wanted to built an old style sextant out of ebony.
The addition of a vernier to the bevel board sound intriguing. I was starting to build a new bevel board, not that there is anything wrong with it, I just have some improvements I’d like to try. I’m going to put a vernier on the list.

-- Jim, Long Island, NY Ancorayachtservice.com home of the chain leg vise

View Brit's profile

Brit

5284 posts in 1565 days


#8 posted 12-23-2012 12:21 PM

Excellent stuff Jim. Thanks for taking the time to put this together.

-- Andy -- Old Chinese proverb say: If you think something can't be done, don't interrupt man who is doing it.

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