# Setting precision angles



## Boatman53 (May 21, 2012)

*The bevel board*

I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds. 
But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.










Start with a square of plywood 32"x32" not much smaller than that. Leave a margin all around and draw a square 30"x30" . Check diagonals and the lengths of the four lines. When you are sure it is square, starting from the lower left hand corner I made a grid of 6" squares I think but they could be any spacing you want accuracy is more important than whether you use 4", 6" or just one at 15". Next you will need to draw an arc with a radius of 28 5/8" or 28.625" if you have decimal measuring tools.










Draw that radius from horizontal to vertical. Every 1/2" measured along that radius is equal to 1 degree. What I did next was layout 10 degrees, measure that distance with dividers and then walk the dividers to the vertical line and see how close I came. Once I had the radius divided into 9 equal spaces they were divided in half and then all the 1 degree marks are added. And of course every 1/8" along the arc is 1/4 of a degree. I never felt it was necessary it add that till I needed it.










I often thought that a vertical and horizontal dado for a miter gauge bar would be handy for setting the miter gauge,but I never did it. 
Hopefully this information is useful to someone and feel free to ask questions if you have them. This is just the first installment on the different ways I handle angles and bevels.


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## DIYaholic (Jan 28, 2011)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Thanks for taking the time to share this!

I can see this being very useful.

I was born & raised on Long Island, Bay Shore to be precise. Family still live there, they're in Brookhaven Hamlet & Mastic Beach now.

Again, thanks for sharing!!!


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## shipwright (Sep 27, 2010)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Good post Jim. 
It's so nice to see you and Eric getting some boat building blogs going.
Keep up the fine work.


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## TopamaxSurvivor (May 2, 2008)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


I'm sure this will help a lot of Ljs. Thanks


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## Dal300 (Aug 4, 2011)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Thanks Jim!

I used one of these when I was repairing and converting over the road buses into motor homes.

Although not as extreme as boats, the angles and curves in a bus are not constant from front to back or even from port to starboard.
Floor levels don't stay the same and roof curve angles change within a foot. Even ceiling heights change from front to rear.
As for finding the exact center of the coach, it can be a real guessing game because the sides aren't straight up and down, they bow out at just below the windows.

Think about that the next time you all see a Trailways or Greyhound going down the road….. they aren't just big boxes on wheels, they have more curves than a the drunk blonde at the office party!


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## dusty2 (Jan 4, 2009)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


I took a shot at remodeling an Airstream travel trailer. I had some really bold ideas about how much better I could do it than did Airstream. Was I ever wrong. The constantly changing curves on the inside of that Airstream got the best of me. I don't think there was a straight line anywhere.

I finished and used the remodel for years but I was never proud of what I had accomplished.


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Thanks for the comments all.
DIY… How did your family fair with Sandy?
Dusty… I too have thought about putting a nautical interior in an Airstream, maybe some day.


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## Dal300 (Aug 4, 2011)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Dusty, I have done a couple of antique Airstreams, one a 1958 and the other a 1971. I had such a good time doing them, especially the interior front and rear corners where the roof panels are cut into rays to come down and meet the walls.


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## mochoa (Oct 9, 2009)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Looks pretty cool Jim. Thanks for sharing the knowledge. Will you show how to use it?


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


The simplest way to use it is just to lay your miter or bevel gauge on the board and adjust to the lines. The other use of finding the bevels form a lofting (the full size drawing of a boat) would require some knowledge of lofting. I'll try if someone really would like me to however.
Mauricio… How did you lay out the angles for your splayed legs on your work bench? Would something like this have helped do you think? 
Jim


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## mochoa (Oct 9, 2009)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Hi Jim, yeah i had a little protractor thingy that I used to make a line on a piece of scrap and then set my bevel guage to that. So yeah, now that I think about it this thing would have come in handy!


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## Sylvain (Jul 23, 2011)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Excellent idea.

For those of us working with the metric system,
if we want 1cm per degree,
it gives R=90 cm/(Pi/2)
or R=180/3.14159…. =57.2958…. , let us say 57.3 cm

By the way, if you replace "cm" by any convenient measure, it is still valid


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## Brit (Aug 14, 2010)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Thanks for a very informative post Jim. One for the favourites.


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Thanks Syllvain for doing the metric math you are correct on all accounts. I'm stll surprised by the world wide audience of the different forums. Thanks again for giving the metric equivalent.

Mauricio… Fortunately you used your little protractor just once to mark that scrap and then after refered to the scrap so at least you had some consistency. And whether or not you were even a half a degree off on you project it was of little consequence as long as they were all the same.

The third installment is geared more toward hand tool use. So hang in there.


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## mochoa (Oct 9, 2009)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Good, I look forward to the hand tool portion of the program, mostly because I could never get my crappy power tools to achieve that kind of precision.


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## BigTiny (Jun 29, 2010)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Thanks for sharing. One more for the favorites list.

Paul


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## BillNel (Jan 11, 2011)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Note there is an easy check here. As Sylvain stated:

it gives R=90 cm/(Pi/2)
or R=180/3.14159…. =57.2958…. , let us say 57.3 cm

The unit of measure is immaterial, so substitute feet. Sylvain's is for one unit per degree while Jim's is for 1/2 unit per degree. So Sylvain's length will be double Jim's.

2×28 5/8" = 57.25 " - close enough that it would be hard to measure the difference.

Also note that the measurements should be along the arc, not a straight line measurement. But since Jim's length is slightly undersized, the straight line cord might work out fine. Sylvain's would be slightly long if using cords instead of arc segments.


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## Eddie_T (Sep 23, 2012)

Boatman53 said:


> *The bevel board*
> 
> I often read posts from people having trouble setting angles on machines or wherever. So I thought I'd share what I've learned over the last thirty years, and I realized I've been using, thinking and in some cases obsessing about angles for a long time. My first career was a land surveyor, and obviously that was nothing if not angles and distances, down to degrees, minutes and seconds.
> But I moved on from surveying to wooden boat building in 1982 and have been doing that ever since. Boats are an amazing combination of angles and bevels constantly changing from one end to the next. Of course a sliding bevel gauge is a primary tool but if you don't have a way to set a particular angle all you can do is compare and transfer. So the first thing I made was a bevel board. It's drawn on about a 32" square of plywood. It's not difficult to make but just a bit tedious. It doesn't wear out so if you make one take your time and accuracy is paramount. As a boatbuilder I would use it to make a bevel stick to quickly find bevels on a lofting so frame bevels could be cut on the bench instead of trial and error once the frames are set up as I have often seen in some shops (professional shops in more than one case). Here is how I made mine. It's very useful even if you don't build boats.
> ...


Using the sine half angle calculation I get r=28.648 for a 0.5" chord per degree, or 26 5/8" to the closest eighth. I just think measuring along the curve would be a bit of a challenge at 1/2" increments.


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## Boatman53 (May 21, 2012)

*The Sine Bar*

The sine bar










The next leap for me in setting angles precisely was the rediscovery of the sine bar. My father was a tool and die maker and although I never worked in his shop I did become familiar with the tools of the trade. The only sine bar I had seen however was 3" long.
Then Fine Woodworking ran an article in the July/August 1992 issue called Simple Instrument Sets Precise Angles by Tom Rose. In it he described how to make a 10" sine bar and use it to set a miter gauge. Ahhhh I was off on my obsession again. I knew it's application in toolmaking and now I could see it's value in woodworking. It was an epiphany and I realized a lot of many trades could easily cross over to other trades.
However before I was able to make one of my own the next issue of FWW came out and a couple of letters lambasted the author about his ability and the instructions to construct a perfect 10" sine bar and the needed gauge blocks of exact length. My enthusiasm wained. I still thought it was a wonderful tool and wanted one and continued to think about it. I was after all still happy with the bevel board.
Eventually I bought into the Festool line for their precision and portability and loved the work table the MFT. But to me it was just a work table till I joined the FOG forum and read about people doing things I never imagined. One post commented that the hole pattern in the top was in fact a very precise grid system and could be used to align the fence and the saw rail to 90degrees precisely and repeatably. As good as Festool is the miter head for the table, like most included miter gauges was not very good. The sine bar would be my after market miter gauge. I built a couple and the best one I made was .001" off from ten inches. But here is what should have been stressed in the article and I didn't understand till later was the fact that it doesn't matter what the length is as long as it is known. If I was real sloppy and had made the bar 9.834" it will still work perfectly because the sine of the angle is multiplied by the length of the bar. Ten inches just makes the math easy, just move the decimal one place. The angular error ignoring the difference from 10" was insignificant for angles under about 35 degrees, so it was put to use as needed. If I needed 45 degrees on the MFT I used the hole grid pattern, it I knew was perfect. I used a different method for cutting my gauge blocks than the article which I will describe. It alone is useful if you need to cut a piece exactly like another that already exists. I do agree that the method described in the article for the gauge blocks is flawed and not accurate enough.

These are the tools needed. The wooden bar is the sine bar, scientific calculator and calipers. I bought the 12" version from Grizzly and they can handle all the measurements needed. 6" calipers would work if you already have them, it just requires an extra gauge block.










To drill the two holes for the round discs I set up a fence on the drill press with a stop block. One hole was drilled, then the calipers were set for 10" and placed against the stop block to index the sine bar over for the next hole. The profile was then cut on the one side to give it the proper clearance. The discs were then epoxied in what remained of the holes. When that was cured the discs were run against the table saw fence and the top was cut parallel to the discs. On this one the discs are 3/4" aluminum rod. Very easy to sand flush to the wood surface. Before the discs are sanded flush I measured them with the calipers to find out how close I came. That number will be used if it is not real close to 10".

This photo shows it in use.









Now to calculate the block of wood labeled 26degrees and cut it exactly.
For this example 26 was entered in the calculator and the sin button was pressed the answer is .438… Since the sine bar is ten inches that answer is multiplied by ten (or the actual length of the sine bar). This is easy just slide the decimal over and set that length on the calipers. If this is just a one time odd angle you need to cut you can use the calipers the set the sine bar as in this photo.










But chances are you might want to cut that angle again so let's make a permanent reference block. Using the miter gauge with a stop block set the block to be several inches longer than the 4+ inches needed and lock it down.










Use the calipers as shown against the stop block to space off a scrap of wood then cut that piece of wood.

Then remove the calipers and slide the small piece of wood you just cut over to the stop block and insert another piece of wood to cut.










You now have a piece of wood the exact same length as the caliper setting because they both occupied the same space at one time.










You now have an accurate and infinitely repeatable reference. This can also be used to set a bevel gauge to set the tilt of the blade also.
If any one is interested in reading how I use this on the MFT they can read my post and discussion on the FOG

http://festoolownersgroup.com/festool-jigs-tool-enhancements/precision-angle-setting/msg195201/#msg195201

Feel free to ask questions.


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## wunderaa (May 15, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Excellent discussion. There have been several great threads lately about accurate measurements, and like the others, I plan to explore this more. Thanks for sharing!


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## mochoa (Oct 9, 2009)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Great information Jim!


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


If it is needed I could build another sine bar on a forum and show step by step construction. I just don't know what forum it should be on.


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## jap (Oct 10, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


thanks, favorited


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## Sylvain (Jul 23, 2011)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Excellent


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Sylvain.. And others you might have figured out that it doesn't matter the length or the unit on this tool. It could be made to 25 cm and the sine constant would then be multiplied by 25 the result is the length of the gauge block in that unit, cm. 
I hope people don't fret over the math as it is only one multiplication. The sine is a constant and if you don't have a scientific calculator (they can be had for around 15$) I have an app on my phone I think it was free or a couple bucks. But they are also published in a lot of reference books and workshop guides and handbooks.
Jim


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## TopamaxSurvivor (May 2, 2008)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Nice discussion. I use trig functions all the time for various things. Never thought of using them in the shop to check angles on the table saw ;-)


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## socrbent (Mar 9, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


As a retired high school math teacher, I really appreciate the elegant simplicity of this device much like a great mathematical proof. QED seems appropriate.
Gene

*QED - An abbreviation of the Latin phrase "quod erat demonstrandum". It literally translates as "which was to be demonstrated", and is a formal way of ending a mathematical, logical or physical proof. It's purpose is to alert the reader that the immediately previous statement, which naturally was arrived at by an unbroken chain of logic, was the original statement that we were trying to prove.


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Thanks for the comments topomax and socrdent. Yes I hated math in high school. How am I going to use that stuff in my life. Once I starred land surveying in college I was hooked, and loved it. 
In part three in this series uses more math, still just a constant and one multiplication and you can accurately set a bevel gauge with a common tool you most likely have in your shop already. I just "discovered" this method over the summer.
Jim


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## waho6o9 (May 6, 2011)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


"If it is needed I could build another sine bar on a forum and show step by step construction. I just don't know what forum it should be on."

This would be awesome Jim, maybe blog it?

Thank you.


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## Sylvain (Jul 23, 2011)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Everybody with a PC with windows has a scientific calculator.
(I don't know for mac and linux)

In the start menu search for accessories (I am not sure but in theFrench version it is "accessoires") 
In "display" You can choose between
simple calculator (+-/*)
scientific
programmer (octal hexadecimal binnary etc)
statistics

and others …


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## Eddie_T (Sep 23, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...












Your method of using of calipers to cut a precise block is neat, and has many other practical applications. Tom Rose (in the FW article) cut blocks a bit long then used an appropriate feeler gauge as an offset for the final cut. Either way beats my method of cutting proud then using skinning cuts hoping for success.

Sine bars don't have to be pretty. Not having a proper bit for drilling precisely located 3/4" holes I glued a dowel section to some end blocks and a backing piece so I could run it across the jointer a few passes to get a flat side. Next I cut two sections and glued the flats to a piece of straight wood at 10" spacing.


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Thanks Eddie for your input. You are right you don't have to set the dowels in a drilled hole and what you made is perfectly useable. I hadn't looked at this blog in a while and was surprised how many views it has gotten.
Jim


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## Eddie_T (Sep 23, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


I am a retired engineer and love articles from which I can learn a new technique, or a new application of something I am familiar with but just didn't think of. Your post and the FW article got me to rethinking trig. If If had anything other than a 3/4" spade bit I think I could have done well with drilling and spacing. Since I didn't I kept pondering for another way. I considered the notched ends as shown for machinist's sine bars but felt that they didn't give enough glue surface to attach the dowels. The letter I saw lambasting Tom Rose's FW article offered a neat way to make an angle gauge with equally spaced pins, he could better have just offered it as his alternate instead of lambasting Tom. Both you and Tom spent quite a bit of time documenting and illustrating the application as well as presenting beautiful tools you can be proud of.

Your bevel board is in my future as well for RAS miter use. I found myself searching online for a PDF protractor rather than using my noggin and knowledge of trig.

Thanks, Ed


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The Sine Bar*
> 
> The sine bar
> 
> ...


Hi Ed, yes I agree that guy hit Tom pretty hard about how difficult it would be to drill those holes exactly 10" etc. That article and subsequent letter stewed around in my head for about 15 years but I couldn't let it go. I definitely was stopped by what I perceived as precision. (I'm not a machinist, my father was, I just pretend) I was studying my dads 3" and 5" sine bars when it hit me, it doesn't matter what the length is as long as you know it. 10" just makes the math easy, you just move the decimal point. It could be 9.865" then that becomes the multiplyer. More difficult but I've got a calculator on my phone so if that is what it is you just write it on the bar. It's too bad Tom wasn't able to explain about the "correction" if ten inches wasn't achieved. I would have made one the next day, and I bet others would have too. That's partly my motivation to post this.
On another note I see you make miniatures. Did you ever see the magazine Scale Woodcraft? It only lasted two years before it folded but I liked it a lot. That was in the late 80's. 
Later, Jim


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## Boatman53 (May 21, 2012)

*The framing square*

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


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## ksSlim (Jun 27, 2010)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


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.


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## macatlin1 (May 5, 2010)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


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


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## jap (Oct 10, 2012)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


awesome idea


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## Sylvain (Jul 23, 2011)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


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.


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## DanKrager (Apr 13, 2012)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


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


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## dontrushme (Jul 23, 2012)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


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.


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


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.


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## Brit (Aug 14, 2010)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


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


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## Islandwoodworker (Mar 24, 2008)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


In the paragraph where you say one setting gives 10, 80 & 100 degrees I think you ment t o say 10, 80, and 90. Just a typo but it might confuse someone new to this. Excellent explanation ( remember that the square is always 90 degrees unless it's out of wack: like you said "adjust it or replace it"


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## Boatman53 (May 21, 2012)

Boatman53 said:


> *The framing square*
> 
> The framing square
> 
> ...


Thanks for your comment but the pics shown above have the bevel square at ten degrees in the first, 100° in the second and 80° in the third. And of course the square itself is 90°. 
Does that help?
Jim


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