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

Feel free to ask questions.

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

## 15 comments so far

wunderaa

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246 posts in 1741 days

#1 posted 12-10-2012 03:09 PM

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!

Mauricio

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7115 posts in 2690 days

#2 posted 12-10-2012 04:32 PM

Great information Jim!

-- Mauricio - Woodstock, GA - "Confusion is the Womb of Learning, with utter conviction being it's Tomb" Prof. T.O. Nitsch

Boatman53

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1016 posts in 1735 days

#3 posted 12-10-2012 04:42 PM

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.

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

jap

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1251 posts in 1593 days

#4 posted 12-10-2012 04:47 PM

thanks, favorited

-- Joel

Sylvain

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645 posts in 2038 days

#5 posted 12-10-2012 09:33 PM

Excellent

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

Boatman53

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1016 posts in 1735 days

#6 posted 12-10-2012 10:38 PM

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

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

TopamaxSurvivor

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17817 posts in 3214 days

#7 posted 12-11-2012 12:35 AM

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 ;-)

-- Bob in WW ~ "some old things are lovely, warm still with life ... of the forgotten men who made them." - D.H. Lawrence

socrbent

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436 posts in 1808 days

#8 posted 12-11-2012 05:15 AM

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.

-- socrbent Ohio

Boatman53

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#9 posted 12-11-2012 12:40 PM

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

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

waho6o9

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7408 posts in 2115 days

#10 posted 12-11-2012 01:06 PM

“If it is needed I could build another sine bar on a forum and show step by step construction. I just donâ€™t know what forum it should be on.”

This would be awesome Jim, maybe blog it?

Thank you.

Sylvain

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645 posts in 2038 days

#11 posted 12-11-2012 07:37 PM

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 …

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

Eddie_T

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195 posts in 1610 days

#12 posted 10-10-2013 04:47 PM

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.

Boatman53

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1016 posts in 1735 days

#13 posted 10-11-2013 02:09 AM

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

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

Eddie_T

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195 posts in 1610 days

#14 posted 10-11-2013 04:11 PM

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

Boatman53

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1016 posts in 1735 days

#15 posted 10-11-2013 11:39 PM

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

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

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