Making a 70.6 cut on miter saw

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On 2/19/10 1:57 PM, J. Clarke wrote:

Did you look at the picture? :-)
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-MIKE- wrote:

Did you read the manual?
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On 2/19/2010 11:09 PM, J. Clarke wrote:

Apparently not...

J., you seem to be referring to the picture of the Incra miter gauge that Leon posted; Mike is referring to the picture of the Biesemeyer fence that I posted, which (if you note the quoting above, none of which I've snipped) is what this branch of the thread is about.
There, I fixed it. :-)
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wrote:

That's what YOU think!
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To everyone on this thread, here's a trigonometry lesson, and for something like this, it is really, really all you need to know.
Who here has ever built a set of stairs, or put up a roof? It's all about the RISE and the RUN, right? The RISE is the vertical distance between the tops of two steps, the RUN is the horizontal distance between the noses of the steps. Or for a shed roof, the RISE is the height of the peak above the low side of the span, and the RUN is the width of the span.
Well the RISE divided by the RUN is what's called the tangent of the angle.
We're starting with an angle that we want on the edge of a board: 70.6. A little thought tells us that to get that on a table saw we need to set our miter gauge at 90 degrees minus 70.6, or 19.4 degrees. That's the angle we need between the miter gauge bar and the face of the gauge. When we put a piece of wood against the miter gauge face and run it through, we'll leave an edge on the board that has an angle of 70.6 degrees with respect to the side that rested against the miter gauge.
Now, we all have PC's right? And they all have a little application called the Calculator. Or we have a hand calculator and if it's a scientific calculator it has a TAN button on it. If it doesn't, fire up your PC.
Start up Calculator, or use your scientific calculator, and type in 19.4, then hit the TAN button. What you'll see is the tangent of 19.4 degrees: 0.3521555 plus a whole bunch of other digits. Now here's the deal: if you think of that in inches, it's the RISE over a RUN of one inch. For each horizontal inch, the line rises about 11/32 inches or a little more. For ten inches of run, it rises 3.521555 inches or about 3 17/32 inches.
Now take a piece of scrap plywood, about 24 inches by 24 inches, with one good straight side. At about the middle of the best side, strike a line across it with your most accurate square - and it should be an accurate one - using a sharp hard-lead pencil or a striking knife. Since we have a 24-inch piece of plywood, let's use most of it: measure up that line exactly 20 inches and strike a mark across it. That 20 inches is going to be our RUN.
With me so far? Now to use the tangent: Multiply the RISE over one inch (0.3521555...) by the RUN (20 inches), and you get 7.0431118... inches. In fractional inches, that's damned close to seven inches plus a 32nd and a half, or 3/64ths. At my age, they might as well not put 64ths on scales any more, so I'd do a 32nd and a half, as best as I could judge it.
Measure that distance to the right from the perpendicular line and strike it on the good edge of the panel.
Finally, draw an angled line between that point and that 20-inch cross-mark you made on the vertical line.
There it is. A line that describes an angle of 70.6 degrees with respect to your good straight edge.
Finally the rubber hits the road: take your miter gauge and turn it over and lay it down on the panel. Swing the bar until it lies along that angled line as closely as your eye can gauge it. Tighten down the screw.
But wait, you might say, what if I'm a little off with my measurements - what angle would I get instead? Well, as the calculator tells us with a little keypunching, if you were to use 7 1/32 instead of 7 3/64 (a 64th short), you'd get 70.63 degrees; if you were to use 7 1/16 (a 64th long) you'd get 70.55 degrees, and in either case we're out no more than 1/64 inch over a board width of 20 inches. Unfortunately our OP didn't tell us how wide his board needed to be, but it's probably nowhere near this wide. At ten inches of width, it turns out, it'll be no more than a thousandth of an inch off.
So put the miter gauge in the table saw and make your cut. Then offer the piece up to see how good your fit is, like we do with every board we've ever cut in our lives. It's going to be perfect, or damned near to it.
And if it's not, what do we do? We reach into our aprons, don't we, and we pull out a block plane and correct the fit by whatever it takes to make the fit air-tight. A 64th of an inch is one and a half thousandths of an inch, remember.
A faster and easier way to do this is to use an accurate protractor, as I've recommended elsewhere in this thread. You'll eyeball the .6 degree on any protractor I've ever seen - even a machinist's protractor- you'll make your cut, and you'll correct the fit with a block plane if you have to. For a reasonably narrow board you'll be damned near perfect. But even then, taking the time to lay it out as I described will get get you closer than the protractor would for a wide board.
Of course, if your miter gauge bar fits loosely in the slot, or there's some spring or flex, no measurement no matter how accurate will give you the results you want. But you need to fix that problem anyway, not just for this one cut.
There it is. I hope this helps a bit. I don't have trig right at my fingertips any more either, even though I've used it a lot in my lifetime, and sometimes I have to bumble around a little to remember what I need to do to solve a problem, but this part of it - the tangent - the rise and the run - is easy to remember and really pays its way.
Hope this helps, Tom Dacon
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On 2/19/2010 1:13 AM, Tom Dacon wrote:

Everything that "you need to know" was posted with Leon's one line post, and my graphic representation of that one line that immediately proceeded it.
Simple, elegant, and with no need for an epic saga.
As Mike says, you doth protest too much ... if you're not a government worker, you missed your calling in life.
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snip

"Typically " an explanation like this is not one of repeated practiced experience, more so a repeat of something published. Those that have done this time and again realize that it is not a complicated feat and that knowing how to place the material on the machine accomplishs correct results in "much" less time than it takes to explain.
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Balderdash, hogwash, nonsense......waitasec...oh...okay.
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Balderdash, hogwash, nonsense......waitasec...oh...okay.
Is that a definite maybe?
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I used to have trouble making up my mind, now I'm not so sure.
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Well, of course it takes much less time to do it than to read about it. I gave a detailed explanation of the process, so that someone using it would have an understanding of what was going on, rather than just following a cookbook. In practice, it takes no more than a minute or two to lay out the angle and set the miter gauge.
I wrote the procedure from my own experience and my own practice in the shop, not from something I read in a book (although I learned trigonometry from a book, of course, back in high school). For most shop requirements, the fixed-stop miter gauges like the Kreg and the Incra and their like do a fine job - quick, accurate, and repeatable. I use one myself. But when they can't do the job, as in the case of the OP, you have to have some other way to handle the problem, and the one I described is both simple and accurate. You just have to read it with an open mind, preferably in the shop where you can try it out and prove to yourself that it works.
By the way, while I didn't mention it in my post, if you have to do an angled cut on a large panel this procedure is almost essential for an accurate cut. In that case, you lay the angle out right on the panel, clamp a straight-edge, and make the cut with a circular saw. Because for long runs the procedure is sensitive to the accuracy of the perpendicular line, I would strike it using the beam compass method, with a modified version of this technique: http://en.wikipedia.org/wiki/Perpendicular, or by the well-known technique of flipping the square and splitting the difference. You could, if you liked, trust the squareness of the panel, but I don't. After you have an accurate perpendicular your accuracy is assured.
Tom
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Actually, ;~) just so we are clear, it takes less time to make the set up and make the cut than simply saying this,
Put your wood on the mitersaw 90 degrees to normal, adjust miter setting to 19.4 degrees and make the cut.
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On 2/19/2010 3:09 PM, Leon wrote:

Or graphically speaking:
Just kidding ... dejavu all over again, I gotta get back to work. :)
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Mutt'n Jeff?
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Leon, maybe you're missing my point. What I have been describing is an accurate method to get the exact 19.4 degrees, not what you do once you get your miter gauge set to it.
Tom
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What you need is a "Precision Universal Bevel Vernier Protractor" http://www.starrett.com/download/371_cat_70_p95.pdf A lot of times you can find these in pawn shops. Set this to the angle and align the saw blade and table to the blades. A model 360 (non vernier) would be very good. Vernier version Is best! New it was $250. Something like it in plastic and lower in precision can be had at office suppliers. This one is rated at 1/12 degree with vernier.
Martin
Tom Dacon wrote:

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You nailed it, Martin. That's the kind of thing I was talking about.
Early on in this benighted thread I talked about using a protractor as a tool to solve a problem which as the original poster posed it was to measure an arbitrary angle to the precision of a tenth of a degree and make a suitable cut. Machinists are accustomed to solving problems like this, and consequently they have the tools to solve them. If a machinist gets an angle called out as 70.6 degrees, he understands that he needs to produce an angle between 70.55 and 70.65 degrees. He HAS to produce an angle to that measurement and those constraints. This is a nice tool, Starrett as you might expect, and well within the constraints of the problem. I have a slightly less accurate machinist's protracter of my own, but I'm going to be on the lookout for one of these. Thanks for the tip. I hope we don't end up in a bidding war :-)
Glad to see someone here who doesn't have something to prove :-)
Tom
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Tom Dacon wrote:

FWIW, Grizzly has a dial protracter readable to 5 minutes for 40 bucks and a digital readable to .1 degree for 90. Not Starrett quality of course but should do most hobbyists just fine.
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On Sat, 20 Feb 2010 00:16:59 -0500, the infamous "J. Clarke"

Aww, who cares, when caulk and putty will fill gaps up to 1/4-inch. <silly grin>
-- "Just think of the tragedy of teaching children not to doubt." -- Clarence Darrow
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scrawled the following:

"Master Carpenter In A Can", eh?
Tom
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