# Understanding Errors in Miter Joints

3956 Views 19 Replies 10 Participants Last post by  JFPNCM
I personally like the looks of a well crafted miter joint. OK purists, I know that there are stronger joints but in my case, I use them where they are strong enough for the intended purpose. In order to produce an appealing miter joint, one needs to understand the relationship between the error in cutting a 45 degree with your favorite tool and the resulting gap in the assembled miter joint. In reality, one might decide what kind of gap is acceptable (1/64", 1/32", ...) and then ask how accurately must my tool be set up to achieve that gap. The attached document presents the equations that relate the gap error and the angle error. For the math challenged, you can still use the equations that are given without understanding the gory details.

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Makes sense to me.
Herb
Solution to miter gap errors.

-Take the time to perfect the setup of your table saw. Blade parallel to the miter slot as close as you can get it and don't quit until it is almost zero. Sometimes the blade isn't really quite flat, in chich case, use a blade stiffener.
-Switch to a full kerf blade, thin kerf deflects during the cut because you are pressing it at a 45 degree angle. My favorite is the Freud Glueline Rip blade.
-Make sure the blade is EXACTLY 90 to the table and that your zero clearance insert is the same height as the table all the way around. Sometimes sawdust builds up under an edge of the insert and raises it.
-When setting up a jig or miter gauge, make sure it is 90 to the blade. Not 89.97.
-Lock the blade height and recheck the tilt (far right side on most saws). If it moves when you lock it, reset it until it is exactly 90. Get a Wixey digital angle gauge.
-Forget using a cheap miter gauge. Incra makes some very accurate ones. Fit the miter bar so it does not move at all side to side, but still slides easily in the slot. -Then recheck the gauge is still parallel to the blade. Some saws shift slightly when you lock down the adjustment
-Move the fence out of the way.
-Put self adhesive sandpaper on the face of a very flat piece of hardwood as your sacrifical fence. About 80-100 grit.
-Get some accurate corner clamps or a band style clamp.
-Trial fit first.
-Get an engneer's square, a good one, or a really nice draftsman's square (Rockler makes a nice one).
-Glue up and assemble, band clamp and double check the corners are SQUARE. If not you probably didn't check the dry fit well enough. You can make slight adjustments.
-Get some Timber Mate wood filler to fill in the inevitable tiny gaps.

I added anothe step. My wife bought me a Lyon (type) miter trimmer, which is like a horizontal gillotine that cuts a very precise 45 degree edge. Trim off about 1/16th to 1/32nd inch only. You can also cut perfect 90 degree joints with it, Cut almost to length, but leave double what you want to trim off. My trimmer came from Grizzly through Amazon. The blades will slice your finger off if you try to lift the trimmer through where the blade slices. It has a handle on top. Use that. Mine is mounted on a sheet of plywood and I bought the long arms with stop block for bigger frames..

Put it together as described and get out the Timber Mate, because nothing and no one is perfect. The Timber Mate comes in many finishes. Rub it into the gap with your fingers, sand and finish the frame. I most often use a semigloss or gloss wipe on poly.

If you want to make sanding easier, get a set of sanding blocks (Rockler) and use 3M's flexible sanding medium. The 3M is far better than paper for this purpose, so I prefer it. I go up to 220 grit, tried 320 but it didn't do any better. If you're a glutton for punishment or a perfectionist, use a curved scraper.

Here's a bunch of pictures, you can tell which is which.

1 commercial frame clamp
3 Miter gauge, higest precision
4 Wixey digital angle gauge
5 Shaped sanding blocks for curves and coves (set)
6 3M flexible sanding medium Wonderful stuff, get it!
7 Lyon type miter trimmer worth it if you make many frames,
Every frame shop has either this or a more comples model
8 Sharp angle flat shaped sanding block (set)
9 Timber Mate, best filler I've ever used. Available in many wood varieties, Amazon

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Makes sense to me.
Herb
me too..
Sure does.

Don't get me wrong knowing the math helps understand the issue and that's important. But visual aids go a long way in clearing up ant misunderstanding. That and having a tool that will allow you to correct the problem. One of the reason I bought the Incra Miter Gauge 1000 with fence is the ability to make very small corrections and the adjustable miter slot rods. Having no wiggle in the miter slot is also important and to be able to make easily adjustable corrections if needed to the gauge even more so. This
explains it very well.
Nice writeup, Ben...

Your summary statement (last line) says it all...
For anyone trying to work through the math the final equation of alpha= 90h/square root 2 pi w it looks like that might read as the square root of 2pi but it's actually the square root of 2 times pi times w.
for anyone trying to work through the math the final equation of alpha= 90h/square root 2 pi w it looks like that might read as the square root of 2pi but it's actually the square root of 2 times pi times w.
√2(3.14)w ????
Thats why I became a carpenter ,threw away the calculus book and bought a framing square.
Just saying.
Herb
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Thats why I became a carpenter ,threw away the calculus book and bought a framing square.
Just saying.
Herb
Good plan Herb. And don't forget the ever handy Tri Square or as we referred to it, that there device with which you TRY to make things square. 😳
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Thats why I became a carpenter ,threw away the calculus book and bought a framing square.
Just saying.
Herb

Nothing like a good framing square and a sharp pencil...and, of course, carefully aligned tools...

I think the message in Ben's writeup is "make sure your tools are aligned and you won't have to resort to scientific calculators, formulas and tricky tables".

"Pie are round, corn bread are square"...:grin:
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I am a simple minded guy, and when things don't fit I make them fit. A good experience for woodworkers is to trim out a house some time......You will find that nothing is absolutely square or plumb. So you make it fit. One of the handiest concepts of carpentry is BISECTING the angle. It can make things fit and never be noticed as not square. They even make tools to lay it out, or just a compass will work too. So if you are dealing with angle that in not perfect you bisect the intersection and the joint will fit perfect. At least that is what I am told.
HErb

https://mathopenref.com/constbisectangle.html

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Nothing like a good framing square and a sharp pencil...and, of course, carefully aligned tools...

I think the message in Ben's writeup is "make sure your tools are aligned and you won't have to resort to scientific calculators, formulas and tricky tables".

"Pie are round, corn bread are square"...:grin:
The point I wish to make is that dealing wood is not an exact science. There are so many factors that even with the most precise machines, milling does not come out perfect. Except maybe for CNC.
Herb
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We used to call those 'Painter fixes', as in, he's the last one to work on it, let him fix it...
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√2(3.14)w ????
It could be written as that but still could be confused as meaning the square root of all those factors rather than just the square root of two times those factors. I would put a space between 2 and pi I think to show that they are separate functions.
It could be written as that but still could be confused as meaning the square root of all those factors rather than just the square root of two times those factors. I would put a space between 2 and pi I think to show that they are separate functions.
√2(3.14) (w)

more gooder????
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I am a simple minded guy, and when things don't fit I make them fit. A good experience for woodworkers is to trim out a house some time......You will find that nothing is absolutely square or plumb. So you make it fit. One of the handiest concepts of carpentry is BISECTING the angle. It can make things fit and never be noticed as not square. They even make tools to lay it out, or just a compass will work too. So if you are dealing with angle that in not perfect you bisect the intersection and the joint will fit perfect. At least that is what I am told.
HErb

https://mathopenref.com/constbisectangle.html
The name that I've seen for that tool is goniometer. It's true that any corner, inside or outside, in a house may not be square. Depending on the builder that could also read probably not square. In that case the proper miter angle would be the total/2 as in 44 and 44 or 46 and 46.
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I trust jigs to make my work consistent and controlled - see my recent post on a miter jig for making boxes, cases, etc. on a small scale for clocks and such:

https://www.routerforums.com/tools-woodworking/143027-mitered-corners-jig.html

For frames and the like, a jig that compensated for blade error is what I look for as tools and blades change over time. Once tested, not worrying about technique but concentrating on the project at hand is where I return to the bliss we all desire in working with wood, Just sayin’...
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Tom: You have a lot of good information in your post. I suggest you start a new thread with that post; as it is, you contribution may get lost when someone searches for miters. I am sure there are other people that have suggestions on how to produce good miters.
We used to call those 'Painter fixes', as in, he's the last one to work on it, let him fix it...
Don't rule out the importance of 1/4" putty. 😁
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