**In
the example above, it would seem like the gap is pretty
big and should be pretty easy to eliminate. But, that
1/8" gap is the result of each cut having only a
very small error. When all the pieces are put together,
the error of each cut accumulates. In an octagon, there
are a total of 16 cuts to be made (two cuts on each of
eight pieces). So, the error in each cut is 1/16 the size
of the gap. **

**Accuracy Required**

**If
the accuracy of miter cuts in measured in terms of
degrees, then the amount of acceptable error depends on
the length and width of each member. Longer joints (from
wider boards) will require higher angular accuracy than
shorter joints. For example, if each joint is 2"
long, then a 1/64" gap results from a total error of
about 0.45 degrees(arc sin (1/64) / 2). For the octagon,
the error in each cut will need to be 0.028 degrees or
less (16 cuts in all). For a 3" joint the total
error goes to about 0.30 degrees and each cut will have
to be accurate to 0.019 degrees. **

**Accuracy Measurements**

**Rather
than determine how long each joint is and convert the gap
width to degrees, it's much easier to measure angular
accuracy in terms of how much gap (or deviation) exists
between the perfect (ideal) angle and the sample being
measured. This is exactly how manufacturers specify the
accuracy of squares and angle blocks. Then it's easy to
predict and measure how accurately each cut must be. For
the example shown in the photo above, the 1/8" gap
is produced by having 1/128" error in each cut (1/8
divided by 16). If 1/64" gap is needed for the
octagon, then each cut must be accurate to 1/1024"
(1/64 divided by 16). In other words, there must be
slightly less than one thousandth of an inch error for
each cut in order to produce an octagonal frame with a
total error of less than 1/64".**

**No
wonder it's so difficult to obtain accurate miters! The
old adage that says working wood to within 1/64" is
"good enough" just doesn't apply to cutting
miters. Such an error would produce a 1/4" gap in
the example above! Even a simple four sided frame would
end up with a 1/8" gap.**

**Method for Success**

**How
is it done? There are basically three methods you can use
to achieve accurate miters. But, before you launch into
one of them you need to know about possible sources of
error and how to avoid them. Please read ****External
Influences on the Accuracy of Results**** in the ****Technical
Documentation****
Section of the web site.**

**1.
Simple Trial and Error**

**Just
like it sounds, you give it a try and see what happens.
For the octagon, it means cutting all eight pieces and
seeing how they fit. You make an adjustment to your
machine based on examination of the results and try again.
Given enough time, patience, and scrap wood, it's
actually possible to obtain good results with this
method. But the word "simple" is a bit
misleading. This is definitely a very difficult task.
You'll be called upon to judge the gap and determine how
much adjustment is necessary. In the end, you'll be
trying to make adjustments to within thousandths of an
inch and these are extremely difficult to do by eye. Most
people who use this method generally settle for a larger
gap than they originally wanted and resort to methods for
hiding that error (like trying to even it out among all
the joints). Many just give up and avoid miters
altogether.**

**2.
Trial and Error with Accurate Measurement**

**If
you could accurately measure the results of a test cut,
then you can save yourself a lot of time and scrap wood.
Precise adjustments to your machine will still require
significant judgment. And, devices that can measure
angles this accurately are fairly expensive. The common
protractors available from woodworking dealers is
completely inadequate. The typical machinists protractor
graduated to five minutes of arc generally starts at
about $140. The big advantage of this method is that you
avoid the need to cut out all the parts for every trial.
Another advantage comes from knowing exactly what your
machine setting produces. When you measure the result
directly, there's no question about what to expect.**

**3.
Accurate Machine Setup**

**In
order to avoid test cuts altogether, you have to know
what your machine setting will produce before the first
cut is made. To do this your machine must be carefully
aligned. You must also be able to make accurate
measurements of the machine settings. This is the
approach that machinists use to produce reliable and
repeatable results. Generally their machines come
equipped with accurate measurement devices.
Unfortunately, the adjustments on most woodworking
machines are very crude by comparison. So, an accurate
alignment/setup tool is needed so that machine settings
can be accurately measured and adjusted. Such a tool
generally starts at about $70. A growing number of
woodworkers are coming to appreciate this approach and
many manufacturers are now producing aftermarket
accessories that help facilitate it. This is the method
that I advocate.**

##### Last revised:
January 21, 2006.