The Science of Inaccuracy
Ever drilled a hole with a bit that was meant to be ‘exactly’ the right size, only to find the hole either too large, or too small?
Ever taken every care measuring the length of board to be cut, and found the result disappointingly long, or worse, too short?
Just how accurate is a ruler?
In the scientific, and particularly the engineering community, every measurement is given a tolerance range (+/- 1mm for example), every tool has a tolerance range, a degree of confidence. There are reasons why this sort of constant monitoring of precision is not translated into woodworking.
For one, it is cumbersome- constantly focusing on accuracy can get in the way of the work. Wood is also rather forgiving- it compresses, there are fillers (and filling techniques), glue can span small gaps, nails can span large ones.
But this doesn’t mean that there is not a lot of benefit to be derived from understanding measuring accuracies, the sources of error and how to control it.
When you are building a house, having a measurement out by 5mm or more is not the end of the world, and the measuring tools used reflect this. If you are making a fine box however, 5mm is an unmitigated disaster. 1mm is a disaster, and is the difference between a fine box, and one made by a 10 year old in a woodshop class at school.
We’ve heard the general rule about not changing what we are using to make the measurements during a project, so as not to introduce an error, but there is an underlying issue there that is glossed over. The accuracy of the device we are using, and while we are at it, let’s ignore the additional errors introduced by thermal expansion.
Any rule, or other measuring device, cheap or expensive has an error. The more you spend, generally the smaller that error is, but it never goes away. Every drill bit, every spanner, bolt, protractor, tape measure, setting block, square. They are all in error. How much they are out, is the difference between whether we can accept the amount of the error or not.
A quality rule, such as one from Woodpeckers are manufactured to be accurate to within +/- 0.025 mm, which for a woodworker’s requirements is pretty good. So if I was to measure the width of a board, does that mean I can be assured that it is (for example) 100mm wide, +/- 0.025mm.
Sorry – not even close! Just because a rule may be manufactured with a high degree of accuracy, it always relies on one other tool – the eyechrometer. (Your eyeball!) The rule for measuring inaccuracy, is you cannot assure an accuracy any better than 1/2 the distance between the two smallest measuring marks. And the error compounds. If I used a normal rule, where the markings do not extend right to the edge, and the rule has markings every mm, then the best I can say is the board is 100mm wide, +/-1.025mm Yuck!
Might explain a few things in the workshop though, when things go wrong.
Take the same example, and let’s ignore the error in the rule itself, and let’s also assume the tablesaw fence is calibrated as accurately as possible (which by definition is +/- the finest measurement shown, so that would typically mean it is accurate +/-0.5mm)
Using a steel rule, which doesn’t have markings extending to the edge, such as this one:
The width of a board is measured as 100mm. The fence on the tablesaw is set to 100mm, and a piece of timber ripped, then laid it on top of the current board, and both stood on edge on the top of the saw. Why are they not the same width? Didn’t I do everything right?
Error has crept in. My original measurement of 100mm is +/- 1mm, so the actual board is somewhere between 99mm and 101mm wide. Let’s say it is actually 101mm. The next board that I rip has been set on the tablesaw, which has its own error of +/-0.5mm, so this board can be anywhere between 99.5mm and 100.5mm.
But wait, not only is the fence out a fraction, the blade itself has some runout which I didn’t know about- happens to be 0.25mm
My cut board can now be anywhere between 99.25 and 100.75mm!
The difference between the board I measured, and the one I cut could be out as badly as 1.75mm. I’m back in my 10 year old woodworking class, and I was being CAREFUL!
Am I doomed to failure?
No: by understanding error, error can be controlled, and minimised.
For one, a rule that has markings extending right to the edge immediately halves the error in measuring. You can feel it is flush with the edge, rather than eyeballing to see the edge is lining up with a marking on the rule’s surface, so that measurement is regarded as accurate.
By switching rules, I can now be confident that the board is 100mm wide, +/-0.5mm
By getting a better rule, with marks laser cut every 0.5mm, I can measure the width to be 100mm +/- 0.25mm
So the board is now somewhere between 99.75 and 100.25mm Already quite a bit better than 99-101mm.
I use the same rule to set the fence to blade distance on the tablesaw, and by knowing the amount of runout of the blade, that error is also taken into account and controlled.
My overall error is controlled, and the resulting board is now also 99.75 – 100.25mm . At worst, the difference in widths of the two boards – the one measured and the one cut is down to 0.5mm. At worst. Probably less, as error is worst-case scenario stuff.
How about another example.
I want to measure the length of a board, and I have 2 ways to measure it on hand. A cheap tape measure, which has it’s own inaccuracy of +/-1mm (a cheap one!), and I also have a good steel rule (the same one as pictured above), accurate to +/- 0.1mm
The board is 2m long. Or is it?
The tape measure measures it as 2000mm +/- 1.5mm (the error of the tape measure, plus the error of the measurement itself)
The steel rule, which is 10x as accurate in its manufacture as the tape measure reads it as
2000mm +/- 15.4mm!!!! How on EARTH did a cheap’n’nasty tape measure absolutely thrash a steel rule?
Simple – every time the rule had to be moved, the error compounded. The steel rule is too short, being only 150mm long, so it had to move a total of 14 times to measure the entire length of the board. Each time, it is +/-1.1mm (because it has 1mm graduations, and the rule itself is already +/-0.1mm) The +/- 15.4mm is a confidence level – you can be sure the length is between 1984.6mm and 2015.4mm. It may be exactly 2000mm, but you cannot say that with certainty. And if you measured it again, it probably wouldn’t come out the same.
What is it they say – measure twice, cut once? But why is that? One big part is that if you repeat the measurement, you might pick up an error you made first time, a total misread. It also increases your sampling, and you can start to average out the measurements. If you measure it twice, and get it to be 0.1mm different, you can increase your confidence you are getting a good reading of the actual width of the board. How many times is enough? How accurate is your rule, and how much variation are you getting each time – at the point you are confident of the measurement, then you are done. If I measure something twice, and I get the same measurement each time, that’s typically good enough. If I was needing some very fine tolerances, such as in precision metal working, 2 is probably no where near enough, and I’d be better off 3 or 4 times, even more, and over an area rather than in the same place. It all depends on how accurate you want to be.
Now you’ve probably been reading all the above and thought “B.something rude”, I can be more accurate than that, and I’m sure that is right. Personally, I’d say I could take a mm rule, and be pretty close to 0.25mm accurately. But the point is, confidence and repeatability. Repeatability from one job to the next, repeatability from one day to the next, repeatability from one tool to the next. Repeatability from one person to the next. But you don’t work with anyone else? Never used someone else’s plans? They were made by a real person, with their own error rate. May not be a big deal, but still worth keeping in mind.
With all that in mind, what do you do? All this has focused on the right tool for the job, and is not saying one person can be more accurate than another. It also looks at being as precise as you need to be. I’d love to build a house to 0.1mm accuracy. But it is not practical (or affordable!) Would be a stunning house though!
If measuring a long board, you need a long rule. A tape measure can be pretty accurate, a Woodpeckers 900mm rule isn’t too bad either. ;)
For small scale stuff, I regularly use a digital calliper, and the Incra rules. They are particularly special. Accurate to 0.001mm, and specifically designed for precision, with the pencil being captive in the rule for the required mark, that precision jumps dramatically compared to a conventional rule. The accuracy when drawing two lines a given distance apart, or a set distance in from an edge will be somewhere in the order of +/-0.1mm or so (it is probably more accurate than that : 0.1 is my conservative estimate.)
Making a mark can be done with a carpenter’s pencil, but at 2-3mm wide, do you then cut to the left, right, or down the middle for accuracy? A fine pencil is better (and a 0.5mm clutch pencil with an Incra Rule is exceptional), and a marking knife produces a razor-sharp line, with no width to speak of. Oh, and don’t forget about parallax error. A good rule is designed to minimise parallax, and again the Incra rule doesn’t have that problem (yes, I am a big fan of Incra rules- can’t you tell?)
There are other ways of dealing with sizing timber correctly. One I do regularly is to cut the first board close to the right length, then mount two together and cut them to the final length simultaneously. This works particularly well when it doesn’t specifically matter how long the two boards are, so long as they are equal.
The Kerfmaker is an exceptional jig for what it is designed for, taking account of board width, saw kerf, blade runout, all without a single rule or scale.
Another useful tool is the story stick, whether this be a simple stick with some marks drawn on it which you then store until the next time you need to make the part in question, or a commercial one which is excellent for the current project, but you don’t keep it dedicated to a single project.
If you want to get into the seriously accurate tools, then the Incra LS positioner, either on the router table or the table saw (or drill press) is one of exceptional accuracy. With the ability to position a fence to within 0.025mm of the required measurement is exceptional. To be able to do it repeatably because of the unique design is quite unbelievable. I have the LS positioner on my router table (love that fence), and am very keen to have one on my tablesaw one day.
If you have ever done any car or motorcycle maintenance, then the concept of a feeler gauge would be quite familiar. Woodpeckers have decided to produce a limited run of an equivalent tool for woodworkers. Called Set Up blocks, these are being produced as part of Woodpeckers One Time range- they will be made to order, and then (at this time), never again. If you are in Australia, you’ll need to order by the 27th June to be part of the manufacturing run from Professional Woodworkers Supplies – cost is $96.50 for the 7 piece metric version (imperial set shown).
The sizes are 0.5, 1.0, 2.0, 4.0, 8.0 and 16mm and there is an additional block which is 25x50x100mm. Like feeler gauges, these can be doubled up to get all the other measurements required. Looks a very cool set- it will be very interesting to see how they work for real. The accuracy of a digital calliper, and no batteries required!
So that is just a brief look into the world of precision, something I am particularly partial to, (and hence why I have a reasonable collection of Incra and Woodpecker.
Quality costs, as does accuracy, but it is a great feeling when you absolutely nail something precisely.
Filed under: Shed, Techniques, Tools | Tagged: Accuracy, Incra, Rule, Ruler, Woodpecker | 2 Comments »