Introduction: You're Up Against It With Fine Woodworking?
Making anything out of wood is a numbers game. It's all about dimensions as in size, length, width & height. Just cut to the dimensions shown and fasten the components. I wish it was that easy though!
The first thing you're Up Against when dealing with wood, is it has characteristics and faults. Things like cup, twist, bow, wind, spring, tension..... Then throw in shrinkage, expansion, swelling....and you could say that, "Wood never dies!"
If all of the above isn't enough of a nuisance, then good old maths comes into play? Namely Deviation and Variance. The strict definition:
Standard deviation measures the spread of the data about the mean value
Variance is the average of the squared differences from the Mean
Might've lost you there, but in plain speak, "Nothing is ever made an identical size!....Close yes, but there's always a degree, a decimal point or an umpteenth fraction difference somewhere?"
Does it really matter all that much anyway? If your knocking up a house frame, a few mm here or there is acceptable, but in small fine woodworking projects, it can be frustratingly annoying if it's not near perfect!
In the following step, I'm going to demonstrate how easily perfection can turn to chaos?
Step 1: Let's Build a Box.
Let's build a box similar to the one in the picture, but on paper first. The box comprises 4 sides mitre cut to butt against a corner post. Looks easy enough, right? I intend to use 30x8mm sides rails and 12mm square posts. I purchase the material from my local timber merchant, it's all dressed and looks great.
Harking back to the last step I need to be aware that the wood I've purchased has nominal dimensions, called the mean. There is a variance that manufacturers are allowed to be within or they may elect to nominate that variance as a "+" and "-" from the mean. For dressed timber at these sizes it can be up to +0.3mm or - 0.3mm. Doesn't sound much hey?
Before I proceed, I'll actually measure the timber I bought. I measured with digital calipers along each length of timber at 5 intervals. The 30x8 maximim deviation was 0.45mm and the 12mm square (wasn't square at all) 0.66mm maximum deviation. Wow!...as a percentage of the overall width, that was like 5.5% difference.
In the next step I'll theoretically build the box using this variance and see what happens?
Step 2: An in Theory Box
In the first pic I want to build a box where the corner posts touch the inside of a 100x100mm square. The sketch uses the nominal dimensions as supplied by the manufacturer. That determines that I need to cut 4 sides 82.059mm long at the longest edge.
Now for the last hiccup to the process? Human error and machine error. How thick is your pencil line? Are you positioning the wood while marking or cutting it looking directly over or from an angle? How's your eyesight? Is your saw blade spinning perfectly plumb? What are you using to measure the length and how accurate is it? How much play in your saws angle setting stops?
Just some of the factors where I guarantee that another 5% error will creep into the equation! If you don't cut each side exactly 82.059mm long based on 8mm wide rail, then you'll never get a perfect 90 degrees angle. Now throw in the variance of timber width as I've already confirmed, and all of a sudden you're doomed to fail to a certain extent!
Using the manufacturers + 0.3mm or - 0.3mm Variance in width and a 5% error factor in cutting the required lengths, I have listed in the 2nd pic the notional final dimensions of all the components of this box. Unknowingly really as I don't bother to check! In the 3rd pic, I start with post P4 and working clockwise, assemble the components.
By the time I've gone around the clock I miss joining up rail L1 to P4 by 1.7mm. Along the way I get a mismatch of margins (final pic). Now I'm in a world of pain! "How could I get it so wrong?" That's a big unsightly gap.
Step 3: How to Fix Things?
"Forewarned is forearmed!" as the saying goes. Every facet from timber selection, measuring,marking and re-checking as well as tool maintenance plays a role in the final outcome of any build. Not to mention your own discipline and expectations to excel or not?
In this example, you must be selective in the orientation of the posts. They were basically rectangles in this instance, not square! Orientate their placement to have the closest similar widths to each other between mitres. If the rails vary in width then it's the shorter edge length that is primary, not the longer edge. Use the most accurate measuring device and best practice method for marking out. Set up a jig for your saw to facilitate accurate repetitive cut lengths. If your blade isn't true or saw has too much play, then either modify or compensate in some way?
Mathematics and Probability dictates that you will never do better than 99.999....% accurate, but hey, that's a hell of a lot better than 90%!
Enjoy your endeavours.
Participated in the
Made with Math Contest