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Math, Metrics, and Mayhem

Going through my "archives", and I ran across this early article I put together some time ago and never published.  It's still good info, so here it is in its unvarnished glory:

Here's a few small tips I use when working to keep my projects on the straight and narrow, and some meandering thoughts on inches, feet, millimeters, fractions thereof and of paranoid machinists who have invaded the souls of today's woodworker.  I can't say it will help you mark the correct side of the inch mark, but maybe it will help.

Calculating Board Feet (BF):

Using board feet is usually done only when purchasing wood - but it's good to know how to convert so that you can understand just how much you are being charged.  The two ways I usually convert - if the length of a board is in feet, then the formula is Thickness (inches) x Width (inches) x Length (Feet) and divide by 12.  If the length is in inches, then divide by 144 instead of by 12.  Therefore, a 5/4 piece of wood, 5.1/4" wide, and 9.5 feet long would be:

1.25 x 5.25 x 9.5 / 12 = 5.2 BF (rounded)

If the dimensions for the board are all inches - say 5/4" x 5 1/4" x 114", the formula would be:

1.25 x 5.25 x 114 / 144 = 5.2 BF (rounded)

Remember that a 1"x12" that is 1 foot long is one board foot.  So is a 2"x6" that is 1 foot long.  Most softwoods (construction lumber) is figured using nominal measurements - a 2x6 actually measures 1-1/2" x 5-1/2", but board feet is figured as a 2"x6", the width of the board before it is planed by the mill. 

Hardwood measurements can vary.  A sawmill is more likely to use nominal measurements, but more often these days in retail lumber stores it is done literally, by the actual measurements - unless you are talking about thickness.  There, a 5/4 (or 1-1/4" thick) board is sold as 5/4 is actually something more akin to 1-1/8" thick, as it "finish" planed for thickness.  In any case, knowing how your local lumberyard "measures up" has it's benefits, as you may be getting more or less for your money.

Converting decimal measurements to fractional:

This is easy, but I've seen many people struggle with converting a decimal figure into a fraction.  All you have to know is the denominator of the fraction you want to end up with... Usually, 16ths are a good final product when working with wood, so I usually work to that accuracy, though if it's critical you can work to 32nds should you wish.  Given that, lets convert 4.429 ft. to a fractional dimension.

The formula is to multiply the right side of the decimal point by 12 for inches then the right side of that decimal point by 16 for sixteenths of an inch (or 32 for thirty-seconds, 8 for eighths of an inch, etc.)

First, we know the 4 on the left side of the decimal is how many feet we are working with, so we need only concern ourselves with what's right of the decimal point, or .429 ft.  To get inches, we multiply it by 12:

.429' x 12 = 5.148"

OK - so we know we have 5" and some change, so now we can just concern ourselves with the right side of the decimal point again, or .148".   To get 16ths of an inch, we simply multiply by 16:

.148" x 16 = 2.368

That would be 2.38/16" (about two-and-a-third sixteenths), which rounds down to a 'strong' 2/16".  Since 2/16 = 1/8" I would just say a 'strong' 1/8".

If you wanted to be more accurate, you could work it to 32nds of an inch:

.148 x 32 = 4.544

That's just over four-and-one-half thirty-seconds, which is closer to 5/32".  I would call it a 'shy' 5/32" if pressed - though I must admit that I generally don't work to 32nds.  I don't find it necessary to work with fractions of an inch that small for my projects.

So - combining it all, our measurement of 4.429' converts to either a shy 4'-5 5/32" or a strong 4'-5-1/8", depending on whether you used 16ths or 32nds.

Staying square with the world

The 3-4-5 formula is a very old formula used for checking that a corner is square - used most often when laying out a shed or building, but it also works with casework.  If one side of a triangle is 3 (inches or feet), and another is 4 (inches or feet), then the third leg will be 5 (inches or feet).  3, 4 and 5 inches can be small, but you can use multiples of the numbers and it will still work out.  3, 4, and 5 multiplied by two is 6,8, and 10. 

Of course, if you want a quick check that something is square, use a fresh piece of printer paper.  The  corner will be square. 

Drafting triangles are very handy and a good plastic set can be had for around $3-$4.  Pick them up along with a couple of different "French curve" templates next time you are in or ordering from an art supply store - or Amazon, even.

 Working with Metrics

I enjoy working with the metric system - it makes sense to  me to have everything divisible by 10.  Much more sense than the imperial system, which has 16th of an inch and 12 inches to a foot.  So when presented with a project that is done in the metric system, I try to work completely with that system.  Of course, many of the tools we use are calibrated to the English system - after all, who's heard of a 19mm wood dado plane (yes, you have - we just call it a 3/4" dado here in imperial math land).

Even with the best of intentions I find myself slipping back, and fighting my own natural tendency to use feet and inches, and then it can get confusing.  So, there are still times when I need to convert.  For that, about.com has a handy conversion chart you can print off and hang up in the shop.

For a more complete setup, Washington State DOT has the best conversion pages I've found, along with a small piece of software called convert.exe that can convert pretty much anything from imperial to metric.

There's no "easy" answer - it's just a matter of committing to whichever system you are using right at the moment and dealing with the consequences.  In any case, it does not hurt to know the metric system and how to use it in your woodworking - the world is not going to go backwards and adapt to an earlier, more archaic mathematic system simply to satisfy the need to work with a 2x4.  Last I heard, there were only 3 countries in the world that didn't use metrics - the U.S., Myanmar, and Liberia...

There is a more basic approach.  You can do away with measuring by either method and use a story stick.  You don't think frontier craftsmen carried around a Starrett rule now, do you?

"Unlearn What You Have Learned"

Here's the "mayhem" part.  A ruler is just a marked up stick.  Without markings on it, you can call it a "story stick".

Though I'm not suggesting you do, you can actually work without using a ruler of any kind, and have just as much success as with - using calipers, story sticks, a straight edge, marking gauges, and a compass. With hand tools, the precise measurement is not that important.  Heresy!  Yes, maybe - but it's important to be able to use the material itself to set widths and depths as well.  Granted, overall measurements to work to help in design, but once the main parts are cut, resist the urge to micro-measure everything. 

Yes you should be precise - but you do not need machine-like.  I've always found I prefer the obvious presence of hand work over a perfectly precise machining. 

PS:  For examples,  I suggest you visit Peter Follansbee's blog site for inspiration.  His work is truly inspiring and is about as hand-wrought as you are going to get.

Comments

Comment: 

 

Another way to check angles is to take any irregular scap of paper and fold it in two giving a straight edge along the fold (180 deg). Now fold the paper in two again carefully laying the previous folded edge ontop of itself this gives a right-angle (90 deg). Repeat again for 45 deg etc.
 
Steve.

Comment: 

it works