# Making a box

September 11, 2012 6:26:23 PM CDT

My projects have a tendency to extend like a telescope, and this is an example. I'm making a box that will house a project that, itself, will be an experimental prototype for still another project.

## Basic parts:

Here's a view of the parts that will become the sides of the box:

The stock is 1/4" oak. The overall dimensions will be 3" x 5" x 8".

The major dimensions come from a designer's math trick: If you want a rectangle that looks good, you use the golden ratio (aka: 'phi' -- about 1.618-to-1). Thing is, it's a pain to try and remember number-and-decimals, and you always end up rounding the numbers to something easier to find on a ruler anyway.

There are many ways to calculate phi, but one of its interesting properties is that it's the limiting value of the ratio between any two consecutive members of the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc). In other words, you can get integer dimensions that meet the golden ratio by taking any two (or in this case, three) consecutive values from the sequence.

The next Fibonacci value is always the sum of the previous two, so you can generate the first dozen or so values on a scrap of paper if you need to. The ratio between values converges on phi pretty fast, too, so the values 13, 21, 34 are already within half a percent of the true golden-ratio values (12.9787, 21, 33.9787).

To scale Fibonacci values, divide your middle dimension by one of the values from the sequence to get a scaling unit, then multiply that by the Fibonacci values on either side to get your dimensions.

### Example:

Say I want a box whose middle dimension is 4".

• Pick a trio of Fibonacci numbers (13, 21, 34 will do).
• Divide the middle dimension by the middle Fibonacci number (4/21 = .1905-ish)
• Multiply the Fibonacci numbers by the result to get dimensions:
• 13 x .1905 = 2.7765 (about 2-3/4")
• 21 x .1905 = 4.0005 (4")
• 34 x .1905 = 6.4770 (about 6-1/2")

## Outsmarting myself:

I was so pleased with myself for coming up with a neat way to calculate dimensions that I forgot a cardinal rule of making decent boxes:

NEVER assemble the body and top separately.

A rectangle is a device for multiplying dimensional errors. If one angle or dimension is slightly out of whack, it will pull others out as well. It isn't hard to glue four sticks together and get an adequate rectangle, but it's very hard to do it twice and get two rectangles that match to within a few thousandths.

Meanwhile, human tactile acuity is easily good enough for people to feel an offset error of .002-.003".

The solution is easy: make a single rectangle that's a bit taller than the base and lid together, then cut a slab off the top. The parts might not be perfect, but they'll match really well.

Cabinetmakers have known that for centuries. I knew it too, centuries ago, but it's been a while since I've made sawdust on any major scale. As you can see from the pictures above, I goofed and cut the top and bottom pieces apart before gluing everything together.

## The handyman's secret weapon:

Fortunately, I recognized the mistake before the glue came out, and know a trick that can compensate:

That's painter's tape, not duct tape, but the spirit is there. As you can see, I laid the pieces together and taped them on both sides to make temporary planks.

Those are machinist's 1-2-3 blocks in the corners. If you don't have a set, I recommend them. They're one of those generically-useful devices for layout and setup work. Here I'm using them as freestanding 3-dimensional squares, because juggling box parts without them is a pain in the tuckus.

I could have clamped the blocks to the long board, then clamped the short boards to the blocks to secure the corners for gluing. Frankly though, that's a nuisance and it doesn't reduce your error that much.

What I did was adjust the Jorgensen clamps so the jaws were parallel with about 1/32" of clearance from the box sides (1/64" on either side, which isn't nearly as exciting as the numbers make it sound), and stood them up on their noses. If you removed the box parts from the pictures above, the clamps would remain standing -- they're built that way.

With the clamps ready, I was able to glue a joint, square it to the 1-2-3 block, slide the clamp over it, and apply light pressure.

"Light pressure" is another of those cabinetmaker's tricks. You want enough pressure to take all the slack out of the system (nothing can rattle or wobble back and forth), but not enough to create significant friction between the parts.

You make your final adjustments under light pressure for a couple of reasons: First, it just works. You can push on the parts to move them around, but when you stop pushing they stay where you left them. Second, parts always squirm when you take the slack out of the system.

As you go from zero pressure to clamping pressure, the parts follow the path of least resistance to the applied force. Unless you take special measures to constrain that path, it will almost certainly take the parts to places you don't want. More complex joints, like rabbets, tenons, and dovetails, have path constraints built in.

For the plain-old butt joint, used here, increasing the clamp pressure gradually does the same thing. You have to do the path-constraint stuff manually, but the friction from light pressure keeps the parts from squirming as you go to medium pressure, or at least it should. If the parts squirm as you go to medium pressure, you knock them back into place with a mallet. Then the friction from medium pressure keeps the parts from squirming as you go up to clamping pressure.

Once you get used to the process, you can do it faster than you can explain it.

## Squaring:

Another trick used above: When possible, only clamp one joint at a time.

Yes, technically there are two joints being clamped in the pictures above, but they're in parallel. Each clamp is only applying pressure to a single joint, and you could release either clamp without affecting the other joint.

Trying to clamp joints in series is a pain because both ends can squirm, and the adjustment you make on one end can pull the other end out of position.

To the contrary, as soon as you glue up one joint, you automatically get a bunch of path constraints that make gluing the next one easier. The workpiece itself becomes part of the clamping fixture, which is always cool.

Here I'm using two tools to constrain the joints for the final side:

The machinist's square in the upper left tells me whether the corner is, well, square.

The other tool is that scrap of wood on the right. It's cut to match the inside dimension on the left, so it guarantees that the inside dimension on the right will match.

According to basic geometry, if you have a four-sided figure whose opposite sides are the same length, the other two sides will be parallel. If both pairs of opposing sides are the same length, you have a parallelogram. If the sides of your parallelogram meet at right angles, you have a rectangle.

So let's do that in wood:

The long strips hold the short sides of the box parallel, the short strips hold the long sides parallel. The short strips are cut square, so laying them flat forces the joints to meet at right angles.

The result will be a box that's pretty darn close to square.

## Done (with this part):

Here are the top and bottom, separated, after the glue had a chance to cure:

I didn't think to take pictures at the time, and I'm further along in the process now, but results were good enough that the top and bottom fit together well in all possible orientations.

# Random brain cookies:

The rhino is a homely beast, For human eyes he's not a feast. Farewell, farewell, you old rhinoceros, I'll stare at something less prepoceros. -- Ogden Nash