# Making a box, part 2

September 15, 2012 4:39:19 PM CDT

When I left off last time, the sides of the box were glued together and square.

Getting the corners square doesn't necessarily mean you've gotten the top and bottom flat though, so that was the next step:

## Flattening:

The gray thing is a 6" x 8" surface plate. It's a 2" slab of granite ground to within .0001" of being perfectly flat.. not the least bit exciting by instrumentation standards, but a handy tool in the shop.

Every measurement relies on something called a datum which defines your frame of reference, and is easier to explain by showing how it can fail:

If you have a single point marked "zero", you can measure the distance from that point to any other. You can't measure angles though, and you can't define shapes:

Even though the distances to the corners of both shapes are the same, the shapes themselves are different. A single datum point just doesn't give you enough information to make meaningful statements about shape.

If you have two datum points, you can triangulate your measurements, which gives you enough information to talk about shapes in a plane. If you have three datum points, you can triangulate from multiple points in a plane, which gives you enough information to talk about solid shapes.

As you can probably guess from the word 'triangulate' though, measuring from a minimal set of datum points involves a lot of trigonometry. In practice it's easier to define your datum as a line, plane, or some other shape that makes the values you care about easier to see.

To demonstrate that last idea, here are the triangulated measurements for a line relative to two datum points:

• (1.414, 7.071), (2.236, 6.083), (3.162, 5.099), (4.100, 4.100), (5.099, 3.162), (6.083, 2.236)

and here are perpendicular measurements from the same line to a straight datum line:

• 1, 1, 1, .9, 1, 1

The second version makes it much easier to see where the dip is.

Thing is, if you use a datum line/plane/etc, you have to be able to rely on it being correct. If you use the line above as your datum, you'll get errors every time you hit that dip at the fourth position, no matter how good your ruler or measurement techniques are.

That, of course, leads back to the old recursive question of all measurement standards, "exactly how do I measure my ruler?"

If you're coming at it from scratch, the answer is, "spend a lot of time and effort comparing and canceling errors." Pragmatically, the answer is, "go buy a certified reference from someone who's already done the hard part."

The shop-grade surface plate above cost \$15 from Grizzly. I consider it a good investment.

This, believe it or not, is one of the accepted uses for a surface plate:

Shove a piece of sandpaper on top of it and use it to mark the high spots on the workpiece.

Normally you just use the sandpaper and surface plate to mark the high spots on a surface you want to flatten, then do the bulk material removal with some other tool. In this case, the box was close enough to being correct that half a dozen light swipes were enough to do the whole job.

## Lining:

Remember those scraps of wood I used to hold the sides parallel and square last time?

They weren't just throwaway pieces:

They were an 1/8" liner that fits inside the part I've already made. The liner sticks up 1/8" beyond the outer shell, creating a lip that will hold the top in place.

I didn't get any shots of the bottom after I took the clamps off (well, okay, I got one):

but apparently I was more excited about showing how square the corners are than about showing the liner itself.

Here's a shot of the top with its liner in place:

That's okay though, because I have plenty of other pictures that show the lip nicely. This one, for instance:

Which I'll talk about next time.