# Making Accurate Straight-Edges from Scratch

An accurate straight-edge is a very useful instrument to have, and it is essential for aligning table saw and jointer tables, as well as truing planes and workbenches. Although commercial, precision straight-edges long enough for woodworking purposes can cost hundreds of dollars, it is possible to make a set of three straight-edges accurate to one or two thousandths of an inch without requiring reference to any standard. Rather, the three straight-edges are compared with each other in such a way as to average out the errors.

Precision straight-edges are typically made of hardened steel, but they can also be made of mild steel, aluminum, rigid plastic, stable wood, or other materials. Lengths of three or four feet can be easily produced, as can longer lengths, although the latter are a little more awkward to handle and tend to sag under their own weights.

I adapted the techniques for making straight-edges from those described for making accurate surfaces, as described in Wayne R. Moore's "Foundations of Mechanical Accuracy", Moore Special Tool Co., 1970. This fascinating book describes how reference tools and machines with accuracies on the order of millionths of an inch are built.

The fundamental principle used to create precision straight-edges is that the only way that three curves can match each other is if the curves are all straight lines. By repeatedly comparing the three developing straight-edges with each other and averaging their shapes where they don't match, the three developing straight-edges will become arbitrarily straight.

## Why Three Straight-Edges Are Necessary

If we have three identical, non-symmetrical developing straight-edges A, B, and C, it may be possible for deviations in straightness to match each other for some orientations. In the second figure below, the hump at A matches the depression at B' and the hump at B matches the depression at A'. However, if we reverse B and B', as shown in the third figure below, the humps at A and B coincide, as do the depressions at A' and B'. From this example we can see why each developing straight-edge must be checked against the others in both directions.

If the deviations in the developing straight-edges are symmetrical it may be possible for two developing straight-edges to match each other in both directions. In the figure above, the hump in A matches the depression in C. However, unless all developing straight-edges are truly straight, the other developing straight-edge B can not match both A and C, as shown in the third figure above. From this example we can see that three straight-edges must be checked against each other in order to verify straightness.

## Getting Started

Begin by selecting three identical pieces of a suitable material with the desired length of finished straight-edges. If mild steel is chosen, hot-rolled steel may be preferable to cold-rolled steel, because the latter can have significant internal stresses that can become unbalanced and cause warping if material is removed asymmetrically. Cold-rolled steel is usually shiny, in contrast to the brownish-black mill scale found on hot-rolled steel.

The thickness and depth of each piece should be great enough to prevent bending significantly under its own weight. In trading off thickness for depth, bear in mind that stiffness increases linearly with the thickness perpendicular to the load, but as the cube of the depth in the direction of the load. That is, although a 1/8"x2" bar and a 1/4"x1" bar are each twice as big as a 1/8"x1" bar, the 1/8"x2" bar is eight times a stiff as the 1/8"x1" bar, but the 1/4"x1" bar is only twice as stiff.

Each piece should be as straight as possible before the refining process begins, and the straight-edges should be smooth to begin with. Wood pieces should be ripped or jointed reasonably straight and smooth, and steel should have any mill scale or rust brushed or filed off. Mark both ends of each piece so that they can be differentiated; for example, A-A', B-B', C-C'.

## The Averaging Process

In a nutshell the averaging process is to:

1. Select one piece as the temporary reference.
2. Compare the temporary reference to the other two pieces in both directions, noting where they don't match.
3. If all pieces match sufficiently closely, we are done. Otherwise:
4. Remove material from the other pieces where they don't match the temporary reference.
5. Select another piece as the temporary reference and return to step 2.

### Notes on the Averaging Process

1. We want to select the straightest piece as the first temporary reference to avoid removing too much material from the wrong piece. If two edges are held together up to the light, points of contact indicate where material must be removed. If the two edges are rubbed together slightly, the points of contact will tend to move with the less-straight edge as they slide along the straighter edge.
2. The easiest way to determine where material must be removed is to coat the temporary reference edge with colored material that can rub off on the other edges when the reference and the test piece are rubbed together slightly. For rough surfaces, colored sidewalk chalk works well, is available in bright colors, and washes off with water. A more traditional material to use is Prussian blue in oil, such as Dykem's Hi-Spot Blue; this is much messier than chalk, although it can be cleaned up with alcohol. A cheaper alternative to Prussian blue is paint pigment in a carrier, in the form of tubes of universal tints for latex and oil-based paints; these are available in a wide selection of bright colors, and can be cleaned off with soap and water.
3. The closeness of the matching of test pieces to the temporary reference can be measured with a feeler gauge. If, for example, a .002" feeler gauge can not slip between the temporary reference and either test piece held next to the temporary reference in either direction, then the maximum deviation is guaranteed to be less than .002". Feeler gauges commonly come in thicknesses down to .0015", which is probably close enough for woodworking purposes. If not, thinner shim stock can be substituted for the feeler gauge.
4. The colored high spots can be removed using any method appropriate for the material, such as planing, sanding, filing, grinding, or scraping. Since we don't generally know if the current temporary reference piece is flatter than the current test pieces, we should remove at most half of the material necessary to make an exact fit. In practice, the deviations are, initially, much greater than the amount of material removed in a given step, and one usually finds that the same areas must be removed each iteration. When this happens, more aggressive material removal can be done until different areas show up as high spots to be removed. Once this happens, the material removed should decrease with each iteration.
5. Selecting the next piece as the temporary reference should follow a round robin order (eg. A B C A B C . . .).
6. After we finish, we have three straight-edges, each as straight as the others. Any or all of them can be used, although it may be useful to keep them all as cross-references for each other. This is especially important for less stable materials like wood or metals with unreleaved internal stresses.

Any of the three straight-edges can be used to make more straight-edges, but when this is done, material is never removed from the reference straight-edge.

## Lapping: Automated Averaging of Edge Deviations

One way to speed up the final averaging process for metal straight-edges is to lap the pieces together. Lapping compounds (abrasives in a grease binder) are applied to two pieces and their edges are rubbed together. This process is repeated for all pairs of pieces in both directions until the edges are sufficiently straight. That is, we lap A:B, A:C, B:A, B:C, C:A, C:B, A':B, A':C, B':A, B':C, C':A, C':B, where A' denotes A reversed. In general, this sequence of lapping is repeated one or more times. Finer abrasives can be used in later stages of the lapping process.

## A Useful Accessory

One useful accessory to the straight-edge is a jig to hold it in position. This can be made by cutting a slot in a block of wood, sufficiently deep to allow the entire depth of the straight-edge to fit inside, and sufficiently narrow to keep the straight-edge from slipping out. This block is pushed over one end of the straight-edge so that its bottom rests on the surface being checked, freeing the operator to look for gaps and to insert feeler gauges between the straight-edge and the surface.