Anisotropy: why the pattern decides how a board behaves

Three directions

Wood does not shrink equally in all directions. The longitudinal direction runs along the grain. Across the grain, the radial direction runs from pith outwards across the rings, and the tangential direction runs along a ring. A sawing pattern decides which direction ends up as the width and thickness of each board.

Typical green-to-oven-dry shrinkage (USDA Wood Handbook, North American species; the articles found no open authoritative table for European species, so no numbers are claimed for Norway spruce, Scots pine, beech or European oak):

Tangential shrinkage is always larger, but the ratio is not exactly two: in the source's selection it runs from about 1.4 to 2.4, and a cited review gives 1.5 to 2.5. "About twice" is a rule of thumb, not a precision claim. Along the grain, shrinkage is only about 0.1 to 0.2 percent for most species, but reaction wood and juvenile wood can shrink about 2 percent along the grain, ten to twenty times more. That difference inside one board produces bow, crook and twist.

Estimating shrinkage with the handbook method

The handbook assumes shrinkage starts at about 30 percent moisture content (MC) and proceeds linearly:

shrinkage (%) = table value x (30 - final MC) / 30

Use tangential values for the width of flat-sawn boards, radial for quarter-sawn, and tangential when ring orientation is mixed or unknown. The method slightly underestimates the true change (about 5 percent of the change), and individual pieces scatter with a coefficient of variation around 15 percent.

Worked example. A flat-sawn bur oak board is 200 mm wide when green, dried to 8 percent MC.

• Tangential: 8.8 x (30 - 8) / 30 = 6.45 percent, so 200 x 0.0645 = 12.9 mm.
• A quarter-sawn board of the same width: 4.4 x 22 / 30 = 3.23 percent, so 6.5 mm.

The quarter-sawn board moves about half as much. This is an illustration of the method, not a measurement.

From anisotropy to warp

All warp is caused by differential shrinkage; growth stresses and irregular grain add to it.

• Cup: in a flat-sawn board the face nearer the bark is more tangential, so it shrinks more across the width. Flat-sawn lumber cups toward the bark side (away from the tree centre). Lumber cut near the pith and from small-diameter trees is more cup-prone (model prediction, not measurement).
• Bow and crook: driven by longitudinal shrinkage differences from juvenile wood (first 10 to 15 rings), reaction wood and sloping grain. Quarter-sawn lumber is the most crook-prone because one edge lies nearer the tree centre. Keep rings centred edge to edge; turning the log 180 degrees after the first face helps.
• Checks: surface checks occur most often on the face of flat-sawn boards. Species with broad rays (oaks, beech, sycamore) are check-prone.

How the pattern changes board behaviour

No source gave measured warp rates for through-and-through or cant sawing; those descriptions follow from geometry.

Practical rules

• Plan for flat-sawn width movement of roughly twice that of quarter-sawn boards of the same species.
• Keep the pith out of boards where flatness matters.
• Match pattern to product: quarter- or rift-sawn where stability matters, flat-sawn where movement is acceptable.
• Dry flat-sawn and quarter-sawn stock in separate charges (portal inference).
• Coat ends of valuable stock to limit end checks.

Key points

• Shrinkage: longitudinal about 0.1 to 0.2 percent, radial moderate, tangential about 1.5 to 2.5 times radial.
• Handbook estimate: table value x (30 - final MC) / 30, with about 15 percent piece scatter; table values here are North American.
• Cup comes from the tangential-radial difference across the board; bow, crook and twist from longitudinal differences.
• Quarter-sawn boards move about half as much in width but are slower to dry and more crook-prone.
• Choose the pattern for the product.