Shrinkage, sawing pattern and warp

Drying defects are shaped by geometry before the schedule. All shrinkage values below are for North American species from the USDA Wood Handbook. The portal did not verify comparable tables for European oak, beech, spruce or Scots pine, so the principles carry over to Europe but the numbers must be replaced with species data.

Three directions, three behaviours

• Longitudinal (along the grain): about 0.1 to 0.2% from green to oven-dry for most species.
• Radial (across the rings): moderate.
• Tangential (along the rings): the largest, roughly 1.5 to 2.5 times radial.

Reaction wood and juvenile wood are the exception: they can shrink about 2% along the grain, ten to twenty times more than normal wood (portal arithmetic). That difference inside one board drives bow, crook and twist.

Values are green to oven-dry, as a percentage of the green dimension. Across the wider Wood Handbook selection the tangential/radial ratio runs from about 1.4 to 2.4, so "about twice" is a rule of thumb.

Estimating dimensional change

The handbook assumes shrinkage starts at FSP (30% if unknown) and falls linearly with MC:

shrinkage % = total shrinkage % x (30 - final MC) / 30

Worked example. A flat-sawn bur oak board is 200 mm wide green and is dried to 8% MC. Tangential shrinkage = 8.8 x (30 - 8) / 30 = 6.45%, so the width falls by about 12.9 mm. A quarter-sawn board uses the radial value: 4.4 x 22 / 30 = 3.2%, about 6.5 mm. The flat-sawn board moves about twice as much. The linear method tends to underestimate true change by about 5% of the change (Bergman, Wood Handbook chapter 13).

For the service range of 6 to 14% MC, Bergman gives a simpler form:

change = initial dimension x coefficient x change in MC

For flat-grained white fir the tangential coefficient is 0.00245 per percentage point. A 232 mm board going from 8% to 11% MC changes by 232 x 0.00245 x 3 = 1.7 mm. Use tangential values for the width of flat-sawn stock, radial for quarter-sawn, and tangential when ring orientation is unknown.

From anisotropy to warp

All warp comes from differential shrinkage (Wengert and Meyer, North America); Bergman adds growth stresses, aggravated by irregular grain and juvenile or reaction wood.

• Cup. In flat-sawn boards the bark-side face is more tangential and shrinks more across the width, so the board cups toward the bark side. Boards cut near the pith, or from small trees, are more cup-prone.
• Bow and crook. Length-wise curvature from longitudinal differences (juvenile, compression or tension wood, sloping grain). Quarter-sawn lumber is the most susceptible to crook.
• Checking. Surface checks occur most on flat-sawn faces; end checks follow fast end drying. Oaks, beech and sycamore check readily because of broad rays.

Sawing pattern

Practical measures: keep grain parallel to edges, keep the pith out of boards where flatness matters, coat the ends of valuable stock, and where possible dry flat-sawn and quarter-sawn stock in separate charges (practical reasoning, not a tested rule). Warp usually forms above 40% MC.

Key points

• Longitudinal shrinkage is about 0.1 to 0.2%, except reaction and juvenile wood at about 2%.
• Tangential shrinkage is typically 1.5 to 2.5 times radial.
• shrinkage = total x (30 - final MC) / 30; use the coefficient method for 6 to 14% MC.
• Cup comes from the tangential/radial difference; bow, crook and twist from longitudinal differences.
• Flat-sawn: more movement and cup. Quarter-sawn: about half the width movement, slower drying, crook risk.
• Do not transfer these North American numbers to European species.