Shrinkage and swelling: three directions and how to estimate them

Wood does not shrink equally in all directions

Wood shrinks and swells because the cell wall changes volume as bound water leaves or enters it. Three directions matter:

• Longitudinal: along the grain, parallel to the stem.
• Radial: across the growth rings, from pith outwards.
• Tangential: along a ring, at a right angle to the radius.

A board's width can be tangential, radial or in between, depending on the cut.

Reference values (North America)

Wood Handbook Table 4-3 gives green-to-oven-dry shrinkage as a percentage of the green dimension:

Tangential is always larger than radial, but the ratio is not exactly two. In the wider selection of the source it runs from about 1.4 to 2.4 (sugar maple: 9.9 / 4.8 = 2.1), and a cited review gives 1.5 to 2.5. "About twice" is a rule of thumb. Longitudinal shrinkage is only 0.1 to 0.2 % for most species, but reaction wood and juvenile wood can shrink about 2 % along the grain. All values are for North American species; no European table was verified.

Method 1: linear shrinkage from the FSP

The Wood Handbook assumes shrinkage starts at the FSP (30 % if unknown) and falls linearly with moisture content:

shrinkage % = S_total x (FSP - MC) / FSP

Use the tangential value for the width of flat-sawn boards, the radial value for quarter-sawn, and tangential when the ring orientation is mixed or unknown. The method tends to underestimate the true change by about 5 % (Bergman), and pieces scatter, with a coefficient of variation of about 15 %.

Worked example 1: bur oak, 200 mm green width, dried to 8 %

• Flat-sawn: 8.8 x (30 - 8) / 30 = 6.45 %, which is 200 x 0.0645 = about 13 mm.
• Quarter-sawn: 4.4 x 22 / 30 = 3.23 %, about 6.5 mm.

The flat-sawn board loses about twice the width of the quarter-sawn one (an illustration of the method, not a measurement).

Worked example 2: the FSP matters

Western redcedar is one of the four entries Bergman treats with an FSP of about 22 %. A 150 mm green flat-sawn board dried to 10 % (tangential 5.0 %):

• With FSP 22 %: 5.0 x (22 - 10) / 22 = 2.73 %, about 4.1 mm.
• With the default 30 %: 5.0 x 20 / 30 = 3.33 %, about 5.0 mm.

Using the wrong FSP overstates the change by nearly a millimetre here.

Method 2: the change coefficient for the service range

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

change in dimension = initial dimension x coefficient x change in MC

For white fir (North America) the tangential coefficient is 0.00245 per percentage point and the radial coefficient is 0.00112, a ratio of 2.2. This method was developed for 6 to 14 % to avoid the underestimate of the linear method.

Worked example 3: white fir in service

A 232 mm flat-sawn board moving from 8 % to 11 % MC: 232 x 0.00245 x 3 = 1.7 mm wider (Bergman's example). A 100 mm flat-sawn board drying from 14 % to 8 % loses 100 x 0.00245 x 6 = 1.47 mm. The same board cut quarter-sawn would lose 100 x 0.00112 x 6 = 0.67 mm.

Length changes

A 2 m board with normal longitudinal shrinkage of 0.1 to 0.2 % shortens by 2 to 4 mm. Juvenile or reaction wood at 2 % would shorten 40 mm per 2 m. This tenfold or greater difference inside one board produces bow, crook and twist (Lesson 6).

Key points

• Shrinkage is smallest along the grain (0.1 to 0.2 %), moderate radially and largest tangentially, roughly 1.5 to 2.5 times radial.
• Linear estimate: S_total x (FSP - MC) / FSP, with FSP 30 % by default, about 22 % for the four named entries.
• Service-range estimate: dimension x coefficient x change in MC (white fir: 0.00245 tangential, 0.00112 radial per point).
• Typical green-to-oven-dry tangential values are 7 to 10 % for common temperate species (North America), lower for western redcedar and redwood.
• Estimates are approximations with scatter.