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Woodworking Math

Wood species

Black willow wood

Black willow is a hardwood (Salix nigra). It weighs about 27 lb/ft³ (437 kg/m³), 2.3 lb (1.03 kg) per board foot.

Also called: willow.

Key numbers

Janka hardness, 12% MC
Not measured
Weight at 12% MC
27 lb/ft³ (437 kg/m³)
2.3 lb per board foot
Specific gravity (oven-dry weight)
0.39 at 12% MC volume
0.36 on green volume
Shrinkage, green to oven-dry
8.7% tangential
Radial 3.3%, volumetric 13.9%

One source: USDA Forest Products Laboratory, the authority for species properties it measured

Why: Measured by the USDA Forest Products Laboratory; black willow's density is worked from its specific gravity with the Handbook's own equation.

Work out what your boards weigh

How much black willow moves

A 12 in wide flatsawn board of black willow that goes from 6% to 12% moisture content swells about 0.22 in (about 7/32 in, 5.6 mm). Quartersawn, the same board moves about 0.08 in (about 3/32 in, 2 mm). Flatsawn faces move 2.6 times as much as quartersawn ones, because the wood shrinks 8.7% around the growth rings but only 3.3% across them.

Worked with the Wood Handbook's dimensional change coefficients for black willow (Table 13-5: 0.00308 tangential, 0.00112 radial per 1% change in moisture content), which hold between 6% and 14%. Individual boards vary: the Handbook gives shrinkage a coefficient of variation of about 15% (p. 4-11).

Work out how much your board will move

Color, grain and working

Color
Grayish-brown or light reddish-brown heartwood, often with darker streaks; whitish to creamy yellow sapwood.
Grain and texture
Uniform texture with somewhat interlocked grain.
Working and character
Light and moderately soft, very weak as a beam or post, fairly tough, with fairly high shrinkage.
Uses
Boxes, pallets, crates, caskets and furniture; small amounts for veneer and charcoal.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-11.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of black willow tested by the Forest Products Laboratory (Wood Handbook Table 5-3b). Knots and cross grain make lumber weaker than these clear samples (Handbook Chapter 5).

PropertyGreen12% MC
Bending strength (MOR)4,800 psi (33 MPa)7,800 psi (54 MPa)
Stiffness (MOE)790,000 psi (5.4 GPa)1,010,000 psi (7 GPa)
Crushing strength (compression parallel to grain)2,040 psi (14 MPa)4,100 psi (28 MPa)
Compression perpendicular to grain180 psi (1 MPa)430 psi (3 MPa)
Shear parallel to grain680 psi (5 MPa)1,250 psi (9 MPa)
Tension perpendicular to grain——

A dash means the Handbook prints no value; none is filled in.

Dust and health

This is what the named authorities publish, not medical advice.

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Why these numbers

Why these numbers?
  1. The situation

    The Wood Handbook prints no side hardness for black willow (Table 5-3b shows "—"), so none is given here.

    One source: USDA Forest Products Laboratory, the authority for species properties it measured , sources [1]

  2. What that means

    Side hardness (Janka) is the load needed to press a 0.444 in (11.28 mm) steel ball halfway into the wood across the grain; a higher number dents less (Handbook p. 5-5).

    One source: USDA Forest Products Laboratory, the authority for species properties it measured , sources [1]

  3. So

    Density at 12% is water's density × specific gravity × (1 + 0.12) (Handbook Eq. 4-14): 62.43 × 0.39 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 27 lb/ft³, or 2.3 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers