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Woodworking Math

Wood species

Douglas-fir wood

Douglas-fir is a softwood; this page covers the douglas-fir (coast and interior), led by coast Douglas-fir (Pseudotsuga menziesii). At 12% moisture content it has a Janka hardness of 710 lbf (3,158 N) and it weighs about 34 lb/ft³ (538 kg/m³), 2.8 lb (1.27 kg) per board foot.

Names and species on this page: Douglas fir, red-fir, yellow-fir, Douglas-spruce.

Key numbers

Janka hardness, 12% MC
710 lbf (3,158 N)
Green: 500 lbf (2,224 N)
Weight at 12% MC
34 lb/ft³ (538 kg/m³)
2.8 lb per board foot
Specific gravity (oven-dry weight)
0.48 at 12% MC volume
0.45 on green volume
Shrinkage, green to oven-dry
7.6% tangential
Radial 4.8%, volumetric 12.4%

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

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

Work out what your boards weigh

How much Douglas-fir moves

A 12 in wide flatsawn board of coast Douglas-fir that goes from 6% to 12% moisture content swells about 0.19 in (about 3/16 in, 4.9 mm). Quartersawn, the same board moves about 0.12 in (about 1/8 in, 3 mm). Flatsawn faces move 1.6 times as much as quartersawn ones, because the wood shrinks 7.6% around the growth rings but only 4.8% across them.

Worked with the Wood Handbook's dimensional change coefficients for coast Douglas-fir (Table 13-5: 0.00267 tangential, 0.00165 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
Reddish heartwood in young, fast-grown trees (“red-fir”); yellowish brown in narrow-ringed old growth (“yellow-fir”).
Working and character
Varies widely in weight and strength; the Handbook advises the denser wood where strength matters.
Uses
Building lumber, beams, plywood, millwork, doors and sashes; some flooring, furniture and boats.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-11 to 2-12.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of coast Douglas-fir 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)7,700 psi (53 MPa)12,400 psi (85 MPa)
Stiffness (MOE)1,560,000 psi (10.8 GPa)1,950,000 psi (13.4 GPa)
Crushing strength (compression parallel to grain)3,780 psi (26 MPa)7,230 psi (50 MPa)
Compression perpendicular to grain380 psi (3 MPa)800 psi (6 MPa)
Shear parallel to grain900 psi (6 MPa)1,130 psi (8 MPa)
Tension perpendicular to grain300 psi (2 MPa)340 psi (2 MPa)

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

The douglas-fir (coast and interior)

The Handbook tests each species separately; they are sold together as Douglas-fir. Across the 4 species measured, Janka hardness at 12% runs from 510 to 710 lbf.

SpeciesJanka, 12% MCWeight, 12% MCTangential shrinkage
Coast Douglas-firPseudotsuga menziesii710 lbf34 lb/ft³7.6%
Interior west Douglas-firPseudotsuga menziesii660 lbf35 lb/ft³7.5%
Interior north Douglas-firPseudotsuga menziesii600 lbf34 lb/ft³6.9%
Interior south Douglas-firPseudotsuga menziesii510 lbf32 lb/ft³—

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 USDA Forest Products Laboratory measured coast Douglas-fir at 710 lbf of side hardness at 12% moisture content, on clear, straight-grained samples (Wood Handbook Table 5-3b).

    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 × 0.48 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 34 lb/ft³, or 2.8 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers