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Woodworking Math

Wood species

Western hemlock wood

Western hemlock is a softwood (Tsuga heterophylla). At 12% moisture content it has a Janka hardness of 540 lbf (2,402 N) and it weighs about 31 lb/ft³ (504 kg/m³), 2.6 lb (1.19 kg) per board foot.

Also called: West Coast hemlock, Pacific hemlock, British Columbia hemlock.

Key numbers

Janka hardness, 12% MC
540 lbf (2,402 N)
Green: 410 lbf (1,824 N)
Weight at 12% MC
31 lb/ft³ (504 kg/m³)
2.6 lb per board foot
Specific gravity (oven-dry weight)
0.45 at 12% MC volume
0.42 on green volume
Shrinkage, green to oven-dry
7.8% tangential
Radial 4.2%, volumetric 12.4%

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

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

Work out what your boards weigh

How much western hemlock moves

A 12 in wide flatsawn board of western hemlock that goes from 6% to 12% moisture content swells about 0.2 in (about 3/16 in, 5 mm). Quartersawn, the same board moves about 0.1 in (about 3/32 in, 2.6 mm). Flatsawn faces move 1.9 times as much as quartersawn ones, because the wood shrinks 7.8% around the growth rings but only 4.2% across them.

Worked with the Wood Handbook's dimensional change coefficients for western hemlock (Table 13-5: 0.00274 tangential, 0.00144 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
Almost white with a purplish tinge; the narrow sapwood may be lighter. Dark streaks from bark maggots are common and don’t reduce strength.
Grain and texture
Small, tight black knots are typical.
Working and character
Moderately light and moderate in strength, hardness and stiffness. It shrinks about as much as Douglas-fir but holds more water green and needs longer kiln drying.
Uses
Framing, sheathing, siding, joists, plywood, flooring, furniture and ladders.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-12 to 2-13.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of western hemlock 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)6,600 psi (46 MPa)11,300 psi (78 MPa)
Stiffness (MOE)1,310,000 psi (9 GPa)1,630,000 psi (11.2 GPa)
Crushing strength (compression parallel to grain)3,360 psi (23 MPa)7,200 psi (50 MPa)
Compression perpendicular to grain280 psi (2 MPa)550 psi (4 MPa)
Shear parallel to grain860 psi (6 MPa)1,290 psi (9 MPa)
Tension perpendicular to grain290 psi (2 MPa)340 psi (2 MPa)

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 USDA Forest Products Laboratory measured western hemlock at 540 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 × 0.45 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 31 lb/ft³, or 2.6 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers