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Woodworking Math

Wood species

Sugar pine wood

Sugar pine is a softwood (Pinus lambertiana). At 12% moisture content it has a Janka hardness of 380 lbf (1,690 N) and it weighs about 25 lb/ft³ (403 kg/m³), 2.1 lb (0.95 kg) per board foot.

Also called: California sugar pine.

Key numbers

Janka hardness, 12% MC
380 lbf (1,690 N)
Green: 270 lbf (1,201 N)
Weight at 12% MC
25 lb/ft³ (403 kg/m³)
2.1 lb per board foot
Specific gravity (oven-dry weight)
0.36 at 12% MC volume
0.34 on green volume
Shrinkage, green to oven-dry
5.6% tangential
Radial 2.9%, volumetric 7.9%

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

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

Work out what your boards weigh

How much sugar pine moves

A 12 in wide flatsawn board of sugar pine that goes from 6% to 12% moisture content swells about 0.14 in (about 1/8 in, 3.5 mm). Quartersawn, the same board moves about 0.07 in (about 1/16 in, 1.8 mm). Flatsawn faces move 1.9 times as much as quartersawn ones, because the wood shrinks 5.6% around the growth rings but only 2.9% across them.

Worked with the Wood Handbook's dimensional change coefficients for sugar pine (Table 13-5: 0.00194 tangential, 0.00099 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
Buff or light brown heartwood, sometimes tinged red; creamy white sapwood.
Grain and texture
Straight and fairly uniform.
Working and character
Light, soft and fairly weak, with very low shrinkage. It dries without warping or checking, stays stable, cuts easily and nails well.
Uses
Foundry patterns, sashes, doors, frames, millwork and building construction.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-16.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of sugar pine 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)4,900 psi (34 MPa)8,200 psi (57 MPa)
Stiffness (MOE)1,030,000 psi (7.1 GPa)1,190,000 psi (8.2 GPa)
Crushing strength (compression parallel to grain)2,460 psi (17 MPa)4,460 psi (31 MPa)
Compression perpendicular to grain210 psi (1 MPa)500 psi (3 MPa)
Shear parallel to grain720 psi (5 MPa)1,130 psi (8 MPa)
Tension perpendicular to grain270 psi (2 MPa)350 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 sugar pine at 380 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 × 0.36 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 25 lb/ft³, or 2.1 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers