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Woodworking Math

Wood species

Sweet birch wood

Sweet birch is a hardwood (Betula lenta). At 12% moisture content it has a Janka hardness of 1,470 lbf (6,539 N) and it weighs about 45 lb/ft³ (728 kg/m³), 3.8 lb (1.72 kg) per board foot.

Also called: Betula lenta.

Key numbers

Janka hardness, 12% MC
1,470 lbf (6,539 N)
Green: 970 lbf (4,315 N)
Weight at 12% MC
45 lb/ft³ (728 kg/m³)
3.8 lb per board foot
Specific gravity (oven-dry weight)
0.65 at 12% MC volume
0.60 on green volume
Shrinkage, green to oven-dry
9.0% tangential
Radial 6.5%, volumetric 15.6%

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

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

Work out what your boards weigh

How much sweet birch moves

A 12 in wide flatsawn board of sweet birch that goes from 6% to 12% moisture content swells about 0.23 in (about 7/32 in, 5.8 mm). Quartersawn, the same board moves about 0.16 in (about 5/32 in, 4.1 mm). Flatsawn faces move 1.4 times as much as quartersawn ones, because the wood shrinks 9.0% around the growth rings but only 6.5% across them.

Worked with the Wood Handbook's dimensional change coefficients for sweet birch (Table 13-5: 0.00319 tangential, 0.00226 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
Dark brown heartwood tinged with red, and light-colored sapwood.
Grain and texture
Fine and uniform in texture.
Working and character
Heavy, hard and strong, with good shock resistance, like yellow birch. Birch shrinks considerably as it dries.
Uses
With yellow birch: furniture, boxes, baskets, wooden ware, cooperage, interior woodwork and doors, and veneer plywood for doors, furniture, paneling and cabinets.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-5.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of sweet birch 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)9,400 psi (65 MPa)16,900 psi (117 MPa)
Stiffness (MOE)1,650,000 psi (11.4 GPa)2,170,000 psi (15 GPa)
Crushing strength (compression parallel to grain)3,740 psi (26 MPa)8,540 psi (59 MPa)
Compression perpendicular to grain470 psi (3 MPa)1,080 psi (7 MPa)
Shear parallel to grain1,240 psi (9 MPa)2,240 psi (15 MPa)
Tension perpendicular to grain430 psi (3 MPa)950 psi (7 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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Buying and finishing sweet birch

Work it out for your project

Why these numbers

Why these numbers?
  1. The situation

    The USDA Forest Products Laboratory measured sweet birch at 1,470 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 × 0.65 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 45 lb/ft³, or 3.8 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers