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Woodworking Math

Wood species

Paper birch wood

Paper birch is a hardwood (Betula papyrifera). At 12% moisture content it has a Janka hardness of 910 lbf (4,048 N) and it weighs about 38 lb/ft³ (616 kg/m³), 3.2 lb (1.45 kg) per board foot.

Also called: Betula papyrifera.

Key numbers

Janka hardness, 12% MC
910 lbf (4,048 N)
Green: 560 lbf (2,491 N)
Weight at 12% MC
38 lb/ft³ (616 kg/m³)
3.2 lb per board foot
Specific gravity (oven-dry weight)
0.55 at 12% MC volume
0.48 on green volume
Shrinkage, green to oven-dry
8.6% tangential
Radial 6.3%, volumetric 16.2%

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

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

Work out what your boards weigh

How much paper birch moves

A 12 in wide flatsawn board of paper birch 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 0.16 in (about 5/32 in, 4 mm). Flatsawn faces move 1.4 times as much as quartersawn ones, because the wood shrinks 8.6% around the growth rings but only 6.3% across them.

Worked with the Wood Handbook's dimensional change coefficients for paper birch (Table 13-5: 0.00304 tangential, 0.00219 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
The Handbook gives no separate color for paper birch.
Working and character
Lighter, softer and weaker than yellow and sweet birch. Birch shrinks considerably as it dries.
Uses
Toothpicks, tongue depressors, ice cream sticks, and turned goods such as spools, bobbins, small handles and toys.

Paper birch grows right across the continent.

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 paper 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)6,400 psi (44 MPa)12,300 psi (85 MPa)
Stiffness (MOE)1,170,000 psi (8.1 GPa)1,590,000 psi (11 GPa)
Crushing strength (compression parallel to grain)2,360 psi (16 MPa)5,690 psi (39 MPa)
Compression perpendicular to grain270 psi (2 MPa)600 psi (4 MPa)
Shear parallel to grain840 psi (6 MPa)1,210 psi (8 MPa)
Tension perpendicular to grain380 psi (3 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 paper birch

Work it out for your project

Why these numbers

Why these numbers?
  1. The situation

    The USDA Forest Products Laboratory measured paper birch at 910 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 × 0.55 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 38 lb/ft³, or 3.2 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers