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Woodworking Math

Wood species

Poplar wood

Poplar is a hardwood (Liriodendron tulipifera). At 12% moisture content it has a Janka hardness of 540 lbf (2,402 N) and it weighs about 29 lb/ft³ (470 kg/m³), 2.4 lb (1.11 kg) per board foot.

Also called: yellow-poplar, tulip-poplar, tulipwood, whitewood.

Key numbers

Janka hardness, 12% MC
540 lbf (2,402 N)
Green: 440 lbf (1,957 N)
Weight at 12% MC
29 lb/ft³ (470 kg/m³)
2.4 lb per board foot
Specific gravity (oven-dry weight)
0.42 at 12% MC volume
0.40 on green volume
Shrinkage, green to oven-dry
8.2% tangential
Radial 4.6%, volumetric 12.7%

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

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

Work out what your boards weigh

How much poplar moves

A 12 in wide flatsawn board of yellow-poplar that goes from 6% to 12% moisture content swells about 0.21 in (about 7/32 in, 5.3 mm). Quartersawn, the same board moves about 0.11 in (about 1/8 in, 2.9 mm). Flatsawn faces move 1.8 times as much as quartersawn ones, because the wood shrinks 8.2% around the growth rings but only 4.6% across them.

Worked with the Wood Handbook's dimensional change coefficients for yellow-poplar (Table 13-5: 0.00289 tangential, 0.00158 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
White sapwood, often several inches wide; yellowish-brown heartwood, sometimes streaked purple, green, black, blue or red (the colors don’t change its properties).
Grain and texture
Generally straight and fairly uniform.
Working and character
Moderately light, soft and fairly weak in bending. It shrinks a fair amount from green but dries easily and is stable afterwards.
Uses
Furniture, interior molding, siding, cabinets, musical instruments and structural parts; also plywood.

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

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Clear, straight-grained samples of yellow-poplar 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)6,000 psi (41 MPa)10,100 psi (70 MPa)
Stiffness (MOE)1,220,000 psi (8.4 GPa)1,580,000 psi (10.9 GPa)
Crushing strength (compression parallel to grain)2,660 psi (18 MPa)5,540 psi (38 MPa)
Compression perpendicular to grain270 psi (2 MPa)500 psi (3 MPa)
Shear parallel to grain790 psi (5 MPa)1,190 psi (8 MPa)
Tension perpendicular to grain510 psi (4 MPa)540 psi (4 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 yellow-poplar 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 × 0.42 × 1.12.

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 29 lb/ft³, or 2.4 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers