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Woodworking Math

Wood species

Purpleheart wood

Purpleheart is a hardwood (Peltogyne spp.). At 12% moisture content it has a Janka hardness of 1,860 lbf (8,274 N) and it weighs about 50 lb/ft³ (798 kg/m³), 4.2 lb (1.88 kg) per board foot.

Also called: amaranth.

Key numbers

Janka hardness, 12% MC
1,860 lbf (8,274 N)
Green: 1,810 lbf (8,051 N)
Weight at 12% MC
50 lb/ft³ (798 kg/m³)
4.2 lb per board foot
Specific gravity (oven-dry weight)
0.67 on green volume
Shrinkage, green to oven-dry
6.1% tangential
Radial 3.2%, volumetric 9.9%

One source: USDA Forest Products Laboratory, collected from the world literature (its Tables 5-5 and 4-4)

Why: From the USDA Wood Handbook, which collected these values from the world literature; purpleheart's density is worked from its specific gravity with the Handbook's own equations.

Work out what your boards weigh

How much purpleheart moves

A 12 in wide flatsawn board of purpleheart that goes from 6% to 12% moisture content swells about 0.15 in (about 5/32 in, 3.9 mm). Quartersawn, the same board moves about 0.08 in (about 3/32 in, 2 mm). Flatsawn faces move 1.9 times as much as quartersawn ones, because the wood shrinks 6.1% around the growth rings but only 3.2% across them.

Worked from the Wood Handbook's shrinkage values (Table 4-4) with its Eq. 13-4; the Handbook gives no movement coefficients for imported woods. 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
Brown when cut, turning deep purple in air and eventually dark brown in light.
Grain and texture
Medium to fine texture, usually straight grain.
Working and character
Strong and heavy, moderately hard to work, and it dulls cutters quickly; dull tools heat it and draw out gummy resin, so the Handbook suggests a slow feed and hardened cutters. Turns easily, glues and finishes well; highly resistant to decay.
Uses
Turnery, marquetry, cabinets, fine furniture, parquet, cue butts and carvings; also heavy construction.

Adapted in our own words from the Wood Handbook, Chapter 2, p. 2-34.

Strength

Bending strength is the modulus of rupture (MOR); stiffness is the modulus of elasticity (MOE). Values for purpleheart from Wood Handbook Table 5-5b (p. 5-24), which the Handbook says were collected from the world literature, on clear, straight-grained specimens. Knots and cross grain make lumber weaker than these clear samples (Handbook Chapter 5).

PropertyGreen12% MC
Bending strength (MOR)13,700 psi (94 MPa)19,200 psi (132 MPa)
Stiffness (MOE)2,000,000 psi (13.8 GPa)2,270,000 psi (15.7 GPa)
Crushing strength (compression parallel to grain)7,020 psi (48 MPa)10,320 psi (71 MPa)
Shear parallel to grain1,640 psi (11 MPa)2,220 psi (15 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 Wood Handbook prints 1,860 lbf of side hardness at 12% moisture content for purpleheart, a value it says was collected from the world literature (Table 5-5b, p. 5-24).

    One source: USDA Forest Products Laboratory, collected from the world literature (its Tables 5-5 and 4-4) , 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, collected from the world literature (its Tables 5-5 and 4-4) , sources [1]

  3. So

    The Handbook gives only the green specific gravity (0.67) for purpleheart, so it is moved to 12% with the volumetric shrinkage of 9.9% (Eqs. 4-9 and 4-11), then multiplied by water's density and 1.12 (Eq. 4-14).

    Arithmetic: exact by definition , sources [1]

  4. The number

    About 50 lb/ft³, or 4.2 lb per board foot (1/12 ft³), at 12% moisture content.

    Arithmetic: exact by definition

How we source these numbers