# Mass Volume Relationship of Timber

## Density

The density of a piece of timber is a function not only of the amount of wood substance present, but also of the presence of both extractives and moisture. In a few timbers extractives are completely absent, while in many they are present, but only in small amounts and usually less than 3% of the dry mass of the timber.

In some exceptional cases, the extractive content may be as high as 10% and in these cases it is necessary to remove the extractives prior to the determination of density. The presence of moisture in timber not only increases the mass of the timber, but also results in swelling of the timber, and hence both mass and volume are affected. Thus, in the determination of density where:

ρ = m/v

both the mass (m) and volume (v) must be determined at the same moisture content. Generally, these two parameters are determined at zero moisture content.

However, as density is frequently quoted at a moisture content of 12% – since this level is frequently experienced in timber in use – the value of density at zero moisture content is corrected to 12% if volumetric expansion figures are known, or else the density determination is carried out on timber at 12% moisture content. Thus, if:

m_{x} = m_{0}(1 + 0.01µ)

where m_{x} is the mass of timber at moisture content x, m_{0} is the mass of timber at zero moisture content, and µ is the moisture content %, and:

v_{x} = v_{0}(1 + 0.01s_{v})

where v_{x} is the volume of timber at moisture content x, v_{0} is the volume of timber at zero moisture content, and s_{v} is the volumetric shrinkage/expansion %, it is possible to obtain the density of timber at any moisture content in terms of the density at zero moisture content, thus:

As a very approximate rule of thumb, the density of timber increases by approximately 0.5% for each 1.0% increase in moisture content up to 30%.

Density therefore will increase, slightly up to moisture contents of about 30% as both total mass and volume increase; however, at moisture contents above 30%, density will increase rapidly and curvilinearly, with increasing moisture content, since, the volume remains constant above this value, while the mass increases.

The determination of density by measurement of mass and volume takes a considerable period of time and over the years a number of quicker techniques have been developed for use where large numbers of density determinations are required. These methods range from the assessment of the opacity of a photographic image that has been produced by either light or b-irradiation passing through a thin section of wood, to the use of a mechanical device (the Pilodyn) that fires a spring-loaded bolt into the timber after which the depth of penetration is measured. In all these techniques, however, the method or instrument has to be calibrated against density values obtained by the standard mass/volume technique.

Timber possess different types of cell that could be characterised by different values of the ratio of cell-wall thickness to total cell diameter. Since this ratio can be regarded as an index of density, it follows that the density of timber will be related to the relative proportions of the various types of cell.

Density, however, will also reflect the absolute wall thickness of any one type of cell, since it is possible to obtain fibres of one species of timber the cell-wall thickness of which can be several times greater than that of fibres of another species. The influence of various growth factors on determining density is provided by Saranpää (2003).

Density, like many other properties of timber, is extremely variable; it can vary by a factor of ten, ranging from an average value at 12% moisture content of 176 kg/m^{3} for balsa, to about 1230 kg/m^{3 }for lignum vitae (Fig. 1).

Balsa, therefore, has a density similar to that of cork, while lignum vitae has a density slightly less than half that of concrete or aluminium. The values of density quoted for different timbers, however, are merely average values, as each timber will have a range of densities reflecting differences between early and latewood, between the pith and outer rings, and between trees on the same site. Thus, for example, the density of balsa can vary from 40 to 320 kg/m^{3} .

In certain publications, reference is made to the weight of timber, a term widely used in commerce; it should be appreciated that the quoted values are really densities.

## Specific gravity

The traditional definition of specific gravity (G, also known as relative density) can be expressed as:

G = ρ_{t}/ρ_{w}

where ρ_{t} is the density of timber, and ρ_{w} is the density of water at 4°C (1.0000 g/ml). G will therefore vary with moisture content, consequently the specific gravity of timber is usually based on the oven-dry mass, and volume at some specified moisture content.

This is frequently taken as zero though, for convenience, green or other moisture conditions are sometimes used, when the terms basic specific gravity and nominal specific gravity are applied, respectively. Hence:

Gµ = m_{0} ÷ V_{µ}ρ_{w}

where m_{0} is the oven-dry mass of timber, V_{µ} is the volume of timber at moisture content m, ρ_{w} is the density of water, and G_{m} is the specific gravity at moisture content m.

At low moisture contents, specific gravity decreases slightly with increasing moisture content up to 30%, thereafter remaining constant. In research activities specific gravity is defined usually in terms of oven-dry mass and volume.

However, for engineering applications specific gravity is frequently presented as the ratio of oven-dry mass to volume of timber at 12% moisture content; this can be derived from the oven-dry specific gravity, thus:

where G_{12} is the specific gravity of timber at 12% moisture content, G_{0} is the specific gravity of timber at zero moisture content, µ is the moisture content %, and G_{s12} is the specific gravity of bound water at 12% moisture content.

The relationship between density and specific gravity can be expressed as:

ρ = G(1 + 0.01µ)ρ_{w}

where ρ is the density at moisture content µ, G is the specific gravity at moisture content m, and ρ_{w} is the density of water. This equation is valid for all moisture contents. When µ = 0 the equation reduces to:

ρ = G_{0} i.e. density and specific gravity are numerically equal.

## Density of the dry cell wall

Although the density of different timbers may vary considerably, the density of the actual cell wall material remains constant for all timbers, with a value of approximately 1500 kg/m^{3} when measured by volume-displacement methods.

The exact value for cell-wall density depends on the liquid used for measuring the volume; densities of 1525 and 1451 kg/m^{3} have been recorded for the same material using water and toluene, respectively.

## Porosity

In above discussion, the cellular nature of timber was described in terms of a parallel arrangement of hollow tubes. The porosity (p) of timber is defined as the fractional void volume and is expressed mathematically as:

p = 1 − V_{f}

where V_{f} is the volume fraction of cell-wall substance. The calculation of porosity is set out in Chapter 3 of Dinwoodie (2000).

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