# Equilibrium moisture content

Equilibrium moisture content of wood versus humidity and temperature, according to the Hailwood-Horrobin equation.

The moisture content of wood below the fibre saturation point is a function of both relative humidity and temperature of surrounding air. The equilibrium moisture content (EMC) is the moisture content at which the wood is neither gaining or losing moisture; this however, is a dynamic equilibrium and changes with relative humidity and temperature.

The moisture content (M) of wood is defined as:

$M = \frac{m-m_{od}}{m_{od}}$

where m is the mass of the wood (with moisture) and $m_{od}$ is the oven-dry mass of wood (i.e. no moisture). If the wood is placed in an environment at a particular temperature and relative humidity, its moisture content will generally begin to change in time, until it is finally in equilibrium with its surroundings, and the moisture content no longer changes in time. This moisture content is the EMC of the wood for that temperature and relative humidity.

The Hailwood-Horrobin equation for two hydrates is often used to approximate the relationship between EMC, temperature (T), and relative humidity (h):[1][2][3]

$M_{\mathrm{eq}}=\frac{1800}{W}\left[\frac{kh}{1-kh}\,+\,\frac{k_1kh+2k_1k_2k^2h^2}{1+k_1kh+k_1k_2k^2h^2}\right]$

where Meq is the equilibrium moisture content (percent), T is the temperature (degrees Fahrenheit), h is the relative humidity (fractional) and:

$W = 330 + 0.452\,T + 0.00415\,T^2$
$k = 0.791 + 4.63\times 10^{-4}\,T - 8.44\times 10^{-7}\,T^2$
$k_1= 6.34 + 7.75\times 10^{-4}\,T - 9.35\times 10^{-5}\,T^2$
$k_2= 1.09 + 2.84\times 10^{-2}\,T - 9.04\times 10^{-5}\,T^2$

This equation does not account for the slight variations with wood species, state of mechanical stress, and/or hysteresis. It is an empirical fit to tabulated data provided in the same reference, and closely agrees with the tabulated data. For example, at T=140 deg F, h=0.55, EMC=8.4% from the above equation, while EMC=8.0% from the tabulated data.

## References

1. ^ Hailwood, A.J.; S. Horrobin (1946). "Absorption of water by polymers: analysis in terms of a simple model". Trans. Faraday Soc. 42B: 84–102.
2. ^ Rasmussen, E.F. (1988). In Forest Products Laboratory, U.S. Department of Agriculture. Dry Kiln Operators Manual. Hardwood Research Council.
3. ^ Eleotério, Jackson Roberto; Clóvis Roberto Haselein, Nestor Pedro Giacomini. "A Program to Estimate the Equilibrium Moisture Content of Wood". Ciência Florestal 8 (1): 13–22. ISSN 0103-9954. Retrieved 2008-11-14.