On the distributions of mass, thickness and density in paper

Data is presented from experimental measurements of the local grammage and thickness made on laboratory formed sheets with a range of structures. We observe that the distributions of local grammage and local thickness are strongly correlated. The correlation between the variances of thickness and grammage are dependent on pulp type but independent of mean sheet grammage, whereas the correlation between their coefficients of variation is independent of pulp type and dependent on mean sheet grammage. A correlation is shown also between the variance of local density and that of grammage and this is sensitive to mean grammage. The variance of local density is however independent of the variance of local thickness. The coefficient of variation of local density is correlated to the coefficients of variation of local grammage and thickness; the correlations being sensitive to pulp type and apparently dominated by the properties of high coarseness fibres in a blended furnish. We note also that the mean density of sheets containing high coarseness fibres increases with improved formation.