1. The in-plane distribution of density in handsheets C.T.J. Dodson, Y. Oba and W.W. Sampson On the distributions of mass, thickness and density of paper Appita J. 54, 4 (2001) 385-389.

2. Introduction Measurements Theory Conclusions Overview

3. Affects pore size distribution, ink transfer, strain distributions under tension, etc. Formation - Distribution of Mass Density

4. Distribution of Density Many physical properties, e.g. tensile index, tear index, light scattering coefficient, permeability, etc. are strongly correlated with mean sheet density. Expect therefore that the local properties of small zones will be dependent on local density.

5. Experimental Sheets with a range of structures and known forming conditions. Measure thickness and grammage of small zones knowing the position of each measurement.

6. 48 conditions

7. Local thickness determination Non contacting double laser triangulation thickness tester Computer controlled x-y stage 0.5 mm pitch. Local average thickness of 1mm square zone taken as average of 4 measure- ments Samples marked 1 mm

9. Local grammage determination Ambertec  -formation tester. Same 1 mm zones measured as for thickness. Formation at scales between 100  m and 7 mm measured.

10.  grammagethickness density

15. Thickness,  m Grammage, g m -2

16. Theory If thickness and grammage are bivariate normally distributed we have: where and if

21. Conclusions Coefficients of variation of thickness and grammage are linearly dependent and independent of furnish. Bulk structure dominated by presence of TMP in blended furnish. Mean thickness depends on formation.

22. Relationship between local grammage and thickness is well described by the Bivariate normal distribution. An approximate model slightly under- estimates density variation.

23. Acknowledgments Funding: Oji Paper Company Ltd., Japan