Elasticity and microfibrillar angle in the wood of Sitka spruce

The initial value of Young's modulus, E, has been measured for small specimens of Sitka spruce wood taken from the annual rings of two disks and has been found in both cases to increase from pith to bark. The decrease from pith to bark in the helical angle $\theta $ of the cellulose microfibrils in the walls of the tracheids averaged over an annual ring has been determined from matched specimens. E has been found to vary regularly with $\theta $. Two mathematical models of the cell involved have been developed and the experimental findings applied to the relations derived between E and $\theta $. The first model was that of a number of helical springs free to slip, twist and bend and gave a relationship between the helical angle and the reciprocal of Young's modulus as proportional to tan$^{2}\,\theta $. The second model, that of an anisotropic homogeneous cell wall, gave 1/E as being proportional to a quadratic function in sin$^{2}\,\theta $. Relative shear in the cell wall has been predicted from this latter model. The tan$^{2}\,\theta $ relation is found to hold provided $\theta $ is less than about 40 degrees. The sin$^{2}\,\theta $ relation holds, on the other hand, over the full range of $\theta $ observed. Some implications of these relations are discussed.