Estimating stem and root-anchorage flexibility in trees

This paper describes a nondestructive method for distinguishing root flexibility from stem flexibility in living trees. It is used here for Sitka spruce (Picea sitchensis (Bong.) Carriere.), but is applicable to any species where the main stem is normally straight and near-vertical. Well-known engineering equations permit the calculation of deflected shape for a vertical cantilever with arbitrary distribution of mass and bending stiffness, when subjected to a lateral force. The equations are used to calculate stem deflections of four Sitka spruce trees for which the stem and branch mass distribution and stem taper have been measured. Free parameters in the mathematical model are a nominal value of Young's Modulus E (assumed uniform and isotropic over the cross section and height of the tree stem) and a root-anchorage stiffness k. The former allows the stem to curve, whereas the latter represents the flexibility of the roots and allows the stem to tilt elastically at ground level. For each of the four trees, the calculated deflection curve is compared with actual deflections measured when the living tree is pulled by a rope at a specified point. By adjusting both E and k, iteratively, a best fit solution is obtained. This provides a simple and effective way to determine both stem stiffness and root hinge stiffness from a single experiment on a living tree.