Estimating stem and root-anchorage flexibility in trees

This paper describes a nondestructive method fbr distinguishing root flexib ility from stem flexibility in living trees. It is used here for Sitka spru ce (Picea sitchensis (Bong.) Carriere.), but is applicable to any species w here the main stem is normally straight and near-vertical. Well-known engin eering equations permit the calculation of deflected shape for a vertical c antilever with arbitrary distribution of mass and bending stiffness, when s ubjected to a lateral force. The equations are used to calculate stem defle ctions of four Sitka spruce trees fbr which the stem and branch mass distri bution and stem taper have been measured. Free parameters in the mathematical model are a nominal value of Young's Mo dulus 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 ste m 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 t rees, the calculated deflection curve is compared with actual deflections m easured when the living tree is pulled by a rope at a specified point. By a djusting both E and k, iteratively, a best fit solution is obtained. This p rovides a simple and effective way to determine both stem stiffness and roo t hinge stiffness from a single experiment on a living tree.