Computing factors of safety against wind‐induced tree stem damage

Abstract

The drag forces, bending moments and stresses acting on stems differing in size and location within the mechanical infrastructure of a large wild cherry (Prunus serotina Ehrh.) tree are estimated and used to calculate the factor of safety against wind-induced mechanical failure based on the mean breaking stress of intact stems and samples of wood drawn from this tree. The drag forces acting on stems are calculated based on stem projected areas and field measurements of wind speed taken within the canopy and along the length of the trunk. The bending moments and stresses resulting from these forces are shown to increase basipetally in a nearly log-log linear fashion toward the base of the tree. The factor of safety, however, varies in a sinusoidal manner such that the most distal stems have the highest factors of safety, whereas stems of intermediate location and portions of the trunk near ground level have equivalent and much lower factors of safety. This pattern of variation is interpreted to indicate that, as a course of normal growth and development, trees similar to the one examined in this study maintain a cadre of stems prone to wind-induced mechanical damage that can reduce the probability of catastrophic tree failure by reducing the drag forces acting on older portions of the tree. Comparisons among real and hypothetical stems with different taper experiencing different vertical wind speed profiles show that geometrically self-similar stems have larger factors of safety than stems tapering according to elastic or stress self-similarity, and that safety factors are less significantly influenced by the 'geometry' of the wind-profile.