Computing factors of safety against wind-induced tree stem damage

The drag forces, bending moments and stresses acting on stems differing in size and location within the mechanical infrastructure of a large wild cher ry (Prunus serotina Ehrh.) tree are estimated and used to calculate the fac tor of safety against wind-induced mechanical failure based on the mean bre aking 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 an d field measurements of wind speed taken within the canopy and along the le ngth of the trunk. The bending moments and stresses resulting from these fo rces are shown to increase basipetally in a nearly log-log linear fashion t oward the base of the tree. The factor of safety, however, varies in a sinu soidal manner such that the most distal stems have the highest factors of s afety, whereas stems of intermediate location and portions of the trunk nea r ground level have equivalent and much lower factors of safety. This patte rn of variation is interpreted to indicate that, as a course of normal grow th and development, trees similar to the one examined in this study maintai n a cadre of stems prone to wind-induced mechanical damage that can reduce the probability of catastrophic tree failure by reducing the drag forces ac ting on older portions of the tree. Comparisons among real and hypothetical stems with different taper experiencing different vertical wind speed prof iles show that geometrically self-similar stems have larger factors of safe ty 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.