Support costs of different branch designs: effects of position, number, angle and deflection of laterals

The structural theory for cantilever beams was used to calculate the dry weight of wood that a branch of Picea sitchensis (Bong.) Carr. must produce to support its own weight plus that of laterals in different positions and numbers, and with different angles and deflections. The endpoint of the branch was maintained at 2% of its length, and constant values or functions (measured on real branches) were assumed for Young's modulus, taper and self weights of wood and foliage. Support costs (branch wood dry weights) were minimized when laterals were positioned so that the center of gravity was close to the base of the branch, and when the branch was angled upward from the horizontal. Small savings in support costs also resulted when laterals were not forward pointing, were angled upward and had endpoint deflections of at least 20% of their length.