Diameters and dry weights of tree shoots: effects of Young's modulus, taper, deflection and angle

The structural theory for cantilever beams was used to calculate the diameters and dry weights of wood that unbranched shoots must produce to support their own weights. The study was done on Picea sitchensis (Bong.) Carr., Pinus contorta Dougl., Larix decidua Mill. and Betula pendula Roth. syn. verrucosa Ehrh. The weights of wood increased in a non-linear fashion with increase in shoot length. A large investment in wood (as measured by diameter and dry weight) was required to maintain a small endpoint deflection (1-5% of the length). By contrast, the degree of linear taper had only a small effect on support costs, as did the Young's modulus of the wood (over the range 1-4 GPa) and the angle of the shoot from the horizontal (over the range 0-45 degrees ). Current year's shoots on young trees of P. sitchensis and P. contorta incur a high support cost in order to maintain small (1-5%) deflections throughout the year: similar shoots of L. decidua and B. pendula have smaller support costs because they deflect by about 20% after leaf expansion in spring.