Ring Width and Ring Diameter as Functions of Ring Number in Suppressed Maples and Oaks

Abstract

Phipps showed that the cross-sectional area of successive tree rings in suppressed red maples and chestnut oaks, sampled at three-foot intervals above the base, is approximately constant. I show that this invariance in cross-sectional area is consistent with ring width varying as the inverse square root of ring number and with mean ring diameter and trunk diameter each scaling as the square root of ring number. These results may be useful in formulating growth rules for tree trunks of selected species, under constant environmental conditions, in terms of a single independent variable. For example, if elastic similarity holds, trunk height is proportional to the two-thirds power of trunk diameter. This relation implies that trunk height scales as the cube root of ring number. Thus, trunk height and trunk diameter may, in principle, both be expressed in terms of one independent variable, ring number.