The power function as a simple stem profile examination tool

Abstract

Formulae are presented for calculating the volume, surface area, centre of gravity, centre of mass, form, taper, and instantaneous slope of the power function. A profile plotting technique is also used that allows visual comparisons between average stem profiles independent of the size and taper of individual stems. The technique is used to demonstrate that the position near 30% of the height from the base of the stem is a position of form stability for volume estimation. Using the paracone profile model (a power function midway between a paraboloid and a cone) with the diameter at the 30% position and the total stem height, individual stem volume estimates within 10% of the true volume (95% confidence) are obtained once again using a sample of 50 yearling aspen (Populustremuloides Michx.). The plotting technique is then applied to the aspen sample, and the average profiles support the hypothesis that juvenile stems may begin life as paraboloids. The average centre of gravity, the average centre of mass, the sectional form, the average form, and the taper of the stems are also examined and are shown to be quantitative indicators of the plotted profile characteristics.