Estimating the accuracy of volume equations using taper equations of stem profile

Abstract

Comparisons of log volume estimation techniques are performed using the equations of Smalian, Huber, and Newton, and a numerical technique using cubic splines. The data utilized were obtained by predicting diameters at various points along the stem from two paper equations for white fir. Results indicate that Newton's and Huber's equations were the most accurate, followed by the cubic spline and Smalian's equation, respectively. This technique facilitated partitioning of the total error in volume estimation into measurement error and error due to model misspecification arising when the taper of logs could not be exactly described by a simple model such as a frustum of a paraboloid. For the taper relationships analyzed it was shown that the error due to the selection of an inappropriate mensurational model is less than 5% for a measurement distance of 16 ft (4.9 m) for all models tested and can be substantially reduced by applying the formulae only to logs positioned above basal swell. Systematic measurement error was assessed analytically and found to range between 1 and 4%. Thus, total error in volume estimation was less than 9% for all methods tested.