Theoretical evaluation of Huber and Smalian methods applied to tree stem classical geometries

Abstract

Huber, Smalian and Newton methods, to estimate tree stem and log volume by sections, were theoretically evaluated applying them to the geometries of paraboloid, cone and neiloid. The study follows approximation procedures from calculus for volume estimation of solids of revolution as function of the number of segments and error analysis methods from forest measurement research. The errors in using Huber and Smalian methods have been determined. Additionally, it was algebraically proved that the Huber's error is exactly one half of the Smalian's error and opposite in sign. The results predict that, for any tree stem modeled classically, Huber's and Smalian's average absolute percent errors should be: less than 13.5 % and 27 %, respectively, for five or more segments; less than 7 % and 14 %, for 10 or more segments; less than 3.6 % and 7.2 %, for 20 or more segments; less than 2.5 % and 5 %, for 30 or more segments. This work provides a quantization on the classical theory of tree stem and log volume estimation. It could help to unify that theory and make it a more compact reference for forest measurement teaching and research.