Error predictions for average end diameter sectional formula in tree stem volume measurement

Abstract

The use of the sectional formula given by the product of the cross sectional area related to the average of segment end diameters, times segment length, is a known method to estimate the volume of a tree stem segment. The whole tree stem volume can be obtained summing volumes of individual segments. There is not a formal study about the errors in using that method that allows comparing it to other conventional methods. In this work, following a theoretical procedure proposed recently in the forest measurement literature, those errors were computed. The method was evaluated applying it to the geometries of paraboloid, cone, and neiloid, to get the errors in tree stem volume estimation as function of a given number of segments, n. The average absolute percent errors were: ≤ 10.9 % for n ≥ 5; ≤ 5.5 % for n ≥ 10; ≤ 2.8 % for n ≥ 20; ≤ 1.9 % for n ≥ 30. Compared to known results, the method is better than Smalian and Huber methods, though it is not for the frustum of cone volume formula. Additionally, there are algebraic proves showing that the segment volume estimated by the method is lower than the volume for frustums of paraboloid and cone; in this work, the proof that it is also lower than the volume for a frustum of neiloid is provided, which completes the corresponding knowledge on the subject.