A Ratio Method for Calculating Stem Volume to Variable Merchantable Limits, and Associated Taper Equations

One method for estimating the volume of the merchantable portion of a tree stem is the volume ratio method. In this study the ratio used with this method was derived from another ratio expressed as ground-to-limit volume to total stem volume. Because of the latter ratio's strong correlation with the ratio of merchantable top diameter/breast height diameter and merchantable height/total tree height, several mathematical models were formed employing these variables for its estimation for red pine (Pinus resinosa Ait.) and sugar maple (Acer saccharum Marsh.). Among the models that were tested, the best for each variable was chosen by assessing its adequacy by the statistical measures of fit index and standard error of estimate. When checked against an independent set of data, these best models performed satisfactorily, with small overall biases. Furthermore, taper equations were derived from these ground-to-limit volume ratio equations.