Représentation mathématique des noeuds dans le tronc des arbres

Abstract

This study is aimed at developing equations describing the shape of any particular knot in the trunk of a tree. The present model differs from previous models in that it is not limited by the assumption of a straight conical knot. The knot is represented by an assemblage of elliptical cone sections with the axis defined by a Hermite-type cubic equation or a straight line, and ends in a half ellipsoid symbolizing the enclosure of an intergrown knot. Simulations of knot shapes are presented to demonstrate the versatility of the model. The model seems flexible enough to adjust to common knot shapes presented in the literature. This model is intended to be incorporated into tree felling, bucking, and sawing simulation softwares.

Modeling jack pine branch characteristics in Eastern Canada

“…Insertion angle tends to decrease with age as its biomass increases and gravity pushes it down. On the other hand, the growth of branches with acute angles in relation to stems is generally higher because they have easier access to light (Samson et al, 1996;Wilson, 2000).…”

Predicting the vertical location of branches along Atlas cedar stem (Cedrus atlantica Manetti) in relation to annual shoot length

“…It could be done by coupling it to a knot form model, which locate precisely the path of the branch inside the bole (e.g. [35]), and using a virtual sawing software (e.g. [20]).…”

Modelling knot morphology as a function of external tree and branch attributes

“…Another possible approach is to directly develop internal knot shape models (Samson et al 1996;Trincado and Burkhart 2008). Fewer studies have used this approach due to the difficulties of obtaining internal data using destructive methods.…”

“…For instance, early knot models represented the knot as a circular cone perpendicular to the longitudinal axis of the stem (Richards et al 1979). An angle of inclination was later added (Leban and Duchanois 1990), although it was known that the axis of a knot is rarely straight (Samson et al 1996). At its initiation point, the angle of insertion of a knot relative to the horizontal is generally positive (i.e., oriented upwards from the horizontal plane), and the curvature is due to the gradual decrease of this angle over time.…”