A Model of Knot Shape and Volume in Loblolly Pine Trees

Guillermo Trincado, Harold E. Burkhart


The shape and structure of branches attached internally to the stem (knots) for loblolly pine (Pinus taeda L.) trees were modeled. Data on knot shape were obtained from the dissection of branches taken from 34 22-yr-old sample trees growing under ten different initial spacings. A total of 341 branches located below the live crown were dissected in the radial/tangential plane. Afterward, a procedure was implemented to reconstruct the branch diameter perpendicular to the branch pith. This information was used to develop a model for representing knot shape, which assumed that the live portion of a knot can be modeled with a one-parameter equation and the dead portion by assuming a cylindrical shape. To study the variability in shape of individual knots (live portion), the model was fitted to 218 branch profiles using nonlinear mixed-effects modeling techniques. A graphical analysis indicated that the random-effects parameter was related to branch diameter. Thus, branch diameter was included as a predictor variable to reduce between-individual variability in knot shape. Reconstructed knots with smaller diameters were more cylindrical; those with larger diameters were more parabolic or conical in shape. Analytical expressions were derived for estimating the volume of knots (live/dead portions) for three types of branch conditions on simulated trees: 1) live branches; 2) nonoccluded dead branches; and 3) occluded dead branches. The knot model assumes a substantial simplification of branch morphology, but should be useful for representing knots as 3-D entities in the stems of loblolly pine trees.


Wood quality;knot shape;knot volume;<i>Pinus taeda</i>

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