A geometrical tree volume model based on the location of the centre of gravity of the bole

Abstract

A tree bole model describing a geometrical form in between a paraboloid and cone "paracone" has been developed. The model is based on empirical evidence that the average centre of gravity of aspen (Populustremuloides Michx.) boles without branches lies at 3/10 of the bole height from its base. Outside bark bole volume, V (cubic decimetres), can therefore be estimated nondestructively from the total height, H (metres), and the diameter outside bark, dK (centimetres), measured at a relative height, K, as follows:[Formula: see text]Based on a sample of 70 aspen stems, this equation estimates individual bole volume from total bole length or height and from a single diameter measurement, either at the 3/10 position or at the breast-height position, as accurately as Smalian's formula using seven diameter measurements. Based on the sample, the 3/10 position should be chosen over breast height wherever breast height lies below 20 or above 60% of the total height. It is important that care be taken in the measurement of the diameter due to the sensitivity of the volume equation to diameter variation. In addition to volume estimation, the paracone model provides a comparison profile around which stem form variation within and among species may be observed.