Determination of stemwood volume using mid-diameter and taper
2004
Felder, S.,Otto-von-Guericke-Universität Magdeburg, Magdeburg (Germany). Institut fuer Sozialmedizin und Gesundheitsoekonomie
The present paper shows that the volume for the theoretical shaft slopes of stemwood can be determined if in the middle of the log, besides the diameter, measurements are also taken and recorded from the shaft's slope. The result is interesting for the stumps of the cone, the neiloid and the cubic paraboloid, all solid bodies that can not only be cubed with the length and the mid-diameter. Huber's formula, widely used in practice, approximates the volume of the stemwood using the cylinder formula. This is not only an exact measurement for the cylinder, but also for the apollonian paraboloid stump, something that has been known in dendrometry for a long time. However, Huber's formula underestimates the volume of the stumps of the cone and the neiloid. In both stumps the error is a cubic function of the length and a quadratic function of the middle taper, whereby it is 30 per cent higher for the neiloid than for the cone. The paper also examines the margin of error of Huber's formula for the stump of the cubic paraboloid. In this case the middle area formula overestimates the actual volume. In comparison with the other solid bodies, however, the margin of error for the cubic paraboloid is limited to a maximum of 5 per cent.
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