A new and improved modification to Smalian’s equation for butt logs

There is still a need to estimate the volumes of butt logs when only the end diameters and length are known. Smalian?s equation averages the cross-sectional area of the ends. This is fairly accurate for upper logs but not for butt logs because of the butt flare. Bruce (1982) modified Smalian?s equation for butt logs by using 25 percent of the butt cross section and 75 percent of the small end cross section. Bruce?s equation is fairly accurate for large, short logs but not small or long logs. Our study used measurements from 500 logs to find the best percentage to use according to butt end diameter and log length. The percentage varied from 45 percent for small, long logs to 25 percent for large, short logs. The new model was validated using two other data sets of 220 and 75 logs. The results indicated that the new model (using diameters inside bark of southern yellow pine) had little bias and was accurate for all diameter classes and lengths studied; thereby, providing a better estimator than that of the Smalian or Bruce equations.

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