CALCULATION OF THE FRUSTUM FORM FACTOR 221 



true of hardwoods with branching crowns. Measured from this point, the frustum 

 of the tree will not differ greatly from that of either a cone or a paraboloid. 



A great source of irregularity in frustum form factors, as in absolute form factors 

 for cubic contents, is found to be the influence of butt swelling extending above 

 B.H. and second, the influence of thickness of bark. Both of these factors reduce 

 the proportion of woody contents to the dimensions and consequently reduce the 

 form factor. 



183. Calculation of the True Frustum Form Factor. A far more 

 serious difficulty in the use of the frustum form factor lies in securing 

 the exact coincidence of the top diameters of the frustums, used as the 

 unit or standard for volume, and the average top diameters of the trees 

 whose volumes are to be compared for the determination of the form 

 factors. There is but one exact method, namely to compute the form 

 factors of a given height separately for each tree whose D.B.H. and 

 top diameter differ even by rjj-inch, by using a frustum whose three 

 dimensions exactly coincide with those of the tree frustum. This 

 method gives the most consistent form factors. The results for long- 

 leaf pine given in the table on p. 222 were obtained by this method. 



This method can be simplified by first averaging together for all 

 the trees in a diameter and height class the four factors, volume, D.B.H. , 

 height, and top diameter. The frustum of a cone having these aver- 

 age dimensions is then used to determine the frustum form factor of 

 the class, by comparing its volume with that of the average tree of 

 the class. While less accurate, this method reduces the computations 

 considerably and is within the required limits of accuracy of the method. 



By this method, the computation of the frustum form factors is 

 the first step in the construction of the volume table for which they 

 are intended. 



184. Calculation of the Volumes of Frustums. Influence of Fixed 

 versus Variable Top Diameters. The purpose of the frustum form 

 factors thus obtained is to make possible the construction of a volume 

 table in board feet, by applying these factors to the volumes of frustums 

 of cones. This may be done in the office, once the factors are known 

 and the dimensions of the frustums determined. 



The second step is therefore to determine these dimensions of frus- 

 tums of cones. The base is fixed, being equal to D.B.H., in 1- or 2-inch 

 classes. But the top diameter of these cones is a source of trouble. 

 As seen in the construction of volume tables (§§ 157-158) the top diam- 

 eters to which trees are actually utilized tends to decrease as height 

 increases, and to increase with D.B.H. The table will be based on 

 one of two plans, a fixed top diameter, or variable top diameters coin- 

 ciding with actual utilization. 



Whichever basis is adopted, the top diameters of the frustums 

 must coincide with the average top diameter of the merchantable boles, 



