220 FRUSTUM FORM FACTORS 



volume form factors of the paraboloid and cone when compared with a cylinder of 

 equal dimensions. 



The nearer the top of the tree this upper diameter falls, or the closer the degree 

 of utilization, the shorter will the completed cone become, until it coincides with 

 the paraboloid in height. In the same manner the frustum form factor will increase, 

 until it reaches a maximum of 1.50 for the completed cone. 



Chandler, 1 in an extensive investigation of the frustum form factor of northern 

 hardwoods, birch, beech and maple, determined that this factor was independent of 

 species, site or other influences, and independent of diameter and height, but was 

 dependent on the two factors, form quotient, and taper ratio. The form quotient 

 agrees in principle with that of Tor Jonson. Based on D.B.H., instead of stump, 

 it was computed for merchantable rather than total height, by first subtracting 

 diameter at top or d from both diameter at B.H. and at middle of merchantable 

 length. Then 



di—d 

 9i= D^d- 



The taper ratio is the ratio between top diameter of merchantable bole, and 

 D.B.H. 



Merchantable cubic frustum form factors were found to diminish as form 

 quotient diminished and as taper ratio increased. The first result is obvious. 

 The second confirms the conclusions set forth above as to the effect of close utiliza- 

 tion in increasing the frustum form factor. 



These researches have definitely proved, on an empirical basis, the fact that, 

 other things being equal, frustum form factors based on a fixed top diameter do 

 not express a scientific relation between the form and volume, but will vary with 

 the relation between cone and paraboloid. In its final analysis, the frustum form 

 factor is an endeavor to express the paraboloidal forms of trees by the use of frustums 

 of cones and the application of a correction or form factor. Although a great 

 improvement over older methods if intelligently applied, it is- not a universal 

 method, since its results vary with taper ratio, butt swelling, bark thickness, and the 

 top diameter utilized. 



On the other hand, the natural divergence in the total form and cubic volume 

 of trees which gives rise to the variation in form quotients of from 0.575 to 0.8 is 

 overcome in a marked degree by the substitution of the merchantable frustum 

 form factor since, first, trees with a high-form quotient and of the same total height 

 will be cut higher in the tops than those with a low-form quotient (§ 179). The 

 merchantable form factor in itself coincides with this greater utilization and there-] 

 fore approaches closer to unity, for both forms. If all trees are utilized to a fixed, 

 top diameter, a cylindrical tree, being cut nearer to its tip than a conical tree,] 

 would have fallen into a larger total height class than the conical tree, hence its] 

 per cent of cylindrical contents would have been much greater for merchantable' 

 form factor than that of the conical tree — a difference not appearing in the frustum 

 form factor. Second, where the actual top diameter is made to coincide with the 

 point at which the tree is commonly utilized instead of with a fixed top, there is apt 1 

 to be still closer approach to unity in the form factors. The length and character 

 of the crown usually determines the amount of taper from the base of the crown 

 to the tip of the tree and consequently its distribution on the stem (§ 172). In' 

 rough utilization, the last saw cut tends to bear a direct relation to the length of 

 crown and to fall nearer to the base of the crown than to its tip. This is especially 



1 Bui. 210, Vermont Agr. Exp. Sta. 1918. 



