CHAPTER XVII 



FRUSTUM FORM FACTORS FOR MERCHANTABLE CONTENTS 

 IN BOARD FEET 



180. The Principle of the Frustum Form Factor. In an effort to 

 simplify the construction and improve the accuracy of volume tables 

 for board feet, based upon merchantable heights and top diameters, 

 a merchantable form factor has been devised by Donald Bruce. 



Timber cruisers in the Pacific Northwest had already made use 

 of the similarity in form of the merchantable portion of the tree to that 

 of the frustum of a cone, but had neglected the possible differences in 

 form and volume between the cone and the merchantable bole. The new 

 method adopts the frustum of the cone as the basic volume, instead of 

 the cylinder as for the form factors discussed in Chapter XVI, and then 

 compares this volume with that of the tree, to determine their true 

 relation. This relation is expressed as a form factor in the usual manner. 



y = volume in tree; 



y = volume in frustum of cone; 



/=form factor. 

 Then 



and 



V^V'f. 



The contents of this frustum were measured as the scaled board- 

 foot contents of cylinders representing the logs into which the bole 

 would be cut. The length of these sections was fixed at 16 feet, and 

 their upper diameters were determined by the diameter of the frustum 

 at the required point. The form factor obtained by comparing the 

 total scaled volume of the merchantable bole with that of the frustum 

 so measured is termed the Frustum Form Factor and is a merchantable 

 form factor having values close to 1, since the deductions from full 

 cubic contents of bole have been made both in the frustum and in the 

 tree. 



The merits of the frustum form factor method for constructing 

 volume tables are that it applies directly to the merchantable portion 



