Net volumes. — The general form of the net volume equations is the same for all volume 

 types : 



NTV = V[1.0 - (PrC) (FC)] 



where 



NV = Predicted net volume of an unforked or forked tree 

 V = Predicted gross volume of an unforked or forked tree 

 ■ - PrC = Predicted probability that a tree of given characteristics will have some 

 cull (that is, the probability that the tree will be unsound) 

 FC = Predicted fraction cull of a tree given that it does have some cull. 



The product (PrC) (FC) estimates the average cull proportion for any tree of given char 

 acteristics. The advantage of separating the average cull rate into its components is 

 the added flexibility it provides when sampling a stand or forest. This method not onl 

 allows the user to predict average cull proportion, but it also allows him to separate 

 the sampled population into completely sound and unsound trees. For example, suppose a 

 sample tree, X., represents n, trees of the same characteristics. The values PrC and 



FC are computed for the sample tree's characteristics and then the following estimates 

 are made: 



Number of sound trees = n.(1.0 - PrC) 



- • Number of unsound trees = (PrC) 



Net volume in one sound tree = Vx (1.0) 

 Net volume in one unsound tree = V x (1.0 - FC) 

 Total net volume in sound trees = V x n.fl.O - PrC) 



Total net volume in unsound trees = V x ^^••(PrC) (1.0 - FC) 



where 



V = Gross volume of a tree of given characteristics. 



It is obvious that this kind of data provides the forest manager with much more infor- 

 mation concerning the structure of a population's net volume than does average cull 

 proportion . 



As mentioned earlier, for a given species. National Forest, and volume type, the 

 specific equations chosen for PrC and FC are not determined on a tree-by-tree basis, 

 but rather by the type of information collected during sampling. In addition to d.b.h. 

 and total tree height, there are two types of additional information that a user could 

 collect and use. One is the forking information previously discussed and the other is 

 information about tree damaging agents. The specific equations chosen will depend upon 

 whether the user collects all, one, or none of these additional pieces of information. 

 Once the choice has been made, the equations will then apply to all trees, whether they 

 be unforked, forked, undamaged, or damaged. 



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