One of the earliest attempts to optimize the spacing of logging roads was 

 presented by Matthews (1942) in his text on logging. Lussier (1961) showed how work 

 road spacings can be optimized using some simplified models and the mathematics .of 

 calculus. For the lesser slopes (<20%) , these methods of Matthews and Lussier give 

 fairly good results when road construction and skidding costs are available. Seihei 

 Kato's (1966, 1967) studies used a similar method of optimization. His studies were 

 concerned with the density of roads within an entire forest area and therefore included 

 all of the development roads. However, none of these analyses consider enough of the 

 variables affecting cost. A more complete method is needed; otherwise the full 

 economic potential cannot be attained. 



Some of the recent research findings of Brown (1967) and Carter (1968) conducted 

 for and in cooperation with the Intermountain Forest and Range Experiment Station's 

 Forest Engineering Research Laboratory, Bozeman, Montana, provide the basis for a 

 more complete analysis procedure. 



Brown developed a method of determining the effects of selected variables on 

 the cost of skidding or yarding. Carter developed cost equations for the principal 

 variables that affect work road costs. In this paper, data from these two studies 

 are combined in a model to optimize the total harvesting operation. A discussion of 

 the general methods employed for each study follows. 



Skidding and Yarding Studies 



A rather large volume of field data on logging production has been obtained in 

 the past 5 or 6 years for the equipment types and site conditions of the Rocky Mountain 

 area. Analysis of early studies established data-collecting techniques and indicated 

 other variables that would have to be included in the analysis. In his early studies. 

 Brown (1967) used an analysis of variance technique developed by Draper and Smith (1966) 

 called "backward elimination procedure" to eliminate the less significant variables 

 and retain those that would give an adequate representation of production. The 

 variables of slope, distance, logs per thousand board feet, and timber stand density 

 are used in most of our prediction (regression) equations. Several publications are 

 available from the Intermountain Forest and Range Experiment Station in Ogden, Utah, 

 reporting on the results of these studies (Gardner and Schillings 1969, Schillings 

 1969a, Schillings 1969b). 



/ Forest Road Studies 



A variety of problems related to the broad subject of forest roads is being studied 

 at our laboratory; this includes design criteria both as related to economics and the 

 environment, and the economics of forest roads associated primarily or exclusively 

 with harvesting. As studies progressed, it became apparent that we would have to 

 include road costs related to harvesting in the total logging cost. This was done 

 by formulating equations to represent the cost of each component. The total cost 

 equation was then optimized (cost minimized) by use of calculus. A description of 

 how this was done follows. 



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