In the preceding equation, we have a situation where as the spacing between skidding roads increases, skidding unit costs increase, while road unit costs decrease. X = A + B + F + C(S/4) + L + H(D/2) + R/(VS) 2.3 Applications of Cost Equations The formula can be extended still further to include the cost of the secondary road system by defining the road construction cost per meter R, and the volume per square meter, V. Where D/2 is the average hauling distance along the secondary road and H is the variable cost of hauling per unit distance. Therefore, the expression C(S/4) would define the variable skidding cost in terms of spacing of the secondary roads.įigure 2.1 Nomenclature for 2-way Skidding to Continuous Landings Among Spur Roads.Ī formula for the cost of logs on trucks at the primary road under these circumstances would be In the expression C(S/4), the symbol S represents the spacing of the secondary roads and the distance S/4 is the average skidding distance if skidding could take place in both directions. If logs were being skidded to a series of secondary roads (Figure 2.1) running into a primary road, then the expression C(D/2) would be replaced by the expression C(S/4) and the cost of truck haul on the secondary roads would appear as a separate item. If C varies with distance, as for example, with animal skidding where the animal can become increasingly tired with distance, the average skidding cost does not occur at the average skidding distance and substantial errors in unit cost calculations can occur if the average skidding distance is used. It is important to note that the average skidding cost occurs at the average skidding distance only when the skidding cost, C does not vary with distance. C is the cost of skidding a unit distance such as one meter and D/2 represents the average skidding distance in similar units. Where the skidding subunit Q has been replaced by symbol F representing fixed costs of skidding such as hooking, unhooking and decking and C(D/2) represents that part of the skidding cost that varies with distance. In skidding, for example, if logs were being skidded directly to a road (Figure 2.1), then the distance skidded is an important factor and the stump to truck unit cost might be written as (Machine rates are discussed in Section 3.)ĭetermine the felling unit cost for a 60 cm tree if the cost per hour of a man with power saw is $5.00, the tree volume is 3 cubic meters, and the time to fell the tree is 3 minutes plus 0.005 times the square of the diameter. The hourly cost of operation is referred to as the machine rate and is the combined cost of labor and equipment required for production. Where C is the cost per hour for the felling method being used, P is the production per hour, V is the volume per tree, and T is the time per tree. The unit cost of felling is equal to the cost per hour of the felling operation divided by the hourly production or The production rate is equal to the tree volume divided by the time per tree. Where T is the time to fell the tree, b is the felling time required per cm of diameter, D is the tree diameter and "a" represents the felling time not explained by tree diameter-such as for walking between trees. For a given felling method, the time required to fell the tree might be expressed as Examples for felling and skidding follow.įor felling, tree diameter may be an important explanatory variable. Functional forms for production in road construction and harvesting are discussed in Sections 4 and 5. To determine the cost per subunit for felling, bucking, skidding, and loading, the factors which determine production and cost must be specified. Where A would be the cost per unit of felling, B the cost of bucking, Q the cost of skidding, and L the cost of loading. If X is the cost per cubic meter of wood loaded on the truck, we could represent the total cost per unit as Let us suppose the cost of harvesting from felling to loading on trucks is being studied. Careful selection of the subunits to express the factors controlling costs is the key to success in all cost studies. Where X is the cost per unit volume such as dollars per cubic meter and the subunits a, b, c will deal with distance, volume, area, or weight. Unit costs can be divided into subunits, each of which measures the cost of a certain part of the total. The use of breakeven and minimum-cost-point formulas require the collection of unit costs.
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