Forest-Based Biomass Basic Computations - Mathematics and Statistics for the Environment - page 333

• Scarlet oak ( Quercus coccinea ) (Clark and Schroeder, 1977)
St + Br: weight = 0.12161 × (DBH 2 × ht) 1.00031
• Chestnut oak ( Quercus prinus ) (Wiant et al., 1979)
St + Br: weight = 0.06834 × (DBH 2 × ht) 1.06370
• Northern red oak ( Quercus rubra ) (Clark and Schroeder, 1977)
WT: weight = 0.10987 × (DBH 2 × ht) 1.00197
• Black oak ( Quercus velutina ) (Bridge, 1979)
WT: ln (weight) = -0.34052 + 2.65803 × ln (DBH)
• Hemlock ( Tsuga canadensis ) (Young et al., 1980)
WT: ln (weight) = 0.6803 + 2.3617 × ln (DBH)
• General hardwoods (Monk et al., 1970)
WT: log (weight) = 1.9757 + 2.5371 × log (DBH)
• General softwoods (Monteith, 1979)
WT: weight = 4.5966 - (0.2364 × DBH) + (0.00411 × DBH 2 )

13.4 TIMBER SCALING AND LOG RULES
With regard to scaling and log rules associated with timber, the measurement of timber to be har-
vested (the cruise), timber cut and removed from the forest (scaling), timber not recovered in the
harvesting process (waste processing), and the use of formulas or tables to estimate net yield for logs
(log rule) are the basis of forest-based biomass harvesting operations.

13.4.1 t heory oF s Caling *
Scaling is the determination (measuring) of the gross and net volume of logs by the customary
commercial units for the product involved; volume may be expressed in terms of board feet,
cords, cubic feet, cubic meter, linear feet, or number of pieces. The cubic foot is an amount
of wood equivalent to a solid cube that measures 12 × 12 × 12 inches and contains 1728 cubic
inches. The cubic meter , used in countries that have adopted the metric system, contains 35.3
cubic feet. The board foot is a plank 1 inch thick and 12 inches square; it contains 144 cubic
inches of wood. Scaling is not guessing; it is an art founded on applying specific rules in a con-
sistent manner based on experienced judgment as to how serious certain external indicators of
defect are in a specific locality.
The measuring standard used in scaling logs, called a log rule , is a table intended to show
amounts of lumber that may be sawed from logs of different sizes under assumed conditions. At
best, a log rule can only approximate salable manufactured volume because of constant changes in
markets, machinery, manufacturing practices, and even the varying skills of individual sawyers.
Thus, a log rule is an imaginary measure. Its application must not be varied according to the mill in
which logs are sawed. The scaled volume of logs must be independent of variations in manufacture.
The difference between the volume of log scale and the actual volume of lumber sawed from the
same logs is called overrun if the volume tally exceeds log scale, or underrun if it is less.
There will generally be an overrun or an underrun when logs are scaled by a particular rule in a
given locality and sawed by a mill. Basic assumptions in the log rules and assumptions in utilization
practices cause overrun to vary with the size of the average log. Experience proves that this is true
even for the International 1/4-Inch rule, although not to the same degree as for the Scribner Decimal
C rule (both rules are discussed further below). This fact does not change scaling practices. Overrun

* This section is based on USDA, National Forest Log Scaling Handbook , FSH 2409.11, U.S. Department of Agriculture,
Forest Service, Washington, DC, 1941; Freese, F., A Collection of Log Rules , General Technical Report FPL-01, U.S.
Department of Agriculture, Forest Service, Forest Products Laboratory, Madison, WI, 1973; USDA, National Forest Log
Scaling Handbook , FSH 2409.11, U.S. Department of Agriculture, Forest Service,Washington, DC, 2006.