United States Department of Agriculture Estimating the Forest Service Forest Board Foot to Products Laboratory Cubic Foot Ratio Research Paper FPL-RP-616 Steve Verrill Victoria L. Herian Henry Spelter Abstract Contents Certain issues in recent softwood lumber trade negotiations Page have centered on the method for converting estimates of 1 Introduction .................................................................... 1 timber volumes reported in cubic meters to board feet. Such conversions depend on many factors; three of the most im- 2 The F3 × F2 × F1 Model.................................................. 2 portant of these are log length, diameter, and taper. Average log diameters vary by region and have declined in the west- 3 The F1 Factor.................................................................. 2 ern United States due to the growing scarcity of large diame- ter, old-growth trees. Such a systematic reduction in size in 4 F3 × F2............................................................................. 3 the log population affects volume conversions from cubic units to board feet, which makes traditional rule of thumb 5 Applying the F3 × F2 × F1 Model to a Population conversion factors antiquated. In this paper we present an of West Coast Logs ........................................................ 3 improved empirical method for performing cubic volume to board foot conversions. 6 Smoothing the F3 × F2 Surface....................................... 4 Keywords: Scribner scaling, diameter, length, taper, 7 Optimal Smoothing Parameter........................................ 4 truncated cone, smoothing, calibration 8 Calibration ...................................................................... 5 9 Problems ......................................................................... 6 10 Computer Program ......................................................... 7 11 Concluding Remarks ...................................................... 7 12 References ...................................................................... 7 Appendix—The F1 Factor .............................................. 8 March 2004 Verrill, Steve P.; Herian, Victoria L.; Spelter, Henry N. 2004. Estimating the SI conversion factors board foot to cubic foot ratio. Res. Pap. FPL-RP-616. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. Inch–pound Conversion factor SI unit 18 p. inch 25.4 millimeter A limited number of free copies of this publication are available to the public from the Forest Products Laboratory, One Gifford Pinchot Drive, foot 0.3048 meter Madison, WI 53726–2398. This publication is also available online at www.fpl.fs.fed.us. Laboratory publications are sent to hundreds cubic foot 0.0283 cubic meter of libraries in the United States and elsewhere. The Forest Products Laboratory is maintained in cooperation with the University of Wisconsin. The use of trade or firm names is for information only and does not imply endorsement by the U.S. Department of Agriculture of any product or service. 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