METHODS FOR ESTIMATING SPECIFIC GRAVITY OF LOGS

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1 U. S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY MADlSON, WIS. In Cooperation with the University of Wisconsin U. S. FOREST SERVICE RESEARCH NOTE FPL-0110 JANUARY 1966 METHODS FOR ESTIMATING SPECIFIC GRAVITY OF LOGS

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3 METHODS FOR ESTIMATING SPECIFIC GRAVITY OF LOGS By DIMITRI PRONIN, Technologist Forest Products Laboratory, 1 Forest Service U.S. Department of Agriculture Introduction It is frequently desirable to have estimates of the average specific gravity of the wood in specified portions of the trunk of a standing tree. Such estimates are commonly obtained by means of regression equations showing the relationship between tree specific gravity and more easily measured characteristics such as age, diameter at breast height (d.b.h.), and the specific gravity of increment cores. To develop such regressions, tree gravity must actually be measured on a certain number of sample trees; however, determining the average specific gravity of the entire trunk would be quite laborious and perhaps an unnecessary refinement. Instead, the sample trees are usually felled and bucked into logs or pulpwood bolts and disks 1 to 2-1/2 inches in thickness are taken at each cutting position as shown in figure 1. The average specific gravity of each log or bolt is commonly estimated as the unweighted average specific gravity of the disks at each end. In combining the bolt specific gravities to estimate tree specific gravity, the bolts may be weighted equally or in proportion to their volume. 1 Maintained at Madison, Wis., in cooperation with the University of Wisconsin. FPL-0110

4 There are two common modifications of this procedure: (1) the lowest disk is frequently taken at breast height or higher to avoid the aberrant specific gravities often encountered at stump height. In this instance, the lowest bolt is assigned the same average specific gravity as that of the lowest disk. (2) The individual disks are divided into several equal wedge-shaped segments (usually four or six) and then one or more of the wedges are selected for determination of the disk specific gravity. Figure 2 shows a schematic plan for cutting the disks and wedges. Specific gravity estimates may be made for all of the wood in the trunk or for the clear wood portions only. Objective of Study The purpose of this study is to compare the log specific gravity values obtained by some of the more common procedures with the actual specific gravity as determined by 100 percent measurement. The comparison is made for both total wood and for clear wood only. Methods There were seven butt logs of shortleaf pine available for the study. All were from trees over 15 inches d.b.h. cut at the Crossett Experimental Forest in Arkansas. Each log was cut into disks 2-1/2 inches thick and each disk divided into six equal wedge-shaped segments. The green volume, ovendry weight, and specific gravity were then determined for each wedge. The weights and volumes of all wedges in a log were pooled to give a weight and volume for the log and from these values the average specific gravity was computed. Estimates follows: of the log specific gravity were made by four basic methods as (1) Weighted average of disks at 0, 8, and 16 feet Disks were taken from heights of 0, 8, and 16 feet above the base of the log. The average specific gravity of the lower 8-foot portion of the log was taken FPL

5 to be the arithmetic average of the specific gravities of the disks at 0 and 8 feet; the average specific gravity of the upper portion was taken to be the arithmetic average of the 8- and 16-foot disk gravities. The volume of each portion of the log was assumed to be proportional to its length times the average of its end diameters squared. In estimating log specific gravity, the specific gravities of the lower and upper portions of the log were combined with weights proportional to their volume. The procedure can be expressed algebraically as follows: where: G L = estimated log specific gravity D = disk diameter G = disk specific gravity The subscripts 0, 8, and 16 indicate the height of the disk above the base of the log. (2) Weighted average of disks at 3.5, 8, and 16 feet Disks were taken at heights of 3.5, 8, and 16 feet above the base of the log. 2 The average specific gravity of the lower 3.5-foot section was taken to be the same as the specific gravity of the disk at 3.5 feet. The specific gravity of the 4.5- and 8-foot sections above this were taken to be equal to the arithmetic average of their end disk specific gravities. The volume of each section was assumed to be proportional to its length times the average of its end diameters squared. Log specific gravity was estimated by combining the specific gravities of the individual portions of the log with weights proportional to their volume. Algebraically, (3) Unweighted average of disks at 0, 8, and 16 feet The log specific gravity was estimated as the arithmetic average of the specific gravities of disks selected at 0, 8, and 16 feet above the base of the log. Algebraically, 2 The stump was assumed to be approximately one foot in height, so that a height of 3.5 feet above the base of the log corresponds to the usual breast height of 4.5 feet. FPL

6 (4) Unweighted average of disks at 3.5, 8, and 16 feet Log specific gravity was estimated as the arithmetic average of the specific gravities of disks selected at 3.5, 8, and 16 feet above the base of the log. Thus, In addition to the estimates obtained by taking whole disks (all six wedges) at each of the specified heights, estimates were made using two randomly selected wedges at each height; also, by using only a single wedge from each height. A further estimate of log specific gravity was made using complete disks selected at heights of 8 and 16 feet. The lower 8-foot bolt was given a specific gravity equal to that of the disk at 8 feet, while the upper 8-foot bolt was assigned a specific gravity equal to the average of the disks at 8 and 16 feet. In estimating log specific gravity, the bolt specific gravities were weighted in proportion to their volume. Expressed algebraically, These 13 procedures were used for estimating average specific gravity for the entire log and also for the clear wood portions only. Finally, two increment cores were taken from each log at a point 3.5 feet from the base (equivalent to cores taken at breast height) and their arithmetic average specific gravity computed. Results and Discussion The specific gravity estimates obtained by each of the 13 methods used in this study are given in tables 1 and 2. In general, results of this research substantiated for southern pines the recognized decrease in specific gravity with increase in height. Increment cores taken at breast height (3.5 feet from the base of the log) gave consistent overestimates of log specific gravity, as had been noted in previous studies. FPL

7 The 13 estimating methods were compared by computing the sums of deviations of estimated specific gravity from log gravity (a possible indicator of bias) and the sum of squared deviations (a measure of accuracy). From the data in tables 1 and 2 it will be noted the most accurate estimates of log specific gravity were obtained when using the weighted specific gravity of disks cut at heights of 3.5, 8, and 16 feet above the base of the log. However, in the field it may not be practical to cut a disk at breast height as it is usually desirable, economically, to retain a butt log length of 8 feet. In this instance, it would be better to select the first disk at the base of the log. Results suggest that when this is done, the unweighted estimate of log specific gravity is as good as the weighted estimate in terms of bias and also in terms of the sum of squared deviations. The use of disks from heights of 8 and 16 feet only resulted in serious underestimates of log specific gravity. In general these results may be explained in light of the recognized hyperboloidal form of most butt logs (which were treated as cones in the weighted estimates) and the known trend of decreasing specific gravity with increased height. The results of this study did not show my clearcut advantage of using a whole disk in place of only one or two wedges from each disk. Increasing the number of wedges, however, would be expected to yield better estimates and until better evidence is obtained, it is recommended that at least two randomly selected wedges be used from each disk FPL

8 M Figure 1.--Disks were cut at heights of 0, 3.5, 8, and 16 feet above the base of the log. Each disk was approximately 2-1/2 inches in thickness.

9 M Figure 2.--Schematic plan for cutting disks from log and subdividing each disk into six wedge-shaped sections. Longitudinal reference lines were marked along the entire length of the log, so that the position and numbering of corresponding wedges (A, B, C, D, E, F) would be the same for all disks as shown. Two increment cores were taken at breast height-the first at random and the second 90 radially from it.

10 FPL-0110 Table I.--Comparison of log specific gravity estimates obtained by 13 methods 1

11 FPL-0110 Table 2.--Comparison of log specific gravity estimated obtained by 13 methods (clear wood portions only) 1

12 PUBLICATION LISTS ISSUED BY THE FOREST PRODUCTS LABORATORY The following lists of publications deal with investigative projects of the Forest Products Laboratory or relate to special interest groups and are available upon request: Architects, Builders, Engineers, and Retail Lumbermen Box, Crate, and Packaging Data Chemistry of Wood Drying of wood Fire Protection Fungus and Insect Defects in Forest Products Furniture Manufacturers, Woodworkers, and Teachers of Woodshop Practice Growth, Structure, and Identification of Wood Logging, Milling, and Utilization of Timber Products Mechanical Properties of Timber Structural Sandwich, Plastic Laminates, and Wood-Base Components Thermal Properties of Wood Wood Fiber Products Wood Finishing Subjects Glue and Plywood Wood Preservation Note: Since Forest Products Laboratory publications are so varied in subject matter, no single catalog of titles is issued. Instead, a listing is made for each area of Laboratory research. Twice a year, January 1 and July 1, a list is compiled showing new reports for the previous 6 months. This is the only item sent regularly to the Laboratory s mailing roster, and it serves to keep current the various subject matter listings. Names may be added to the mailing roster upon request.

13 The Forest Service of the U. S. Department of Agriculture is dedicated to the principle of multiple use management of the Nation s forest resources for sustained yields of wood, water, forage, wildlife, and recreation. Through forestry research, cooperation with the States and private forest owners, and management of the Notional Forests and National Grass- Ionds, it strives-as directed by Congress--to provide increasingly greater service to a growing Nation.

14 FOREST PRODUCTS LABORATORY