How to calculate the usable volume of a wooden log?/Calculating the Hoppus cu ft. volume of a wooden log.

How to calculate the usable volume of a wooden log?/Calculating the Hoppus cu ft. volume of a wooden log.

Measurement of Logs

Logs are tree sections that are to be converted to products such as lumber, veneer, and plywood. Many log measurement systems have been developed and can be very confusing. In this chapter, a number of important domestic and foreign log measurement systems, often called log scales or log rules, are described. Also presented are methods for estimating conversion factors, and some conversion factors commonly used by statistical reporting agencies.

Criteria for a Good Log Rule Log scaling is the process of estimating the weight or volume of a log while allowing for features that reduce product recovery. Scaling in terms of volume has been the predominant method, but weight scaling is common in some industries and for small logs. Many log rules for estimating volume have unique characteristics. Many were devised when lumber was the principal product. Rather than measuring the total volume of the log, they apply lumber manufacturing assumptions to estimate the quantity of lumber a given log will yield. Since lumber is measured in board feet, these are called board foot rules. While these rules may have been adequate in the past, their emphasis on a single product and their antiquated assumptions regarding lumber processing make them poor choices today.

In today's complex, multiproduct environment, a good log rule should (1) provide a good estimate of the total wood fiber content, (2) provide a good basis for estimating the yields of alternative products, (3) have the property that when a log is cut into shorter segments, the segment volumes sum to the volume of the original log, and (4) involve simple, easy-to-take measurements (Snellgrove and Fahey 1982).

Gross Versus Net Scale Since log features such as rot and lack of straightness reduce product recovery, an adjustment, usually referred to as defect scaling, must be made. Gross scale is the volume based solely on the actual log dimensions. Net fiber (firmwood) scale is the gross scale adjusted for defects (voids, decay, charred wood, etc.) that reduce the amount of wood usable for pulping and other chip products. Net product scale has additional adjustments for defects (sweep, cracks, shake, etc.) that affect the yield of solid wood products such as lumber and veneer.

Log volume may be reported on either gross or net scale basis; net scale is more common. Manuals of the appropriate scaling agency should be consulted to understand the types of defects involved and how gross scale is adjusted to net scale. Only gross scale is considered in this chapter. The difference between gross and net scale is much less for today's young-growth resource than was the case with the old-growth, which often had a high percentage of scaling defects.

In weight scaling, the principal adjustment is for moisture content, hence the counterparts to gross and net volume are green and oven-dry weight. Additional reductions in weight can be made for malformed logs, rot, or other factors. 

Cubic Volume Log Scaling With a few exceptions, cubic log rules attempt to estimate total wood volume and make no assumptions regarding eventual product recovery and use. Product recovery generally follows a consistent pattern with total cubic volume. Cubic systems have been widely adopted by organizations wishing a good accounting of primary products and residues. A common unit that evolved with the use of cubic foot scaling is the cunit (100 cubic feet = CCF).

In the past, widespread standard procedures for cubic scaling did not exist in the United States. Various organizations picked a particular formula and developed their own measurement and defect scaling standards. Using length as an example, assume that a log specification requires nominal 32 foot logs to have at least 8 inches of trim allowance. A log actually measured as 33.1 feet long could be recorded as 32.0, 32.7, or 33.1 feet. Differences in diameter and length recording procedures result in volume differences that can be magnified when different cubic formulas are used.

In theory, cubic formulas all yield volume as a function that increases smoothly with diameter and length. In practice this may not happen, for two reasons: (1) length and diameters may be recorded in nominal or rounded forms (these could be one or two foot length intervals or one or two inch diameter classes); (2) the resulting volume may be rounded. These practices convert the smooth cubic volume function into a step function.

Cubic Volume Formulas Geometric Solids. Several formulas which assume that a log conforms to a geometric shape such as a cylinder, cone, or paraboloid can be used to estimate volume in cubic feet or cubic meters. Assuming a circular cross section of diameter, D, measured in inches (centimeters), the area in square feet (square meters) is 0.005454 D2 (0.00007854 D2). Table 2-1 presents several common cubic rules that use different assumptions as to cross section area measurements. Some of these formulas average the log end areas, some average the log end diameters, and so on. Generally, they do not give the same result and each has a bias from the true volume that depends on how much the assumed geometric shape differs from the actual log shape. Smalian's formula is the statute rule in British Columbia and is the basis for the Interagency Cubic Foot scaling system discussed below. Since Smalian's formula assumes a paraboloid log shape, it has a bias toward overesti

mation, especially for butt logs. Hence a variation, Bruce's butt log formula, was developed. The Huber formula assumes that the average cross section area is at the midpoint of the log, but this is not always true. It is intermediate in accuracy but has limited use due to the impracticality of measuring diameter inside bark at log midlength. Sorenson's formula is derived from the Huber formula by assuming taper of 1 inch per 10 feet of log length. This assumption allows measurement of log diameter inside bark at the small end. Its accuracy depends on the validity of the taper assumption. Newton's formula is the most accurate, but by requiring measurement of diameter at both ends and the midlength of a log, it is more time consuming and suffers from the same impracticality as the Huber formula. The subneiloid formula is often confused with Smalian's formula, and is often more accurate. When multi-plied by 12 board feet per cubic foot, the subneiloid formula becomes the Brererton board foot log rule discussed in the section on Board Foot Log Scaling below (p. 25). The two-end conic formula assumes that the log shape is a cone. It is the basis for the "Northwest cubic foot log scaling rule" (Anon. 1982b) which was developed to use the West-side Scribner diameter and length measurements (see p. 27). 

Hoppus. The most widespread cubic log rule that includes an assumption regarding processing loss is the Hoppus rule, sometimes called the quarter-girth formula. It was derived in Britain and is widely used internationally. The formula is 

Some common cubic volume formulas. 

Name                                  Formula 

 1. Smalian                        V      = f (ds2 + dl2) L / 2 

 2. Bruce's butt log                     = f (0.75 ds2 + 0.25 dl2) L / 2 

 3. Huber                                    = f dm2 L 

 4. Sorenson                               = f (ds + 0.05 L)2 L 

 5. Newton                                 = f (ds2 + 4 dm2 + dl2) L / 6 

 6. Subneiloid                            = f [(ds + dl)/2]2 L 

 7. Two-end conic                     = f (ds2 + ds dl + dl2) L / 3   

where     f = 0.005454 (Imperial) or 0.00007854 (metric) 

               V = volume, in cubic feet or cubic meters 

 ds, dm, dl = small, midlength, and large end diameters, in inches or centimeters 

              L = length, in feet or meters