RTI

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 thegross 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 organiza-tions 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 proceduresfor 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.

Table 2-1. 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

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 overestimation, 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 logit 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).

Table 2-2. Partial list of recorded log lengths and scaling segments for the Interagency Cubic Foot

		Scaling segments
Measurement (ft)	Recorded as	Bottom	Middle	Top

8.0-8.5	8	8	—	—
8.6-9.5	9	9	—	—
· · ·
19.6-20.5	20	20	—	—
20.6-22.0	21	11	—	10
22.1-23.0	22	12	—	10
23.1-24.0	23	12	—	11
· · ·
40.1-41.0	40	20	—	20
41.1-42.0	41	14	14	13
42.1-43.0	42	14	14	14
43.1-44.0	43	15	14	14
etc.
Logs 61-80 feet in length are divided into four segments.

Source: USFS (1991).

Table 2-3. Interagency Cubic Foot log scale applied to 15 sample logs.^a

Diameter^b				Scaling segments
Small (in)	Large (in)	Length (ft)	Recorded size	Top	Middle	Bottom	Total vol. (ft³)

13.8	20.4	27.0	14 x 20 x 26	14 x 17 x 12		17 x 20 x 14	42.2
17.0	27.5	41.0	17 x 28 x 40	17 x 23 x 20		23 x 28 x 20	116.2
12.3	19.4	44.9	12 x 19 x 44	12 x 15 x 14	15 x 17 x 14	17 x 19 x 16	61.0
14.5	22.1	44.3	14 x 22 x 44	14 x 17 x 14	17 x 20 x 14	20 x 22 x 16	83.4
7.2	13.0	20.9	7 x 13 x 21	7 x 10 x 10		10 x 13 x 11	12.2
6.0	10.6	28.8	6 x 11 x 28	6 x 9 x 14		9 x 11 x 14	12.2
17.7	27.3	27.1	18 x 27 x 27	18 x 23 x 13		23 x 27 x 14	78.2
6.3	12.8	23.5	6 x 13 x 23	6 x 10 x 11		10 x 13 x 12	12.9
10.4	16.1	26.9	10 x 16 x 26	10 x 13 x 12		13 x 16 x 14	25.0
17.4	23.2	35.3	17 x 23 x 35	17 x 20 x 17		20 x 23 x 18	77.5
5.5	9.0	39.0	6 x 9 x 38	6 x 8 x 18		8 x 9 x 20	12.8
7.0	15.0	40.9	7 x 15 x 40	7 x 11 x 20		11 x 15 x 20	28.2
15.0	17.2	34.7	15 x 17 x 34	15 x 16 x 16		16 x 17 x 18	47.8
12.6	18.3	34.9	13 x 18 x 34	13 x 16 x 16		16 x 18 x 18	47.0
6.4	8.3	14.9	6 x 8 x 15	6 x 8 x 15			4.1

						Total	660.7

^aThe sample logs, while taken from intensively managed young plantations, are intended only to illustrate methodology. They should not be construed as representing any particular log sort or the resource in general. The results obtained and differences between the log rules discussed in this chapter may change significantly with a different sample.

^bThe diameters were obtained from logs of circular cross section. The rule to obtain recorded size requires that two diameters be taken at right angles (both 13.8 inches for the small end of the_ first log). These are rounded to the nearest inch, and averaged with any remaining fraction dropped. Thus the recorded diameters of the first log are 14 and 20 inches, respectively.

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
Volume, in cubic feet = (C/4)² _* L/144

Volume, in cubic meters = (C/4)²_*L/10,000

where

C = log circumference, in inches or centimeters (since C = πD, some versions show this substitution where D is the diameter in inches or centimeters)

L = log length, in feet or meters.

When volume is obtained in cubic meters, it is often referred to as a Francon cubic meter to distinguish it from the solid cubic meter estimated by other formulas. When it is obtained in cubic feet, some multiply by 12 to give board feet. These are often termed Hoppus superficial feet, quarter-girth superficial feet, or Haakondahl superficial feet.

Hoppus rule gives 78.5% of the actual cubic volume of the log, making a 21.5% lumber processing allowance for slabs, edgings, and sawdust. Since 78.5% of 12 BF/ft³ yields 10 BF/ft³, a Hoppus cubic foot is considered equal to 10 BF (Freese 1973). Standards for measuring and recording length and circumference vary among countries. For example, circumference or diameter may be taken inside or outside bark at the log end or midlength, and there may be assumptions regarding log taper and bark thickness. As a result, there are numerous variations. Hoppus measure, as expressed in the above formulas, can be converted to an estimate of the full cubic volume of the log by multiplying by 1/0.785 = 1.2739. Multiplying the Hoppus formula by this adjustment results in

Total ft³ = (C/4)²L/113

Total m^{3 =}(C/4)² L/7,850.

Interagency Cubic Foot Log Rule

In recognition of the advantages of replacing antiquated board foot rules with cubic measure and the need to have a standardized method for cubic scaling, the Interagency Cubic Foot system was developed and was officially adopted by the U.S. Forest Service and Bureau of Land Management in 1991 (USFS 1991). The general procedure to follow is outlined below:

Scaling diameter: At each end, take a pair of inside bark diameters at right angles, round each to the nearest inch, average, drop any fraction, and record the result.

Scaling length: Measure length to 0.1 foot and record the nominal length according to Table 2-2.

Scaling segments: (1) If the recorded length is 20 feet or shorter, apply Smalian's formula to these recorded measurements. (2) If the log is longer than 20 feet: subdivide into segments as shown in Table 2-2; estimate taper as the difference in the recorded diameters (allocate taper in whole inches as evenly as possible to the segments; when taper cannot be evenly allocated, place greater taper in the top segment); and apply Smalian's formula to the segments and sum. See Example 1.

Recorded volume: Record the volume to the nearest 0.1 cubic foot.

The use of segment scaling is intended to reduce the bias from the paraboloid log shape assumption of Smalian's formula. For complete details on this scaling system see the cubic scaling handbook (USFS 1991).

Table 2-3 presents actual measurements of 15 sound, straight logs with circular cross section and the resulting cubic foot volumes with this system.

Example 1

A log measures 43.8 feet long, 13.2 and 14.8 inches diameter on the small end, and 20.9 and 24.4 inches diameter on the large end. The small end diameters round to 13 and 15 with an average of 14. The large end diameters round to 21 and 24, with an average of 22.5. Assuming that 0.8 feet meets trim allowance requirements, the log is recorded as 43' x 14" x 22". It is scaled as three segments and the 8 inches of taper is used to obtain intermediate diameters as follows:

Diameter (in)

Length Volume

Segment (in) Small Large (ft³)

Top 14 14 17 18.5

Middle 14 17 20 26.3

Bottom 15 20 22 36.2

Total 81.0

Japanese Log Rules

Four log rules are commonly used in Japan. With a few exceptions, log length is generally measured in full 20 cm intervals (i.e., 7.76 m is recorded as 7.6 m = L in the formulas below). Procedures for obtaining a recorded diameter differ among the systems as discussed in the following sections. Volume, in cubic meters, is recorded to three places.

Japanese Agricultural Standard (JAS) Scale.
Scaling diameter (D) is measured on the small end only. For logs 14 cm or less in diameter, round down to the nearest whole 1 cm class. For logs larger than 14 cm, measure the long and short axes and round down to even 2 cm class. Find the difference between the rounded long and short axes. The scaling diameter is the short axis after applying the following adjustment rule.

If the short axis is between 14 and 40 cm, add 2 cm to the short axis for every 6 cm of difference. If the short axis exceeds 40 cm, add 2 cm to the short axis for every 8 cm of difference.

_{Short axis 14 to 40 cm}		_{Short axis > 40 cm}

^{Difference (cm)}	^{Add (cm)}	^{Difference (cm)}	^{Add (cm)}
< 6	0	< 8	0
6 - 11.9	2	8 - 15.9	2
12 - 17.9	4	16 - 23.9	4
etc.		etc.

_Examples:	_Axis
				_Scaling
	_Short	_Long	_Difference	_diameter

	18	22	4	18
	18	24	6	20
	18	28	10	20
	18	30	12	22
	40	44	4	40
	40	50	10	42

Scaling length (L) is in full 0.2 m (20 cm) intervals, as previously noted, but certain others (1.9, 2.1, 2.7, 3.3, 3.65, 4.3) are inserted into this scheme.

Volume in cubic meters

= D² L /10,000 if L ≤ 6 m

= [D – (INT(L) – 4) / 2]² L / 10,000

if L > 6 m.

INT(L) is the length rounded down to the nearest meter and the term (INT(L) – 4) / 2 is a taper adjustment of 1 cm per meter of length (about 1 inch per 8 feet). This formula views a log as a square cant with a side equal to the scaling diameter.

Revised JAS. Also termed the United American Investigation Form, the JAS formula for logs 6 meters and longer is modified by including a factor, f, to adjust the original taper assumption. For 6 meter and longer logs, the volume in cubic meters

={[D – (INT(L) – 4) / 2] _* f}² L/10,000

where f = 0.6 if D ≤ 28 cm

= 0.8 if D ≥ 30 and ≤ 58

= 1.0 if D ≥ 60 cm.

Hiragoku (Hirakoku or Heiseki) Scale. For scaling diameter, measure and record diameter at the small end using the South Sea Log procedure (below).

Volume in cubic meters = D² L / 10,000.

Hiragoku also views a log as a square cant with a side equal to the recorded small end diameter. However, unlike JAS, there is no taper adjustment.

South Sea Log (SSL) Scale or Brererton. For scaling diameter, measure the long and short axis on each end and round down to 2 cm class (i.e., 69.1 cm and 63.5 cm measures from one end become 68 and 62 respectively). Average the rounded measures and record to 1 cm (i.e., the average of 62 and 68 is 65 cm). Average the above results for each log end and round down to 1 cm. Call this result D.

Volume in cubic meters = 0.7854 D²L / 10,000.

This is the metric form of the subneiloid formula (Table 2-1) and is applied to hardwood logs from tropical Asian sources. This formula is often called Centi-Buleletin in several South Sea countries and is sometimes called Brererton since the subneiloid formula is the basis of that rule.

Comparing the Japanese Log Rules. While these four rules yield volume in cubic meters, they can produce very different results for a particular log. Table 2-4 gives the metric sizes of the 15 sample logs described in Table 2-3, along with volumes in cubic meters in three of these Japanese systems. Briggs and Flora (1991) present these methods in greater detail along with translation of Japanese scaling books. Table 2-4 also presents conversion ratios among these rules and between them and the Interagency Cubic Foot rule (Table 2-3). Beneath each column of ratios are the ratio statistics. See Sample Scaling for a Conversion Factor (pp. 31-32). Some important conclusions are:

1. Variation of the ratios is large. The South Sea Log and Interagency Cubic Foot rules are the most consistent (least variation). This is not too surprising since they are the ones that utilize actual log taper.

2. In theory, 35.315 cubic feet equal a cubic meter, but this is generally not true for these rules.

3. The ratio of the total volumes is not the same as the average of the individual log ratios (bottom line of Table 2-4). The former can be viewed as the correct weighted average in which larger logs contribute disproportionally more, since volume is a function of diameter squared.

Table 2-4. Japanese scaling of the 15 sample logs in Table 2-3.
Metric diameter				JAS		Hiragoku		South Sea
Small (cm)	Large (cm)	Length (m)	Recorded length (m)	Diam. (cm)	Vol. (m³)	Diam. (cm)	Vol. (m³)	Diam. (cm)	Vol. (m³)

35.1	51.8	8.23	8.2	34	1.063	35	1.005	43	1.191
43.2	69.9	12.50	12.4	42	2.624	43	2.293	56	3.054
31.2	49.3	13.69	13.6	30	1.691	31	1.307	40	1.709
36.8	56.1	13.50	13.4	36	2.198	36	1.737	46	2.227
18.3	33.0	6.37	6.2	18	0.224	18	0.201	25	0.304
15.2	26.9	8.78	8.6	14	0.220	15	0.194	20	0.270
45.0	69.3	8.26	8.2	44	1.735	44	1.588	56	2.020
16.0	32.5	7.16	7.0	16	0.214	16	0.179	24	0.317
26.4	40.9	8.20	8.2	26	0.643	26	0.554	33	0.701
44.2	58.9	10.76	10.6

Chapter 2. Measurements of Logs

Chapter 2. Table of Content

Criteria for a Good Log Rule

Gross Versus Net Scale

Cubic Volume Log Scaling

Cubic Volume Formulas

Interagency Cubic Foot Log Rule

Japanese Log Rules

Korean Log Rules

Log Rules for Indonesia, Malaysia,
and the Philippines

British Columbia Log Rules

Chilean Log Rules

Russian Log Rules

New Zealand Log Rules

Board Foot Log Scaling

Board Foot and Overrun

Board Foot and Overrun (continued)

Formula Board Foot Log Rules

Diagram Board Foot Log Rules

Log Rule Conversion Factors

Conversions for Formula Log Rules:
Algebraic Approach

Conversion Using Log Rule Tables

Sample Scaling for a Conversion Factor

Institutionalized Log Conversion Factors

Log Weights

Chapter 2. Measurement of Logs

Criteria for a Good Log Rule

Gross Versus Net Scale

Cubic Volume Log Scaling