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Timbeter measurement formulas, its equations and descriptions

May 26, 2022
Timbeter measurement formulas, its equations and descriptions

There are a variety of log scaling methods around the world. However, there is a vast variability between each region, making transparent communication difficult. Describing each method and its parameters are vital for enabling clear and transparent measurement between all partners, and thus eradicating any attempts at fraud.

Typically, each method utilizes length and diameter information to determine volume in cubic units. Several log-scaling methods require small-end diameter measurement while others require diameters at both ends of the log. The majority of methods use the diameter measurement under the bark.

Some methods are based on mathematical formulas (JAS; Doyle) and others use fixed values for certain diameters that come from tables (GOST).

A very important part of the log volume calculation is rounding the diameter. While many of the formulas use the conservative mathematical rounding (meaning 25.5cm 26cm and 25.4 25cm), for example, the Japanese Agricultural Standard requires rounding down to the nearest even number (meaning 25.9cm is rounded down to 24). This, of course, raises questions about the log’s true volume – but these are the rules that must be abided by.

For the Timbeter team, this was puzzling when applying the rounding rules, because our solution shows diameters with mm accuracy.

Timbeter has the following formulas inside the application:

A. Nilson (Estonian formula)Cylindrical formula
Doyle log Scale
GOST 2708-75
Hoppus Imperial
Hoppus Metric
International ¼ Rule
JAS Scale
Latvian standard 82:2003
Lithuanian formula
Lithuanian with bark
Maine Log Rule
Ontario Scaler’s Rule
Polish Formula*
Roy Log Rule
Scribner Decimal C Rule
Slovenian formula*South African Standard
Pulgada Maderera Tica (PMT)*
Georgian Formula*

*Polish formula, Slovenian formula, Pulgada Maderera Tica and Georgian formula are available upon request.

A. Nilson (Estonian formula)

Estonians use this formula developed by Arthur Nilson to calculate the volume of logs. This method uses both a formula and a support table with coefficients, depending on the tree type.

Formula:

cbm = (d² * L*(a1+a2*L)+a3*L²)/10 000

Where:

d – small-end diameter

L – length in dm

a1, a2, a3 – coefficients, that are defined by the tree species

Species a1 a2 a3
Pine 0.0799 0.000146 0.0411
Spruce 0.07995 0.00016105 0.04948
Birch and other hardwoods 0.0783 0.000236 0.045
other conifers 0.0800 0.000154 0.0453

Cylindrical formula

The Cylindrical Formula is the most straightforward and used formula for fast measurements. That said, it doesn’t mean that the method is the most accurate and should not be used to calculate all kinds of logs, due to their unique structures and timber being a highly valued and prized commodity.

Cylindrical formula is mostly used to measure pulp- and fuelwood and is the conventional method used in Central-Europe.

Formula:

V = π x r² x h

Where:

π – mathematical constant

r = radius

h = height

Doyle log Scale

The Doyle Log Rule is used in East and Central parts of North America. It originates from 1825. Different from the Scribner rule, Doyle is based on a formula.

Formula:

Board Feet Doyle = (D-4)2 x (L/16)

Where:

D = Diameter inside bark at the small end in inches
L = Log length in feet

GOST 2708-75

The Interstate Standard GOST 2708-75, called Round Timber. Tables volumes was a table implemented by the soviet government in 1977.

The formula determines the standard volume of roundwood by the thickness of the upper end and the length of the logs.

This table is still commonly used in Russia and some CIS countries as a standard of quality for log measurements.

Hoppus Imperial

This older system of measurement was practiced in the UK and former British colonies. It was made popular in 1736, and it’s still used in Asia, Africa, South America and Oceania. It can be used both in the metric and imperial systems.

Imperial:

Hoppus ft³ via girth = (mid-girth in inches/4)² x length in feet / 144

NB! Round to the nearest tenth ft³

Hoppus ft³ via diameter = mid-diameter in inches² x length in feet x 0.004283

NB! Round to the nearest tenth ft³

Hoppus superficial feet = Hoppus ft³ x 12

Hoppus ton = hoppus ft³ / 50

Hoppus Metric

This older system of measurement was practiced in the UK and former British colonies. It was made popular in 1736, and it’s still used in Asia, Africa, South America and Oceania. It can be used both in the metric and imperial systems.

Metric:

Hoppus m³ via girth = (mid-girth in cm/4)² x length in meters / 10.000

NB! Round to the nearest three decimal points

Hoppus m³ via diameter = mid-diameter in cm² x length in meters x 0.000061685

NB! Round to the nearest three decimal points

International ¼ Rule

This rule was published in 1917 and used primarily in the eastern half of North America. It is especially popular in the New England and Quebec regions. Also, it has been adopted by the US Forest Service in several regions.

Formula:

V = (0.199 x diameter in inches²) – (0.642 x diameter in inches)

Where:

V = volume in board feet for 4-foot section

D = d.i.b on small end of 4-foot length

Standardized taper of 0.125″ is used to calculate log segments. Each segment consists of 4′ cylinders and the result of the segment is rounded to the nearest 5FBM (157.3 ~ 155FBM, etc.)

JAS Scale

The Japanese Agricultural Standard Scale was developed for measuring roundwood in the late 1940s and became popular in Eastern Asia, Oceania (including Australia) and Chile. Used by companies exporting timber to China and Japan.

Formula:

For logs less than 6m long:

V(m3) = (D2*L)/10000

Where:

D – Small-end diameter (cm), for less than 14 cm the diameter is rounded down and after 14 cm the diameter is rounded down to the nearest even integer.

L – Length (m)

For logs equal to or greater than 6m:

V(m3) = (D + [L’-4]/2)2*(L/10000)

Where:

D – Small-end diameter (cm), for less than 14 cm the diameter is rounded down and after 14 cm the diameter is rounded down to the nearest even integer.

L – Length (m)

L’ – Length in meters rounded down to the nearest whole number

Latvian standard 82:2003

Latvian standard of Measurement of Round Timber

Formula:
V = π x (d² + s x l)² x l/4 x 2 x 10000

Where:

V – Volume (m3)

π – mathematical constant

d – log diameter

s – taper (cm·m-1)

l – length

Lithuanian formula

Used in Lithuania. Formula based on a table with a rounding down to the nearest whole number.

Lithuanian with bark

Used in Lithuania. Formula based on a table with adding bark to diameter, rounding down to the nearest whole number.

Maine Log Rule

This rule was devised by Charles T. Holland, a surveyor, in either 1856 or 1867. It is a diagram rule based on 1-inch boards with a minimum width of 6 inches and an allowance of 1/4 inch for kerf.

Ontario Scaler’s Rule

Used by mills in the Province of Ontario, Canada. It was adopted as the official rule in 1952.

Formula:

BF = (0.55D² – 1.2D) * L/12

Where:

BF – board feet

D – scaling diameter in inches inside the bark on the small end of the log

L – log length in feet

Polish Formula*

Polish standard for roundwood measurement.

Formula:

Where:

V – Volume (m3)

π – mathematical constant

d – log diameter

z – taper (cm·m-1)

l – log length

Rounding down to nearest integer

Roy Log Rule

This formula is used in the province of Quebec, Canada. It’s quite accurate for 14 and 16 foot logs.

Formula:

BF = (d – 1)² L / 20

Where:

BF = board feet

d = scaling diameter in inches inside the bark on the small end of the log

L = log length in feet

Scribner Decimal C Rule

The Scribner Decimal C Rule is used in the Midwestern and Northern regions of North America. It was published in 1945 in the University of Minnesota and uses the help of a table.

Formula:

(0.79*D² – 2D – 4) * L/16 = FBM, rounded to the nearest 10 FBM (313 ~ 310, 317 ~ 320 etc.)

Where:

D – Small-end diameter in inches, rounding half down if the diameter is exactly .5

L – Length in feet

Slovenian formula*

Slovenian standard.

Formula:

Where:

V – Volume (m3)

π – mathematical constant

d – log diameter

l – log length

Rounding down to nearest integer

South African Standard

South African Standard.

Formula:

Where:

V – Volume (m3)

π – mathematical constant

d – log diameter

l – log length

s – taper , Taper is fixed at 1.0 for softwood and 0.8 for hardwood. This means that timber species selection affects the volume

Rounding to the nearest uneven number.

Pulgada Maderera Tica (PMT)*

Roundwood measurement standard in Costa Rica.

Georgian Formula*

Roundwood measurement standard in Georgia based on tables.

For cases where timber has been stacked with both the ends mixed, we suggest using the Cylindrical (also known as “True content of cylinder”) formula, which is also available in Timbeter. This is the dominant method used in most of continental Europe.

Most of the formulas listed in this article originate from Matthew A. Fonseca’s book, the author of “The Measurement of Roundwood”. Our team had the honor to meet him at the Timber Measurement Society Annual Meeting in Coeur d’Alene last year. We agree with him that log scaling needs to be simplified, unified and harmonized. This industry needs to change in order to become more transparent and effective. Using Timbeter is the way to begin increased transparency and ease to business.


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