Board-foot log rules in North America

In much of North America, logs are bought by the thousand board feet (MBF) according to a log rule, a table or formula that predicts how many board feet of lumber a log of a given small-end diameter and length should yield. This lesson shows how the rules differ, why a European cubic-metre price cannot be compared with an MBF price without care, and what the portal's sources say about their accuracy.

What a board foot is

By definition, 1 board foot (bf) is 1 in x 12 in x 12 in = 144 cubic inches. With 1 in = 0.0254 m exactly, that is 144 x 0.0254^3 = 0.002359737 m3. For lumber the formula is bf = thickness (in) x width (in) x length (ft) / 12, using nominal sizes.

Worked example. A nominal 2 x 4 in, 8 ft piece is 2 x 4 x 8 / 12 = 5.33 bf, or 0.01259 m3 by the definition above (own calculation). The actual dressed piece is smaller than the nominal size, so board-foot recovery based on nominal dimensions differs from cubic recovery (Steele 1984, USDA Forest Products Laboratory).

One thousand board feet (MBF) is therefore 2.3597 m3 nominal. The portal's articles also use 1.623, 1.59 and about 2.36 m3 per MBF in different documents, and these could not be reconciled. Convert only with the factor named in the source document and state which you used.

Three rules, three answers

The USDA Forest Service handbook NA-FR-15 (Ashley, United States, 1989, internet version revised October 2001) prints board-foot volumes for 16-foot logs by small-end diameter. The Scribner and Doyle columns are headed "(tens)" and the scaling could not be confirmed unambiguously from the extracted text, so the values below are shown as printed.

Compare Doyle with International (own calculations): at 10 in. Doyle gives 36 / 65, which is 44.6% less; at 12 in. it is 32.6% less; at 16 in. it is exactly 20% less; at 20 in. 11.7% less; and at 30 in. the two are within 0.1% of each other. Scribner is 7.7% below International at 10 in. and 11.1% below at 16 in.

The pattern is the point. The rules disagree most on small logs and converge on large ones. A buyer paying the same price per MBF under Doyle and under International is paying very different prices for the same wood when the logs are small. On this table, a seller of small logs gains from International and a buyer from Doyle.

How good are the rules?

Spelter (Journal of Forestry, United States, June 2004) found in the abstract that the three rules generally underestimate true recovery, inconsistently, and that the undercount grows sharply for smaller logs; the author argued for cubic measurement. Only the abstract was readable, so the portal quotes no recovery percentages from it.

The consequence shows up in mill statistics. Lumber overrun is the lumber tally minus the log-rule volume, divided by the log-rule volume. Keegan and co-authors (2010) call it imprecise because log rules do not reflect solid-wood volume. The portal's yield article also lists the lumber recovery factor (LRF, board feet of lumber tally per cubic foot of log volume) and cubic lumber recovery (CLR, green lumber volume divided by log volume). A CLR of 0.50 means 50% in green-lumber terms. LRF values reported for western US mills (6.72 to 8.67) depend on log-rule conventions and are not comparable with a European volume percentage.

Comparing across systems

A price in "MBF Scribner" cannot be compared with a price per Fm o.R. without a size-dependent conversion agreed in writing. Three problems stack up:

1. The unit differs (board feet of predicted lumber against solid cubic metres of wood).
2. The rule underestimates recovery by an amount that depends on log size.
3. The diameter is measured differently (small end in North America, mid-diameter in the RVR).

A conversion that is right for 30 in. logs is wrong for 10 in. logs, so ask for the log size distribution first.

Key points

• 1 bf is 144 in3, or 0.002359737 m3; 1 MBF is 2.3597 m3 nominal, though portal sources also use 1.623 and 1.59 and these were not reconciled.
• Doyle gives 44.6% less than International at 10 in., 20% less at 16 in., and the two converge at 30 in. (own calculations from NA-FR-15, as printed).
• Spelter (2004) found log rules generally underestimate true recovery, with the undercount growing sharply for small logs (abstract only).
• Overrun, LRF and CLR depend on log-rule conventions and do not compare directly with a European volume percentage.
• A price in MBF Scribner cannot be compared with a price per Fm o.R. without a size-dependent conversion agreed in writing.