by Professor Gene Wengert

President, The Wood Doctor抯 Rx, LLC

**How much wood can a woodchuck chuck...?**

Logs are really truncated cones. Lumber is, however, a rectangular parallelepiped. When measuring logs, the real question is 揌ow many rectangular parallelepiped fit in a truncated cone??If you know the answer, then you know how many board feet of lumber a log contains and can begin to determine the log抯 value. IMPORTANT NOTE: Scaling measures volume; grading determines quality. Scaling and grading are different operations.

One way to answer the question I have posed is to draw a circle, representing the small end of a log. Then, if I assume that the log doesn抰 curve or bend, I can easily draw a bunch of rectangles inside the circle, representing the ends of pieces of lumber, to get the board footage. Of course, I better include a space between each rectangle to represent the sawdust. Another way to determine the answer would be to get a bunch of logs that are all the same size (as close as possible) and then saw these logs into lumber and measure the output.

These methods are okay for a certain log size and straightness, using a certain thickness saw blade. But what about the fact that 10 logs with 20 BF each will take a lot more time and effort to saw than one log of 200 BF? Maybe I should adjust my numbers slightly so that when I find a smaller log, I estimate a smaller number of BF of lumber than actually is present to offset the extra handling expense? Or maybe I should just give the correct footage answer but pay less for smaller logs? Or maybe, I should just have my own rules on how to measure logs and convert them to footage?

The fact is that all of the above methods have been used to measure logs. The end result is that there are over 100 different log measurement (or estimation?) techniques, called log rules, in the U.S. and Canada. There are three widely used log rules, however桽cribner, Doyle, and International. Let抯 look at these three rules in more detail.

*International*

Of all the log rules, the International 1/4-Inch Log Rule is the rule that comes closest to estimating the actual lumber footage that is in a log. The rule uses 1/4-inch kerf. It is approximately as accurate with smaller logs as with larger logs. However, because such a rule requires log prices to be based on diameter in order to accommodate the extra handling expense from smaller logs, this rule is not widely used by sawmillers.

*Scribner*

The Scribner Rule is widely used in the East and North. Its estimates are based on fitting rectangles into a circle. It does under-estimate the volume from smaller logs.

*Doyle*

The Doyle rule is widely used in the Southern U.S. Although empirically based, the estimates are quite close to the Scribner Rule.

**Using a log rule**

All the major log rules use the small end diameter, inside the bark, as the basic size measurement; this diameter is called the Scaling diameter. If the log is not perfectly round, then two readings are taken at 90 degrees to each other and averaged. Many rules will stipulate that the diameters are measured to the closest inch, and if the average of two diameters is exactly on the half, round up once and then round down the next time. In any case, the diameter measurements are supposed to represent a cone; butt swell, dipsy-doodles, or other small weird protuberances or depressions would be ignored.

The log length is the length to the last full foot (especially for hardwood logs); do not round up to the next foot. Softwoods are often measured to the last full even foot (i.e., 8, 10, 12, etc.). Hardwoods used to be measured to the even foot, but not so much anymore.

What about log defects, like a squirrel hole, fire scar, forks, or ?? The person measuring the log, often called a scaler, may decide that the last two feet of a log is not useful and will then scale the log as being 10 feet long instead of 12 feet actually measured. Or if there is a bad defect on one side, the scaled footage can be reduced proportionately. For gentle sweep (or crook), there are tables that indicate how much to deduct from the scaled answer.

In most cases, the footage numbers are given to the closest 10 BF (sometimes to the closest 5 BF; very seldom would the footage be more precise). Because all the numbers then will end in zero, the results are sometimes given without the zeros-璮or example, 240 BF is given as 24. With such a procedure, the log rule will have the word 揹ecimal?added to it.

**Make it simple?**

There are some people who believe that such a complicated scaling system for logs should be made easier. The way to do that is to measure the diameter at both ends of the log and also the actual length. Then, using the basic formula for volume of a cone (7th grade geometry class?), then we could figure out the cubic footage梠ops, I mean cubic meters. In fact, the U.S. Forest Service now requires timber sales to be in cubic metric values. Of course, conversion between the 搊ld?system and metric system is nearly impossible, unless you know diameters, log rules, etc. In other words, 10,000 cubic meters of pulpwood logs will have very little board footage compared to 10,000 cubic meters of 20" diameter and larger logs. (Plus, I learned the 搊ld?way of scaling and I am not anxious to change at my age!)

**Actual numbers**

There are three ways to get the actual footage number.

*Tables*

The footage values have been tabulated for the three rules for different diameters and lengths. Simply, look up the numbers. (A few sample numbers are given in Table 1. A tabular listing is available in the archives at WOODWEB and perhaps other Internet Sites, in many forestry books, and at many state forestry offices. Many logging and sawmill machinery companies also provide log scale information.) Often a tabular value is the preferred technique with today抯 fast computers.

*Formula*

A second method is to use a formula that represents the log rule; often one rule may have several slightly different formulas. These formulas use diameter (D) and length (L) with volume (V) in board feet.

Scribner is V = (0.0494 x D x D x L) - (0.124 x D x L) - (0.269 x L)

International is V = 0.905 x ([0.22 x D x D] - [0.71 x D]) for every 4 foot length of log.

Doyle is V = [L x (D - 4) x (D - 4)] / 16

Doyle is also V = [0.0625 x D x D x L] [0.500 x D x L] + [1.000 x L]

*Scaling Stick*

A third method, and the most common, is to use a scaling stick. This is a piece of wood (about 1/4 inch thick and 1-1/2 inches wide) that has the footage numbers printed on the stick. The numbers are located on the stick at the spot that represents the diameter for that number. (For example, a 16" diameter log that is 16 feet long scales as 360 BF; the number 360 will be located 16 inches from the end of the stick.) There will be several sets of numbers representing different log lengths. The stick is held up to the end of the log (running across the log measuring the diameter) with one end of the stick at the edge of the bark and wood. Where the bark and wood cross the other end of the stick, the appropriate number scale is read to determine the footage. (Here is how I measure oval logs with a scaling stick: The diameter is measured at the largest spot and then I mark this measurement on my stick holding my fingernail at the correct spot. Then I move the stick to measure at 90 degrees and note the second (and smaller) diameter reading. I then move my fingernail to a spot halfway between the first and second readings and use that spot for getting the footage value.)

Table 1. A selection of scaling values for Scribner, Doyle and International 1/4-Inch Rule for a 12 foot straight log.

Diameter | Scribner | Doyle | International |

(Inches) | ---Board Feet--- | ||

6 | 10 | 5 | 10 |

10 | 30 | 30 | 50 |

16 | 120 | 110 | 130 |

22 | 250 | 240 | 260 |