## Bulletin E2915 How Much Lumber in that Tree?

November 16, 2015 - Author: <petersog@msu.edu>

There are times when a woodland owner may want to determine the board foot volume of certain trees in his or her woodlot for building purposes or for sale. Measuring the volumes of standing trees enables the property owner to select the proper combination of available trees to provide the desired amount of lumber. Volume calculations can also help the woodland owner avoid harvesting more trees than necessary and can give him or her an accurate accounting of the number of board feet for sale.

Large trees that will yield boards for lumber are called sawtimber trees. Sawtimber is measured and sold in terms of board feet. A board foot is 1 inch thick, 1 foot wide and 1 foot long. The first step in determining the board foot contents of standing trees is measuring their diameters and usable heights. Tables 2, 3 and 4 summarize these volumes using various log rule techniques.

Anyone can determine the board foot content of their trees by following a few simple steps. This bulletin describes how to estimate the amount of lumber in a tree with easy-to-make tools. If an estimate of the entire woodlot is needed, however, the owner should contact an area forester or a consulting forester for this service. More complex techniques are involved in estimating volumes on a large scale, which are beyond the scope of untrained individuals.

## Measuring Diameter

Tree diameters are measured at breast height, which is 41 ⁄2 feet above the average ground level. Although diameter tapes are often used to take this measurement, another tool, called a Biltmore stick1, is easy to construct in the home workshop. Use a straight piece of hardwood that is free from knots or other defects, as shown in Fig.1. The stick should be 30 inches long, 1 ⁄2 inch thick and 11 ⁄2 inches wide, and beveled on one edge.

Fig. 1. Dimensions of Biltmore stick designed to measure tree diameter on one side and merchantable tree height on the other side.

Sand the sides and edges of the stick smooth. The stick is then graduated on the unbeveled side according to the figures given in Table 1.

1The Biltmore stick may also be purchased from forestry equipment catalogues such as Forestry Suppliers or Ben Meadows.

Table 1. Biltmore rule graduations.

 Diameter-graduations on a stick Distance in inches from end of stick to diameter graduations Diameter-graduations on stick Distance in inches from end of stick to diameter graduations 5 4.6 18 13.7 6 5.4 19 14.3 7 6.2 20 14.9 8 7.0 21 15.5 9 7.7 22 16.0 10 8. 23 16.6 11 9.2 24 17.1 12 9.8 25 17.7 13 10.5 26 18.2 14 11.2 27 18.7 15 11.8 28 19.2 16 12.5 29 19.7 17 13.1 30 20.2

Measure tree diameters with the Biltmore stick in the following way (see Fig. 2):

1. Hold the stick 25 inches from your eyes in a horizontal position. Hold the beveled edge of the stick against the trunk of the tree at breast height.

2. Look straight at the tree without moving your head from side to side. Adjust the stick so that the left or zero end is lined up with the left side of the tree.

3. Without moving your head, shift the line of sight to the right-hand side of the trunk.

4. Read the diameter on the stick nearest the point at which the line of sight crosses it.

Tree diameter can also be measured using an ordinary tape measure. Wrap the tape around the circumference of the tree at 4.5 feet above its base. Divide the circumference by 3.14 (π) to calculate the diameter of the tree.

Fig. 2. Measuring tree diameter with a Biltmore stick.

## Measuring Height

Tree heights are measured in units of 16-foot logs or fractions thereof. In slender, straight trees, this measurement is taken to a point on the upper trunk of the tree where the diameter inside the bark is 8 inches. With older trees, however, excessive branching or forks may reduce the usable height. One should then measure the distance between stump height and usable height.

A Merritt rule for measuring tree heights can be inscribed on the reverse side of the Biltmore stick; then both rules, one for measuring tree diameter and the other for measuring tree height, will be on the same stick.

To inscribe the Merritt rule on the stick, simply mark graduations of 6.1 inches from the zero end of the stick (see Fig. 1). Each graduation represents a 16-foot log length. Inscribe half-log marks halfway between the 16-foot log marks. Make the graduation for both the diameter scale and the height scale with a sharp pencil or marker. Then give the stick a coat of clear var nish or polyurethane. This will bring out the color of the indelible lead, as well as protect the stick from moisture and discoloration.

Measure tree heights with the Merritt rule by the following method (see Fig. 3):

1. Stand 66 feet from the base of the tree. Hold the stick vertically at a distance of 25 inches from your eye.

2. Adjust the stick so that the zero end is in the line of sight with the upper limit of usable height.

3. Without moving your head or the stick, shift your line of sight to the stump height at the base of the tree (usually 12 to 16 inches above ground level). From the scale, read the number of logs (or fractions of logs) in the tree.

If the ground is not level, stand on a spot that has about the same elevation as the base of the tree.

Fig. 3. Measuring tree height in 16-foot log units with a Merritt rule.

## Determining Tree Volume

After the diameters and heights of the trees have been measured, the board foot content for each tree can be read from a volume table. Board foot volume is estimated in many ways. Because many of these calculations were developed before the benefit of calculators, estimations are simplified formulas that are easy to tabulate by hand. Other, later formulas are more complex but ultimately more accurate in estimating the amount of useable wood. The International log rule (Table 2), one of these more recent estimation systems, gives a very accurate measure of the amount of lumber that a sound, straight tree will yield at the sawmill.

Local customs, however, sometimes require using other log rule calculations when standing timber is sold. Estimated volumes from two other log rules, Doyle and Scribner Decimal C, are given in Tables 3 and 4.

If you are going to fell the trees yourself and haul the logs to the mill, read the board foot values in Table 2, the International rule. However, if you are selling standing trees in the Lower Peninsula (and if the buyer insists), use the values in Table 3. If your trees are in the Upper Peninsula and the buyer demands it, use the values based on the Scribner Decimal C rule (Table 4).

In using these tree volume tables, increase the volumes by 10 percent for the following trees: balsam fir, spruce, white oak, yellow poplar, black cherry, beech and ash. Also, make suitable deductions for visible defects, such as rot.

Table 2. Tree volume table based on International log rule.

 Diameter 4 ½ feet above ground (inches) Number of 16-foot logs 1 2 3 4 Volume in board feet 10 35 60 11 45 75 12 55 90 120 13 65 110 145 14 80 130 175 15 90 155 200 16 180 240 285 17 205 280 330 18 235 315 375 19 265 360 425 20 295 400 480 21 330 450 540 22 370 500 605 23 405 550 665 24 440 605 725 25 485 665 800 26 725 880 27 790 950 28 850 1,030 29 920 1,110 30 990 1,070

Table 3. Tree volume table based on Doyle rule.

 Diameter 4 ½ feet above ground (inches) Number of 16-foot logs 1 2 3 4 Volume in board feet 10 15 20 11 20 30 12 30 45 50 13 40 60 70 14 50 75 95 15 60 95 120 16 115 150 170 17 140 180 210 18 165 215 250 19 195 255 300 20 225 295 350 21 260 345 400 22 295 390 460 23 330 445 520 24 370 495 580 25 415 560 660 26 620 740 27 685 815 28 750 890 29 825 980 30 900 1,070

Table 4. Tree volume table based on Scribner Decimal C rule.*

 Diameter 4 ½ feet above ground (inches) Number of 16-foot logs 1 2 3 4 Volume in board feet 10 3 4 11 4 6 12 5 8 10 13 6 9 12 14 7 11 15 15 8 14 18 16 16 21 25 17 18 25 29 18 21 28 33 19 24 32 38 20 27 36 43 21 30 41 49 22 34 46 55 23 37 51 61 24 41 56 66 25 45 62 74 26 68 81 27 74 89 28 80 96 29 86 104 30 93 112

*The figures shown in this table must be multiplied by 10 to obtain board foot values.

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