by Will Blozan » Mon Nov 17, 2014 4:21 pm
Maybe it is time to revisit Colby Rucker's Rule of 73...
The Rule of 73
Colby B. Rucker
July 2003
Trees are often compared by measurements of the trunk circumference taken at breast height (4 ½ feet, or 54 inches above grade). National and state bigtree registries use this measurement, often known as cbh, by adding one point for each inch of cbh to points for height and average spread in their periodic lists of champion trees. When a fork, burl or lowbranching habit causes the trunk to have its smallest girth at some point below breast height, many of the bigtree registries have allowed that lower girth to be entered as cbh. This has given such trees an unfair advantage over competitors that have a similar lower girth but taper to breast height, where their circumference is less.
I felt that some simple formula was needed to allow a fair comparison between trees with a low “waist,” and those that taper in a typical fashion. An old list of national champions provided the elevation of 35 circumferences of trees measured below breast height. I found that those trees averaged eight feet in circumference. I then measured actual mature trees of ten species, which also averaged eight feet in girth at the same height. After taking circumferences at numerous elevations, I devised a formula to fit the actual flaring contours of the trunks measured. That formula, which I call “The Rule of 73,” is as follows:
Measure the smallest trunk circumference at or below 54 inches. Add onehalf the elevation (in inches) of the circumference to 73. Apply the sum as a percentage of the measured girth. The product is the hypothetical circumference at breast height.
As an example, in 1988 the Liberty Tree measured 31’ 7.5” (379.5”) in circumference at 24” above grade. Onehalf of 24 is 12, which added to 73 gives 85. 85% of 379.5 is 322.6. By the formula, the hypothetical cbh is 322.6”. The actual 1988 measurement of the tree at breast height was 26’ 11”, or 323.0”. Although some trees have greater or less taper than is typical, the accuracy of the Rule of 73 is often quite surprising. Since the rule is based on percentages, it is applicable to trees of various sizes. Also, because of the nature of percentages, hypothetical circumferences (from breast height to grade) do not increase by fixed increments, which would produce a conic structure. Instead, circumferences increase by gradually greater increments, which produce a concave curve, which corresponds to the flaring base of a typical tree, as may be seen below.
Column “A” shows the elevation above grade in inches.
Column “B” shows the hypothetical circumference.
Column “C” shows the increase in inches over the girth just above.
Column “D” shows the increase as a percentage of the girth just above.
A B C D
54 100.00
52 101.01 1.01 1.01
50 102.04 1.03
48 103.09 1.05 1.03
46 104.17 1.08
44 105.26 1.09 1.05
42 106.38 1.12
40 107.53 1.15 1.08
38 108.70 1.17
36 109.89 1.19 1.09
34 111.11 1.22
32 112.36 1.25 1.13
30 113.64 1.28
28 114.94 1.30 1.14
26 116.28 1.34
24 117.65 1.37 1.18
22 119.05 1.40
20 120.48 1.43 1.20
18 121.95 1.47
16 123.46 1.51 1.24
14 125.00 1.54
12 126.58 1.58 1.26
10 128.21 1.63
8 129.87 1.66 1.29
6 131.58 1.71
4 133.33 1.75 1.33
2 135.14 1.81
0 136.99 1.85 1.37

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