p. United States @ Department of 

Agriculture Butt-log Grade Distributions 

Forest Service for Five Appalachian 

NortheasternForest ~ardwoo~~pecies Experiment Station 

@ John R. Myers 

Gary W. Miller 

Harry V. Wiant, Jr. 

Joseph E. Barnard 
The Authors 

John R. Myers is a graduate research assistant in the Division of Forestry, West 

Virginia University, Morgantown. 

Gary W. Miller is an economist with the timber management project at the Timber 

and Watershed Laboratory, Northeastern Forest Experiment Station, Parsons, West 

Virginia. 

Harry V. Wiant, Jr. is professor of forestry in the Division of Forestry, West Virginia 

University, Morgantown. 

Joseph E. Barnard is manager of the National Vegetation Survey Research and 

Development Application Program at the Forestry Sciences Laboratory, Southeastern Forest Experiment Station, Research Triangle Park, North Carolina. 

Manuscript received for publication 21 January 1986 

Abstract 

Tree quality is an important factor in determining the market value of hardwood 

timber stands, but many forest inventories do not include estimates of tree quality. 

Butt-log grade distributions were developed for northern red oak, black oak, white 

oak, chestnut oak, and yellow-poplar using USDA Forest Service log grades on 

more than 4,700 trees in West Virginia. Butt-log grade distributions indicate the 

probabilities associated with each grade for each species and d.b.h. class. These 

estimates are useful for predicting the value of timber stands for which stand tables are available. 

Northeastern Forest Experiment Station 

370 Reed Road, Broomall, PA 19008 

August 1986 
Introduction Results 

Timber cruises usually involve the estimation of board-foot 

sawtimber volumes, cordwood volumes, and stand growth. 

One variable that is not commonly measured, but is important in estimating the actual value of a stand, is the stem 

quality of trees sampled in the cruise. Butt-log grade is a 

measure of stem quality that can be estimated from empirical equations relating butt-log grade to tree d.b.h. (Ernst and 

Marquis 1979). We developed equations and butt-log grade 

distributions for five Appalachian hardwood species. The 

distributions are useful for estimating average tree quality 

and stand value when stem quality data are not available. 

Methods 

Empirical grade equations were derived from Forest Survey 

point samples containing information on species, d.b.h. (D), 

and butt-log grade. The species included northern red oak, 

black oak, white oak, chestnut oak, and yellow-poplar. Data 

were from 4,781 sawtimber trees ranging from 10 to 25 

inches d.b.h. on point samples placed throughout West Virginia.' USDA Forest Service log grades (Rast and others 

1973) were used to grade the butt 16-foot log of each sample tree. 

Three regression equations were developed for each 

species. The equations related the inverse of tree d.b.h. 

(D-') to: 

(1) The proportion of sawtimber trees with a grade 1 butt 

log; 

(2) The proportion of sawtimber trees with a grade 3 butt 

log; 

(3) The proportion of sawtimber trees with a butt log below 

grade 3. 

All regressions were weighted by the actual number of sawtimber trees in a diameter class times 1/D2, because trees 

were selected by point sampling. Analyses of covariance 

indicated that the following combinations of oak species 

were acceptable: red and black oak, and white and chestnut 

oak. 

'Data were provided by the Forest Inventory and Analysis 

Research unit of the USDA Forest Service, Northeastern 

Forest Experiment Station, for the State of West Virginia. 

Butt-log grade distributions for yellow-poplar, red and black 

oak, and white and chestnut oak are presented in Tables 

1-3. The grade distributions were predicted from the regression equations presented in Table 4. Coefficients of determination (RZ) ranged from 0.49 to 0.90. For each grade 

distribution, the percentage of sawtimber trees with butt logs 

in grade 1, 3, or "below grade" were predicted from the 

equations. The percentage of trees with grade 2 butt logs 

was found by subtraction. 

For each species group and diameter class, the percentage 

of sawtimber trees with below-grade butt logs was computed 

first. Below-grade logs are not used to produce factory grade 

lumber. They include construction logs used for ties and 

timbers and local-use logs (Rast and others 1973). The predicted percentage of trees with below-grade butt logs decreased as d.b.h. increased in each species group (Tables 

1-3). 

From 10 to 11 inches d.b.h., the percentage of trees with 

grade 3 butt logs was determined by subtraction. In these 

diameter classes, grade 3 is the best possible grade due to 

size limits in the grading rules (Rast and others 1973). From 

13 to 14 inches d.b.h., the percentage of trees with grade 

3 butt logs was computed from the equations, and the percentage with grade 2 butt logs was determined by subtraction. In these diameter classes, the butt logs are too small to 

be grade 1. For trees 15 inches d.b.h. and larger, the percentage of trees with butt-log grades 1 and 3 were computed from the equations, and the percentage with butt-log 

grade 2 was determined by subtraction. Thus, the percentage of trees in each grade category for a particular diameter 

class totals 100. 

Making Value Determinations 

Forest Service tree grades (Hanks 1976) are useful for predicting lumber grade yields and the market value of individual sawtimber trees. Although tree grades and butt-log 

grades differ with respect to scaling diameter and allowable 

cull, surface requirements are the same in both grading 

systems. With some minor changes, the butt-log grade distributions presented here can be transposed to tree grades 

for estimating stumpage values. 

The minimum diameters for tree grades I, 2, and 3 are 10, 

13, and 16 inches d.b.h., respectively (Hanks 1976). To 

approximate tree grade distributions from those presented in 

Tables 1-3, assume that no 12-inch trees are grade 2 and 

that no 15-inch trees are grade 1. This will increase the 

percentage of I Pinch trees that are grade 3 and the percentage of 15-inch trees that are grade 2. The total distribution in each diameter class equals 100 percent. 
Table 1 .-Butt-log grade distributions for yellow-poplar 

D.b.h. No. of Below 

(inches) trees Grade 1 Grade 2 Grade 3 grade 

Percent ................................. 

10 123 - - 74 26 

11 99 - - 78 22 

12 112 - 9 71 20 

13 123 24 59 17 

14 1 08 - 37 48 15 

15 85 29 19 39 13 

16 82 36 20 32 12 

17 73 4 1 23 25 11 

18 46 47 25 19 9 

19 28 51 28 13 8 

20 34 56 29 8 7 

21 23 59 31 4 6 

22 18 63 30 1 6 

23 7 66 29 1 5 

24 6 69 26 1 4 

25 9 72 23 1 4 

Total 976 

Table 2.-Butt-log grade distributions for red and black oak 

D.b.h. No. of Below 

(inches) trees Grade 1 Grade 2 Grade 3 grade 

---------------------------.----- Percent ------------------------------. -- 

10 161 - - 81 19 

11 144 - - 83 17 

12 141 - 11 74 15 

13 130 - 23 64 13 

14 164 - 34 54 12 

15 126 19 25 46 10 

16 133 25 27 39 9 

17 110 30 29 33 8 

18 105 35 30 27 8 

19 87 39 32 22 7 

20 79 43 33 18 6 

2 1 63 46 34 14 6 

22 58 49 36 10 5 

23 40 52 36 7 5 

24 42 54 38 4 4 

25 31 57 38 1 4 

Total 1,614 
Table 3.-Butt-log grade distributions for white and chestnut oak 

D.b.h. No. of Below 

(inches) trees Grade 1 Grade 2 Grade 3 grade 

................................. Percent ................................. 

10 264 - - 76 24 

11 255 - - 79 21 

12 233 - 5 76 19 

13 208 - 15 68 17 

14 229 - 23 61 16 

15 196 6 25 55 14 

16 142 10 27 50 13 

17 126 14 29 45 12 

18 105 17 31 4 1 11 

19 94 20 32 38 10 

20 99 23 34 34 9 

2 1 65 25 36 3 1 8 

22 54 27 36 29 8 

23 34 29 38 26 7 

24 37 31 38 24 7 

25 23 33 39 22 6 

Total 2,164 

Table 4.-Regression statistics for dependent variable of percentage of trees in given grades 

Grade 1 Grade 3 Construction 

Species Equationa R2 Equationa R~ Equationa R~ 

Yellow-poplar Y=135.6-1601.4 .62 Y= -86.2+1885.5 .90 Y= -11.0+365.9 .79 

D- ' D-' D-' 

Red, black oaks Y=112.7-1403.1 .73 Y= -67.4+1702.2 .89 Y= - 6.4+252.6 .49 

D-' D-' D-' 

White, chestnut oaks Y = 73.8 - 1021.4 .61 Y = -27.8 + 1241.0 .83 Y = - 6.0 + 302.3 .62 

D-' D-' D-' 

" Y = Percentage of trees by grade; D' = 1ld.b.h. (percentage of trees with grade 2 butt logs is found by subtraction.) 

The adjusted grade distributions indicate how many trees in 

each diameter class are grade 1, 2, 3, or below grade for 

each species group. For example, a stand table reveals that 

a 50-acre stand contains 126 northern red oaks in the 18- 

inch diameter class. The grade distribution for the red oakblack oak group (Table 2) estimates the number of trees 

in each grade (Table 5). This procedure is repeated for each 

diameter class and for each species until all trees have 

been "graded." 

The final step is estimating the market value of individual 

trees in each species group. Table 6 lists the average lumber yields and current lumber prices for a northern red oak, 

18 inches d.b.h., with a grade 1 butt log and a merchantable 

height of 32 feet. The sum of current lumber prices (Lemsky 

1985) applied to each lumber grade yield is the total value of 

lumber in the tree, $100.05. The value of lumber in a similar 

tree with a grade 2 butt log is $85.74. With a grade 3 butt 

Table 5.-Tree grade distribution of 126 northern red 

oaks on a 50-acre forest tract 

Estimated no. 

of trees in 

Tree grade Probability each grade 

1 0.35 44 

2 0.30 38 

3 0.27 34 

4 0.08 10 

log, the value drops to $65.32. The value of products in 

trees below grade 3 depends on local-use markets. For this 

example, we assumed the value of products in trees below 

grade was $40. 
Table 6.-Value of lumber in a northern red oak, 18 inches d.b.h., with a grade 1 

butt log and merchantable height of 32 feet 

Lumber 

grade 

FAS 

1 F 

No. 1C 

No. 2C 

No. 3A 

Total 

Board feet 

35.9 

26.0 

66.1 

65.5 

44.0 

237.5 

Lumber priceb Lumber 

per M bf value 

.................... Dollars ..................... 

$71 5 $ 25.67 

705 18.33 

525 34.70 

207 13.56 

177 7.79 

100.05 

" From Hanks 1976. 

From Lemsky 1985. 

Stumpage prices can be obtained by subtracting conversion 

costs and a margin for profit and risk. In this example, the 

lumber grade yields (Hanks 1976) and current lumber prices 

(Lemsky 1985) for 126 northern red oaks resulted in an 

average lumber value of $361 per thousand board feet (M 

bf). If conversion costs and a margin for profit and risk equal 

$220 per M bf, the stumpage price for 18-inch red oaks is 

$141 per M bf. This could be expanded to include trees 

in all d.b.h. classes for red oak and result in one average 

stumpage price for the species. As lumber prices and conversion costs change, individual-tree values and average 

stumpage prices can be adjusted accordingly. 

Discussion 

Butt-log grade distributions can be used to estimate individual-tree and stand values when actual grade data are not 

available. Regression equations or grade distribution tables 

predict the percentage of trees in each grade for a particular 

species and diameter class. This information provides a 

basis for estimating lumber grade yields, total lumber value, 

and the residual stumpage value for any number of sawtimber trees. The user should first develop a stand table that 

indicates the number of trees by species and d.b.h., and an 

estimate of average merchantable height. 

The regression equations can be used to incorporate grade 

distributions into stand value computer programs. An important advantage of using butt-log grades when estimating 

stand value is that dollar values include the effect of timber 

quality and current lumber prices. In cases involving timber 

trespass, for example, the grade distributions can be used to 

estimate the total value of losses based on the probable 

grade of the trees cut. Similarly, the distributions provide a 

basis for computing potential stand value from projections of 

individual-tree diameter growth and the accompanying 

changes in grade. In both examples, the value estimates 

include the effect of stem quality as well as species, tree 

size, and total volume. 

Because butt-log grade data for this study were collected in 

unmanaged, central Appalachian hardwood stands throughout West Virginia, the distributions may have limited use 

outside the general study area. In addition, intensive timber 

management practices may result in grade distributions 

significantly different from those presented here. The user 

should be aware that such differences may occur and that 

additional grade distributions may be needed for some 

stands. 

Literature Cited 

Ernst, R. L.; Marquis, D. A. Tree grade distributon on 

Allegheny hardwoods. Res. Note NE-275. Broomall, PA: 

U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station; 1979. 5 p. 

Hanks, L. F. Hardwood tree grades for factory lumber. 

Res. Note NE-33. Broomall, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment 

Station; 1976. 81 p. 

Lemsky, Abe. Appalachian hardwoods. Hardwood Market 

Report 63(48):4; 1985. 

Rast, Everette D.; Sonderman, David L.; Gammon, Glenn L. 

A guide to hardwood log grading. Gen. Tech. Rep. 

NE-1. Upper Darby, PA: U.S. Department of Agriculture, 

Forest Service, Northeastern Forest Experiment Station; 

1973. 132 p. 
Myers, John R.; Miller, Gary W.; Wiant, Harry V., Jr.; Barnard, Joseph E. 

Butt-log grade distributions for five Appalachian hardwood species. 

NE-RP-590. Broomall, PA: Northeastern Forest Experiment Station; 1986. 

4 P. 

Tree quality is an important factor in determining the market value of hardwood timber stands, but many forest inventories do not include estimates of 

tree quality. Butt-log grade distributions were developed for northern red oak, 

black oak, white oak, chestnut oak, and yellow-poplar using USDA Forest 

Service log grades on more than 4,700 trees in West Virginia. Butt-log grade 

distributions indicate the probabilities associated with each grade for each 

species and d.b.h. class. These estimates are useful for predicting the value 

of timber stands for which stand tables are available. 

ODC 561.53 76.1 

Keywords: Appalachian hardwoods; tree quality; tree grade; probability 

distributions; stand value