. e- United States 9 ( 'I Department of 

Agriculture Butt Log Quality of Trees 

Forest Service in Pennsylvania Oak Stands 

Northeastern 

Station Martin E. Dale 

Resibarch Paper 

NE-568 Robert L. Brisbin 
The Authors 

Martin E. Dale, research forester, joined the USDA Forest Service in 

1957, specializing in forest management and silviculture research at Berea, 

Kentucky. 'In 1973, he received a Ph.D. degree in forest biometry from Iowa 

State University, and was assigned to the Northeastern Forest Experiment 

Station's Forestry Sciences Laboratory at Delaware, Ohio. Currently, he is 

engaged in research on the growth and yield of managed upland oaks. 

Robert L. Brisbin, research forest products technologist, received a B.S. 

degree in forestry from Iowa State University in 1961 and an M.S. degree in 

wood technology from the Pennsylvania State University in 1969. He joined 

the Northeastern Station in 1961, and currently is studying the managementand utilization of nonindustrial private forests at the Forestry Sciences Lab 

at Delaware, Ohio. 

Manuscript received for publication 22 October 1984 

Abstract 

Describes the distribution of sawtimber trees by diameter at breast height 

(d.b.h.) and grade for eight hardwood species in upland oak stands of 

Pennsylvania. The proportion of trees by d.b.h. and grade revealed 

differences between species. The quality of northern red oak, white oak, and 

yellow-poplar appeared inherently better than that of red maple, chestnut 

oak, and a group of other hardwoods. Grade predictions by size and species 

allow more precise timber appraisals and enable managers to evaluate 

alternative management strategies more accurately. 
Introduction 

The dollar value of a hardwood tree depends 

largely on its suitability for conversion into various 

types of wood products. Some hardwood trees are 

converted to high-value products such as face veneer 

or First and Second and Select grade factory lumber; 

others are used only for their fiber or as fuelwood. 

Hardwood log and tree grading systems have been 

used since the early 1900's by foresters, timber 

buyers or sellers, and others to appraise timber 

values. USDA Forest Service standard grades for 

hardwood factory lumber logs have not changed since 

they were first published in 1949 by the Forest 

Service's Forest Products Laboratory. However, 

guides for applying the rules have been revised and 

now provide greater detail and more clarification 

(Rast et al. 1973). Lumber grade yields associated 

with the log grades have been tabulated and expanded 

to include other hardwood species (Hanks et al. 1980). 

In addition to the grades for factory lumber logs, 

specifications have been developed for other major 

use classes of logs, including veneer, construction, 

and local use. Grade specifications within each class 

of logs are designed to separate logs into value 

groups based on product requirements. 

It is possible to determine the precise relative 

value of a tree if yields in factory lumber grades or 

other product classes are available by log grade, 

species, and diameter at breast height (d.b.h.1. Treevalue conversion standards reported by (Mendel et al. 

1976) measure a tree's relative worth based on the 

quantity and quality of its expected yield of 4/4 (1- 

inch) lumber. This approach to tree or stand evaluation is beneficial to foresters and others because it is 

easy to use, objective, and provides a realistic ranking of relative tree or stand values. The only information needed is d.b.h., merchantable height, tree 

grade, and species. 

Unfortunately, there is little information on tree 

grades in most forest inventories or growth and yield 

simulators. Although we can not determine accurately the value of individual trees, it is still possible 

to evaluate stands. This requires an appropriate 

distribution of trees for each species that gives the 

percentage by grade in each d.b.h. class. Such grade 

distributions have been described mathematically for 

six hardwood species on the Allegheny Plateau (Ernst 

and Marquis 1979). Trimble (1965) presented freehand curves that described the grade distribution for 

factory-grade butt logs for six hardwood species in 

West Virginia. It was apparent from these findings 

that there were large differences between species in 

the d.b.h.-grade relationship arid by geographic area. 

Our objective in this study was to develop estimates of the d.b.h.-grade relationship for an expanded list of species for upland oak stands of Pennsylvania. These distributions could be used to evaluate 

typical stands for timber sale appraisals or used in 

growth simulators to assign a grade to individual 

trees. Although the specific grade distributions 

developed in this study apply only to the Pennsylvania 

oak stands, the methodology is applicable to other 

timber types or geographic areas. 
Methods 

Data 

Our data on log grades were extracted from 10- 

point cluster plots used in the USDA Forest Service's 

1978 forest survey of Pennsylvania. Original field 

plots were first screened to select all plots where oak 

and hickory species constituted a plurality of the 

stand basal area. From 506 plots representing the 

oak-hickory type in Pennsylvania, we tabulated the 

number of trees by species, grade, I-inch diameter 

class, and productivity class. Our sample of hardwood sawtimber trees, excluding all conifers, consisted of 15,716 observations by species and grade (TabIe 

1). Sugar maple, hickory, and beech were later pooled 

with other hardwoods because data were insufficient 

for analysis. 

Grades were assigned by survey field crews using 

Forest Service standard grades for hardwood factory 

lumber logs for log grades 1 through 3. If the butt 

log failed to meet specifications for a factory lumber 

log but met specifications of Forest Service standard 

hardwood construction logs (Tie and Timber logs), it 

was assigned grade 4. The major factors that affect 

quality for the tie and timber logs are size and condition of log defects, straightness, and soundness of 

heart (Rast et aI. 1973). Culls and other sawtimbersize trees not meeting these specifications were 

assigned grade 5. Trees generally were graded on the 

butt 16-foot section rather than on the shorter sections permitted by the grading rules. However, to 

prevent underestimating log quality, if a 12-r 14- 

foot section qualified as a higher grade compared to 

the entire log, then the higher grade was assigned to 

the entire 16-foot log. 

Four productivity classes originally were tabulated on the basis of the ability of the site to produce 

wood, and were expressed as growth in cubic feet 

(ft3) per acre per year. The best sites were those 

capable of producin a mean annual increment 

greater 4 than 120 ft /acre; the mean annual increment on the poorest site was less than 50 ft3/acre. 

Intermediate sites ranged from 50 to 84 and from 85 

to 120 ft3. We later foundlhat productivity class 

had no significant effect onjthe distribution of grades 

by d.b.h. class. As a result,'this variable was dropped 

from our analyses. 

Table 1.-Number of trees by grade and species 

Species Percent No. 1 No. 2 No. 3 No. 4 No. 5 Total by species 

White oak 

Chestnut oak 

Northern red oak 

Other oaks 

Red maple 

Y ellow-poplar 

Walnut ash 

Sugar maple 

Hickory 

Beech 

Other hardwoods 

Total 

Percent 11 2 3 5 1 04 11 -- 100 
Analysis I 

I The proportion of trees in each grade within a 

I diameter class was computed and plotted over the 

range of diameters for a species (Fig. 1). From these 

plotted distributions we were able to hypothesize 

I mathematical models to describe the grade distributions. A nonlinear model was developed to fit the , distribution of grade 1 trees of the form: 

I 

where: 

! Yi,l = proportion of trees in the ith diameter 

class that are grade 1 

I 

I Di = midpoint of the ith diameter class 

Co = a constant to be estimated. Interpreted 

as the minimum d.b.h. that qualifies as a grade 1 

tree; hence, Co = 15.5 inches 

80, 81,82 = model parameters to be estimated: 

80'0; B1<0 

Data analysis indicated that the percentage of 

grade 1 trees reached a maximum at a d.b.h. of 18 to 

20 inches. For most species, the proportion of grade 

1 trees declined beyond 20 inches in d.b.h. The coefficient, Bo in model 1, is the asymptote and 

represents the maximum percentage of grade 1 trees. 

We determined the approximate value of 60 by 

reading the maximum value from free-hand curves. 

Values of fil and 8~ were then computed by nonlinear 

regression using data through the 20-inch d.b.h. class. 

The shape of the grade 2 frequency distribution 

was more difficult to describe mathematically, but 

when grade 1 and grade 2 trees were combined the 

shape of the curve resembled that for model 1 (Fig. 

1). We used the combined grade 1 and 2 data to fit 

model 1 and then by subtracting the estimate for 

grade 1 obtained the estimated percentage for grade 

2 trees for a specified diameter. The model parameter 8, was read from the hand-fitted curves as 

before. Minimum d.b.h. for a grade 2 hardwood log is 

13 inches, so Co was assigned the value 12.5. Estimates of @, and &were computed by nonlinear 

regression for all data through the 20-inch d.b.h. 

class. 

A?-- K ' Grades 

\ ' '-. 

-\Q / 

I 

Grade 3 

I I I I I I I I I I I 

12 14 16 18 20 2 2 2 4 

DIAMETER AT BREAST HEIGHT (Inches3 

Figure 1.--Distribution of butt-log grade for white oak trees. 
Results 

For all trees larger than 20 inches in d.b.h., we 

used a linear regression model to estimate the 

proportion of trees in grade 1 and the combined log 

grades 1 and 2. This regression was conditioned so 

that when the d.b.h. was 20.5 inches, model 1 or 2 

provided identical estimates. The intercept term, a, 

in the model: 

was set equal to the solution of model 1 using a d.b.h. 

of 20.5 inches. Linear regression was used to 

estimate the value ofay for each species. 

The distribution of grade 3 trees was fitted to a 

nonlinear model of the form: 

where: 

Y(i,3) = proportion of trees in the ith diameter 

class that are grade 3 

I 

! Co = a constant. The minimum sawtimber size 

hardwood was 11.0 inches in d.b.h., hence, Co = 11.0 

inches ao .Bo ,81,82 = model parameters to be 

estimated. ac>0;ao>f30; B~<O 

Approximately 95 percent of white oak trees that 

are 11.0 inchesbd.b.h. are grade 3 (Fig. 1). The 

parameter a. was set equal to this value, or 0.95. 

Figure 1 also shows that the proportion of grade 3 

trees seems to have some minimum value which is 

approached asymptotically with large trees. 

Therefore, we determined the value of this 

asymptote as (a0 -60 ) from the free-hand curve value 

for a 25-inch tree. Data from all diameter classes 

were used to estimate the parameters 81 and 82 as 

before. 

Trees that were grade 4 made up a relatively 

small percentage of all trees for most species and 

accounted for only 4 percent of the entire sample 

(Table 1). We did not attempt to separate grade 4 

from grade 5 trees since both grades combined 

accounted for only 15 percent of the total, and both 

grades represent low value or unmerchantable 

material. Plotted data indicated that grade 5 trees, 

or culls, generally tended to increase with d.b.h. 

class, particularly for trees more than 20 inches 

d.b.h. The percentage of grade 4 and 5 trees 

combined was obtained for any d.b.h. class by 

substracting the combined percentages of grades 1, 2, 

and 3 from unity. 

We were unable to detect significant differences 

in grades due to site quality, so this variable was 

dropped from the final analyses. Also, sample size 

was too small or poorly distributed across d.b.h. 

classes to obtain reliable equations for hickory, sugar 

maple, or beech, so these species were pooled with 

other hardwoods. 

Estimated parameters and statistics are given 

for predicting the proportion of trees in each grade in 

Tables 2, 3, and 4. Prom observed and predicted 

values we calculated ~2 values for each species and 

grade and the root mean square residual. For a given 

species, higher computed ~2 values were obtained for 

grade 3 trees than grade 1 or grade 1 and 2 combined 

(Table 4). However, the root mean square residual 

indicates that data fitted the model for each grade 

about equally well since there was little difference in 

the statistic between the models. Some species, 

generally those with the most observations, provided 

slightly better estimates of the parameters. The root 

mean square residual ranged from 0.05 or 0.06 to 0.15 

for each of the three models. Overall, the models 

seemed to fit northern red oak, white oak, and other 

oaks somewhat better than the other species, 

particularly red maple and the black walnut/ash 

group. 

Model parameters for white oak were used to 

predict the proportion of trees by grade for each 

diameter class (Table 5). As expected, similar calculations for other species revealed considerable differences between species. Table 6 gives the percentage 

of combined grade 1 and 2 trees; red oak, white oak, 

and yellow-poplar usually have inherently better 

quality than chestnut oak, red maple, or the group of 

other hardwoods. 

Discussion 

The results of this study indicated large differences among species in the d.b.h.-grade relationship. 

Similar findings were reported by Trimble (1965), who 

believed that these differences were due to inherent 

differences in branching habit and frequency of dormant buds. There are similar'inherent differences 

between Allegheny hardwood species (Ernst and 

Marquis 1979). The latter found the highest proportion of grade 1 or 2 trees in the black cherry/yellowpoplar group, whereas the beech/birch group consisted of higher proportions of grade 3 or lower quality 

trees. 
Table 2.-Model parameters for predicting the proportion of grade 1 trees 

Species Trees520.5 inches d.b.h. Trees 220.5 inches d.b.h. Root mean 

Bo B 1 82 ao a 1 square residual 

White oak 

Chestnut oak 

Northern red oak 

Other oak 

Red maple 

Y ellow-poplar 

Walnutlash 

Other hardwoods 

Table 3.-Model parameters for predicting the proportion of grade 1 

and grade 2 trees combined 

- -- 

Species " Trees'20.5 inches d.b.h. Trees 220.5 inches d.b.h. Root mean 

B o B 1 8 2 ao a 1 R2 square residual 

White oak .88 

Chestnut oak .72 

Northern red oak .go 

Other oak .79 

Red maple .59 

Yellow-poplar .94 

Walnutlash .76 

Other hardwoods .61 

Table 4.-Model parameters for predicting the proportion of grade 3 trees 

Species All trees 211.0 inches d.b.h. Root mean 

ao Bo B1 B 2 R2 square residual 

White oak 

Chestnpt oak 

Northern red oak 

Other oaks 

Red maple 

Y ellow-poplar 

Walnutlash 

Other hardwoods 
Table 5.-Predicted grade distribution of white oak 

by d.b.h. class. 

-- - - 

D.b.h. Grade 1 Grade 2 Grade 3 Grade 4 and 5 

11 - - -- .950 .050 

12 - - -- .914 ,086 

13 - - .I84 .724 .092 

14 -- .489 .488 .023 

15 -- .667 .308 .025 

16 .275 .491 .I96 .038 

17 .476 .343 .I32 .049 

18 .5.35 .312 .098 .055 

19 .552 .311 .080 .057 

20 .558 .313 .070 .059 

21 .552 .309 .065 .074 

2 2 .537 .300 .063 .lo0 

23 .523 ,290 .061 .I26 

24 .508 -281 .061 .I50 

2 5 .494 .271 .060 .I75 

2 6 .480 .261 .060 .I99 

27 .465 .252 .060 .223 

Table 6.-Percentage of sawtimber trees with grade 1 or 2 butt log, 

by species and d.b.h. class. 

White Chestnut Northern Other Yellow- Walnut Red D.b.h. oak Other 

oak red oak oak poplar ash maple hardwoods 
Our sample data on tree quality represent a much 

broader spectrum of various forest conditions than 

was reported in earlier studies. Because of this diversity in ownerships, management practices, and 

forest condit'ions, our sample quality data should 

represent average stand conditions for the Pennsylvania upland oak type. Although our sample included 

data on some of the same species discussed in earlier 

studies, no comparisons were attempted because both 

geographic areas and forest conditions differed. It 

should be noted that the quality of trees in individual 

stands may vary widely from the average values reported here because of the great variation in forest 

conditions sampled. 

Our grade distributions also differ from earlier 

results in that beyond a d.b.h. of 20 inches all species 

show a decline in the proportion of grade 1 and 2 

trees. Many of our sample stands have been cut indiscriminately over the years, leaving culls or lowvalue trees to occupy the lands. 

The 31-percent drop in grade 1 or 2 walnut or ash 

trees between 20 and 25 inches may reflect the fact 

that high-value, high-quality trees that are more than 

20 inches in d.b.h. are more likely to be cut. 

The computed percentages by grade and d.b.h. 

class for each of the various species are useful when 

estimating stand or tree values for typical stands 

where specific grade information is lacking. In broad 

regional economic analyses, grade distributions are 

helpful in determining current and projected timber 

resources by species, quality class, and value. When 

grade distributions are used in conjunction with 

growth simulators, more precise economic evaluations are possible for alternative management strategies. 

The equations presented here provide a means of 

building grade predictions into growth simulators for 

eight species groups. Thus, as the simulator grows a 

tree in height, d.b.h., and volume, we can change the 

grade over time with these equations. For example, 

if we have a 14-inch grade 3 white oak, what is the 

probability of it becoming grade 1 or grade 2 when it 

reaches 16 inches? Using Table 5 or the equations, 

we can determine that about 29 percent of such 

grade 3 trees will become grades 1 or 2 by the time 

they grow to 16 inches (.488-.196=.292). 

The grade distributions by d.b.h. class (Table 5) 

should be an important reminder that quality and, 

therefore, value are closely linked to size. Less than 

50 percent of 14-inch white oak trees are expected to 

be better than grade 3. If these trees grow 4 more 

inches, then 85 percent should qualify as grade 1 or 2. 

Coho and Wysor (1980) showed that most logs more 

than 17 inches in scaling diameter that were delivered to sawmills were grade 1. However, they added 

that the most frequent scaling diameter of logs delivered at their sample sawmills in West Virginia was 

only 12 to 14 inches; thus, these logs were of low 

quality. Since the stumpage price of grade 1 or 2 

trees is several times that of grade 3 trees, managers 

should look at the economics of growing their small 

sawtimber trees a few more years so that more would 

qualify as grade 1 or 2. 
Literature Cited 

Ernst, Richard L.; Marquis, David A. Tree grade distributions in Allegheny hardwoods. Res. Note NE275. Broomall, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station; 1979. 5 p. 

Goho, Curtis D.; Wysor, Paul S. Characteristics of 

factory-grade hardwood logs delivered to Appalachian sawmills. Res. Pap. NE-166. Upper Darby, 

PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station; 

1970. 17 p. 

Hanks, Leland F.; Gammon, Glenn L.; Brisbin, 

Robert L.; Rast, Everette D. Hardwood log 

grades and lumber grade yields for factory lumber 

logs. Res. Pap. NE-468. Broomall, PA: U.S. 

Department of Agriculture, Forest Service, 

Northeastern Forest Experiment Station; 1980. 

92 p. 

Mendel, Joseph J.; DeBald, Paul S.; Dale, Martin E. 

Ree value conversion standards for hardwood 

sawtimber. Res. Pap. NE-337. Broomall, PA: U.S. 

Department of Agriculture, Forest Service, 

Northeastern Forest Experiment Station; 1976. 

74 p. 

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. 31 p. 

Trimble, George R., Jr. Improvement in butt-log 

grade with increase in tree size, for six hardwood 

species. Res. Pap. NE-31. Upper Darby, PA: U.S. 

Department of Agriculture, Forest Service, 

Northeastern Forest Experiment Station; 1965. 

15 p. 
Dale, Martin E.; Brisbin, Robert L. Butt log quality of trees in 

Pennsylvania oak stands. Res. Pap. NE-568. Broomall, PA: 

U.S. Department of Agriculture, Forest Service, Northeastern 

Forest Experiment Station; 1985. 8 p. 

Describes the distribution of sawtimber trees by diameter at breast 

height (d.b.h.) and grade for eight hardwood species in upland oak 

stands of Pennsylvania. The proportion of trees by d.b.h. and grade 

revealed differences between species. The quality of northern red 

oak, white oak, and yellow-poplar appeared inherently better than 

that of red maple, chestnut oak, and a group of other hardwoods. 

Grade predictions by size and species allow more precise timber 

appraisals and enable managers to evaluate alternative management 

strategies more accurately. 

I ODC: 853:561.5:652.3 

I Keywords: Grading; quality; value 

*U. S. GOVERNMENT PRINTING OFFICE2 1985-505-028:20028 
Headquarters of the Northeastern Forest Experiment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of 

Massachusetts. 

Berea, Kentucky, in cooperation with Berea College. 

@ Burliigton, Vermont, in cooperation with the University of 

Vermont. 

Delaware, Ohio. 

Durham, New Hampshire, in cooperation with the University of 

New Hampshire. 

Hamden, Connecticut, in cooperation with Yale University. 

Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown. 

Orono, Maine, in cooperation with the University of Maine, 

Orono. 

Parsons, West Virginia. 

Princeton, West Virginia. 

Syracuse, New York, in cooperation with the State University of 

New York College of ~nvikmental Sciences and Forestry at 

Syracuse University, Syracuse. 

University Park, Pennsylvania, in cooperation with the 

Pennsylvania State University. 

@ Warren, Pennsylvania.