Predicting Volumes and 

Forest Service Numbers of Logs by Grade 

Northeastern Forest 

Experiment Station from Hardwood Cruise Data 

Research Paper NE-613 

Daniel A.. Yaussy 

Robert L. Brisbin 

Mary J. Humphreys 
Abstract 

The equations presented allow the estimation of quality and quantity of commercial logs produced from a hardwood stand based on cruise data. The gross International %inch board-foot volume and number of logs by log grade for trees of 11 

species can be predicted based on dbh, merchantable height, and tree grade. A 

two-stage estimation procedure was developed utilizing regression techniques 

and linear discriminant analysis. The volumes by log grade are estimated with 

multivariate multiple linear regression equations. These volumes, the tree dimensions, and grade are then used in discriminant functions to estimate the number 

of logs by log grade. This information, when packaged in appropriate computer 

software, will provide the mill manager with the means to estimate the quantity 

and quality of logs that would be added to a mill yard inventory from a timber 

sale. The software also will help a timber buyer or landowner set purchase price 

based on stumpage prices or delivered log prices and conversion costs. 

The Authors 

DANIEL A. YAUSSY, research forester, received a B.S. degree in natural resources 

(forestry) from the Ohio State University in 1976, an M.S. degree in forest biometrics from Virginia Polytechnic Institute and State University in 1978, and an M.S. 

degree in statistics from Ohio State in 1984. He joined the USDA Forest Service in 

1979 and is with the Northeastern Forest Experiment Station project on management and utilization alternatives for nonindustrial private forests at Delaware, 

Ohio. 

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 is located at Delaware, Ohio, on the staff of the Station's forest inventory, analysis, and economics project. 

MARY J. HUMPHREYS, research forest technician, is working toward a B.S. 

degree from Michigan Technological University. She joined the USDA Forest Service in 1987 and is currently assigned to the project on management and utilization 

alternatives for nonindustrial private forests at Delaware, Ohio. - - 

Manuscript received for publication 9 February 1988 

Northeastern Forest Experiment Station 

370 Reed Road, Broomall, PA 19008 

April 1988 
Introduction Methods 

The equations in this paper were developed to be used in 

the computer program STUMP (Brisbin et al. 1988) for 

estimating the quality and quantity of commercial logs that 

can be produced from individual hardwood trees. The gross 

International %-inch board-foot volume and number of logs 

by log grade for each tree are predicted based on diameter 

at breast height (dbh or D), merchantable height to an 

8-inch top (H), and USDA Forest Service tree grade (Hanks 

1976). When used in conjunction with a taper equation, a 

bucking simulator can be developed to estimate scaling 

diameter, log length, and log grade for each log cut from a 

tree. This bucking routine can be integrated into a growth 

and yield simulator. This information, when packaged in appropriate computer software, will provide a mill manager 

with the means to estimate the quantity and quality of logs 

that would be added to a mill yard inventory from a timber 

sale. This same software will help a timber buyer set 

stumpage prices based on conversion costs and delivered 

log prices. 

Blinn et al. (1983) developed a method for estimating the 

multiproduct value of a hardwood stand. The method is 

field intensive and does not lend itself to computer simulations. Another method of partitioning volume into roundproduct classes was developed by Yaussy and Sonderman 

(1984), but the classes were too broad to accommodate 

estimation of numbers of logs by log grade. These methods 

require that an estimate of total height be obtained in some 

manner. Reed et al. (1987) distributed gross board-foot 

volume of a tree between the log grades of sugar maple. 

Reed's method could be substituted as the volume estimator for this study. For practical application of the results of 

this study, the independent variables used in these equations were limited to those commonly collected in a field 

cruise. 

Data 

The data set used in this study is part of an extensive data 

base collected in the 1960's and early 1970's and includes 

the major Appalachian, central, and northern hardwood 

species. The standing trees were measured and graded 

using Forest Service tree grades. They were then felled, 

bucked, and diagrammed, and the resulting logs were measured and graded using Forest Service log grades (Rast et al. 

1973). The logs were bucked in lengths from 8 to 16 feet to 

maximize log grade and minimize scalable defects such as 

sweep, crook, and rot. The study reported here includes the 

11 species listed in Table 1 of the Appendix. The data set 

contained 2,800 trees. One-quarter of the trees from each 

species were set aside in a validation data set. 

The object of this research was to provide a means of predicting the volume and the number of logs by log grade that 

a standing tree would produce based on cruise data. Analysis indicated that the only way to obtain a satisfactory prediction of the number of logs by log grade could be 

obtained only the use of volume by log grade. Since neither 

of these variables is measured in a normal cruise, a twostage estimation procedure was appropriate. An equation 

was developed to predict volumes by log grade. These 

volumes were then used in a second set of equations to 

estimate the number of logs by log grade. 

Multivariate linear regression analysis was used to develop 

the equations for predicting gross International %-inch 

board-foot volumes by log grade. This form of analysis is 

preferable to Ordinary Least Squares (OLS) methods since 

there is a relationship between the log grade volumes within 

the tree, i.e., they must sum to the total factory grade 

sawlog volume. The usual variables representing base 

diameter (D), basal area (D2), surface area (DH), and cylindrical volume (D2H) were used in conjunction with the 

dummy variables representing tree grade (G, G,, defined in 

Table 2) in univariate stepwise regressions to find the five 

most descriptive variables for each log grade in each species. These variables were then combined in a multivariate 

linear equation across log grades for each species (Table 3). 

Variables were deleted by means of backward elimination if 

the associated coefficients were not statistically different 

from zero at the ,051 level of significance based on the Wilk's 

Lambda criteria. Coefficients are found in Table 4. 

The next step involved developing equations to predict the 

number of bucked logs by log grade that an individual tree 

would produce. OLS regression analysis was not appropriate for predictions of this type since the dependent variable is not continuous. A prediction of 2.38 grade 2 logs 

would not be acceptable. Linear discriminant analysis 

develops equations which can be used to estimate the 

probability that an observation fits into a certain category. In 

this instance, the categories were the numbers of logs of 

each log grade that a tree will produce (i.e.. 0,1,2,3,4). This 

meant that there would be an equation for each possible 

category in each of three log grades, in each of 11 species, 

198 equations. With this in mind, it was decided to limit the 

number of variables in each equation to five. The linear discriminant function used was: 
The coefficients for the linear discriminant functions are 

listed in Table 5. Many species in the development data set 

had trees which produced four or more logs per log grade, 

others did not. That is why some species in Table 5 have 

fewer coefficients than others. For example, the paper birch 

sample had no trees that produced more than one grade 1 

log; therefore, it only has coefficients for two equations. 

Validation 

The multivariate equations were applied to the trees in the 

validation data set. The results (Table 6) indicate that total 

merchantable volume by species is predicted within 5 percent of the actual. With the exception of log grade 3 chestnut and northern red oaks, all log grade volumes are within 

20 percent. Actual log grade volumes of the validation trees 

were used as input to the discriminant functions for testing. 

The total predicted numbers of logs is within 10 percent for 

all species except one, and is acceptable for each log grade 

within species except for grade 3 northern red oak. It is 

interesting that the multivariate equations overestimated the 

grade 3 volume for this species by such a wide margin, yet 

the discriminant functions underestimated the number of 

logs by the same percentage. This might be due to the 

low number of grade 3 northern red oak logs in the study 

(Table 2). 

For the predicted values that deviated from the actual, the 

deviations are usually negative. This is due to the nature of 

the system being modeled. The probability of a tree producing no logs or one log of a certain grade is much higher 

than the probability of producing two, three, or four logs of 

that grade. And this model, like most models, tends toward 

the mean and avoids the extremes. This yields a slight negative bias even when the model is used with the development 

data set. 

Applying the Models 

Log grade volumes are estimated for each tree based on 

equation set (1). The discriminant equations are then applied to the values of dbh, merchantable height, tree grade, 

and the predicted volumes from equation set (1). The largest resulting values indicate the numbers of logs by log 

grade the tree is most likely to produce. 

I One of the drawbacks of additive models, like the multivariate equations, is that a volume is always estimated even if it 

is negative or close to zero. These small volumes produce 

no logs when entered in the discriminant functions. Log 

grade volumes of this type may be handled in two ways: 

1. The volume is distributed evenly to the volumes of the 

remaining log grades and the value is set to zero. In this 

manner the total merchantable sawlog volume for the tree is 

maintained. 

2. The volume is added to the volume of the next tree of 

the same species. This will more closely estimate the log 

grade volume and number of logs of the stand. 

An example of the use of the equations is given in Table 7. 

Conclusion 

The objective of this study was to produce equations to 

predict volumes and numbers of logs by log grade from 

information that is commonly tallied in a timber cruise. The 

resulting models work satisfactorily. More accurate models 

probably could be developed if more descriptive, less obtainable variables were considered. 

The next phase of this research is to apply a taper function 

to the volumes and number of logs to predict log length and 

small-end diameter for each log in a tree. 

Acknowledgment 

This project was partially funded by the Forest Resources 

Systems Institute, which receives Federal financial assistance. Benefits of the Forest Resources Systems Institute 

are available to all eligible persons regardless of sex, race, 

color, national origin, religion, handicaps, or age. 

Literature Cited 

Blinn, C. R.; Sinclair, S. A.; Ek, A. R. 1983. A method for 

estimating the multi-product value of hardwood timber 

stands. Forest Products Journal. 33(3): 49-54. 

Brisbin, R. L.; Yaussy, D. A.; Fuller, L. G. 1988. STUMP - a 

system of timber utilization and mill processing. The 

Compiler. 6(1): 9-13. 

Hanks, L. F. 1976. Hardwood tree grades for factory lumber. 

Res. Pap. NE-333. Upper Darby, PA: U.S. Department of 

Agriculture, Forest Service, Northeastern Forest Experiment Station. 80 p. 

Rast, E. D.; Sonderman, D. L.; Gammon, G. L. 1973. 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. 31 p. 

Reed, D. D.; Lyon, G. W.; Jones, E. A. 1987. A method for 

estimating log grade distribution in sugar maple. Forest 

Science. 33(2): 565-569. 

Yaussy, D. A.; Sonderman, D. L. 1984. Multivariate regression model for partitioning tree volume of white oak into 

round-product classes. Res. Note NE-317. Broomall, PA: 

U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment Station. 4 p. 
Appendix 

Table 1.-Number of trees and logs by species and tree grade for the development and 

validation data sets (numbers in parentheses are percentages) 

Development Validation 

N~, of NO. of logs NO. of NO. of logs 

Species Tree trees Grade Grade Grade trees Grade Grade Grade 

and code grade 123 123 

Total 

Black 

cherry 2 

(BLC) 

Total 

Total 

Chestnut 

oak 2 

(CW 

Total 

Continued 
Table 1 .-Continued 

Development Validation 

N~, of NO. of logs NO. of NO. of logs 

Species Tree trees Grade Grade Grade trees Grade Grade Grade 

and code grade 123 123 

Northern 

red oak 2 

(NW 

Total 

Paper 

birch 

(PW 

Total 

1 

Red 

maple 

(REMI 

3 

Total 

1 

Sugar 

maple 

(SUM) 

3 

Total 

Continued 
Table 1.-Continued 

Development 

NO. of NO. of logs 

trees Grade Grade Grade 

123 

100 99 125 94 

(36) (88) (46) (27) 

Validation 

NO. of NO. of logs 

trees Grade Grade Grade 

123 

Species 

and code 

Tree 

grade 

1 

White 

oak 

(WHO) 

3 

Total 

1 

Yellow 

birch 

(YEB) 

3 

Total 

1 

Yellowpoplar 

(YEP) 

3 

Total 
Table 2.-List of variables and definitions 

D = dbh, tree diameter, outside bark, at 4.5 feet 

H = merchantable height, height to an 8-inch diameter, inside bark, or to 

the point that the main stem breaks up 

"i = gross International %-inch board-foot volume for log grade i, i=1,2,3 

Gk = dummy variable indicating tree grade, k=2,3: 

Tree grade G2 G3 

1 0 0 

2 1 0 

3 0 1 

b- 11 = coefficients determined by regression, j=0, ..., 11 

fin = linear discriminant function value for log grade i and number of logs n, 

n=0, ..., 4 

ainm = coefficients determined by discriminant analysis, m=0, ..., 5 

'-i = number of grade i logs in a tree, Li = the "n" associated with maxn(fin) 
Table 3.-Model forms and variables used for predicting volumes by log grade 

Equation set (1) model form: 

V. = b + b. X. + b X. + ... + billXill i = 1,2,3 1 10 1' 11 12 12 

PAB D2 

REM D 

SUM D 

WHO D2 

YEB D 

Species Xi, Xi2 

BAS D H 

BLC D2 D2*H 

BLO D H 

CHO D D2 

NRO D*H D2*H 

H 

D2 

H 

D*H 

H 

YEP D*H D2*H 
Table 4.-Multivariate regression coefficients to predict volumes by log grade 

i bio bil biz bi3 bi4 bi5 bi6 bi7 bi8 big bile bill 

BAS 

1 124.4676 -1.56267 -1 16.795 7.428632 -0.41 31 6 -.96.33ll 17.8701 7 -1.1 18 

2 89.091 93 -6.2618 -45.0312 4.814644 0.207677 792.8332 -1 11.084 3.587002 

3 -500.424 32.86177 145.2025 -8.09048 0.138984 -316.591 47.72614 -1.22285 

BLC 

1 -40.0789 0.505623 0.022593 -0.42124 0.023633 -0.72066 3.041069 

2 -25.5242 0.1991 81 0.044957 0.1 52841 0.0731 34 0.31 2790 -1.91 674 

3 40.92406 -0.23153 0.1 2770 0.000909 0.01 4509 0.1 07651 0.81 3458 

BLO 

1 -28.5531 8.349625 -41.2948 0.131248 -0.39456 -0.15321 

2 -14.9287 3.456186 -34.9253 0.131475 0.245983 -0.02877 

3 24.7471 9 -4.09842 40.43329 0.039805 0.097044 0.095157 

CHO 

1 -1030.04 119.5710 -2.93541 503.5838 -59.2919 1.658894 -25.0837 0.902412 10.68945 -0.50995 -0.31793 -0.32453 

2 -355.341 11.95751 0.271 448 4.420796 5.98471 9 -0.1 9765 54.7031 5 -2.44229 -1 9.2414 0.927707 13.72388 -0.56886 

3 1526.879 -137.292 2.862889 -500.197 47.80283 -0.97528 -42.1716 2.165500 14.07657 -0.73187 -22.2291 1.285556 

NRO 

1 122.3440 -1 0.2673 0.549595 -1 .OBI 9 -0.1 I966 -7.8551 1 0.042438 81 .I6464 -0.241 30 

2 -25.451 1 5.259903 -0.08475 -1.23754 0.096733 60.56266 -2.88872 -271.742 0.585807 

3 56.4721 2 -0.34953 0.00991 5 -3.03426 0.086864 -86.7301 4.877621 303.4664 -0.881 90 

PAB 

1 -1 6.5397 0.485952 -6.53406 -0.35776 178.6421 -23.0975 0.747528 -0.41 788 1.991921 -0.09785 

2 83.24077 0.00101 0 -1 5.61 32 -0.24188 -204.682 23.27547 -0.43230 -0.32030 -7.481 09 0.6461 59 

3 -80.6021 0.053629 60.26620 0.386348 -1 20.077 14.25352 -0.58485 0.31 701 8 0.0681 02 -0.07493 

REM 

1 -22.0244 -7.97003 0.975629 -0.01742 9.1 971 41 -0.89884 0.001 650 8.51 7887 -0.81 466 -0.01 730 

2 167.5897 -1 8.5903 0.283858 0.1 73881 -4.93892 0.992506 -0.1 5668 -1 4.2928 1.395580 -0.21 456 

3 -237.854 35.95310 -1.20282 0.073460 -0.1 31 71 -0.26224 0.1 24409 8.686255 -0.71 907 0.1 72893 

SUM 

1 82.83013 -0.03570 -44.1 681 0.201989 -2.05552 -0.1 1932 -0.27442 -0.05718 

2 40.1 8536 3.837562 -41.2307 0.096812 -3.59342 0.1 8487 -0.54040 0.209947 

3 -238.336 9.391353 78.66990 -0.07997 3.420974 -0.03584 0.835311 -0.17571 

WHO 

1 82.42034 0.1 14695 -4.90782 0.257628 -0.30051 -0.30031 -0.03631 

2 -55.2884 0.1 15733 0.7901 78 0.088963 0.1 12273 0.409885 -0.23695 

3 -85.651 3 0.1 20743 4.268837 -0.09586 0.1 58384 0.1 95562 0.089931 

YEB 

1 -39.5768 7.565891 18.43794 -7.16096 0.350975 -5.01494 -58.9563 11.48668 -0.44884 7.149255 -0.71674 

2 -224.931 13.58281 -21 .go86 8.41 0861 -0.29970 5.568782 169.6781 -23.8634 0.7231 78 2.36521 7 -0.1 8458 

3 109.5665 -8.02168 11 3.6866 -11.0371 0.367923 1.142733 -228.61 1 22.79333 -0.54453 -9.70899 0.820814 

YEP 

1 124.1392 -6.04278 0.346507 -1 9.8908 0.721 81 3 7.488989 -0.41 292 -0.34244 -0.031 72 

2 32.01724 -1 .%I96 0.185181 -17.8547 1 .O363OO 6.049651 -0.28623 -0.41000 0.07851 3 

3 0.409898 2.144933 -0.02501 7.890494 -0.45646 -4.78722 0.296917 0.211873 0.077016 
Table 5.-Linear discriminant function coefficients for predicting the number of logs by 

log grade 

BAS 

29.23947 

9.897940 

14.68596 - 

18.67562 

1 7.09449 

17.49262 

20.74589 

16.33567 

19.421 33 

16.93973 

16.64529 

15.72571 

17.11509 

BLC 

23.051 32 

13.71 652 

21.1 1360 - 

- 

22.95071 

17.281 60 

18.13481 

25.84078 - 

18.09682 

17.09623 

15.23348 

16.1 8072 - 

BLO 

21.99984 

1.875626 

0.212283 

-0.76108 - 

13.581 25 

12.2381 9 

12.73075 

15.51461 - 

22.38560 

15.58454 

10.98221 - 

- 

23.60029 

15.521 80 

12.52378 

9.981720 

6.368033 

10.09766 

19.9691 8 

28.73801 

35.98256 

50.50779 

32.42247 

26.02659 

20.37389 - 

- 

32.39095 

27.59525 

19.421 01 

17.05780 - 

29.97801 

49.35207 

72.71268 

93.31 171 

- 

16.34590 

8.692768 

-1.05359 

-7.64187 - 

16.981 72 

9.927046 

3.372948 

2.442764 - 

Continued 
Table 5.-Continued 

13.54840 

9.189846 

5.761827 

4.062538 - 

CHO 

17.00297 

11.15577 

17.22099 - 

12.90514 

13.00943 

15.47643 

15.8571 2 

- 

12.32869 

11.68221 

11.43332 

10.8801 5 

- 

NRO 

24.83825 

8.469391 

8.1 49256 

7.411188 

6.070625 

10.8461 1 

9.558031 

9.3131 87 

11.53423 

11.12551 

11.05702 

7.236086 

2.677372 

1 1.39122 - 

PAB 

29.37293 

35.1 2669 

- 

- 

7.998236 

47.24703 

84.35400 

11 2.4821 - 

23.00735 

11.87230 

1.459532 - 

- 

23.1 1 646 

12.4721 4 

6.1 82095 

3.338323 - 

18.77531 

52.91 449 

82.3961 0 

1 17.2000 - 

36.93330 

23.90157 

20.80553 

20.79236 

15.49281 

29.02894 

22.35797 

18.52543 

18.75486 

13.76342 

1 7.62662 

51.82179 

93.36548 

128.2080 - 

28.9941 7 

6.080971 - 

- 

- 

Continued 
Table 5.-Continued 

34.69084 

37.20074 

45.6731 9 

49.83071 - 

30.47835 

27.70859 

26.66292 

25.09376 - 

REM 

31.43903 

10.92691 

11.48646 - 

- 

21.79864 

20.84694 

22.1 5043 

23.06293 - 

23.90431 

20.99925 

19.06962 

19.84916 

19.65262 

SUM 

18.67638 

12.39526 

15.11249 

15.88579 - 

16.40248 

13.87071 

16.1 6728 

16.87634 - 

14.62629 

12.401 25 

12.56379 

11.651 29 

13.16876 

30.4571 0 

20.16537 

17.45698 

9.309786 - 

16.32866 

39.74486 

60.83406 

73.26560 - 

33.89331 

17.85137 

10.60369 - 

- 

33.55805 

24.08137 

19.79676 

18.80464 - 

18.82301 

35.68753 

50.32214 

70.601 17 

59.25131 

31.41 859 

24.18096 

26.941 64 

28.3591 9 

- 

28.96448 

22.51 21 7 

19.39242 

16.301 43 

- 

29.53050 

50.70147 

72.36822 

97.38596 

98.861 70 

Continued 
Table 5.-Continued 

WHO 

21.11756 

9.541 529 

14.1 2656 - 

- 

16.02093 

13.50678 

12.93143 

15.11850 

1 1.871 70 

17.31752 

13.48480 

13.88476 

11.75160 

7.235757 

YEB 

22.61053 

13.421 75 

16.89758 

18.71 390 

- 

19.09565 

16.85377 

19.18828 

20.00756 - 

17.28062 

16.05029 

14.79576 

15.60289 

14.59744 

YEP 

18.00787 

8.757671 

14.73622 - 

- 

12.13002 

11.17330 

12.23943 

13.8501 2 

13.4901 2 

11.57775 

2.796366 

-4.27862 - 

- 

11.90309 

5.778838 

3.001601 

0.1 80557 

-2.96547 

2.072930 

21.281 08 

40.51661 

60.26592 

71.53659 

30.17830 

23.04481 

22.1 31 56 

1 8.24740 - 

29.38369 

24.59036 

21.20388 

23.521 50 - 

24.06342 

44.40267 

72.01 447 

78.8961 5 

95.40305 

14.02178 

8.956738 

4.720561 - 

- 

15.4141 3 

8.361 107 

3.1 74894 

-0.20739 

-6.42525 

Continued 
Table 5.-Continued 

Table 6.-Comparison of actual values and those predicted by the models using the validation data set 

Tree Value BAS 

Actual 3300 

1 Predicted 2923 

% Difference -1 1.4 

Actual 3750 

2 Predicted 3978 

% Difference 6.1 

Actual 3645 

3 Predicted 3798 

O/O Difference 4.2 

BLC BLO CHO NRO PAB REM SUM WHO YEB YEP 

GROSS BOARD-FOOT VOLUME (Int. % inch) 

Total 

74880 

73757 

-1.5 

92660 

91 196 

-1.6 

72270 

7471 1 

3.4 

Actual 10695 14455 21370 27080 28975 7180 19630 25165 32680 17500 35080 239810 

Total Predicted 10699 13840 21513 27376 30349 6822 19266 25938 32619 16941 34301 239664 

O/O Difference 0.0 -4.3 0.7 1.1 4.7 -5.0 -1.9 3.1 -0.2 -3.2 -2.2 -0.1 

NUMBER OF LOGS 

Actual 22 28 38 42 53 12 36 40 46 20 34 371 

1 Predicted 22 28 34 41 51 12 36 40 47 21 34 366 

% Difference 0.0 0.0 -10.5 -2.4 -3.8 0.0 0.0 0.0 2.2 5.0 0.0 -1.3 

Actual 42 66 45 89 85 32 76 88 76 78 84 761 

2 Predicted 38 58 45 92 72 31 75 86 74 75 83 729 

O/O Difference -9.5 -1 2.1 0.0 3.4 -15.3 -3.1 -1.3 -2.3 -2.6 -3.8 -1.2 -4.2 

Actual 63 56 71 68 42 53 106 77 116 89 157 898 

3 Predicted 63 52 64 68 33 53 105 68 115 78 158 857 

O/O Difference 0.0 -7.1 -9.9 0.0 -21.4 0.0 -0.9 -11.7 -0.9 -12.4 0.6 -4.6 

Actual 127 150 154 199 180 97 218 205 238 187 275 2030 

Total Predicted 123 138 143 201 156 96 216 194 236 174 275 1952 

O/O Difference -3.1 -8.0 -7.1 1.0 -13.3 -1.0 -0.9 -5.4 -0.8 -7.0 0.0 -3.8 
Table 7.-Example of the use of the models 

Species: 

Dbh (D): 

Merchantable height (h): 

Tree grade: 

Black cherry (BLC) 

20 inches 

3 logs 

2 (G2=l, G3=0) 

Multivariate equations: 

V1 = -40.0789+.505623*D2+.022593*D2*H-.42124*D2*G2 

+.023633*D2*H*G2-.72066*D2*G3+3.041069*D*H*G3 

= 31 board feet 

v2 = 210 

V, = 62 

Discriminant functions: 

flo = -22.5491+22.1 948*G2+23.0513*G3+34.7579*V1/D2 

f,, = no calculations 

f14 = no calculations 

L, = 0 grade 1 logs (f,, = max,(fln)) 

fz0 = -22.8420+20.4264*G2+22.9507*G3+62.3885*Vl/D2 

+9.99473*V2/D2+32.3910*V3/D2 

= 12.7 

fP1 = 31.0 

fZ2 = 32.3 

fZ3 = 28.6 

f24 = no calculations 

L2 = 2 grade 2 logs 

Continued 
Table 7.-Continued 

f, = no calculations 

L, = 1 grade 3 log 

After adjusting the grade 1 log volume to reflect the estimate of no grade 1 logs: 

Grade 1 Grade 2 Grade 3 

Volume I 0 225 78 

Number of logs 0 2 1 

15 

*U. 5. GOVERNMENT PRINTING OFFICE: 19881748-076/600 17 
Table 7.--Example of the use of the models 

Species : Black cherry (BLC) 

Dbh (D): 20 inches 

Merchantable height (h): 3 logs 

Tree grade: 2 (G2=1, G3=0) 

Mu1 tivariate equations : 

= 49 board feet 

vz = 257 

Discriminant functions: 

f lo = -22.5491+22.1948*~~+23.0513*~ +34.7579*~,/0~ 3 

+28.7885*~,/~~+.32.422511, L /D~ 

-t 

= 32.1 

f,, = 11.7 

f12 = -48.8 

13 = no calculations 

f14 = no calculations 

L1 = 0 grade 1 logs (f10 = rnan(fln)) 

Continued 
Table 7. Continued 

f2, = 44.6 

fz2 = 49.8 

fi3 = 48.0 

fi4 = no calculations 

L2 = 2 grade 2 logs 

2 

f30 = -21.2797+15.9264*~~+18. 0968*G3+55. 5755*V1/D 

2 +33.2239*~,/~ +29. 9780*v3/~ 2 

= 31.8 

f = 36.1 31 

f32 = 36.4 

f = 33.7 3 3 

34 = no calculations 

L3 = 2 grade 3 logs 

After adjusting the grade 1 log volume to reflect the estimate of no grade 

1 logs: 

Volume 

Number 

of logs 

Grade 1 

0 

Grade 3 

144 
Yaussy, Daniel A.; Brisbin, Robert L.; Humphreys, Mary J. 1988. Predicting 

volumes and numbers of logs by grade from hardwood cruise data. 

Res. Pap. NE-613. Broomall, PA: U.S. Department of Agriculture, 

Forest Service, Northeastern Forest Experiment Station. 15 p. 

The equations presented allow the estimation of quality and quantity of logs 

produced from a hardwood stand based on cruise data. When packaged in 

appropriate computer software, the information will provide the mill manager with the means to estimate the value of logs that would be added to a 

mill yard inventory from a timber sale. 

ODC 832.1 5-525.1 :853 

Keywords: Multivariate regression; discriminant functions 
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. 

Burlington, Vermont, in cooperation with the University of Vermont. 

Delaware, Ohio. 

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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 Environmental Sciences and Forestry at Syracuse University, 

Syracuse. 

University Park, Pennsylvania, in cooperation with the Pennsylvania State 

University. 

Warren, Pennsylvania. 

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should be reported to the Secretary of Agriculture, Washington, DC 20250.