United States 

Department of 

Agriculture 

Forest Service 

Southern 

Research Station 

Weight and Volume 

Determination for Planted 

n North Louis 

Ray A. Newbold; V. Clark Baldwin, jr.; and Gary Hill 

Research Paper 

SRS-26 
The Authors 

Ray A. Newbold, Professor, buisiana Tech University, School of Forestry, Ruston, 

LA; V. Clark Balduin, Jr., Supervisory Research Forester, U.S. Department of 

Agriculture, Forest Service, Southern Research Station, Asheville, NC; and Gary 

Hill, Production Analyst, Willmette Industries, he., Ruston, LA, respectively. 

October 2001 

Southern Research Station 

P.O. Box 2680 

Asheville, NC 28802 
Weight and Volume Determination 

for Planted Loblolly Pine in North Louisiana 

Ray A. Newbold; VB Clark Baldwin, Jc; and Gary Hill 

Abstract 

'The objective of this study was to assess the variability in weight-tovolume relaionships in loblolly pine (Pinus tm& L.) plantations and to 

determine predictability based on stand age, site quality, and/or tree size. 

Tree ages ranged from 1 I to 443 years, with diameters to 21 inches and 

heights to 91 feet. Measured site indices ranged from 45 to 72 at base age 

25. A total of 75 planted loblolly pine trees were felled and processed to 

assess the variability in bole weight to volume relationships. Cubic volume, 

green weight, and dry weight relationships were investigated; and the 

predictability of these variables with respect to age, site index, and tree size 

was determined. 

Keywords: Loblolly pine, Pinus tueda, plantation, volume, weight. 

Introduction 

Arguably, loblolly pine (Pintss taeda L.) is the most 

important commercial softwood species in the South and the 

most widely planted southern pine. The volume of wood 

coming from plantations is increasing, and the age at which 

plantations first support a commercial thinning continues to 

decline. Much of the commerce in purchasing roundwood is 

based on green weight, while initial manufacturing output is 

measured by dry weight, e.g., paper, or volume, e.g., lumber. 

The weight-to-volume relationship then becomes an 

important consideration for forest industry. A number of 

studies have been done on biomass estimates, which 

indicate that there are several interacting factors that 

influence green weight and dry weight per volume unit. The 

USDA Forest Service now markets timber sales on a cubicvolume basis, as opposed to a board-foot-volume basis that 

uses log scales such as Doyle, Scriber, or International 114- 

inch rule. Weight-to-volume relationships that change with 

age, tree size, or site quality carry important economic 

implications. 

A review of previous publications on this topic reveals that 

equations based on project data frequently carry coefficients 

of determination ranging from 0.94 to 0.99, although weight 

and volume equations among studies often yield varying 

results. Based on a Mississippi study (Nelson and Switzer 

1975), a 12-inch (in.) diameter at breast height (d.b.h.) tree 

70 feet (ft) tall would have a green weight of 1,362 pounds 

(Ib) on a poor site and 1,400 Ib on a good site. Based on a 

Texas study (Wiswell and others 1986), the same tree would 

weigh 1,502 Ib. Baldwin (198'7) would predict 1,430 Ib at 

age 27. Another study in Mississippi (Shelton and others 

1984) detedned that the green weight of a 20-year-old tree 

could exceed that of the same size 10-year-old tree by 15 

percent. With weights of loblolly pine vwing from 

Mississippi to Texas and sensitive to both site quality and 

age, justification exists for developing local tables for more 

specific regions of application. In this paper quations are 

developed for north Louisiana, where there is a substantial 

concentmtion of loblolly pine production and numerous 

product-manufacturing organizations that use this species. 

Comparisons are made with Baldwin's (1987) table, which 

is based on central Louisiana data. Our study assesses the 

variability in weight-to-volume relationships in loblolly pine 

plantations and determines predictability based on stand age, 

site quality, andor tree size. 

Methods 

A cross section of loblolly pine plantations was selected 

from lands of Willamette Industries, Inc., through data base 

queries. Stands selected were located across six Louisiana 

parishes: Bienville, Claibome, Jackson, Lincoln, Union, and 

Winn. To sample the influence of diameter on weight, two 

trees from the dominant, codominant, or intermediate crown 

classes were selected. One tree had a relatively large 

diameter and the other had a relatively small diameter. In 

some stands, a tree of a diameter between the other two was 

also sampled. The selected trees were a distance of at least 

1.5 times their height fiom the stand boundary and were 

proximate (usually within 50 ft) to each other. This removed 

edge effect on tree growth and kept the site quality constant. 

Difference in tree size was, therefore, due to growth rates 

and not age or site quality. 

Seventy-five trees were felled from 33 stands, 20 of which 

were age 25 or older. Sampling was carried out over a 

period of about 1 year. Wenty-three age classes raging 

from 1 I to 40 years were sampled. Tree d. b. h. ranged from 

5 to 2 1 in., and height ranged from 50 to 9 1 ft (fig. I). Site 

quality (25 years) ranged from 45 to 72 ft. 

Ekch tree was cut at or near ground level. The felled stem 

was then limbed and bucked into 3-ft bolts to a 3-in. 

merchantable top. The large end of each bolt was nubered 

to identify the tree number and bolt number. A 13-in. heavyduty commercial hanging scale (600 Ibs by 8 ounces) set up 

on a tripod was used to weigh each bolt. Weights for each 
0J , i 

0 2 4 6 8 10 12 14 16 18 20 22 24 

D.b.h. (in.) 

Figure 1-Data distribution of sample trees by d.b.h. and total height. 

bolt were recorded to the nearest 0.25 lbs along with the Results and Discussion 

stand number code, d.b.h., and total tree height. Diameters 

outside bark for both ends of each bolt were measured to the Effects of Site Quality and Age 

nearest 0.1 in. using a diameter tape. Disks were then sawn 

from the end of each bolt (with tree and bolt numbers) and 

placed in plastic bags. These samples were taken to the 

laboratory where they were either processed or stored in a 

cooler prior to processing. 

Laboratory weighing was done using a 3,000-gram (g) 

electronic balance. Weights for each disk were recorded to 

the nearest 0. lg. Processing involved first weighing the 

green disks with the bark attached. The disk was then 

debarked and using calipers, two perpendicular inside bark 

diameters were then averaged to get the diameter of the disk 

to the nearest 0.1 in. Green weight without bark was 

recorded, and the disks were placed in a forced air oven at 

105 "C. The first sample of disks was weighed three times 

daily during drying to monitor weight loss. After 48 hours, 

the dry weight had stabilized. All subsequent samples were 

dried for approximately 48 hours. The oven dry weight of 

each disk was then recorded. Aftewards, the disks were 

sanded, and growth rings were counted. The data collected 

to this point provided the basis for detemining cubic-foot 

volumes, green weight per cubic foot, moisture contents 

(MC), dry weight per cubic foot, and height growth as a 

measure of site quality. 

The hypothesis that bole green weight is influenced by site 

quality and age was tested. Site quality (SQ,,) was defined 

as total tree height at age 25. This was determined by first 

counting growth rings on the cross-section disks; then, using 

only dominant and codominant trees at least 25 years of age 

(n = 24), the point on the stem at which the ring count was 

25 rings less than the total ring count was assumed to be the 

height achieved in 25 years and was considered the actual 

site index. Both age and site index variables proved to be 

nonsignificant at the 0.05 probability level (F = 0.32, P = 

0.58 and F = 1.29, P = 0.27, respectively) when tested 

against bole green weight outside bark using the model 

LnWT = bo + b,LnDBH + b,LnHT + b,LnAGE + b,LnSI ( 1) 

where 

WT = bole green weight (Ibs) outside bark, 

DBH = tree diameter outside bark at 4.5 ft, 

AGE = tree age in years, 

SI = total tree height of dominantlcodominant trees at 

age 25, 

HT = total tree height, 

Ln = natural logarithm, and 

bo, b,, b,, b,, and b,= equation coefficients to be estimated. 
Day of year 

Figure 2-Moisture content of sample trees by sampling date. 

Green and Dry Wood Density 

Wood MC was calculated on a dry weight basis as 

MC = (green weight - dry weight) / (dry weight) X 100 (2) 

Tree age influenced MC and, therefore, dry weight. The data 

showed a wide variation in MC, but seasonal variations 

were not significant (fig. 2). The larger diameter sample 

trees had higher MC; but in intemdiate-to-large d.b.h. 

trees, it was inconsistently so. Because there were only 

seven sample trees in this data class, these observations 

were removed. Age was broken into six 5-year age classes 

to test for a critical age of MC change using the model 

MC = bo +b,(size) + b,(age class) + b,(size X age class) (3) 

where 

MC = moistwe content, 

size = small or large, 

bo, b,, b,, and b,= equation coeficients to be estimated, and 

age class = 11 to 15, 16 to 20, 21 to 25,26 to 30, 3 1 to 35, 

or 36 to 40 years. 

The statistic& difTerence between MC for the large trees and 

the small trees was then highly significant (F = 18.5 1, P = 

0.0001). Average MC for large (faster growing) trees versus 

small (slower growing) trees in the stand was 108.3 percent 

and 94.7 percent, respectively. Age class was also a highly 

significant variable (F = 10.02, P = 0.W1). The MC for 

trees aged 11 to 20 years versus 21 to 40 years averaged 

122.7 percent and 96.0 percent, respctively (table 1). 

Interaction between size and age proved to be nonsignificant 

(F = 1.43, P = 0.2280). 

Density (pounds per cubic foot) was also tested against the 

relative size of the tree in the stand. Tree size was not a 

significant variable for green weight per cubic foot, either 

inside bark (F = 0.89, P = 0.41) or outside bark (F = 0.19, 

P = 0.12). Across the entire data set, the inside bark green 

weight was 62.6 lbs per cubic foot, and the outside bark 

green weight was 55.5 lbs per cubic foot. The dry weight 

Table 1-Effect of age on bole moisture content 

Age class Observations MC" 

Number Perrent 

8 124.4 a 

6 120.5 a 

14 99.5 b 

12 98.2 b 

12 93.7 b 

16 93.0 b 

MC = moisture content. 

"Means followed by the same letter are not significantly different 

(Duncan's Multiple Range Test, P < 0.05). 
did, however, vary significantfy with tree size (faster versus 

slower growing trees) in concert with MC (F = 9.64, P = 

0.0002). Small tree (slow growth) dry weight averaged 32. f 

Ibs per cubic foot and large tree (fast growth) dry weight 

averaged 30.1 Ibs per cubic fwt, 

Considering the characteristics of the ple trees from both 

an age and size perspective, it was concluded that green 

weight per cubic foot is not affected by either of these 

variables. But in the faster growing, young plantations up to 

age 20, it was determined the weight was made up of more 

water and less wood fiber. Adjwting weight conversions as 

a wood procurement practice would be awkward, but 

correction of price based on expected dry fiber yield would 

be appropriate in wood procurement activity, This is the 

practice in agricultural grain markets where MC is measured 

at the delivery scales. 

Volume and Green Weight Prediction 

Weight afad volume predictions in this analysis were to a 

3-in. top diameter (merchantable bole). For weights by log 

height, the weights were to an 8-in. top. Therefore, whether 

estimated from the total tree height or the merchantable 

height, weights are for the merchantable portion of the bole. 

Figure 3 is a plot of actual tree weights from this study, 

which suggests that weight is a predictable variable. A set of 

equations based on these plantation data was developed, 

Table 2 displays the resulting coefficients of the regression 

amlysir, using the following mcxie2 

LnY = bo + b, LnDB H + bzLnHT (4) 

where 

Ln = natural logarith, 

Y = variables for cubic-foot volume outside bark, cubic-foot 

volume inside bark, and green weight outside bark in 

pounds, 

bo, b,, and b, = equation coefficients to be estimated, 

DBH = tree diameter outside bark at 4.5 ft, and 

HT = total tree height or merchantable height to a 3-in. top 

diameter for all trees except those expressed in log 

heights that are to an 8-in. top (table 2). 

The equations are for cubic-foot volume outside bark, 

cubic-foot volume inside bark, and green weight outside 

bark, both by total tree height and merchantable height to a 

3-in. top diameter for all trees except those expressed in log 

heights that are to an 8-in. top. Tree d.b.h. measurements are 

0 2 4 6 8 10 12 14 16 18 20 22 24 

D.b.h. (in.) 

Figure 3-Data distribution of tree weights by d.b.h. 
Table %Coefficients for various bole volume and green weight equations 

Dependent 

variable 

CFOB 

GFIB 

WT 

CFOB 

CFIB 

WT 

DBH 

bo b, 

-6.08947 1.93996 

-6.70 152 1.97460 

- 1.90705 2.00230 

-5.37160 1.82063 

-5.90076 1.85502 

-1.20192 1.90120 

TOTHT MCHT 

b2 b* 

LOGHT 

b? FI SE 

CFOB (16.5 ft logs) - 1.63258 1.54659 - - 1.05228 .989 1.97 

CFIB (16.5 ft logs) -2,28907 1.75 195 - - .97262 ,981 2.20 

WT (16.5 ft logs) 2.14989 1.668 1 1 - - ,95809 .980 147.74 

CFOB (1 7.5 ft logs) - 1.57067 1.54659 - - 1.05228 989 1.97 

GFIB (17.5 ft logs) -2.23 184 1.75 195 - - .97262 .981 2.20 

W (17.5 ft logs) 2.20626 1.668 1 1 - - .95809 ,980 147.74 

- = Not applicable. 

Equation form: LnY = bo+ b,LnDBH + b,LnHT 

CFOB = cubic foot volume outside bark; CFIB = cubic foot volume inside bark; WT = weight in pounds; DBH = diameter at breast 

height (4.5 in.); TOTHT = total tree height; MCHT= merchantable tree height (3-in. top diameter outside bark); LOGHT = number of 

logs to an 8-in. top diameter outside bark; H = fit index; SE = standard error of the estimate. 

in inches and heights are in feet. Logs are either 16.5 or 17.5 

ft to allow for trim on either saw log or ply log bolts, 

respectively. 

Figure 4 reveals that on an individual tree basis, the 

predictions from the equations developed in this study can 

be somewhat variable as a percent of bole weight, ranging 

from - 17 percent to +26 percent. Compared to the actual 

measured weight, more than 75 percent of the 75 predicted 

weights were within 10 percent of the actual tree weight 

using total tree height (equation 3 in table 2). A similar 

outcome was found using merchantable height (equation 6 

in table 2). Percent bark in this study varied by tree volurne 

and weight, but averaged 19.4 percent of volume and 9.1 

percent of weight (fig. 5). 

As previously noted, different equations developed for the 

same species have produced different results. It is difficult 

to determke the reasons for these differences because 

comparisons must involve at least comparable data and the 

same model form. Most of these requirements were met 

with the Baldwin (1987) equations and the data and 

equations developed in this study. The same model form 

was used and the tree sizes and ages were fairly close, but 

Baldwin (1987) did not actually make measurements to a 

3-in. top for the trees in his study. In this study, there was no 

differentiation between trees that came from thinned or 

unthinned stands, but suspected differences between these 

classes of trees was a main testing point in the Baldwin 

( 1987) study. 

Nevertheless, because Baldwin (1987) data were available, 

the following manipulations were accomplished in order to 

test for similarity or differences between the green weight 

and cubic-foot volume equations. The measured upper-stem 

diameter-height measurements from the Baldwin (1987) 

data were used to estimate height to a 3-inch top for each 

tree within those data, and all trees from thinned and 

unthinned stands were combined so comparable data were 

available for testing. hch test was done for both green 

weight and cubic-foot volume using model (4). The first test 

used was an F-test to determine if one equation was 

adequate for both data sets, or if separate equations would 

be better. This test revealed that there were significant 

differences between the two populations in both the green 
i 1 ------------------------------- -1 rn Equation 6 I - 

------------------------------------------ 

#a a, 

l2.b.h. (in.) 

Figure &Predicted green weight as a percent of actual weight. 

Volume outside bark (ft3) 

Figure 5-Percent of bole weight and bole volume in bark. 
weight (F = 15.24, P = 0.0001) and volume (F = 12.01, P = 

O'ooo I). 

An opprtslnity was taken to validate the Baldwin (1987) 

systern using these new data. Comparisons of mean 

predicted and observed values, and mean percent 

dserences, using a t-test, showed no significant differences 

between the Baldwin (1987) predictions and these data (for 

merchantable weight outside bark, t = 0.64, P = 0.52; and for 

mean volume outside bark, t = 1.605, P = 0.11). These 

apparently conflicting results led to some more exhaustive 

analyses. The most revealing was the test for normality of 

the two data sets using both measured and logarithmically 

tmnsfomed values. These analyses revealed that the 

logarithmically transformed values for the new data set were 

nomally distributed; but for the Baldwin (1987) data set, 

they were mot. For both data sets, the untransformed values 

were not nomafly disbributed. From this we can conclude 

that the F- and t-tests performed were probably indicative of 

the actual situation, but not strictly valid. 

Thus, we can reasonably conclude the following-the new 

data equations are somewhat diEerent from Bddwin's 

(1987) and are more likely to be applicable for the north 

Louisiana region; although, the differences are minor and 

have much to do with the range of observations, digerent 

expe~ental goals, and methodology used. Were 

merchantable green weight and cubic-foot volume to a 3-in. 

top diameter are desired in north Louisianq these new 

equations can be used with codidence. Some tables 

generated by the equations are found in the Appendix. 

bo, b,, and b, = equation coefficients to be estimate& 

DBH = tree diameter outside bark at 4.5 ft, and 

d = top diameter. 

The following rearrangement of terms expresses the 

relationship as the ratio of the bole accounted for to a 

specified top diameter 

R,,, = 1 - (2.0576 X d2-5654911)BH3.io2g3) (6) 

where 

%ore = the ratio (proportion) of the bole weight to a top 

diameter (d), and 

DBH = tree diameter outside bark at 4.5 ft. 

Table 3 shows the results of these partial stem weights as a 

proportion of total merchantable weight for use with weight 

estimates in loblolly pine plantations. For example, a 17-in. 

d.b.h. tree with a total height of 82 ft would weigh 3,421 Ibs 

(by equation 3 in table 2). The proportion of that green 

weight to a 6-in. top is 0.969 (equation 6 or table 3); 

therefore, the estimated bole weight to a 6-in. top is 3,3 15 

lbs (3,42 i by 0.969). Similarly, bole weight to a 10-in. top is 

3,029 lbs (3,42 1 by 0.885). 

Table %Ratio of partial bole weight to a top diameter 

as a proportion of total weight (to a 3-inch top) 

Top diameter 

Weight Adjustment for Top Diameter Limits 

Eurkhart (1977) published volume ratio equations to 

estimate tree volumes to various top diameters as a 

proportion of the total tree volume. The data collected in this 

study provided an opportunity to do similar calculations for 

weight ratios. A reg~ssion equation for topwood green 

weight (outside W) from top diamters 10 in., 8 in., 6 in., 

and 4 in., to a 3-in. top was fitted using a variation of 

Burhm" technique. For changing top diameters, topwood 

weight was subtracted from total merchantable bole weight 

(3-in. top) and the result expressed as a proprtion of the 

total. The model was solved (fit index = 0.803, SE = 0.008) 

where 

Ln = natural logarithm, 

TOP = the proportion of the total merchantable stem weight 

above the spcified (d) to a 3-in. top, 

------------ Inches - - 

0.557 0.750 

.662 309 

.736 $5 1 

.790 .882 

.83 1 .904 

.86 1 .922 

.885 .935 

.904 .946 

.9 19 ,954 

.93 1 '96 1 

.940 .966 
Conclusions Literature Cited 

The data in this study do not support the hypothesis that 

weight per cubic-foot volume varies significantly with site 

qdity and tree age. There was weight variation acceding 

to growth rates; but it was apparently a combination of 

influences including stand density, site qudity, tree age, and 

perhaps genetics. Differences in merchantable green weight 

and volume of planted loblolly pine for north and south 

Louisiana were also tested. Unfortunately, those tests were 

inconclusive. We conclude, however, that the new equations 

are valid and can be used with confidence in the north 

Louisiana region. The Baldwin (1987) equations can be used 

for other plantation management and merchantability 

situations. Further validation of these weight and volume 

estimates should be made in the field and under market 

conditions to determine the equations' robustness. 

Acknowledgments 

Funding for this project was provided by a Challenge-Cost 

Share Grant SRS-3MA-9r4-072, "Development of 

Loblolly Stem Weight and Cubic Volume" for the period 

July 1,1996, until September 30, 1998, through the U.S. 

Department of Agriculture, Forest Service, Southern 

Research Station. Monetary support was provided by 

Willamette Industries, Inc., Ruston, LA, with in-kind 

support from Louisiana Tech University. 

Baldwin, V.C., Jr. 1987. Green and dry-weight equations for above-ground 

components of planted loblolly pine trees in the west gulf region. 

a1 of Applied Forestry, 1 l(4): 2 12-21 8. 

Burwart, Harold E. 1977. Cubic foot volume of loblolly pine to any 

merchantable top limit. Southern Journal of Applied Forestry. l(2): 7-1 1. 

Nelson, L-E; Switzer, G.L. 1975. Estimating weights of Ioblolly pine 

trees and their components in narural stands and plantations in central 

Mississippi. Tech. Bull. 73. Mississippi State, MS: Mississippi 

Agricultural & Forestry Experiment Station. 15 p. 

Shelton, M.G.; Nelson, L.E.; Switzer, G.L. 1984. The weight, volume and 

nutrient status of plantation-grown loblolly pine trees. Tech. Rep. 12 1 

Mississippi State, MS: Mississippi Agricultural & Forestry Experiment 

Station. 25 p. 

WisweU, TJ.; Blackard, J.; Ldart, J.D. 1986. Estimating the green 

weight of individual loblolly pine trees planted in east Texas. Rep. 6. 

Nacogdoches, TX: Stephen F. Austin State University, School of 

Forestry, Center for Applied Studies. 10 p. 

Table A1-Cubic-foot volume (outside bark) by d.b.h. and total tree height 

Weight 

In. 

5 

6 

7 

8 

9 

10 

11 

12 

I3 

14 

15 

16 

17 

18 

19 

20 

- = Not applicable. 
ubie-foot volume (inside bark) by d,b.h. and total tree height 

Height 

- = Not applicable. 
Table ALCubic-foot volume (outside bark) by d.b.h, and height to a 

3-in* top 

Height 

- = Not applicable. 
Table AkGubic-ht volume (inside bark) by d.b.h. and height to a 3-in. 

top 

Height 

- = Not applicable. 
Table A§-Bole weight (pounds) by d,b.h, and total tree height 

Height 

fa. ------------------------------Feet------------------------- 

- = Not applicable. 
Table AGBole weight (pounds) by d.b.h, and height to a 3-in. top 

Height 

- = Not applicable. 
Table A7-Cubic-foot volume (outside bark) by d.b.h. and 16.5-ft logs 

- = Not applicable. 

Table A&Cubic-foot volume (inside bark) by d.b.h, and 16.5-ft logs 

Logs 

In. 

-- - Not applicable. 
Table A9-Bole weight (pounds) by d.b.h. and 163-ft logs 

In. 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

- = Not applicable. 

Table AlO-Cubic-foot volume (outside bark) by d.b.h. and 17.5-ft logs 

In. ----------------------Feet----------------------- 

- = Nor applicdble. 
Table All-Cubic-foot volume (inside bark) by d.b.h. and 17.5-ft logs 

In. ----------------------Feet----------------------- 

- = Not applicable. 

Table Al2-Bole weight (pounds) by d.b.h. and 17.5-ft logs 

In. 

- = Not applicable. 
Newbold, Ray A.; Baldwin, V. Clark, Jr.; Hill, Gary. 2001. Weight and 

volume detednation for planted loblolly pine in North Louisiana. Research 

Paper SRS-26. Asheville, NC: U. S . Department of Agriculture, Forest 

Service, Southern Research Station. 19 p. 

The objective of this study was to assess the variability in weight-to-volume 

relationships in loblolly pine (Pinus taeda L.) plantations and to determine 

predictability based on stand age, site quality, andlor tree size. Trees ages ranged 

from 11 to 40 years, with diameters to 2 1 inches and heights to 9 1 feet. Measured 

site indices ranged from 45 to 72 at base age 25. A total of 75 planted loblolly 

pine trees were felled and processed to assess the variability in bole weight to 

volume relationships. Cubic volume, green weight, and dry weight relationships 

were investigated; and the predictability of these variables with respect to age, site 

index, and tree size was determined. 

Keywords: Loblolly pine, Pinus taeda, plantation, volume, weight. 
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