POND PINE WEIGHT EQUATIONS

Thesis for the Degree of M. S.
MICHIGAN STATE UNIVERSITY
FLOYD IL CURTIS
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ABSTRACT

This study, conducted in North Florida, presents pond pine

(Pinus serotina) tree weight prediction equations for rough

 

green weight to 2-, 4—, and 8-inch top diameters outside bark.
The data range is from 4 to 17 inches DBH. Prediction equations
are also given for bark weight, peeled green tree weight and the
proportion of oven dry wood in the peeled tree.

Scatter diagrams with regression lines plotted through the
basic data are shown for each of the response variables. Also,
the proportion of oven dry wood, at four locations in the tree
stem,is shown graphically. Numerous statistics, develOped by
multiple regression analysis are included in the Appendix.

The prediction equations accounted for 93 to 98 percent of
the variation in rough green tree weight and bark weight. The
prOportion of oven dry wood variable had less variation explained;
at best only 54 percent of the variation in this variable could
be accounted for by the dependent variables in the prediction
equation.

The conclusions of this study are that pond pine tree and

bark weights can be reliably predicted within the data range for
the study area; that the proportion of oven dry wood decreases
rapidly from the butt to the top of the stem; and that the large

ii

amount of unexplained variation in the proportion of oven dry
wood is probably caused by experimental error, natural vari—

ation and seasonal variation in moisture content of the tree.

iii

POND PINE WEIGHT EQUATIONS

BY

Floyd H. Curtis

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Forestry

1969

5‘7
/[/22/69

ACKNOWLEDGEMENTS

For his encouragement, guidance and counsel in
making this study possible, the author is deeply
indebted to his major professor, V.J. Rudolph.

The author is grateful to The Buckeye Cellulose
Corporation of Perry, Florida, for making the data
for this study available.

For typing and retyping this manuscript, as
well as offering constructive suggestions, the author
thanks Grace B. Colson.

The author's grateful appreciation goes to his
wife for being understanding and patient during the

preparation of this thesis.

iv

TABLE OF CONTENTS

ABSTRACT . . . . . . . . . . .
ACKNOWLEDGEMENTS . . . . . . .
TABLE OF CONTENTS . . . . . .
LIST OF FIGURES . . . . . . .
LIST OF TABLES . . . . . . . .
INTRODUCTION . . . . . . . . .
POND PINE CHARACTERISTICS . .
THE STUDY AREA . . . . . . . .
PROCEDURE . . . . . . . . . .
DATA ANALYSIS AND RESULTS . .

Rough Green Tree Weight .

Tree Bark Weight . . . .

Proportion Oven Dry Wood
DISCUSSION . . . . . . . . . .
CONCLUSIONS . . . . . . . . .
LITERATURE CITED . . . . . . .
APPENDIX . . . . . . . . . . .

Definitions of Statistics

Presented

Multiple Regression Statistics . .

Correlation Coefficients

Page
ii

iv

vi

vii

13
17
24
29
32
33
34
36

42

LIST OF FIGURES
Page

Figure l. Pond pine study area in north Florida . . . . 5
Figure 2. Data and regression line for pond pine

rough green tree weight to a 2—inch top

D.O.B. . . . . . . . . . . . . . . . . . . . 14
Figure 3. Data and regression line for pond pine

rough green tree weight to a 4-inch top

D.O.B. . . . . . . . . . . . . . . . . . . . 15
Figure 4. Data and regression line for pond pine

rough green tree weight to a 8—inch top

D.O.B. . . . . . . . . . . . . . . . . . . . 16
Figure 5. Data and regression line for pond pine

tree bark weight to a 2-inch top D.O.B. . . . 18
Figure 6. Regression line for pond pine peeled

green weight to a 2—inch top D.O.B. . . . . . 19
Figure 7. Pond pine bark weight as a percent of

rough green tree weight to a 2-inch top

D.O.B. by (DBH)2 (Ht.) and DBH class . . . . 20
Figure 8. Average proportion oven dry wood in fresh

green pond pine disks by location in the

tree . . . . . . . . . . . . . . . . . . . . 23
Figure 9. Data and regression line for pond pine

prOportion oven dry wood in peeled green

tree 0 O O O O O O O O C O O O O O O O O O O 25

vi

LIST OF TABLES
Page
Table 1. Number of trees in multiple regression

program by DBH class . . . . . . . . . . . . 10

Table 2. Mean values of variables in multiple

regression program . . . . . . . . . . . . . 12
Table 3. Mean values and standard deviations for

sample disks from 61 trees . . . . . . . . . 22
Table 4. Pond pine rough green tree weight to a

2—inch top D.O.B. by DBH and height

class . . . . . . . . . . . . . . . . . . . 27
Table 5. Pond pine rough green tree weight to a

4—inch top D.O.B. by DBH and height

class . . . . . . . . . . . . . . . . . . . 28
Table 6. Pond pine peeled green tree weight to a

2-inch top D.O.B. by DBH and height

class . . . . . . . . . . . . . . . . . . . 30

vii

INTRODUCTION
This study's purpose is to develop rough green, peeled
green and oven dry weight equations for pond pine (Pinus

serotina)l/located in the "Big Bend" of north Florida. The

basic data were collected in Jefferson, Madison, Lafayette
and Taylor Counties during the spring and summer of 1962.

Tree stem weight equations, as discussed here, are pre—
dicting equations, derived by multiple regression analysis,
for estimating merchantable stem weight in pounds. They are
similar to predicting equations developed for estimating tree
volume in units such as cubic feet, cords or board feet.

Tree weights are of interest since considerable quantities
of felled timber are bought and sold by weight, especially in
the southeastern United States. While this trend toward weight
purchases has been primarily with the pulp and paper industry,
southern pine sawmills and treating plants are beginning to
purchase timber by weight. This trend toward weight and away
from volume has occurred because weight measurements are faster,
simpler, more consistent and more easily checked than volume
measurements. Also, working directly with tree weight eliminates

the necessity of using volume-to—weight conversion factors.

 

_L/Scientific and common names are according to Little, (1953).

In addition, in the pulp and paper industry, many pro—

duction variables such as final product yield, amount of bark,

moisture percent, and by-product yield are measured by weight.

Weight is

of timber

also an important factor in regulating the movement

over railroads and public highways. Thus, it is

logical for those organizations and individuals dealing in

timber to
This

pond pine

be interested in tree weight.

study presents equations for predicting the following
stem weights above the stump:

rough green weight to a 2—inch top D.O.B.

rough green weight to a 4-inch top D.O.B.

rough green weight to a 8—inch top D.O.B..

bark weight to a 2—inch top D.O.B.

peeled green weight to a 2-inch top D.O.Bcg/
proportion of peeled green weight, to a 2-

inch top D.O.B., that is oven dry wood.

While the study is localized, the equations and statistics

should be

Pond

of interest in other areas.
POND PINE CHARACTERISTICS

pine is one of the minor southern pines. It ranges,

in the coastal plain, from the southern tip of New Jersey south-

 

2 ' = _
.L/By subtraction, yP y2 yB.

ward to central Florida and westward to southeastern Alabama.
It occurs as far inland as the Piedmont Plateau through the
Carolinas and Georgia (Collingwood and Brush, I964).

Pond pine is characterized by a comparatively short trunk
and a shaggy appearance caused by heavy needle clustering at
branch ends. The limbs and trunk have a tendency to produce
needle and twig sprouts. Pond pine, unlike most pines, sprouts
readily and many stands are established after logging or fire
in this manner. The cones are serotinous and consequently
cones of varying ages are found on the same tree. The cones
Open rapidly after a fire or after the tree is felled.
Apparently, fire is necessary for the establishment of well
stocked natural stands (Fowells, 1965).

Pond pine inhabits the poorly drained mineral and organic
soils of the lower coastal plain. On the wet organic soils it
often occurs in almost pure stands, while on the poorly drained
mineral soils it is found associated with species such as lob-

lolly pine (Pinus taeda), slash pine (Pinus elliottii), cypress

 

(Taxodium spp.), and sweetgum (Liguidambar styraciflua).

 

 

Pond pine growth is slow compared to pines such as loblolly

and slash. However, the adverse site on which it occurs often

accounts for the poor growth rate. Growth can be improved by

the elimination of fire and providing adequate land drainage.

THE STUDY AREA
The study area is in the lower coastal plain of north
Florida (Fig. l). Elevations are generally less than 100 feet
above sea level, while the topography is flat and for the most
part poorly drained. Lesser vegetation includes wax myrtle

(Myrica cerifera), gallberry (Ilex glabra), saw—palmetto (Serenoa

 

 

repens) and titi (Cyrilla spp.). Pond pine is found primarily
on organic soils and poorly drained mineral soils, such asthe
Leon and Portsmouth series.

The area's climate is typical of the southeastern United
States; summers are hot and humid, while the winters are
normally dry, with large fluctuations in daily temperature. The
mean annual temperature for Perry, Florida, is 68.7OF; the
January mean is 55.80F and the August mean is 81.4OF.

Annual precipitation for the area is about 55 inches with
almost half of it occurring during the months of June, July,
August and September. There is an average of 245 days between
dates of 32°F or below.

PROCEDURE
The study was conducted in the spring and summer of 1962

on the lands of The Buckeye Cellulose Corporation. A series of

sample points was randomly located on timber type maps. These

points were then located in the field and a 4-man crew moved

-4-

T 11 h ee . i O JaCkSOnville
a a ass _

.Perry

0 Tampa

Miami .

 

Study Area

Fig. l. Pond pine study area in north Florida.

3 Jacksonville
Tallahassee o

 

0 Tampa

Miami .

 

Study Area

Fig. l. Pond pine study area in north Florida.

equipment to the point. The equipment consisted of a small
winch equipped crawler tractor, a specially designed skidding
and hoisting arch, hydraulic scales with a 3,600—pound capacity,
a chain saw, peeling spuds, diameter tapes, numerous small hand
tools and miscellaneous materials. Sample trees were selected
by making a clockwise sweep with a lO—factor prism and marked
by numbering those trees occurring within the sample. Each
sample tree had an increment core, reaching to the pith, ex—
tracted at breast height (4.5 feet above ground). The increment
core was given the same number as the tree, placed in an air—
tight bottle, and taken to the laboratory for specific gravity
determinations.

The sample trees were then felled, keeping stump height as
low as possible, limbed and tOpped at 2 inches D.O.B., or where
the main stem was no longer identifiable and larger than 2 inches.
The following measurements and weighings were then made:

1. Diameter outside bark, at breast height, to the nearest

.l-inch.

2. Total tree height to the nearest foot.
3. Bark thickness, at breast height, to the nearest .05-

inch.

4. Diameter inside bark, at 16.5 feet above stump, at
the butt, at a point one—third of the way up the stem
from the butt, at a point two-thirds up the stem from

—6—

the butt, and at the top of the used stem, all to
the nearest .l—inch.

5. Tree age.

6. Rough green tree weight, to a 2—, 4—, and 8—inch
top D.O.B., all to the nearest 5 pounds.

7. Peeled green weight of every fifth tree to a 2—
inch top D.O.B.

The tree stem was weighed on the hydraulic scales by
attaching the scales to the tree with two tongs separated by
a spreader bar and hoisting the load with the tractor winch
line which ran on a fixed roller at the top of the skidding
arch. The tree weight was read directly off the scales which
had been tared for the log tongs. Every fifth tree was peeled
by hand and reweighed.

Four 2—inch thick disks were cut from each sample tree at
the butt, at a point one—third of the way up the stem from the
butt, at a point two—thirds up the stem from the butt, and the
top of the used stem. These disks were given the same number as
the tree, placed in plastic bags and taken to the laboratory for
oven dry weight determinations.

The disks cut from each sample tree were brought into the

laboratory, loose material was brushed from their surfaces, and

they were weighed and recorded fresh green to the nearest .2-gram.

-7-

Next, they were placed in drying ovens at 1000C. The disk
weights were checked periodically until a constant weight was
reached, indicating cessation of moisture loss. Most samples
reached a constant weight within 32 hours. The proportion of
fresh green weight that was oven dry wood was calculated by
dividing oven dry weight by fresh green weight.

The increment borer used to extract the increment core
has a bore diameter of .170 inches which makes the end area of
the core .1464 square centimeters. The fresh green volume of
the increment core was calculated by multiplying the core length
by the core end area. This gave increment core volume in cubic
centimeters.

The increment cores were placed in drying ovens at a
temperature of 1000C. The cores were removed periodically, put
in drying chambers and weighed to the nearest .OOl-gram.
Weighing had to be accomplished rapidly as the cores quickly
picked up moisture from the air. Oven dry weight was reached
when increment core weight remained constant. Increment core
Specific gravity was calculated by dividing the oven dry weight
in grams by the fresh green volume in cubic centimeters. The
average increment core specific gravity for 61 samples is .585
with a standard deviation of .059.

DATA ANALYSIS AND RESULTS
The purpose of this study was to provide pond pine pre—

—8—

diction equations for the following dependent variables: y2,
y4, y8, yB, yP and yOD' There were 57 sample trees used for
Y2’ 54 for y4, 29 for y8, 11 for yB, and 61 for YOD'

The reasons for using differing numbers of trees is that
61 trees were sampled and used for yOD; some of these trees had
data missing and were not useable for y2; 3 trees used in y2
did not have a 4—inch top and thus could not be used for Y47
only 29 trees had an 8-inch top useable for y8; and only 11
trees were peeled for yB. Table 1 shows the number of trees by
DBH class used for each dependent variable.

After checking the field and laboratory work for errors,
the data were punched into cards for multiple regression analysis
using a stepwise program on an IBM 7080 computer.

Rough Green Tree Weight: The three rough green tree weight
response variables, y2, y4 and y8 had eight independent variables
used in the program. They were:

X1 = DBH, diameter breast height in inches.

X2 = Total tree height in feet.

X3 = Tree age in years.

X4 = Form class or d.i.b. at 16.5 feet above stump.

DBH o.b.
X = (DBH)2
5
X6 = Logarithm of total tree height.
X7 = Logarithm of DBH.

Table 1. Number of trees in multiple
regression program by DBH

 

 

 

 

class.
DBH Variable
Class y2 Y4 y8 yB you
Inches
4 7 4 9
5 4 4 2 5
6 6 6 6
7 5 5 l 5
8 6 6 1 6
9 6 6 6 2 7
10 4 4 4 l 4
ll 3 3 3 l 4
12 5 5 5 2 5
13 6 6 6 6
l4 1 1 l 0
15 2 2 2 2
16 1 1 1 l
17 1 1 l l 1
Totals 57 54 29 11 '61

 

-10-

X = (DBH)2 (total tree height) = (X )(X )
8 5 2

The mean values of the variables in the rough green weight
programs are shown in Table 2.

The program produced predicting equations for those vari-
ables with a partial F larger than 1.00. However, for y2 and
y4, practically all of the variation was accounted for by the
combined variable X8, (DBH)2(total tree height). For ya, in--
dependent variable x5, (DBH)2 accounted for most of the vari-
ation. The rough green weight predicting equations and the
amount of variation accounted for by the independent variables

are as follows:

2 -

 

 

 

 

 

Response Equation R _§L SyX y 2
Percent Pounds Pounds

§2 = .148(X8) - 21 97 57 112 663 4,631 = E8

y4 = .149(x8) - 54 97 54 117 685 4,956 = Q8

ya = 11.38(X5) - 757 93 29 173 878 143.7 ='§5

Appendices 2, 3 and 4 show the multiple regression program
output respectively for y2, y4 and y8.

These equations are practical in that the transformed values
of DBH and height, easily measured characteristics, are used to

estimate weight---a value difficult to measure. The inclusion of

additional variables only increased the percent of variation

accounted for by 1.0, 1.3, and 3 percent, respectively, for Y2'

-11-

 

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y4 and y8. Figures 2, 3, and 4 are scatter diagrams showing
the regression lines plotted through the basic data for y2,

y4 and y8 respectively.

Tree Bark Weight: As only every fifth tree used in the

 

rough green weight analysis was peeled, there are only eleven
bark weight sample trees. The independent variables used in

the yB program are:

X3 = Tree age.
X8 = (DBH)2(total tree height) or (X5)(X2).
X9 = Double bark thickness in inches.

The mean values of these variables are shown in Table 2.
As was the case with rough green tree weight, X8 accounted
for most of the variation in bark weight. The equation and some

statistics are as follows:

2

 

 

 

Response Equation R hi Syx §B X8
Percent -__ Pounds Pounds
§B = .o17(x8) + 9 98 11 12 97 5,156

Appendix 5 shows the multiple regression program output
for yB. Figure 5 shows the regression line plotted through the
basic data.

By subtracting the equation for yB from the equation for

y , a peeled green weight equation yP is obtained. Thus, yP =

2
_[_—._148(x8) - :I ’Bl7IX8) +_—_9] = .131(x8) - 30. Figure 6 shows

-13-

Weight in Pounds

2,500

2,000

1,500

1.000

500

Fig.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A I
y =.ld8£Xq) I—,_l
N = 57 Trees
r2 = .97
SyIX = 112 Pounds
$2 = 663 Pounds
2 = 4631 o//
5)) = 632 ll
SX = 4213
l
l
' l
K
I .
/ °
/
/'
:K
7/
J
.J'
0/
5,000 10,000 15,000
(DBH)2 (Ht.) = x8
2. Data and regression line for pond pine rough green

tree weight to a 2—inch top D.O.B.

-14-

 

 

 

 

Weight in Pounds

2,500

2,000

'1,500

1,000

500

Fig.

 

= .149 (x2) - 4

 

= 54 Trees

 

 

X = 117 Pounds /

 

= 635 Pounds /

 

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M A)

 

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SA

= 4137

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.

5,000 10,000 15,000
(DBH)2 (Ht.) = x8

Data and regression line for pond pine rough green
tree weight to a 4-inch top D.O.B.

-15-

Weight in Pounds

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

§ = 11.32 (xqi J 7:7
N = 29
r2 = I93
SyX = 173
2,500 Y = 878
SE = 143 . '7
Sy = 648
sx = 54.9
2,000 ,//
/
/
__ //
j/l.
1,500 //
I
O r .
1,000 V/f
//’
1 Z .
/
500 .
//%/’
. /°
//
o /
100 150 200 250

(DBH)2 = xs

Fig. 4. Data and regression line for pond pine rough green
tree weight to an 8—inch top D.O.B.

-16-

the regression line for this equation. A conservative estimate

 

 

of Sny is Szyzx + SZyBX = \JI112)2 +~(12)2 = 113.

Bark weight as a percent of rough green weight varies con-
siderably. Figure 7 shows how this percentage varies over the
range of X8. By fitting a curve of DBH over X8 and then super-
imposing DBH on X8 in Figure 7, bark weight as a percent of
rough green weight is estimated for each DBH class.. Bark percent
varies between 19 percent for the 6—inch DBH class and 12 percent

for the l6-inch class.

Proportion Oven Dry Wood: The oven dry wood in a tree as
a proportion of the peeled green weight was obtained by calcul-
ation rather than direct measurement, as was the case with rough
green tree and bark weight. The calculation was made in the
following manner:

Let:

A1 = Diameter inside bark of the tree's butt disk.

A2 = Diameter inside bark of the tree's second disk.

A3 = Diameter inside bark of the tree's third disk.
A4 = Diameter inside bark of the tree's top disk.
D1 = Proportion of oven dry wood in the butt disk.
D2 = Proportion of oven dry wood in the second disk.
D3 = Proportion of oven dry wood in the third disk.
D = Proportion of oven dry wood in the top disk.

Since the area of a circle is proportional to its diameter

-17-

Bark Weight in Pounds

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

§ = 017 (x ) ‘ 9 A/

N = 11 [/I

rZ = L98 //

SyX = 12 [I
250 I = 97

i = 5,156 1/

Sy = 82 //

sx = 4,752 //

‘ l
1
200 . ///
/
150
/F
/
///'
100
l?’
/
/ o
50 1/
l/.
I o
0
5,000 10,000 15,000

(DBH)2 (Ht.) = x8

Fig. 5. Data and regression line for pond pine tree bark
weight to a 2-inch D.O.B.

-18-

Weight in Pounds

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9P = 0? -‘9R = .131 (xi) 4 I0
2,500 ~ ///
e/
,/
2,000 ’//r
//
[I
A/
l , 500 /
/
5/
[V’
1,000
/
/
/
500
1
z”
/
0 /
5,000 10,000 15,000

(DBH)2 (Ht.) = x8

Fig. 6. Regression line for pond pine peeled green weight
to a 2—inch top D.O.B.

-19-

Bark Percent
of Rough Green Tree Weight

 

Irk PCrcen = (Qu

r §2)(1C0)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-25
20
15
\\
\\
\
10
5 I l l l 1 I l
6 8 1C 12 14 l6 18
I Average DBH .
5,000 101000 15,000 20,000
(DBH)2 (Ht.)
Fig. 7. Pond pine bark weight as a percent of rough green

tree weight to a 2-inch top D.O.B. by (DBH) (Ht.)

and DBH class.

-20-

squared, the proportion of oven dry wood in the used tree stem,

YOD' is estimated by:
y = A2 D + A2 D + A2 D + A2 D
OD 1 1 2 2 3 3 4 4

 

A2 + A2 + A2 + A2
l 2 3 4

Mean values for all sample disks are shown in Table 3.
The relationships for disk locations within the tree are

shown graphically in Figure 8.

The independent variables used in the yOD programs are:

X1 = DBH in inches.
X2 = Total tree height in feet.
X3 = Tree age in years.
X8 = (DBH)2(tota1 tree height).
Xlo = Increment core specific gravity.
X11"—L
X3

X13 = ___1.-_
x10
X3

A single variable equation using X10, increment core
specific gravity, accounted for 45 percent of the variation in
proportion of oven dry wood in peeled green pond pine. A

three—variable equation increased the amount of variation ex-

-21-

 

 

 

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-22-

Proportion Oven Dry Wood

 

Butt One—third Two-thirds 2-inch
used length used length top

Disk Location in Tree

Fig. 8. Average proportion oven dry wood in fresh green
pond pine disks by location in the tree.

-23-

plained to 54 percent.

The proportion oven dry wood equations are:

 

 

 

 

Response Equation R2 EL _§yX ,y 2
Percent
l. YOD .642 (X10)+ .151 45 61 .043 .526 .585
2. YOD .489 (X10)+ 54 61 .039 .526 .585
.0025 (X2)- 41.9
.006 (Xl)+ 8.7
.187

Appendices 6 and 7 show the multiple regression program
output, respectively, for equations 1 and 2. Figure 9 is the
scatter diagram for yOD with the regression line for equation

No. 1, above, plotted through the data.

DISCUSSION
The objectives of the study were partially met with the
development of weight equations that explain moSt of the vari-
ation in rough green tree weight and bark weight. Unfortunately,
the best prediction equation for the proportion of oven dry wood
in peeled green pond pine, could, at best, only account for 54
percent of the variation associated with this variable.

2

There may be several reasons for the lack of a high R for

yOD' First, for the variables chosen, this may be as much vari-

ation as can be accounted for. Second, many detailed measurements

-24*

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-25-

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and oven drying could have induced large experimental errors.
Certainly, experimental error contributed to unexplained vari-
ation. Third, yOD was not a direct measurement, but calculated
from four stem samples, assumed to consistently represent the
entire tree.' Fourth, there is variation in tree stem moisture
content from season to season. Peck (1959) reported seasonal
moisture variation on an oven dry basis for loblolly pine,

which, when converted to a green weight basis, is as follows:

 

Season Sapwood Heartwood
Percent Percent
Winter 52.3 37.1
Spring 51.7 32.4
Summer 51.7 36.3
Autumn 50.0 31.9

Bishop and Markworth (1933), also working with loblolly
pine, found green weight moisture percent varied between 36.3
percent in May and 42.9 percent in November.

The weight prediction equations presented here can be
used in forest inventories in the same manner as volume equations
are used, or by using Tables 4 and 5, which have pond pine tree
weights calculated by DBH class and lO-foot total height inter—
vals, respectively, for a 2- and 4—inch top D.O.B.

Peeled green weights for a 2-inch top D.O.B. are shown in

-26-

Table 4.

Pond pine rough green tree weight to a 2-inch

top D.O.B., by DBH and height class.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DBH Total Tree Height in Feet
Class 30 40 50 80
Inches -------------------- Pounds ——————————————————————
5 89 26
6 138 191 245
7 196 268 341
8 262 357 451
9 , 338 457 577
10 422 570 718
11 515 694 873 1409
12 ‘ 830 1043 1681
13 978 1227 1977
14 1137 1427 2296
15 1309 ‘1641 2639
16 1492 1870 3005
17 2114 3396
18 2373 3811
A 2
y2 = .148 (DBH) H - 21
N = 57 Trees sampled
r2 = .97
Syx = 112 Pounds
y = 663 Pounds
Mean DBH = 9.0 Inches
Mean Height = 43 Feet
Sy = 632 Pounds

-27-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 5. Pond pine rough green tree weight to a 4—inch
top D.O.B., by DBH and height class.
DBH Total Tree Height in Feet
Class 30 4O 50 60 70 80
Inches -------------------- Pounds ----------------------
5 58 I 95
6 107 161 214
7 165 238 311 384
8 232 327 422 517 612
9 308 429 550 671 792
10 393 542 691 840 989
11 487 667 847 1027 1207
12 804 1019 1234 1449 1664
13 953 1205 1457 1709 1961
14 1114 1406 1698 1990 2282
15 1288 1623 1959 2294 2630
16 1473 1854 2236 2618 3000
17 1670 2100 2531 2962 3393
18 2361 2844 3328 3811
A 2
y2 = .149 (DBH) H - 54
N = 54 Trees sampled
r2 = . 97
sy,x = 117 Pounds
§ = 685 Pounds
Mean DBH = 9.4 Inches
Mean Height = 44 Feet
Sy = 628 Pounds

-28—

Table 6 by DBH class and lO-foot total height intervals. Bark
percent by DBH class as shown in Figure 7 may also be used to
estimate peeled green weight.

To use the yOD equation, an increment core specific
gravity sample is necessary. From average increment core
specific gravity, an estimate of the proportion of oven dry

wood in the peeled green tree stem can be made.

In addition to using the equations as mentioned, consider-
able statistical information is included. A summary of the
multiple regression program outputs are included in the Appendix.
In addition, simple correlation coefficient matrices for each
problem are in the Appendix, along with definitions (from Steele
and Torrie,1960) of the statistics presented. These data
should be of value to anyone planning similar studies.

CONCLUSIONS

The following conclusions are drawn from the results of
this study:

1. Pond pine rough green tree weight can be predicted

quite reliably for 2-, 4-, and 8—inch top D.O.B.

within the data range. The sample trees ranged be-

tween 4 and 17 inches. DBH.

2. Bark weight can also be reliably predicted for trees
to a 2-inch tOp D.O.B. While the sample size was

small, (11 trees), the regression equation accounted

—29-

 

 

 

Table 6. Pond pine peeled green tree weight to a 2-inch
top D.O.B. by DBH and height class.
DBH Total Tree Height in Feet
Class 30 40 50 60 70 80
Inches -------------------- Pounds ----------------------
5 68 I 101
6 111 159 I 207 255
7 163 227 291 355 419
8 222 305 388 471 554
9 288 394 394 500 606
10 363 494 625 756 887
11 446 604 762 920 1078 1236
12 725 913 1101 1289 1477
13 856 1077 1298 1519 1740
14 997 .1254 1511 1768 2025
15 1149 1444 1739 2034 2329
16 1311 1647 1983 2319 2655
17 1863 2242 2621 3000
18 2092 2517 2942 3367

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A
YP = y2 - YB = .131 (Kg) — 30

-30;

for 98 percent of the bark weight variation.

There is a substantial difference in bark as a percent
of rough green weight to a 2-inch top D.O.B. by DBH
class. The 6—inch DBH class has about 19 percent of

its rough green weight in bark, while the 10— and 17-
inch DBH classes have 13 and 12 percent,respective1y.
The proportion of oven dry wood weight to peeled green
weight is highest in the butt of the tree and lowest

in the top. There is almost a straight line relation—
ship in the decline of oven dry wood from butt to top.
The decline is from .561 in the butt to .407 in the top.
The variation in proportion oven dry wood was not satis—
factorily explained. Possibly natural variation, ex-
perimental errors and seasonal variation in moisture
content contributed to the large amount of unexplained

variation.

-31-

LI TE RATURE C ITED

Bishop, G.N. and G.D. Marckworth.
1933. Some Factors Influencing Resin Concen—
tration in Loblolly and Slash Pines.
Jour. Forestry 31(8): 953-960.

Collingwood, G.H. and W.D. Brush.
1964. Knowing your Trees. The American
Forestry Association. 349 pp.

Fowells, H.A.
1965. Silvics of Forest Trees in the United
States. U.S.D.A., Forest Service,
Agriculture Handbook No. 271. 761 pp.

Little, E.L., Jr.
1953. Check List of Native and Naturalized
Trees of the United States (Including
Alaska). U.S.D.A., Agric. Handbook 41.
472 pp.

Peck, E.C.
1959. The Sap or Moisture in Wood. U.S.D.A.
Forest Service, Forest Products Labor—
atory Publ. No. 768. 5 pp.

Steele, R.G-D. and J.H. Torrie.

1960. Principles and Procedures of Statistics.
McGraw-Hill Book Company, Inc. 481 pp.

-32-

APPENDIX

-.33-—

Appendix 1. Simple regression statisticsl/

 

 

 

 

 

 

 

 

 

y = Predicted value for dependent variable.
y = Response or dependent variable.
§ = Mean of observed dependent variables.
x = Independent variable.
i = Mean of observed independent variables.
N = Number of observations.
r2 = Proportion of variation explained by prediction
equation = Z(y -§)2
2(y - {NZ
Syx = Standard error of estimate = 23y2 - (ny22 = Residual M Sq.
EX
N — 2
SY = Standard deviation of dependent variable = Eyz - (Zy)2
N
N - 1
SX = Standard deviation of independent variable = 2x2 - (EXQZ
N
N - 1
Confidence limits for a predicted y =Ԥ : t Residual MSq)(1 + (x0- x)

N Zx31£xf
N

Where: x0 selected value of x

fl
II

t for given probability level and degrees of
freedom for residual mean square.

 

l/For several independent variables see Steele and Torrie, 1960.

_34-

b coefficient = ny - (§x)(Ey)
N
2x2 — (Ex)

N

 

2

 

 

Standard error of b coefficient = Residual MS
Ex

2 _ (Zx)2

N

 

Confidence interval for B = bl: t Sb

Where: t = t for given probability level and degrees
of freedom for residual mean square.
Standardized = Regression coefficient when each variable
b coefficient is in deviations from the mean of its

standard deviation. Used for comparing the
relative importance of the independent
variable = b.§§

3y

_35-

Appendix 2. y2 multiple regression program statistics

Dependent variable: y2 - rough green pond pine
tree weight in pounds

to a 2—inch top D.O.B.

Independent variable: X8 (DBH)2 (tree height)
Number of observations: 57
R2, percent of variation explained: 97
Standard error of y2: 112
Mean of y2: 663

Standard error as a percent of mean: 17
Analysis of variance:
Source D.F. Sum Square Mean Square F
Total 56 22,397,860
Regression 1 21,707,460 21,707,460 1,729**
Residual 55 690,402 12,553
Tabular F .01 with 1/55 df = 7.08
B coefficients and 95 percent confidence limits:

95 Percent
Confidence Limits Standard Standardized

 

 

Variable Mean B coeff Upper Lower Error b Coefficient
X8 4632 .148 .155 .141 0004 .984
Constant term in prediction equation = ~21

Equation: y2 = .148 (X8) -21

~36-

Appendix 3.

Dependent variable:

Independent variable:

Number of observations:
R2,
Standard error of y4:

Mean of Y4:

Standard error as a percent of mean:

Analysis of variance:

y4 multiple regression

percent of variation explained:

CD

54
97

117
684

17

program statistics

— rough green pond pine
tree weight in pounds

to a 4-inch top D.O.B.

(DBH)2 (tree height)

 

 

Source D.F. Sum Sggare Mean Sgpare F
Total 53 20,885,770
Regression 1 20,175,480 20,175,480 1,477**
Residual 52 710,283 13,659

Tabular F .01 with 1/52 df = 7.19

B coefficients and 95 percent confidence limits:

95 Percent

Confidence Limits Standard Standardized

Variable Mean B coeff Upper

 

 

Lower Error b Coefficient
X8 4957 .149 .157 .141 .004 .982
Constant term in prediction equation = —54
Equation: Y4 = .149 (X8) -54

.‘-37-

Appendix 4. Y8 multiple regression program statistics

Dependent variable: Y8 - rough green pond pine
tree weight in pounds

to a 8-inch top D.O.B.

Independent variable: X5 (DBH)2
Number of observations: 29
R2, percent of variation explained 93
Standard error of Y8: 173
Mean of y8: 879

Standard error as a percent of mean: 20

Analysis of variance:

 

 

Source D.F. Sum Square Mean Square F
Total 28 11,752,940

Regression 1 10,941,420 10,941,420 364**
Residual 27 811,516 30,056

Tabular F .01 with 1/27 df = 7.68
B coefficients and 95 percent confidence limits:

95 Percent
Confidence Limits Standard Standardized

 

 

Variable Mean B coeff Upper Lower Error b Coefficient
X5 143.7 11.38 12.61 10.16 .597 .965
Constant term in prediction equation = -757

Equation: y8 = 11.38 (X5) -757

—38-

Appendix 5.

yB multiple regression program statistics

 

 

 

Dependent variable: yB - pond pine bark weight
to a 2-inch top D.O.B..
Independent variable: X8 (DBH)2(Tree Height)
Number of observations: 11
R2, percent of variation explained: 98
Standard error of yB: 12
Mean of yB: 97
Standard error as a percent of mean: 13
Analysis of variance:
Source D.F. Sum Square Mean Square F
Total 10 66,551
Regression 1 65,216 65,216 440**
Residual 9 1,335 148

Tabular F .01 with 1/9 df

10.

56

B coefficients and 95 percent confidence limits:

95 Percent

Confidence Limits Standard Standardized

 

Variable Mean B coeff Upper

X 5157

8 .017

.019

Constant term in prediction equation

Equation: YB = .017 (X8) +9

-39-.

Lower

.015

9

Error

b Coefficient

.0008 .990

Appendix 6. YOD multiple regression program statistics

Dependent variable:

 

 

 

yOD - proportion oven dry
wood in peeled green
pond pine stem.
Independent variable: X10 — Increment core specific
gravity.
Number of observations: 61
R2, percent of variation explained: 45
Standard error of YOD: .043
Mean of yOD: ‘ .526
Standard error as a percent of mean: 8.1
Analysis of variance:
Source D.F. Sum Square Mean Square F
Total 60 .1947
Regression 1 .0874 .0874 48.07**
Residual 59 .1073 .0018

Tabular F .01 with 1/59 df = 7.08
B coefficients and 95 percent confidence limits:

95 Percent
Confidence Limits Standard Standardized

 

 

Variable Mean B Coeff Upper Lower Error B Coefficient
Xlo .585 .642 .824 .461 .093 .670

Constant term in prediction equation = .151

Equation: y0D = .642 ()io) +.151

-4o-.

Appendix 7. yOD multiple regression program statistics

Dependent variable: YOD - Proportion oven dry wood

in peeled green pond pine

 

 

stem.
Independent variables: X10 - Increment specific gravity
X2 - Total tree height
Xl — Tree DBH
Number of observations: 61
R2, percent of variation explained: 54
Standard error of YOD: .039
Mean of YOD: .526
Standard error as a percent of mean: 7.5
Analysis of variance:
Source D.F. Sum Square Mean Square F
Total 60 .1947
Regression 3 .1058 .0353 22.62**
Residual 57 .0889 .0015

Tabular F .01 with 3/57 df = 4.13
B coefficients and 95 percent confidence limits:

95 Percent
Confidence Limits Standard Standardized

 

 

 

Variable Mean B Coeff Upper Lower Error B Coefficient
X10 .585 .489 .685 .295 .010 .511
X2 41.9 .0025 .004 .001 .001 .586
X1 807 -0006 -0001 _0011 .003 .366
Constant term in prediction equation = .187
Equation: yOD = .490 (X10) + .003 (X2) — .006 (X1) + .187

_41-

 

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Appendix 11.

Correlation coefficients for
variables in pond pine bark

weight (yB program).

 

 

 

 

 

x3 X8 X9 Y8
X3 1.00
X8 .81 1.00
X9 .52 .59 1.00
yB .85 .99 .60 1.00
Mean 46 5157 1.75 97
Std. Dev. 16 4752 .38 82
N = 11

 

_45_

 

 

 

 

 

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