Volume tables plantation grown white pine, Pinus strobus L. in Connecticut

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Bulletin 427 June, 1939

Volume Tables
Plantation Grown White Pine,

PINUS STROBUS, L.
IN CONNECTICUT

Henry W. Hicock, Arnold D. Rhodes and A. Richard Olson

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Olmtitetttatt

^griatUural ^Experiment jiiatum

New Syauen

Volume Tables
For Plantation Grown White Pine

Henry W. Hicock, Arnold D. Rhodes
and A. Richard Olson*

PREFACE

D,

"uring the last 40 years many thousands of acres of coniferous plan-
tations have been established throughout the East. Northern white pine,
Pinus Sirobus, L., has been the species most commonly planted. In Con-
necticut alone some 10,000 acres have been set out to this species, either
pure or in mixture with other conifers. Today the older plantations are
producing merchantable material, the best stems measuring 12 to 14 inches
in diameter at breast height and 50 to 60 feet tall. Already profitable
thinnings have been made on a commercial scale in stands less than 30
years of age. In the future an ever increasing number of such stands will
attain merchantable proportions.

Where efforts have been made to determine the volume of standing
timber or to predict growth and yield, it has become increasingly evident
that existing volume tables are unsuitable. Such tables, based on natural
stands of large timber, prove inadequate when applied to plantation
grown trees of dimensions only slightly greater than the lower limits of
merchantability. Furthermore, the adaptation and correction of these
tables to fit the desired conditions seems a less reasonable and less satis-
factory solution than the construction of new tables made for and from
plantation grown timber.

The hurricane of 1938 afforded the opportunity for carrying out such
a project. At that time the School of Forestry, Yale University, with the
aid of funds from the Charles Lathrop Pack Foundation, cooperated with
the Connecticut Agricultural Experiment Station in gathering the necessary
taper measurements from wind-thrown plantation trees. From these data,
three volume tables for white pine have been constructed, two in cubic
feet and one in board feet. Labor for the field work was provided by
the Civilian Conservation Corps and the National Youth Administration.

Five hundred and thirteen trees were measured at the Rainbow Forest
in East Granby and Windsor in plantations of the Connecticut Agricultural
Experiment Station, and 323 in the vicinity of New Haven on the Eli Whit-
ney Forest of the New Haven Water Company. In addition, 95 taper
measurements, which had been previously taken by the Yale School of
Forestry during the process of thinning plantations, were used with those
more recently secured, making a total of 931 such measurements avail-
able for the construction of the volume tables. Of this number, 747 were
incorporated into the board foot table and 921 into the two cubic foot
tables.

*Mr. Hicock is Associate Forester, Conn. Agri. Exp. Sta., New Haven. Mr. Rhodes is Instructor in
Applied Forestry, School of Forestry, Yale University, New Haven. Mr. Olson is Research Technician,
Conn. Agri. Exp. Station, New Haven.

4 Connecticut Experiment Station Bulletin 427

DESCRIPTION OF PLANTATIONS

The stands represent a wide variety of planting sites and planting
conditions. The Rainbow plantations are situated on a site of very low
productive capacity. The tract is part of an extensive glacial outwash plain
about 160 to 180 feet above sea level. The soil is a coarse sand to a depth
of many feet. Natural forest stands of the region are composed chiefly
of pitch pine and inferior hardwoods such as gray birch, red maple, and
black and scarlet oak. Prior to the establishment of the plantations, the
land had been abandoned for ordinary agricultural crops for a number of
years and was reverting to forest growth. Recently much land of a similar
character has been reclaimed for the cultivation of shade grown tobacco.
Its value for this purpose would be prohibitive for the growing of forest
crops. The oldest plantations sampled were planted in 1902, the youngest,
in 1907. Measured trees varied in breast high diameters from 2.4 to 12.0
inches, and in height from 23 to 49 feet. Growing space at the time of
planting ranged from 20 to 50 square feet per tree. Thinnings were made
in 1932 and 1936.

On the Eli Whitney Forest, plantations were established on soils of
superior quality, representing the best sites for white pine in the region.
Originally, these areas were farmed with fair success. The soil is, in the
main, a good quality loam somewhat better than the usual run of forest
soils. Organic content, texture and moisture conditions are excellent.
Growth has been rapid and well sustained with some of the better stands
supporting 8,000 to 10,000 board feet of low grade material per acre at 30
years. In all cases, plantings were made on recently cultivated fields, or
on pasture or mowing fields, which were relatively free of shrub and tree
growth. Spacing was 6 by 6 feet. The youngest stand sampled was 17 and
the oldest, 30 years old. Breast high diameters ranged from 1.7 to 12.5
inches and heights from 16 to 55 feet.

SECURING THE FIELD DATA

In the field, the following measurements were taken on each tree:

a. Total height to the nearest tenth of a foot.

b. Diameter outside bark and bark thickness to the nearest tenth

of an inch at —

1. Stump height, usually taken at 6 inches.1

2. Two and one-half feet above ground.

3. Breast height.

4. Intervals of one-, two-, three-, and four-fifths of the
length of stem above breast height plus an additional
measurement at mid-point for form quotient.

OFFICE COMPUTATIONS AND CONSTRUCTION OF TABLES

In view of the varied character of the stands sampled, particularly the
differences in age, density of stocking and site conditions, it seemed desir-
able to examine the data for differences in tree form. Form quotients in-
side bark were co nputed for all trees. The range of individual quotients
varied from 0.472 to 0.862. Ten of the most widely varying individuals

'In some cases, the position of the wind-thrown trees necessitated cutting at other levels.

Plantation Grown White Pine 5

were discarded, reducing these limits to 0.542 and 0.808, respectively.
The average form quotient of the 921 trees used in the volume tables was
0.681.

The field measurements of the 921 trees finally accepted as being
suitable were recorded on U. S. Forest Service Form 558a. For each tree,
three volumes were determined: (a) total peeled volume, in cubic feet, of
the stem including stump ; (b) volume of the stem with bark, in cubic feet,
between a stump height of 0.5 foot and a top diameter of 2.0 inches, out-
side bark ; and (c) the volume of the stem, in board feet by the Interna-
tional Rule (0.25-inch saw kerf), between a stump height of 0.5 foot and a
top diameter of 5.0 inches, inside bark. All volume determinations were
made directly from the plotted taper measurements. Cubic contents
were obtained by the conversion of planimetered areas, board foot vol-
umes by graduated transparent overlays.1 In the latter case, each tree was
scaled as a composite of 8-foot logs plus a top log of shorter length,
including allowance for stump height and trimming length. Trees with top
diameters of less than 5.0 inches, inside bark, at 8.65 feet above ground
were considered unmerchantable. The top log, when less than 8 feet in
length, was scaled by a separate calculation in units of 2, 4, or 6 feet of
length and the top diameter, inside bark, to the nearest tenth of an inch
at that point. Thus, a top log which measured 7.5 feet in length to a 5.0-
inch top diameter, inside bark, was treated as a 6-foot log with atop diam-
eter, inside bark, somewhat larger than 5 inches. Since this top diameter
rarely exceeded 5.5 inches, the possible combinations of diameter and
length were so few that it was a simple matter to make up a table giving
the volume of any combination at a glance.

The three sets of volumes, properly arranged and tabulated, were
worked into tables by the alinement chart method as described by Bruce
and Reineke.2 Base charts were furnished by the U. S. Forest Service.
The resulting volume tables and charts are presented on the following
pages. Tables 1, 2, and 3 were read from Charts I, II and III, respec-
tively. The alinement charts are somewhat easier to use for fractional di-
ameters and odd heights because interpolation is unnecessary. If diame-
ters are grouped by whole inch classes and heights by 5- or 10-foot classes,
the tables are preferable.

Two measures of accuracy were applied to the completed alinement
charts, the aggregate difference in percent and the average percentage
deviation. The first measure compares the sum of all the measured volumes
with the sum of the corresponding chart volumes for the same trees. By
this standard, Charts I, II and III give volumes 0.08 percent low, 0.03 per-
cent low and 0.06 percent low, respectively. These charts obviously fit the
basic data, in the aggregate, well within the 1 percent tolerance usually
allowed.3

The second measure is an average of the deviations of the measured
volumes from their corresponding chart volumes, each deviation being ex-

1ReiDeke, L. H. The Determination of Tree Volume by Planimeter. Journal of Forestry, 24: 183-
189, 1926.

2Reineke, L. H. and Bruce, Donald. An Alinement-Chart Method for Preparing Forest Tree Volume
Tables. Technical Bui. No. 304 U.S.D.A. Washington, 1932.

3Item 37a, Committee Report: Methods of Preparing Volume and Yield Tables. Journal of Forestry,
24. 653-666, 1926.

6 Connecticut Experiment Station Bulletin 427

pressed as a percent of the corresponding chart value. These values for
Charts I, II and III aie 4.59 percent, 4.70 percent and 8.5 percent, respec-
tively.

READING THE ALINEMENT CHART

A straightedge is necessary for reading the alinement chart. One
made of a strip of transparent celluloid with a fine line scratched on the
underside throws no shadow and makes reading accurate and rapid. The
dimensions of the strip should be about 1 by 12 by 1/32 inches. The
heavier grade of celluloid used for automobile side curtains is entirely
satisfactory. To construct: (see sketch below) Scribe a very fine,
straight line down the middle. Remove any burr with the thumb nail,
and rub India ink into the line to make it more visible. Near one end of
the straightedge, cut a V- notch as shown, being careful that the inked
line bisects the angle at "X" formed by the sides of the notch. A needle
mounted in a cork with the point exposed completes the equipment needed.

I * _

The volume of a tree of any given dimensions may be obtained from
the chart by connecting its D.B.H. value on the left hand scale with its
total height value on the right hand scale by a straight line, and reading
volume at the intersection of this line with the middle scale. For example,
to secure the volume of a tree 6.3 inches D.B.H. and 38.2 feet in total
height using Chart I, place the point of the needle on the diameter scale
at 6.3 inches, hook the straightedge around the needle and pivot it until
the inked line intersects the height scale at 38.2 feet. The volume, 4.05
cubic feet, will be found at the intersection of the inked line with the
volume scale.

The long axis of the needle should always be held perpendicular to
the surface of the chart and the inked line should always be on the under-
side of the straightedge next to the chart.

APPLICATION OF THE VOLUME TABLES

As previously stated, the data for the volume tables included were
secured entirely in Connecticut. If the tables are to be used in other
regions, their applicability should be tested. To do this, fell 20 to 25
trees, selected to give a good range of diameters and heights, and measure
after the manner employed in the construction of the table. Compute the
volumes of these trees by standard methods using the same units (cubic
feet or board feet) and the same limits of utilization as in the table.

Plantation Grown White Pine 7

Express the deviation for each tree as a percentage of the tabular volume
of a tree of the same dimensions. Compute the average of these percent-
age deviations for comparison with the average percentage deviation as
shown in the table.

Compare the total volume of the felled trees with the total of the
tabular volumes of these trees to arrive at the aggregate difference. If
the average percentage deviation of the local trees is not appreciably
greater than that of the table, and if their aggregate difference is not more
than two and one-half times the average percentage deviation of the table
divided by the square root of the number of trees used in the test, correc-
tion for locality is unnecessary.

If the volumes of the local trees differ consistently from the tabular
values, the table should be corrected. If the table is to be used for limits
of utilization other than those used in its construction, it must be cor-
rected to give volumes adjusted to the new limits.1

A volume table for local use, reading in terms of diameter only, may
be made as follows :

1. Obtain sufficient heights in the field to plot a height-on-diameter
curve. From this, read heights corresponding to one-inch diameter classes
and tabulate, as in column 2 of the table below.

2. From the chart, read the volumes for the several paired diameter-
height values and enter these in column 3 of the table.

D.B.H.

in Inches

(1)

Total Height
in Feet

(2)

Volume in

Cubic Feet2

(3)

2.0

14.4

.16

3.0

17.7

.44

4.0

20.3

.87

5.0

22.7

1.52

etc.

etc.

etc.

Columns 1 and 3 now constitute a local table reading in terms of full
inches of diameter. These values may be curved to discover errors in
chart reading or to provide for fractional-inch diameters.

1For information on the correction of volume tables for locality and for different limits of utilization,
the reader is referred to Miscellaneous Publication No. 50, U. S. Department of Agriculture, Washington,
D. C. Volume, Yield and Stand Tables for Second-Growth Southern Pines, prepared by Office of Forest
Experiment Stations, Forest Service, and Cooperating Agencies.

'Read from Chart I.

Connecticut Experiment Station Bulletin 427

ACKNOWLEDGMENTS

The writers wish to express their appreciation to the following persons
and organizations:

To Mr. L. H. Reineke, Silviculturist, Northeastern Forest Experiment
Station, New Haven, Conn., for help and advice in the preparation of the
manuscript and charts.

To Dr. A. R. Kienholz, Research Technician, Civilian Conservation
Corps, Connecticut, and men from C.C.C. Camp Robinson, East Hartland,
Conn., for assistance in obtaining taper measurements at the Rainbow
Forest.

To Mr. 0. A. Kelsey, temporarily employed by the Connecticut
Agricultural Experiment Station, for careful and painstaking work in the
preparation of the charts and tables.

To the men of the National Youth Administration assigned to the
School of Forestry, Yale University, New Haven, Conn., for assistance
in field and office work.

Plantation Grown White Pine

D. B.H.
INCHES

TOTAL

VOLUME

CU. FT.

50-
40-

1.0-
0.9-
0.8-
0.7-
0.6-
0.5-

0.1-
0.09-

TOTAL

HEIGHT

FEET
-65

PLANTATION GROWN WHITE PINE

P/nus Strobus,L.

CONNECTICUT

1939

ENTIRE STEM, LESS BARK.

STUMP, 0.5 FOOT HIGH, MEASURED AS A CYLINDER.

VOLUME MEASURED BY PLANIMETER.

BASIS: 921 TREESj DIAMETERS, 1,7 TO 12.5 INCHESj

HEIGHTS, 17 TO 55 FEET; AGES, 16 TO 40

YEARS; AVERAGE FORM QUOTIENT, 0.681.
AGGREGATE DIFFERENCE' CHART 0.08% LOW.
AVERAGE PERCENTAGE DEVIATION' 4.59%.
MEASURED 8Y THE CONNECTICUT AGRICULTURAL

EXPERIMENT STATION AND THE SCHOOL OF

FORESTRY, YALE UNIVERSITY.

Chart I. Alinement chart for volumes of plantation grown white pine showing total
contents of the stem, without bark, in cubic feet.

10

Connecticut Experiment Station

Bulletin 427

D. B.H.

INCHES

16-

15-
14-
13-
12
II -

MERCHANTABLE
VOLUME
CU. FT.
60—=
50—=
40-

30-

TOTAL
HEIGHT

FEET
-65

10-
0.9-
0.8-
0.7-
0.6-
0.5-

0.4-

PLANTATION GROWN WHITE PINE

Pinus StrobusX-

CONNECTICUT

1939

MERCHANTABLE STEM WITH BARK.

STUMP, 0.5 FOOT HIGH, EXCLUDED.

TOP DIAMETER OUTSIDE BARK, 2.0 INCHES.

VOLUME MEASURED BY PLANIMETER.

BASIS; 921 TREES; DIAMETERS, 1.7 TO 12.5 INCHES-.

HEIGHTS, 17 TO 55 FEET; AGES, 16 TO 40

YEARS; AVERAGE FORM QUOTIENT, 0.681.
AGGREGATE DIFFERENCE: CHART 0.03 % LOW.
AVERAGE PERCENTAGE DEVIATION 4.70 %.
MEASURED BY THE CONNECTICUT AGRICULTURAL

EXPERIMENT STATION AND THE SCHOOL OF

FORESTRY, YALE UNIVERSITY.

Chart II. Alinement chart for volumes of plantation grown white pine showing mer-
chantable contents of the stem, including bark, in cubic feet.

Plantation Grown White Pine

11

PLANTATION GROWN WHITE PINE

Pinus Strobus,L

CONNECTICUT

1939

INTERNATIONAL LOG RULE

!V' SAW KERF

VOLUME
BD. FT.

100-

90 —

80-

70

60-

MERCHANTABLE VOLUME.

STUMP, 0.5 FOOT HIGH, EXCLUDED.

TOP DIAMETER, INSIDE BARK, 5.0 INCHES.

BASIS: 747 TREES; DIAMETERS, 5.6 TO 12.5
INCHES; HEIGHTS, 28 TO 55 FEET(
AGES, 18 TO 40 YEARS; AVERAGE
FORM QUOTIENT, 0.675.

AGGREGATE DIFFERENCE: CHART 0.06%
LOW.

AVERAGE PERCENTAGE DEVIATI0N(58I TREES,
6.6 INCHES PLUS), 8.5%.

MEASURED BY THE CONNECTICUT AGRICULT-
URAL EXPERIMENT STATION AND THE
SCHOOL OF FORESTRY, YALE
UNIVERSITY.

"35

'30

~ss

Chart III. Alinement chart for volumes of plantation grown white pine showing mer-
chantable contents of the stem, without bark, in board feet.

12

Connecticut Experiment Station

Bulletin 427

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