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http://www.archive.org/details/tablesprocedures659wian

Tables and Procedures for
Estimating Weights of Some
Appalachian Hardwoods

: Bulletin 659T ie FEB 15 197
. December 1977

re ENGR. LIBRARY
WEST VIRGINIA UNIVERSITY

_ West Virginia University
_ Agricultural and SEES Experiment Station

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AUTHORS

Harry V. Wiant, Jr. is Forest Scientist in the West Virginia University Agri- |

cultural and Forestry Experiment Station. Junior authors were graduate students
in the Division of Forestry, West Virginia University.

ACKNOWLEDGMENTS

Appreciation is extended to the Westvaco Corporation, and especially Mr. |

Bruce B. Brenneman, Research Center Leader at Rupert, West Virginia, for their
cooperation and review of the manuscript and to the West Virginia Department
of Natural Resources for the use of the West Virginia University Forest. Thanks
are expressed to others who reviewed the manuscript, including Dr. Harold E.
Young, University of Maine; Mr. Jeffrey L. Wartluft, USDA Forest Service; and
Professor William R. Maxey, West Virginia University

West Virginia University
Agricultural and Forestry Experiment Station
College of Agriculture and Forestry
Dale W. Zinn, Director
Morgantown

778-2308

PREFACE

The weight tables in this publication, while based on data collected in
northern West Virginia, may prove useful in other areas of the Appalachian
region; however, they should be adequately tested before they are utilized else-
where. The sampling procedures described are of more general utility.

Contents

ENTE STGS s 24 Seat Sek 25 ee tae Se emg or a ie a ae ee ee 1
EOS BEGGS Oss SAR es ie eee np CSE Sees he epee Ol SON 1
SRS LES Te oe GR re Co aie ae Ne Gan eee Shs co auaaee WP th 2

SPE SHTeSAOHIMVCIGNE: 25 512), 88a nos Flee eee epee Moy aes ne 2
Weight Estimates When Marking Timber ................ 15
Weight Estimates Using Fixed-Area Plots ................ 15
Mveightestimates Using Point'Samples .... 22.2222. 2 2.5522. 17
Weight Estimates Using Point and 3P Sampling ..........2... 18
EeIRACECHEACOPATIDROGEIN = ic: colstae = eset: via sue eee cay See ee 21
Combined Equations for Red and White Oaks .........2.2.22.. 22

PUR LCEMERCECTCHIECSIr ey. 2) Sette 2 iiscee) ase URES Sk ee Tea ny he ee ee 36

TABLES

PeEERCCIGTCCHWCIGhE = ears ee Se et BS Se See eg 3
PEEAETEC OL WCIGht= ee) its 6 a) oso) ain ee et cc oe Lees 4
werota mee ary weight without bark <<: ... ) 62. ea eb be ee 5
PRR EAACe Cry, WEIGhL OF Dank. seis Sie oe Se eg ee 6
Peer RUsC ITE Oty IN ANIGIIES ©, Siena! Sos es heced Abe &: eet met cee Ge We 7
PEEP UV CIA OMDIdnChes = anaes ees Gea ee ee ee SOR ae 8
Pamryaweight of branches without bark . 2... 02 2 bk ee es 9
PPI hEO Mm DFAaMch Dales Sfyceie SOR Wr 2 i eee ae 10
SeeGicemweigne toa 4 inch GOD. 26.0... ss 2s se eG kee ee ee 11

PeePiMCighitO aA -InehWGOD 92 en's. 2 cae ew SR es Se es 12

Pee mnyviweight withoutbarktoa4-inchidob .......2..-5....5.. 13

-Pimawecight.On bark toa4-inchidob .. 2... 2. ee eee eee 14

13. Total tree green weight per acre per in-tree (BAF =10) ......... 23

14. Total tree dry weight per acre rer in-tree (BAF=10) .......... 24

15. Total tree dry weight without bark per acre per in-tree (BAF = 10) ... 25

16. Total tree dry weight of bark per acre per in-tree (BAF =10) ...... 26

17. Green weight of branches per acre per in-tree (BAF =10)........ 27

18. Dry weight of branches per acre per in-tree(BAF=10) ......... 28

19. Dry weight of branches without park per acre per in-tree (BAF = 10) . . 29

20. Dry weight of branch bark per acre per in-tree(BAF=10) ....... 30

21. Green weight to a 4-inch dob per acre per in-tree(BAF=10) ...... 31

22. Dry weight to a 4-inch dob per acre per in-tree (BAF =10) ....... 32

NNMN
oS

. Dry weight without bark to a 4-inch dob per acre per in-tree (BAF = 10) 33

Dry weight of bark to a 4-inch dob per acre per in-tree (BAF =10) .. . 34

. Weight equations for the red oak and white oak groups ......... 35

Tables and Procedures for
Estimating Weights of
Some Appalachian Hardwoods

Harry V. Wiant, Jr., Carter E. Sheetz, Andrew Colaninno,
James C. DeMoss, and Froylan Castaneda

WEIGHT TABLES

The introduction of whole-tree chipping operations in West Virginia forests
has stimulated interest in the development of weight tables for field use. These
tables facilitate the estimation of weight of standing trees to be chipped and
eliminate the need to convert from cords or cubic feet to weight. Weight tables
were developed for some Appalachian hardwoods in northern West Virginia.

Procedure

Nineteen to 22 trees, ranging from 2 to 16 inches in diameter at 4.5 feet
(dbh), were selected for study on or near the West Virginia University Forest?
near Morgantown for each of the following species:

Code Species

NRO northern red oak (Quercus rubra)

BO black oak (Q. velutina)

SO scarlet oak (QO. coccinea)

WO white oak (Q. a/ba)

CO chestnut oak (Q. prinus)

VE yellow-poplar (Liriodendron tulipifera)
H hickories (Carya spp.)

BC black cherry (Prunus serotina)

RM red maple (Acer rubrum)

Trees were felled, sectioned, and weighed in the field, and oven-dried weights
were determined from wedge-shaped samples taken at 4-foot bucking points and
from branch samples. All stem material less than 4 inches, diameter outside bark
(dob), and limbs were considered as branches. Stumps, approximately ‘-foot,
roots, and leaves were not included in this study.

The West Virginia University Forest is evenaged, about 45 years old, with an average
site index, using Schnur’s (1937) curves, of 73.

1

Results

Analyses indicated dbh accounted for most of the variation in total oven-
dry weight. Inclusion of total or merchantable heights did not improve relation-
ships appreciably. This indicates the value of local weight tables, using dbh
alone, for weight estimations. Tables 1 to 12 give green and dry weights for the
various species.

Regression models tested included:

W=a+bD?
W=a+bD+cD?
W = ab?

where: W = weight in pounds
D =dbh
a, b, and c = regression constants

Although there are more sophisticated statistical procedures, models providing
the best R-values (or r?) were accepted and are given with their standard errors
and standard errors as a percent of the W-means below each table. It should be
noted that the reliability of equations, as indicated by standard errors, was better
for total tree weights than for branch material.

If weights for species not included in this study are desired, it may be
possible to use values for a closely related species in terms of growth habit, wood
density, etc. For example, four trees for each of several minor species, selected
to span the dbh-range, indicated total weights of cucumbertree (Magnolia
acuminata) and bigtooth aspen (Populus grandidentata) are approximated by
yellow-poplar; and sweet birch (Betu/a /enta) by black cherry.

FIELD ESTIMATES OF WEIGHT

Weight estimates in the field can be made using the same basic techniques
utilized for cubic-foot or board-foot volume determinations. An unrealistically
simple example will be used to illustrate the procedures, much of which could be
computerized. Assume we are interested in total dry weights of species A and B,
and that those species occur in only two diameter classes, 5 and 10 inches, as
follows:

Total dry weight (Ibs.)

Dbh Species A Species B
5 100 125
10 650 730

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14

Weight Estimates When Marking Timber

Weight estimates are easily derived when each tree to be harvested is visited
and marked with paint. A tally of the number of trees by species and diameter is
made. For example:

Number of trees

Dbh Species A Species B
5 Dia Ex
10 mis Bd :
Weight estimates are:
Dbh Species A Species B Totals
5 (23) (100)'= 2300 (24) (125) = 2625 4 4925
10 (5) (650) = 3250 (12) (730) =8760 12010

Totals 5550 11385 |16935

Our total weight estimate is 16935 pounds, and, as each member of the
population of interest has been measured, there is no sampling error in the
statistical sense.

Weight Estimates Using Fixed-Area Plots

If cruising is done using fixed-area plots, a separate tally of trees by species
and diameter class is made at each plot. Suppose the following data are collected
on 1/10-acre plots:

Number of trees

Plot Dbh Species A Species B
we 5 al ne
10 se es
2 5
10
3 5 :
10 4 6
4 5 : :
10 o ¢@

15)

Weight estimates for plots are:
Plot Dbh Species A Species B Totals
1 5 (6) (100) = 600 (2) (125) = 250 850
2230
10 (1) (650) = 650 (1) (730) = 730 1380
2 eS = a @
3 5 (1) (100) = 100 = 100
3020
10 = (4) (730) = 2920 2920
4 5 (1) (100) = 100 CI RG25) aah 5 225
1525
10 (2) (650) = 1300 — 1300
Totals 2750 4025 (6775
Average per-acre estimates are:
Dbh Species A Species B Total
5 i) 8004-1002100} 2000 io)| 2808125] = 937.5 2937.5
10 (10)| $801300 | = 4875 in0)| 79022020]. 9125 14000

10062.5 |16937.5

The average 1/10-acre estimate is 6775/4 = 1694 pounds. The standard
error (Sz) for that estimate is:

}
Sy = | >x2 - (=X)2/n
n (n-1)

Totals 6875

where: X = weight estimate for a given plot
n = number of plots
Therefore:

S- = / (2230)? + (0)? + ae et (1525)? - (6775)7/4 _ 642

Expressed as a percent of the mean, our sampling error Is:

642
on} WUCO) = Seo
1694

16

On an acre basis, our weight estimate is:

(10) (1694 + 642) = 16940 + 6420 pounds
or 16940 + 38%

About two in three times we expect the true population mean to be within
these limits. Limits are doubled for a 19 in 20 chance or tripled for a 99 in 100
chance. The usual assumptions of random sampling are made here, of course.

Weight Estimates Using Point Samples

If point sampling (BAF=10) is to be used, weights in the basic table are
multiplied by the appropriate conversion factors (see Kulow 1965), as follows:

Total dry weight (Ibs.) per acre per in-tree?

Dbh Species A Species B
5 (73.34) (100) = 7334 (73.34) (125) = 9168
10 (18.34) (650) = 11921 (18.34) (730) = 13388

The following data are collected:

Number of in-trees

Point Dbh Species A Species B
1 5 on :
10
2 5
10
3 5 it
10 e e
4 5 ie
10

TT oa

2 An “in-tree’”’ is a tree selected as “in” with a prism or similar instrument.

U7

Weight estimates per acre for points are:

Point Dbh Species A Species B Totals

1 5 (2) (7334) = 14668 (1) (9168)= 9168 23836 j
49145
10 (1) (11921) = 11921 (1) (13388) = 13388 25309

. |.

3 5 — —
53552,
10 — (4) (13388) = 53552 53552
4 5 (5) (7334) = 36670 — 36670
36670
10 — — |
|
aia 63259 76108 (30565
Average per-acre estimates are:
Dbh Species A Species B Totals”
5 14668+ 36670) _ 19935 ae = 2292 15127
4 4
10 fees = 2980 {ag osbbal = 16735 19715
4 4 ee
Totals 15815 19027 [34842 :

The average per-acre estimate is 34842 pounds. The standard error is:

_ | (49145)? + (0)? + (53552)? + (36670)? - (139367)2/4
4 (4-1)

S

x
= 121152

Sampling error, as a percent, is:

12152 |
| (100) = 35% |

34842

Weight Estimates Using Point and 3P Sampling

Much time can be saved in the field by combining 3P and point sampling.
Again, we will assume BAF=10. Before the cruise, determine:

18

(1) the number of point samples desired. This can be done statistically
(see Wiant 1976), but in most situations will be at least 30 and not
more than 100.

(2) the number of 3P sample points needed for the desired accuracy.
Wiant (1976) provides a formula for a statistical determination,
but 15 to 20 should suffice in most cases.

(3) the approximate sum of basal areas (= KPI) expected at the point
samples. For example, if you assume point samples will average 40
square feet of basal area, and you plan to have 100 point samples:

= KPI = (40) (100) = 4000

Develop a list of random numbers, one for each point sample, from 1
through KZ, where:
=KPI

number of 3P samples desired
lf 20, 3P samples are desired:

Kz = 4000
20

= 200

In the field, record the number of in-trees by species on a point sample.
Then, total the number of in-trees and multiply by 10 to obtain the per-acre
basal area estimate for that point sample.

If that basal area is less than the random number for that point sample, go
the next point. If that basal area equals or exceeds the random number for that
point, measure the dbh of each in-tree.

After field work is completed, calculate:

(1) the ratio of per-acre weight (Y) at each 3P point sample to the
basal area at that point sample, or Y/KPI.

(2) the total per-acre volume estimate, which equals the average basal
area on all point samples times the average Y/KPI-ratio. That ratio
times the average basal area for a given species provides a per-acre
weight estimate for that species; however, if there are sufficient
data, an average Y/KPI-ratio should be calculated for the individual
species to provide a better estimate.

(3) the approximate sampling error, which includes that due to the
point samples and that related to 3P, plus a covariance term which
will be ignored in this paper as is usually done in practice.

19

As an illustration of calculations, the example in the previous section will be
used:

DKPI
Point Randomno. Species A Species B Total a Y/KPI
1 23 30 20 50 49145 983
2 11 0 0 0 — =
$3 8 0 40 40 53552 Talso9
4 64 50 0 50 — =
Total 80 60 140 2322
Average 20 15 35 1161

Total per-acre weight = (35) (1161) = 40635
Species A per-acre weight = (20) (1161) = 23220

If there were sufficient data, a better estimate for Species A is obtained by
calculating its own average Y/KPI-ratio, as:

Point KPI Y Y/KPI
1 30 26589 886
Average 886

Per-acre weight = (20) (886) = 17720
Species B per-acre weight = (15) (1161) = 17415

Again, a better estimate for species B is:

Point KPI Y Y/KPI
1 20 22556 1128
6} 40 53552 1339
Average 1234

Per-acre weight = (15) (1234) = 18510
When separate Y/KPl-ratios are calculated for the different species for
weight estimates, the sums of per-acre weight estimates for all species may not
equal the total per-acre estimate, but the difference should be minor.
The standard error for point samples is based on basal area values:

_ /|(50)? + (0)? + (40)? + (50)? - (140)2/4
4 (4-1)

S

x
=11.9

20

_ = (100)

The standard error for 3P samples is based on the Y/KPI-ratios:

_ /(983)2 + (1339)? - (2322)2/2
2 (2-1)

SX
= 178

The sampling error as a percent for the cruise

Se for point samples] 2 Sx for Y/KPI-ratios]?
Le ee Se ee ae ae
average basal area average Y/KPI-ratio

| 2 2
= (100) ino]? . fa78
35 1161

= 37%

The per-acre weight estimate is, then, 40635 + 37%.

Tables 13 to 24 are provided for point sample estimates using these

' techniques (BAF=10).

Computerized Approach

As Lenhart et a/. (1973) point out, formulae, such as those in tables 1 to
12, can be modified for computerized applications. Using the one for total tree
green weight for northern red oak as an example:

W = 2.87249D7-°°°°°

| which is divided by 0.00545415D°, the basal area (BA) in square feet for a

diameter class, expressed in inches:

Ww DST2ZAID a Cee
0.00545415D2 0.00545415D?
giving:
W/BA = 526.66135D°-°°?°8

Suppose a single point sample tally (BAF=10) of northern red oak is as
follows:

No. in-trees

21

Using Table 13, the per-acre total tree green weight estimate is:
Dbh Per-acre weight

5 (2) (15472) = 30944
6 (3) (17481) = 52443
7 (1) (19382) = 19382

Total 102769
Using the formula approach, W/BA is calculated for each tree, summed, and
multiplied by the BAF, as follows:
W/BA = [526.66135(5)°-°°?°8] (2) = 3094.4
= [526.66135(6)°-°°9°°] (3) = 5244.3
= [526.66135(7)°-©°?58] (1) = 1938.2

10276.9
(BAF=10) (10276.9) = 102769 pounds per acre, the same answer obtained using
Table 13.
In actual practice, in-trees should be measured to the nearest tenth inch.
Equations of the form exemplified by the green weight of branches for
northern-red oak are modified as follows:
W = 116.07240 + 4.58936D? - 24.66151D

W/BA = 116.07240 is 4.58936D2 _24.66151D
0.00545415D2 + 0.00545415D? 0.00545415D2
= 21281.48291D + 841.44367 - 4521.60465D°!
A simpler method for BAF=10 is to multiply equations given in tables 1 to
12 by 1833.46495 to obtain per-acre estimates. The per-acre total green weight
for a 7-inch northern rad oak, for example, is:
1833.46495 [2.87249(7)2-66958]
(7)?

19382

W per acre =

This procedure was used to produce tables 13 to 24.

Combined Equations for Red and White Oaks

Data for the red oaks (northern red oak, black oak, and scarlet oak) and
white oaks (white oak and chestnut oak) were combined to yield equations
shown in Table 25. Foresters wishing to tally oaks in these two groups rather
than by species will find these equations useful and can develop local or point
sampling weight tables using the procedures previously discussed.

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SELECTED REFERENCES

Belanger, R. P. 1973. Volume and weight tables for plantation-grown sycamore.
USDA For. Ser. Res. Paper SE-107.

Burkhart, H. E., and J. L. Clutler. 1971. Green and dry weight yields for old
field loblolly pine plantations in the Georgia piedmont. Ga. For. Res.
Council Report 22.

Curtis, F. H. 1965. Tree weight equations—their development and use in forest
management planning. Soc. Amer. For. Proc. pp. 189-191.

Kulow, D. L. 1965. Elementary point-sampling. W. Va. Univ. Agr. Exp. Sta. Cir.
116.

Lenhart, J. D., J. R. Hasness, D. R. Hicks, D. M. Hyink, and S. |. Somberg. 1973.
Estimating cubic foot volume, green weight, or dry weight per acre of
planted loblolly pine using variable-radius-plot cruising techniques. Stephen
F. Austin State Univ. Texas Forest. Paper 21.

Ribe, J. H. 1973. Puckerbrush weight tables. Univ. Maine Life Sci. & Agr. Exp.
Sta. Misc. Report 152.

Schnur, G. L. 1937. Yield, stand, and volume tables for even-aged upland oak
forests. USDA Tech Bul. 560.

Young, H. E. 1976. A summary and analysis of weight tables studies. Complete
Tree Institute, Univ. of Maine.

Wartluft, J. L. 1977. Weights of small Appalachian hardwood trees and
components. USDA For. Ser. Res. Paper NE-366.

Wiant, H. V., Jr. 1976. Elementary 3P sampling. W. Va. Univ. Agr. & Forest.
Exp. Sta. Bul. 650T.

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