Stephen F. Austin State UniversitySFA ScholarWorks

Informal Project Reports East Texas Pine Plantation Research Project

10-1986

Research Report No. 5, Estimating the Cubic FootVolume of Individual Loblolly Pine Trees Plantedin East TexasThomas J. Wiswell

Jock A. Blackard

J. David LenhartArthur Temple College of Forestry and Agriculture, Stephen F. Austin State University

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Recommended CitationWiswell, Thomas J.; Blackard, Jock A.; and Lenhart, J. David, "Research Report No. 5, Estimating the Cubic Foot Volume of IndividualLoblolly Pine Trees Planted in East Texas" (1986). Informal Project Reports. Paper 69.http://scholarworks.sfasu.edu/etpprp_project_reports/69

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by

Thomas J . Wiswel I

Jock A. Blackard

J_ Dovid Lenhart

REPORT NUMBER 5

TO

PARTICIPATING COl1PANIES

IN THE

EAST TEXAS PINE PLANTATI ON RESEARCH PROJECT

A STUOV OF

L06LOLLV AND SLASH PINE PLANTATIONS

IN

CENTER FOR APPLIED STUDI ES

SCHOOL Of FO RESTRY

STEPHEN f . AUSTIN STATE UNIVERSITY

NACOGDOCHES, TEXAS 75962

Ocf.ober, 1 966

This is the fifth in a continuing series of reports

describing results from the East Texas Pine Plantation Research

Project.

Subject and content of eoch ETPPRP report 'w'ill be

regional in scope and of particular i riterest to lob lolly and slash

prne plantation owners in East Texas.

Anu suQgestions, ideas or comments vill always be

we 1 corned .

*********

Support from the participating companies ...

Champion International Corporation,

lnternatfonel P~per CompF.iny and

Temple- EasTex, Inc.

is gratefully appreciated.

*********

Hiis report is ba3ed ori work by:

1. Mr. Thomas J. Wis'w'ell during the Spring '86

~rnester, &~ e doctoral student et SFASU on

a T. L. l. Temple Fello,11ship.

2. Mr . . Jock A. 81ock&rd, as s Graduate Assi.:,toilt.

3. Dr.'"'· [>avid Lenhart.

J . David Lenhart

Project Di rector

October 16, 1986

EST IMAT ING THE CUB IC FOOT VOL UME • OF

INDIVIDUAL LOBLOLL Y PINE TREES PLANTED IN EAST TEXAS

by

Thomos J. Wiswell furmtlr tlodorial carlfJ>il61e, Sc/I()()/ uf forestry, Sf ASL/

Jock A. Blackard lbrmer grliO'oale student, t/Sf '86, Sc//(I(}/ of forestry, Sf'4Sll

J . Davf cJ Lenhart Professor, Sc/JotJI uf rurestrv, SrrJSll

ABSTRACT. Equati ons are presented to estimate the cubi c f oot content of

the 1noocJ and bark in the stem end branches of i ndiYidual loblolly pine

trees planted on site-prepared lend in E6st Tex6s. Taper funcUons are

also developed.

2

INTRODUCTION

The estimetion of the content of. individu6l trees is a rrincip61

component in the meosurement process to detennine per acre yields. In

particulflr, the content of individua l trees is a value needed in the lest

stages of the diometer distribution yield prediction method. Also, tree

information is use ful in timber cruising.

In this report, we present equations to estimflte the cubic foot

content of individual planted l oblolly pines in non-old-fields in East Texas

flS:

1. hornplete Iree hubic feet Wood ond §ork: CTCFWB.

2. ,Cornplete Iree r;ubi c feet 'wood only: CTCF'w.

3. I otfil ~tern Cubic feet Y./ood and §ork: TSCFWB.

4. fartial ~tern hubic feet Wood and §erk: PSCFWB . 5. Iotal ~tern kUbic feet Wood only: TSCFW.

6. fartia l ~tern Cuttic [eet Wood only: PSCFW.

By fippropriete subtraction, the cubic feet of berk Bnd the cubic feet of

branches cen be determined. Di fferences bet ween total stern and perlial

stern values can be. obtcine.d for l/e1-ious rnultiple-producl cornpulations.

3

TREE MEASUREMENTS

A totol of 68 lot.lolly pine somple trees Iocoted 111 the buffer

zones of 34 of our 176 ETPPRP permt:Jnent plots in loblolly pine plontalions

were f elled during Jonuory - March, 1986. Two trees were sampled per

plontotlon. Three of the trees were eventuetlly eliminoted due to sompllng

errors. The dlstnbulion of the resulting 65 stimple trees by county and by

dbh and height closses is shown in Figure 1.

Prior to felling o tree, the dbh ond crown cless were

determined. After felling, the branches were removed and weighed. A

typicel branch wes weighed with ond without needles. Eight brench

segments ( 12" long) were cut ond weighed with ond without bork.

Al 3-foot c:u t points a1 0119 the stern, dob was recorded. Ttre11

the stem wos bucked into 3-f oot long bolts. Eoch boll wos weighed. At

the bottom of eBch boll, a 1- to 2-inch disk was cut. Each disk was

weighed with and without bark. In oddition, dib for- etich disk wes noted.

The top stern segment was ol so weighed ond considered port of n1e stem.

The necessary field d6lo wt1s now 6'v't1iloble lo compute

observed cubi c foot tree volume wHh and without berk es:

1. PorUal ~ t t.n-: to the t op of ecci·1 successive bolt.

2. Total stem.

3. Brnnr.hes.

BrMch volume was calculated using appropriate ratios of cubic feet to

green Weight . Complete tree cubic feet WBS determined by summing total

stem find branch values.

s

COMPLETE TREE ESTIMATION

PlotUngs of CTCF\¥8 end CTCFW over dbh (D) and total tree.

heigr'1 t (H) indicoted o model origin61Jy suggested by Schumocher and Hflll

( 193J3) OS

Tree content = bODb 1 Hb2 ( 1)

repre~ented the relotionships seen in the plottings.

Non-lineer regression enfllysis of the dete set produced the

fol loW- ing predictic1n equeUons as

CTCFWB = 0.00638902.242262H0.668729 (2)

and

CTCFW = 0.002 l 96D2.263525H0.572B31 , (3)

witt1 R2 = 99% for bot11 equations*.

___ __. _____ _ I

All R2 val ~es in this report 'w'ere calculated using non-l inear regression res ult~ ss:

R2 ~ ({n- 1 )(:std dev dep v~r) 2 - Residuol 55}/((n-1 )(std dev dep var)2)( 100)

6

PARTIAL AND TOTAL STEM ESTIMATION

In a dissertation by McTague ( 1985), a new stem content -

estimation modeJ was presented, that has several desirable properties:

1. Treats totaJ stem content as a special case of partial

stern content.

2. Predicts stem content between stump and any

upper stem diameter limit.

3. Convertible to a wel l-beheved taper function.

4. Also, suitable for estimating green or dry weight of the

to tel or pert iaJ stem.

Subsequently, P1enaor and others ( 1955) developed variations of the

original McTague model as

Volume wood & Bark in the stern = b0ob 1 Hb2

- b3(db4;ob4 - 2)(H - 4.5), .

where d = upper stem diameter o. b. and

b3=0.00545415(1-2/b4),

Volurne wood only 111 the stem::: c0oc 1 Hc2

(4)

(5)

7

Equotion (4) wes used in non-hnetsr regression analysis withe

do to set comprised of 745 c6ses of cubic feet wood 6nd bork . The

resu_lling equotion is

PSCFWB = 0.0021030 1.958489H 1.062346

_ 0_0020323d3_ 1 a1s1e0-1 .1 s7878(H _ 4_5) (6)

With R2 = 98%.

If the value ror the variable d (upper stem diameter o. b.)1n EQ. 6 ls set to

zero (or the top of the stem), the lotter part of EQ. 6 diseppeors, and we

now have an equet1on to estimate

TSCFWB = 0.00210301 .958489H1 .062348_ (7)

Equotion (5) was used in non-linear regression onolysis with a

deta set comprised or 745 cases of cubic feet wood only . The resulting

equation is

PSCFW = 0.0009280 1.973735H 1.2 13909

_ 0.0017S 1 d2.9035B90-0.903589(H _ 4.S) (8)

ond

TSCFW = 0.00092801.973735H 1.213909 (9)

Tebles I end 2 show predicted cubic foot volumes for verious

cornbinetions of D, Hand d based on Eqs. 6 and 8, respectively.

TABL E 1. ESTIMATED CUBIC FEET OF WOOD AND BAR K IN THE STEM TO SPECIFIED UPPER DIAMETER L I~ITS FOR INDIVIDUAL LOBLOLLY PINE T~~ES ON NON-OLD-FIELD PLANTATIONS IN EAST TEXAS .

--------------------------------~----------------UPPER TOTAL TR EE HEIGHT (F EE T) STEM

DB H DIAMETER -----·----- -------- - --- ------·-----CI N> LIMIT CIN) 20 30 40 so 60 70 80

---------- ---------------------- ------·-----2 0 0

4 0 1 1 2 1 1

6 0 3 4 4 2 3 3 4 4 2 3 4

8 0 6 8 1 0 2 6 8 ~ 4 6 7 9 6 4 6 7

10 0 1 2 1 ) 1 7 2 12 1 5 1 7 4 1 2 1·4 1 7 6 10 1 3 1 5

12 0 2 1 25 29 2 21 25 29 4 21 24 28 6 1 9 23 26 8 1 7 20 23

14 (J 2Y 3 " 39 ~ 2 •} 31, •c ·' . 4 20 33 38 6 2 ? 32 37 8 ~) 29 3t.

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

TABLE 2 . ESTIMATED CUBIC FEET OF WOO D ONLY IN THE STEM TO SPECIFIED UPPER DIAMETER LIMITS FOR INDIVIDUAL LOBLOLLY PINE TREES ON N ON- OL~- FIELO PLANTATI ONS IN EAST TEXAS .

--------------------------------------- -----------UPPER TOTAL TR EE HE I GHT (Ff-ET> STEM

DB H DIAME TER ----------------------- ------·-----(IN) LI MI T (IN) 20 30 40 so 6U 70 80

---------- -------~-------------------------2 0 0

4 a 1 1 2 a 1

6 0 2 3 4 2 2 3 4 4 1 2 3

8 0 s 6 s 2 5 6 cS 4 4 0 I 6 3 4 5

10 a 10 1 j 1 s 2 10 1 2 1 s 4 10 l2 1 4 6 8 1 u 1 3

12 u 1 6 22 26 2 1 8 22 25 4 1 ., 2 1 25 6 1 6 20 23 8 1 4 1 7 20

1 L. 0 2 t.. ?. 9 3 i; 2 ~~

") ,, .... 35 4 2 l. 29 34 () ~ .5 28 32 b 21 25 3('

--------------------------------~----------------

10

TAPER FUNCTIONS

86sed on 6 procedure outlined by Clutter ( 1960) 6nd Pien6ar

et ol. ( 1965), Eq. 6 wos converted into the following toper equotions

EIS

Upper stem dob = D((H - L)/(H - 4_5))0.641637, ( 10)

Where L =Position on upper stem where dob occurs,

ond

L = H - (H - 4.S)(dob/D) 1. l 87676. ( 1 1)

EQ. 8 wos converted into the following toper equations os

Upper stern dib = 0.685652D((H - L)/(H - 4.s))0.722175, ( 12)

and

L = H - 1. HJ2741(H- 4.5)(dib/D) 1.384706. ( 13)

'"'here L =Position on upper stern where dib occurs,

1 1

LITERATURE CITED

Clutt•.."r, J. L. 1980. Development of toper functions from verieble-top

rnerchontoble volume equotions. For. Sci. 26( 1):117- 120.

McTogue, J. P. 1985. Growth and yield of slosh ond lob lolly pine in the

state of Senta Catarina, Brnzi 1. Univ. of Ga., Ph.D. Di ss. 219 p ..

Pienoor, L. V., B. D. Shiver ond J. W. Rheney. 1985. Revised stern volume

and weight equations for site-prepared slash pine plentelions.

Univ. of Ge., Sch. of For. Resources, Plcmtation Manege. Res.

Coop. Tech. Rep. No. 1985-5. 22 p.

Schurmicher, F. X. tmd F. S. Holl. 1933. Logorithrnic expression of timber­

tree volume. J. Agr. Res. 47:719-734.