United States

Department of

Agriculture

m

W

3 Forest Service

 Southern Forest

Research Note

so-355

Experiment Station October 1989

Merchantable Volume and Weights of Mahoe in

Puerto Rican Plantations

John K. Francis

SUMMARY

Mahoe (Hibiscus e/&us SW.), a fast-growing tree

whose wood is considered valuable, is planted and managed primarily in the West Indies. Until now, volume and

weight tables have not been available for the species.

Data used in this paper were collected from 50 felled

trees in a range of sizes from plantations across Puerto

Rico. Using linear regression techniques, equations

were derived to construct tables for merchantable bole

volume, with and without bark, and green and dry

weights of merchantable boles. A local volume curve is

also presented that can be used to estimate merchantable volumes with bark from diameter measurements at breast height. Heartwood diameter can be predicted from inside-bark diameter and height on the stem.

INTRODUCTION

Hibiscus e/a&s S W., commonly known as mahoe or

blue mahoe, is native to Cuba and Jamaica. This upland

tree is impressive with a straight, clean form and rapid

growth. Its wood is of moderate density with a streaked

metallic gray color, and it works easily (Chudnoff 1984).

Mahoe is being planted and managed in its natural range

and in a number of other tropical countries (Weaver and

Francis 1988). Growth rates of mahoe have been reported for Hawaii (Whitesell and Walters 1976), Jamaica

(Wadsworth 1960, Swabey 1940), Puerto Rico (Francis

and Weaver 1988), and St. Lucia (Weaver and Lugo

1981, Ward and Charles 1982). Also, site quality (site

index) curves from St. Lucia and Puerto Rico are available (Ward and Charles 1982, Mark and others 1988). A

stand table for volume over bark per hectare based on

basal area and average dominant height was developed

for Grenada (Johnson 1985). However, no individual

tree volume or weight tables have been published to

date.

METHODS

Sample trees were chosen from plantations in five

different forests and numerous plantations distributed

throughout the moist, central area of Puerto Rico. Fifty

trees were selected that ranged from 15 to 59 cm in

diameter at breast height (d.b.h.); the commercial bole

lengths ranged from 6 to 26 m. Commercial bole length

was defined as the distance between the stump and a

lo-cm bole diameter or an obstruction such as a major

ramification that would render material above that point

unmerchantable. Most trees tapered evenly to the minimum diameter. The d.b.h.‘s were measured to the

nearest 0.1 cm with a diameter tape. Then each tree was

felled. Stump height was measured to the nearest

1 .O cm, and total height was measured to the nearest

0.1 m. Starting at the stump, diameters to the nearest

0.1 cm of the commercial bole were measured at l-m

intervals with calipers. The commercial bole length to the

nearest 0.1 m and diameter to the nearest 0.1 cm at

commercial height were also measured. Bark thickness

was determined at each meter with a bark gauge. Disks

5 to 8 cm thick were cut from each tree at four of the 1 -m

intervals scattered up the bole. The disks were measured for thickness (nearest 0.1 cm), weighed, and then

oven dried (85 “C) to constant moisture. After drying, the

wood and bark were separated and weighed individually.

Heartwood thickness and inside-bark diameter of the dry

disks were also measured.

Southern Forest Experiment Station/T-10210 U.S. Postal Services Bldg., 701 Loyola Avenue, New Orleans, La. 70113

Forest Service, U.S. Department of Agriculture.

Serving Alabama, Arkansas, Louisiana, Mississippi, E. Oklahoma, Tennessee, E. Texas, Puerto Rico, U.S. Virgin Islands

1
Commercial volumes of the sample trees both with

and without bark were obtained by summing the volumes of the 1 -m sections whose individual volumes had

been calculated with Smalian’s formula (Avery 1967). A

weighted linear regression, using a natural log transformation of the dependent variable, was employed to predict merchantable volumes with and without bark from

d.b.h. and merchantable heights. The bias associated

with the regression log-transformed data was ignored

after tests with Baskerville’s approximate correction

(Baskerville 1972) resulted in very small changes. In

addition, a “local” volume equation for merchantable

bole volume with bark was developed using a polynomial

model (with the dependent variables d.b.h. and d.b.h.

squared). Green and dry weight relationships of the merchantable bole with bark was developed as follows. First,

green- and dry-weight densities of the disks were used

to calculate the weights of adjacent l-m sections. Then

a linear regression equation based on the weights, diameters, and heights on the tree of the disks sampled

was employed to predict green and dry weights of the

remaining 1 -m segments. The calculated and predicted

weights of the 1 -m sections were summed to obtain the

green and dry weights of each tree. These weights became the dependent variables in a linear model based

on d.b.h., d.b.h. squared, and commercial bole length. A

linear model was constructed to predict heartwood thickness from inside-bark diameter at any point on the bole

and height at that point. Residuals were plotted for all the

models constructed, and no obvious trends were noted.

Because of the small sample size in each plantation,

tests for differences of models between plantations were

not conducted.

RESULTS

The following linear regression equations were used

to construct the tables for commercial volume with bark

(table 1) and commercial volume without bark (table 2) of

mahoe:

In Vwb = -3.8699 + 0.1069D

- 0.0006829D2 + 0.04355L

n = 50; Sy.x = 0.1159; R2 = 0.984

In Vwob = -4.0111

+ 0.1053D - 0.0006568D2 + 0.04426L

n = 50; Sy.x = 0.1266; R2 = 0.981

DIAMETER AT BREAST HEIGHT (CM)

Figure 1 .-Graphical representation of the relationship between diameter at breast height and merchantable bole volume of

mahoe (Hibiscus elatus).

where:

In Vwb = natural log of commercial volume with

bark (m3)

In Vwob = natural log of commercial volume without

bark (m3),

D = d.b.h. (to the nearest 0.1 cm),

D2 = d.b.h. squared,

L = merchantable bole length (to the nearest

0.1 m),

Sy.x = root mean square error, and

R2 = multiple regression coefficient.

The graphical presentation (fig. 1) of a local volume

equation is based on the relationship:

Vwb = 0.1112 - 6.01312D + 0.0009599D2

n = 50; Sy.x = 0.1305; R2 = 0.961

Both the green and dry weights of merchantable boles

of mahoe presented in tables 3 and 4, respectively, are

given by the following equations:

John K. Francis is research forester at the Institute of Tropical Forestry, U.S. Department of Agriculture, Forest Service, Southern Forest Experiment

Station, Rio Piedras, Puerto Rico, in cooperation with the University of Puerto Rico, Rio Piedras, Puerto Rico.

2
Wg = 2.4372 + 0.1387D - 0.001 13D2 + 0.04244L

n = 50; Sy.x = 0.1330; R2 = 0.980

Wd = 1.7850 + 0.1342D - 0.001 07D2 + 0.04508L

n = 50; Sy.x = 0.1372; R2 = 0.979

where:

Wg = green weights of commercial boles (kg)

Wd = dry weights of commercial boles (kg)

The heartwood diameter within mahoe stems can be

predicted by the relationship:

HD = -3.2082 + 0.9659Dib - 0.1904Hs

n = 187; Sy.x = 1.5910; R2 = 0.969

where:

HD = heartwood diameter at any point on stem

Dib = diameter inside bark, and

Hs = height on stem.

In large diameter stem pieces, heartwood is well defined, richly colored, and occupies most of the stem

thickness. In small stems and at the small diameters

located high on merchantable stems, heartwood is light

colored, poorly defined, and disappears altogether at

around an 8-cm diameter.

The average stump height for the 50 trees cut was

0.28 + 0.02 m. The variation appeared to be associated

with tree size and topography; the higher stumps had a

tendency to be found on larger trees and on steeper

slopes.

Table 1 .-Cubic-meter merchantable stem volume (outside bark) of mahoe (Hibiscus elatus)

D.b.h.

Merchantable bole length (m)

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

c m __________-________-____________________- Cubicmete~*-----------------------------------------

1 5 0.10 0.11 1 0.12 0.13 0.14 0.15 0.16 0.16 0.19 0.21 0.23 0.25 0.26 0.30

2 0 0.16 0.17 0.19 0.21 0.23 0.25 0.27 0.30 0.32 0.35 0.36 0.42 0.46

2 5 0.23 0.26 0.26 0.30 0.33 0.36 0.40 0.43 0.47 0.51 0.56 0.61 0.67

3 0 0.33 0.36 0.40 0.43 0.47 0.51 0.56 0.61 0.67 0.73 0.79 0.67 0.94

3 5 0.45 0.50 0.54 0.59 0.64 0.70 0.77 0.64 0.91 0.99 1.06 1.16 1.29

4 0 0.65 0.71 0.76 0.85 0.93 1.01 1.10 1.20 1.31 1.43 1.56 1.71

4 5 0.84 0.91 0.99 1.08 1.18 1.29 1.41 1.54 1.68 1.83 2.00 2.18

5 0 1.34 1.46 1.59 1.74 1.90 2.07 2.26 2.46 2.69

5 5 1.60 1.74 1.90 2.07 2.26 2.47 2.69 2.94 3.21

6 0 1.84 2.01

6 5

2.19 2.39 1 2.61 1 2.84 3.10

2.24 2.44 2.66 2.90 3.17 3.46

"Block outline indicates general extent of basic data.

Table P.-Cubic-meter merchantable stem volume (inside bark) of mahoe (Hibiscus elatus)

D.b.h.

Merchantable bole length (m)

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8

c m ---______-----------____________________- Cubic meters* - - - - _-_-_____----____-_------------------

1 5 0.08 0.09 1 0.10 0.11 0.12 0.13 0.14 0.15 0.17 0.18 0.20 0.22 0.24 0.26

2 0 0.14 0.15 0.16 0.18 0.19 0.21 0.23 0.25 0.28 0.30 0.33 0.36 0.39

2 5 0.20 0.22 0.24 0.26 0.28 0.31 0.34 0.37 0.40 0.44 0.48 0.53 0.58

3 0 0.28 0.31 0.34 0.37 0.40 0.44 0.48 0.52 0.57 0.62 0.68 0.75 0.81

3 5 0.39 0.42 0.46 0.50 0.55 0.60 0.66 0.72 0.78 0.85 0.93 1.02 1.11

4 0 0.56 0.61 0.66 0.73 0.79 0.87 0.95 1.03 1.13 1.23 1.35 1.47

4 5 0.71 0.78 0.85 0.93 1.02 1.11 1.21 1.32 1.45 1.58 1.73 1.89

5 0 1.15 1.26 1.38 1.50 1.64 1.79 1.96 2.14 2.34

5 5 1.38 1.51 1.65 1.80 1.97 2.15 2.35 2.57 2.80

6 0 1.60 1.75 1.91

6 5

2.09 1 2.28 1 2.50 2.73

1.97 2.15 2.35 2.56 2.80 3.06

'Block outline indicates general extent of basic data.
Table X-Green weights for merchantable boles ofrnahoe (Hibiscus elatus)

D.b.h.

Merchantable bole length (m)

2 4 6 6 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8

c m ________________________________________-- Kilograms’ ________________________________________--

1 5 77 84 1 92 100 109 118 129 140 152 166 181 197 214

2 0 127 138 150 164 178 194 211 230 250 272 297 323 351

2 5 214 233 254 276 301 328 357 388 423 460 501 545

3 0 314 342 372 405 441 480 523 569 620 675 734 799

3 5 435 474 516 562 611 666 725 789 859 935 1017 1108

4 0 570 621 676 735 801 1 871 949 1033 1124 1224 1332 1450

233

383

594

870

1206

1579

4 5 768 836 910 991 11078 1174 1278 1391 1514 1649 1795 1954

5 0 1064 1159 1261 1373 1495 1627 1771 1928 2099 2285

5 5 1281 1394 1518 1652 1798 1958 2131 2320 2525

6 0 1338 1456 1585 1728 11879 12045 2226

'Block outline indicates general extent of basic data.

Table 4.-Dry weights for merchantable boles of mahoe (Hibiscus elatus)

D.b.h.

Merchantable bole length (m)

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 2 6 2 8

c m ________________________________________-- Kilograms* ________________________________________--

15 38

20 62

2 5

3 0

3 5

4 0

4 5

5 0

5 5

6 0

42 1 46 50 55 60 66 72 7 9 8 6

68 74 82 89 98 107 117 128 140

105 115 125 137 150 164 180 197 215

152 167 183 200 219 239 262 287 314

211 230 252 276 302 331 362 396 433

276 302 330 361 396 433 474 518 567

342 375 410 449 491 537 588 643 704

528 578 632 692 757 828

644 705 771 844 924

9 4 103 113

153 168 183

235 258 282

343 376 411

474 519 568

621 679 743

770 843 922

1011 1106 1210 go6 1992

I

124

201

309

450

621

813

1009

1188

1324 I I

681 745 815 892 1 976 I1068 1169

"Block outline indicates general extent of basic data.

LITERATURE CITED

Avery, T. Eugene. 1967. Forest measurements. New

York: McGraw-Hill Book Company. 290 p.

Baskerville, G. L. 1972. Use of logarithmic regression in

the estimation of plant biomass. Canadian Journal of

Forest Research. 2: 49-53.

Chudnoff, Martin. 1984. Tropical timbers of the world.

Agric. Handb. 607. Washington, DC: U.S. Department

of Agriculture. 464 p.

Francis, John K.; Weaver, Peter L. 1988. Hibiscus e/&us

SW. Mahoe. Res. Note SO-ITF-SM-14. New Orleans,

LA: U.S. Department of Agriculture, Forest Service,

Southern Forest Experimental Station 7 p.

Johnson, M. S. 1985. Forest inventory in Grenada.

Surry, England: Overseas Development Administration. 169 p.

Mark P.; Ashton, S.; Lowe, J. S.; Larson, B. C. 1988. An

initial site index for mahoe (Hibiscus e/a&s SW.) in the

moist limestone region of Puerto Rico. New Haven,

CT: Tropical Resources Institute, Yale School of

Forestry and Environmental Studies. 13 p.

Swabey, C. 1940. Blue mahoe of Jamaica. Caribbean

Forester. l(4): 1 l-l 2.

4

Wadsworth, Frank H. 1960. Datos de crecimiento de

plantaciones forestales en Mexico, lndias Occidentales y Centro y Sur America. Caribbean Forester.

21 (Supplement): l-200.

Ward, Tom; Charles, Gabriel L. 1982. Preliminary results

from St. Lucia blue mahoe. In: Forestry In the

Caribbean: Proceedings of the First Workshop of

Caribbean Foresters; 1982 May 24-28; Castries; St.

Lucia: Washington, DC: U.S. Man and The Biosphere

Program. 121-l 29.

Weaver, Peter L.; Francis, John K. 1988. Performance of

Hibiscus e/a&s in Puerto Rico. Commonwealth

Forestry Review. 67(4): 325-338.

Weaver, Peter L.; Lugo, A. E. 1981. Forestry in St. Lucia.

Rio Piedras, PR: U.S. Department of Agriculture,

Forest Service, Southern Forest Experiment Station,

Institute of Tropical Forestry. 64 p.

Whitesell, C. D.; Walter, G. A. 1976. Species adaptability

trials for man-made forests in Hawaii. Res. Pap. PSW118. Honolulu, HI: U.S. Department of Agriculture,

Forest Service, Pacific Southwest Forest and Range

Experiment Station. 30 p.