Willow Oak Volume

Forest Service

Southern Forest

Experiment Station

New Orleans,

Louisiana

and Weight Tables

Research Paper

so-1 73

for the Mississippi

September 1981

Delta

0

‘EG,X/KS9

Bryce E. Schlaegel
SUMMARY

A sample of 79 trees from the Mississippi Delta is used to construct volume

and weight tables for willow oak (Quercus phellos L.). By using the allometric

model, D2H (squared diameter at breast height multiplied by total tree height)

can predict volumes and weights of bole wood, bole wood plus bark, and bole

wood plus bark plus limbs. Equations are presented for estimating

merchantable bole volumes and weights at 2-inch intervals to top diameters of 2

to 12 inches. Additional equations are given for estimates using upper bole

diameters at relative heights of 0.25H, 0.33H, and OJOH, which are significant

improvements over the D’H equations.
Willow Oak Volume and Weight Tables for the

Mississippi Delta

Bryce E. Schlaegel

INTRODUCTION

Willow oak (Q. phellos L.) is a common bottom land

species ranging from Long Island to Georgia and from

the Atlantic Coast to eastern Texas (fig. 1). On good

sites, it is a moderately rapid grower reaching heights

over 120 ft and with a dbh (diameter at breast height)

in excess of 3 ft.

intervals for trees 5 inches dbh and larger and at 3-ft

intervals for trees smaller than 5 inches dbh. All limbs

were weighed on 65 of the trees.

In the laboratory, both wood and bark moisture content and specific gravity were determined as follows:

1. Wood and bark were separated with a hammer

and chisel.

In recent years there has been considerable demand

for volume and weight tables for bottom land hardwood species. This paper is the first of a series of six

giving both volume and weight tables for some of the

major bottom land hardwood species. Species analyzed

in later series are Nuttall oak (Q. nuttuZZii Palmer),

overcup oak (Q. lyrata Walt.), sugarberry (Celtis laevigata Willd.), sweetgum (Liquidambar styraciflua L.),

and green ash (Fraxinus pennsylvanica Marsh.).

2. Each component was weighed green.

3. Both wood and bark were soaked in water for at

least an hour to ensure complete swelling.

4. Volumes were obtained by immersion (Heinrichs

and Lassen 1970).

5. Wood and bark were dried in a forced air oven at

105°C for at least 48 hours or until weight loss

was completed.

Wood or bark moisture content =

green weight-ovendrywwjght

ovendry weight

METHODS Specific gravity =

Data were collected from 10 natural bottom land

hardwood stands in Mississippi. Nine of the stands

were uneven-aged, mixed species, and one of the

stands was even-aged and pure.

ovendry wood (bark) weigh&&)

green wood (bark) volume (cm31

Each stand was measured for species composition

and diameter distribution. Chosen for destructive

sampling were 79 trees ranging from 2 to 37 inches

dbh. Both understory and overstory trees were judged

as growing stock with healthy crowns and no visible

signs of disease or decay. When available, three trees

were selected from each diameter class.

Average tree moisture content and specific gravity

were calculated from weighted averages of the disk

values; specific gravity or moisture content of each

disk was weighted by its squared average diameter.

Stump height, height to crown, and total height

were measured on each felled sample tree. One-inch

thick disks were cut from the bole at regular intervals

and sealed in separate polyethylene bags for laboratory determination of moisture content and specific

gravity. The first disk was at stump height and the

remaining disks were from ground to tree top at 5-ft

Taper functions were calculated for each tree both

inside and outside the bark. Cubic foot volumes were

obtained by integrating the taper function to heights

of specific top diameters. Moisture content and specific

gravity were assumed to be uniform along the bole.

Bole green and dry weights were calculated from estimated tree volume and average tree density and moisture.

Allometric regression equations were used to estimate volume, green weight, and dry weight of bole

wood, bole wood plus bark, and bole wood plus bark

plus branches.

Bryce E. Schlaegel is Mensurationist at the Southern Hardwoods Laboratory, maintained at Stoneville, Miss., by the Southern Forest

Experiment Station, Forest Service-USDA, in cooperation with the Mississippi Agricultural and Forestry Experiment Station and the

Southern Hardwood Forest Research Group.

1
Figure l-The range of willow oak is from Long Island to Georgia and from the Atlantic Coast to eastern Texas

RESULTS Individual tree volumes and weights were fitted to

.,. n,. 1. the allometric model: .I. , Characteristics or the trees usea in this stuciv are:

Range

19-111

1.7-37.0

20-124

LN(Y) = LN(a) + b LN(D2H)

where

Average (1)

Age (years) 59

Dbh (in) 15.7

Total height Cft) 76

Wood moisture

content (percent) 80

Bark moisture

content (percent) 67

Wood specific gravity 0.593

Bark specific gravity 0.625

Wood + bark green

density (lblfi?) 66.18

Wood + bark dry

density (lbift”) 37.23

Wood + bark moisture

content (percent) 78

Wood + bark

specific gravity 0.596

2

68-99

45-171

0.499-0.651

0.396-0.989

57.69-69.37

32.17-41.02

66-93

0.515-0.657

Y = the volume or weight variable of interest,

D = tree dbh in inches,

H = total height in feet, and

LN is a natural logarithm;

LN(a) and b are coefficients estimated from the

data.

Estimates of the coefficients LN(a) and b are presented in table 1 for predicting cubic foot volume and

green and dry weight of bole wood, total bole, and total

tree. Additional statistics presented are the component average, fit index (FI), regression standard error

of estimate (S,,,) based on residuals after converting to

actual units, and coefficient of variation (C.V.) of predictions in arithmetic units. Fit index, which is similar

to R2, is used to judge equation efficiency when the

dependent variable has been transformed (Farrar
19781 and is calculated in actual units from the total

and residual sums of squares.’ The fit index and RP are

equal when a simple linear regression analysis is performed on an untransformed dependent variable.

Fit indices range from 0.884 for dry bole bark weight

to 0.978 for bole wood volume. A fit index of 1.0 indicates that predictions can be made without error when

the data are used to fit the model. Coefficients of variation, which are indices of relative precision of prediction, range from 33.0 percent for dry bark weight to

15.2 percent for bole wood volume.

Using measures of individual tree dbh and total

height, estimates can be made for tree volume (table

21, green weight (table 31, and dry weight (table 4) for

bole wood, bole wood plus bark, and for bole wood plus

bark plus limbs.

MERCHANTABLE BOLE ESTIMATES

The merchantable bole is defined as the tree bole

from a 1-ft stump to a specific top diameter, ignoring

limbs. Merchantable bole volume or weight can be

expressed as a proportion of the total bole by a simple

asymptotic model proposed by Stevens (1951):

where

RI = a + P,y” (2)

D = tree dbh outside bark,

RI =ratio of merchantable bole volume or

weight to total bole volume or weight,

where I = top outside bark diameter of

merchantable bole;

Measuring two upper bole diameters at one-fourth

and one-half total height result in greater precision

with bark predictions being more precise than the D2H

model. Improvements over the D2H model range from

53 to 71 percent for bole wood and total bole and from

28 to 31 percent for bark.

01, l3, y = parameters to be estimated from the

data, where

fy = the upper asymptote of the ratio,

l3 = the change in the ratio estimate as D

goes from 0 to infinity, and

y = the factor by which the deviation of the

ratio is reduced from its asymptotic

value by each unit step of D.

For a specific top diameter, the ratio of merchantable bole to total bole is the same for volume, green

weight, dry weight, and inside and outside bark. Moisture and density trends within the bole are ignored.

Table 5 gives the parameter estimates for Model 2

using nonlinear techniques proposed by Stevens

(1951). Intervals are measured by 2-inch top diameters

outside the bark. Volume or weight to any top diameter I is found by multiplying the ratio estimate from

one of the equations in table 5 with the total bole

volume or weight estimate from tables 2, 3, or 4.

V4 = R4 + VT,

Taking additional bole measures means a higher

inventory cost since more time will be spent at each

tree. Much of the inventory cost is in traveling to the

candidate tree. Data presented in this paper allow

total and merchantable bole estimates to be made with

high reliability. Each user has to decide when increased precision is needed and whether the need will

offset the higher cost.

LITERATURE CITED

Farrar, R.M., Jr.

where VT is the total bole volume or weight ofinterest.

1978. Silvicultural implications of the growth response of naturally regenerated even-aged stands

of longleaf pine (Pinus palustris Mill.) to varying

stand age, site quality, and density and certain

stand structure measures. Unpublished Ph.D. dissertation, Univ. Ga., Athens. 132 p.

Heinrichs, J. Frank, and L.E. Lassen.

1970. Improved technique for determining the

volume of irregularly shaped wood blocks. For.

Prod. J. 20(4):24.

Stevens, W.L.

’ FI = { 1 - [Z: (Yi - Pi)~l/ 12: (Yi - P)‘]) 1951. Asymptotic regression. Biometrics 7:247-267.

IMPROVED TOTAL BOLE ESTIMATES

The precision of the merchantable bole estimate depends upon accuracy in measuring total bole. Total

bole estimates can be significantly improved by

measuring one or two additional diameters. Tables 6

and 7 give regression statistics for total bole volume

and weight under two different model forms:

Ln(Y) = Ln(a) + b Ln(D*Dt/,*H)

and

Ln(Y) = Ln(a) + b Ln[(D*Dvz + D’i,b)*H]

where D, H, and Y are defined previously, and Dl/,,

Dv~/,, and Dj/, are diameters measured outside the bark

at one-third, one-half, and one-fourth the total height.

Statistics from tables 6 and 7 show the significant

improvement over the previous D2H equations of table

1. Measuring one additional diameter at one-third the

tree height reduces standard error of estimate, Sy.X, by

32 to 40 percent for bole wood and total bole. Bark

standard errors are reduced but not significantly.

3
Table l-Regression statistics for predicting willow oak tree volumes and weights;’ Ln(Y)=Ln(a) + b Ln(D’H)

Component

Average

Y Ln(a)

Fit

b index

Volume icubic feet)

L

C.V.

percent

Bole wood 54.7 -6.047 0.97301 0.978 8.32 15.2

Bole bark 7.3 -7.026 0.89551 0.913 2.04 27.9

Total bole 62.0 -5.798 0.96166 0.975 10.01 16.1

Total tree 101.0 -5.719 0.98243 0.961 19.01 18.8

Green weight (pounds)

Bole wood 3634 -1.856 0.57354 0.974 610 16.8

Bole bark 464 - 2.903 0.88049 0.907 136 29.4

Total bole 4098 - 1.590 0.96001 0.971 713 17.4

Total tree 6687 -1.546 0.98398 0.949 1460 21.8

Dry weight (pounds)

Bole wood 1991 -2.381 0.96703 0.969 359 18.1

Bole bark 299 -3.870 0.93109 0.884 99 33.0

Total bole 2290 -2.179 0.96142 0.965 435 19.0

Total tree 3728 -2.102 0.98175 0.947 812 21.8

‘All predictions from a l-ft stump to tree tip.

Table 2-Cubic foot volume for willow oak bole wood, bole wood plus bark, and complete trees

Dbh

in

inches

Total height in feet

2 0 3 0 4 0 5 0 6 0 7 0 80 90 100 110 120 130

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ --------.............-.----cubic feet -_--- -----...- _________ _________

0.17l 0.25*

0.2P 0.30

0.243 0.36

0.33

0.40

0.48

0.55

0.66

0.80

0.96

1.15

1.41

0.73 0.90

0.87 1.08

1.07 1.33

1.27 1.58

1.52 1.88

1.88 2.34

1.96 2.44

2.33 2.88

2.91 3.62

2.80 3.48

3.30 4.10

4.16 5.18

3.78 4.69

4.45 5.51

5.63 7.02

4.90 6.08

5.75 7.12

7.33 9.12

6.16 7.65

7.21 8.93

9.23 11.5

1.89

2.24

2.79

2.91 3.38

3.44 3.99

4.33 5.04

4.15 4.82 5.49

4.88 5.66 6.44

6.20 7.21 8.22

5.60 6.51

6.57 7.61

8.39 9.76

7.27 8.44

8.49 9.84

10.9 12.7

9.14 10.6

10.6 12.3

13.7 16.0

7.41 8.31

8.66 9.70

11.1 12.5

9.61 10.8

11.2 12.5

14.5 16.2

12.1 13.6 15.0

14.0 15.7 17.4

18.2 20.5 22.7
Table Z.-Cubic foot volume for willow oak bole wood, bole wood plus bark, and complete trees-Continued

Dbh

in

inches

10

11

12

1 3

14

15

16

17

18

19

20

21

22

23

24

25

26

Total height in feet

20 30 40 50 60 70 80 90 100 110 120 130

9.39

10.9

14.1

11.3

13.1

17.0

13.4

15.5

20.2

15.6

18.1

23.7

18.1

20.9

27.4

20.7

23.9

31.4

23.4

27.0

35.6

__________ cubic feet --.__

11.2 13.0 14.8

13.0 15.1 17.2

16.9 19.7 22.4

13.5 15.7 17.9

15.7 18.2 20.6

20.4 23.7 27.1

16.0 18.6 21.2

18.5 21.5 24.4

24.2 28.2 32.1

18.7 21.7 24.7

21.6 25.0 28.5

28.3 32.9 37.6

21.6 25.1 28.6

24.9 28.9 32.8

32.8 38.1 43.5

24.7 28.7 32.7

28.4 33.0 37.5

37.5 43.6 49.8

28.0 32.5 37.0

32.2 37.3 42.4

42.6 49.5 56.5

31.5 36.6 41.7

36.2 42.0 47.7

48.0 55.8 63.6

35.2 40.9 46.6

40.4 46.8 53.2

53.7 62.5 71.2

39.1 45.4 51.7

44.8 52.0 59.1

59.7 69.5 79.2

43.2 50.2 57.2

49.4 57.3 65.2

66.0 76.8 87.6

47.5 55.2 62.9

54.3 63.0 71.6

72.7 84.5 96.4

52.0 60.4 68.8

59.4 68.9 78.3

79.6 92.6 106

56.7 65.9 75.0

64.7 75.0 8s5.3

86.9 101 115

61.6 71.6 81.5

70.2 81.4 92.6

94.5 110 125

77.5 88.3

88.1 100

119 136

83.7 95.3

95.0 108

129 147

16.6 18.4

19.2 21.3

25.2 27.9

20.0

23.1

30.4

23.7

27.3

36.0

27.7

31.9

42.2

32.0

36.8

48.8

36.6

42.0

55.9

41.5

47.5

63.4

46.7

53.4

71.5

52.2

59.6

79.9

58.0

66.2

88.9

22.2 24.3

25.6 28.0

33.7 37.0

26.3 28.8

30.3 33.2

40.0 43.9

30.7 33.7

35.3 38.7

46.8 51.4

35.5 38.9

40.7 44.6

54.1 59.4

40.6 44.5

46.5 50.9

62.0 68.0

46.0 50.5

t52.6 57.7

70.3 77.3

51.8 56.8

59.1 64.8

79.2 87.0

57.9 63.5

66.0 72.3

88.7 97.4

64.3 70.5

73.2 80.2

98.6 108

64.1

73.0

98.3

70.5

80.2

108

77.2

87.7

119

84.2

95.5

129

91.4

104

141

99.0

112

152

107

121

165

71.0 77.9

80.8 88.6

109 120

78.1 85.7

88.8 97.3

120 132

85.5 93.8

97.1 106

132 144

93.2 102

106 116

144 158

101 111

115 126

156 171

110 120

124 136

169 186

118 130

134 147

183 201

55.0

62.7

84.2

61.8

70.4

94.8

69.1

78.6

106

76.8

87.3

118

84.8

96.3

130

93.3 101

106 114

144 155

102 110

116 125

157 170

111 120

126 136

172 186

121 131

137 148

187 202

131 142

148 160

202 219

141 153

160 172

218 236
Table 2.-Cubic foot volume for willow oak hole wood, bole wood plus bark, and complete trees-Continued

Dbh Total height in feet

in

inches

2 7

2 8

29

3 0

31

3 2

3 3

3 4

3 5

3 6

20 30 40 50 60 70 80

-------------------------------------------------------cubic feet ----

90.0 103

102 116

139 158

96.6 110

110 125

149 170

103 118

117 133

159 182

111 126

125 142

170 194

118 134

133 151

182 207

125 143

142 161

193 221

133 152

150 171

206 234

161

181

248

170

191

263

3 7

3 8

39

4 0

‘Bole wood volume only, from a l-ft stump to tip of tree.

2Bole wood plus bark volume from a l-ft stump to tip of tree.

“Complete tree volume, including branches, from a 1-ft stump to tip of tree.

*Italicized numbers denote limits of the data.

90 100 110 120 130

_.. .__._ _ ___ _____ _ ___ .- _._ _____.

115 127 140 152 164

130 144 158 172 185

177 197 216 235 255

123 137 150 163 176

139 154 169 184 199

190 211 232 253 273

132 146 161 175 189

149 165 181 197 213

204 226 249 271 293

141 156 172 187 202

159 176 193 210 227

218 242 266 289 313

150 167

170 188

233 258

199 215

224 242

309 334

160 177

180 200

248 275

183

206

283

l/95

219

302

212 229

238 257

328 355

170 188 207 225 243

191 212 232 252 272

263 292 320 349 378

180 199 219 238 258

203 224 246 267 289

279 309 340 370 400

191 211 232 252 272

214 237 260 283 305

295 327 360 392 424

201 223 245 266 288

226 250 274 298 322

312 346 380 414 448

212 235 258 281 304

238 264 289 314 340

329 365 401 437 473

224 248 272 296 320

251 278 304 331 357

347 385 423 460 498

235 261 286 311 336

264 292 320 348 376

365 405 445 485 524

247 274 300 327 353

277 307 336 365 395

384 426 468 509 551
Table 3.-Green weight in pounds for willow oak bole wood, bole wood plus bark, and complete trees

Dbh

in

inches 20 30 40

______-_____________-----.

2 11’ 1P 22

l42 20 2 7

163 24 31

3 3 6 4 8

4 4 5 8

5 3 7 0

4 6 4 8 4

7 6 101

93 123

5 130

155

191

6 186

219

273

7 251

295

370

8 325

381

481

9 409

478

607

10

11

12

13

14

15

16

17

1 8

.___ _____ -- _________ ---_- _______ pounds ---- ____ ____________________. -----_-_

Total height in feet

5 0 6 0 7 0 8 0 90 100 110 120

6 0

7 2

8 7

105 125

125 149

153 183

162 193 224

192 228 265

238 284 331

231 275 320 364

272 324 376 427

340 407 474 540

311 372 432 492 552

365 435 505 574 643

461 551 642 732 822

404 482 560 638 716

472 563 652 742 830

599 717 834 952 1069

508 606 705 803 900 997

592 705 818 930 1041 1152

756 904 1052 1200 1347 1494

623 745 865 985 1105 1224

725 864 1001 1138 1275 1410

930 1112 1295 1476 1658 1839

751 896 1042 1186 1330 1474 1617

871 1037 1202 1367 1531 1693 1856

1121 1342 1562 1781 2000 2218 2436

889 1062 1234 1405 1576 1746 1916

1029 1226 1421 1615 1809 2001 2193

1331 1592 1853 2113 2373 2632 2891

1039 1241 1442 1642 1842 2041 2239

1200 1429 1657 1884 2109 2334 2557

1558 1864 2169 2474 2778 3082 3385

1200 1434 1666 1897 2127 2357 2586

1383 1648 1911 2172 2432 2691 2948

1803 2157 2510 2863 3214 3565 3916

1373 1640 1905 2170 2433 2696 2958

1579 1881 2181 2479 2776 3072 3366

2065 2470 2875 3279 3682 4084 4485

1557 1859 2160 2460

1787 2129 2469 2807

2344 2805 t3264 3723

2759

3143

4180

3105

3530

4710

3470

3940

3057 3354 3651

3477 3810 4142

4637 5093 5548

2092 2431 2768

2392 2774 3153

3160 3678 4195

2339 2717 3094

2670 3095 3519

3440 3775 4108

3906 4280 4653

,5225 5738 6251

3845 4219 4592

4359 4777 5193

3537 4116 4694 5271 5847 6421 6995
Table 3.-Green weight in pounds for willow oak bole wood, bole wood plus bark, and complete trees-Continued

Dbh

in

inches

1 9

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Total height in feet

20 30 40 50 60 70 80 90 100 110 120 130

---- -----.....-----......--------......--------.......~~~poun& ____ -.-.--.._______.....______-----...........--

2598 3019 3438 3856 4272 4687 5102

2962 3434 3904 4371 4836 5300 5761

3934 4578 5221 5863 6503 7142 7781

2871 3336 3799 4261 4721 5180 5638

3268 3789 4308 4823 5337 5848 6358

4352 5064 5776 6485 7194 7901 8607

3157 3668 4178 4685 5191 5696 6200 6702

3589 4161 4731 5297 5861 6422 6982 7540

4790 5575 6,358 7139 7919 8697 9475 10251

3456 4016 4574 5129 5683 6236 6787 7337

3924 4550 5173 5792 6408 7022 7634 8244

5249 6109 6967 7823 8678 9fi31 10383 11234

3769 4379 4987 5593 6197 6800 7401 8001

4274 4956 56c34 6308 6979 7648 8314 8978

5729 6668 7604 85738 9471 10402 11332 12261

4095 4758 5418 6076 6733 7t387 8040 8692

4638 5378 6113 6845 7574 8299 9022 9743

6230 7250 8268 9284 10299 11311 12322 13332

5151 5866 6579 7290 7998 8706 9411

5816 6612 7403 8191 8976 9758 10537

7857 8960 10061 11160 12257 13353 14447

5560 6332 7101 7868 8633 9396 10158

6271 7129 7982 8832 9678 10521 11361

8487 9679 10868 12056 13241 14424 15607

5984 6815 7643 8468 9291 10113 10932

6742 7664 8582 9495 10405 11312 12215

9142 10425 11706 12985 14262 15537 16810

6423 7315 8203 9089 9973 10855 11735

7230 8219 9203 10182 11158 12130 13099

9820 11199 12575 13948 15320 16689 18057

6877 7832 8783 9732 10678 11622 12564

7734 8792 9844 10892 11935 12975 14012

10522 11999 13474 14946 16415 17883 19348

7346 8366 9,383 10396 11407 12416 13422

8254 9383 10506 11624 12738 13848 14954

11248 12827 14404 15977 17548 19116 20683

7831 8918 10001 11082 12159 13234 14307

8790 9993 11189 12380 13566 14748 15926

11998 13682 15364 17042 18717 20391 22062

8330 9487 10639 11788 12935 14078 15219

9343 10621 11892 13158 14419 15675 16927

12771 14564 16354 18141 19924 21705 23484

8844 10072 11296 12516 13733 14947 16159

9911 11267 12616 13959 15296 16629 17957

13568 15474 17375 19273 21168 23060 24950

10675 11972 13265 14555 15842 17126

11932 13360 14782 16198 17610 19016

16410 18426 20439 22449 24456 26460

11295 12667 14036 15400 16762 18120

12615 14125 15628 17126 18618 20105

17373 19508 21639 23767 25891 28013
Table 3.-Green weight in pounds for willow oak bole wood, bole wood plus bark, and complete trees-Continued

Dbh Total height in feet

in

inches 20 3 0 4 0 50 60 70 80 90 100 110 120 130

_.._..........__._______________________----------------- pounds _____._.............____________________--.-...

36 13382 14827 16269 17707 19142

14910 16497 18077 19652 21222

20620 22873 25122 27367 29610

37 14115 15639 17160 18677 20191

15715 17388 19054 20714 22368

21763 24140 26513 28883 31250

38 14867 16473 18075 19672 21267

16541 18301 20055 21802 23543

22935 25441 27942 30440 32934

39 15638 17328 19012 20693 22370

17387 19237 21080 22917 24747

24138 26775 29408 32036 34662

40 16429 18204 19973 21739 23500

18253 20195 22130 24058 25980

25371 28143 30910 33673 36432

‘Bole wood weight only, from a l-ft stump to tip of tree.

“Bole weight of wood plus bark from a l-ft stump to tip of tree.

“Complete tree weight, including branches, from a l-ft stump to tip of tree.

“Italicized numbers denote limits of the data.

Total height in feet

60 70 80 90 100 110 120 130

________________ pounds ____________________---------.-----.-.-.....----

20 3 0 4 0 50

_____

6’ 9 ” 13

82 1 1 15

P 13 18

21 27 34

2 5 3 2 40

3 0 4 0 49

3 6 4 8 5 9 71

43 5 6 70 83

52 70 8 7 103

74 91 109 127

87 107 128 148

108 134 160 187

105 130 1.55 180 205

123 153 182 211 240

154 192 229 267 304

141 175 209 243 276 309

166 205 245 284 322 361

209 260 311 361 412 462

183 227 270 314 357 400

214 265 316 367 417 467

271 338 404 470 535 601

Table 4.-Ovendry weight in pounds for willow oak bole wood, bole wood plus bark, and complete trees

Dbh

i n

inches

2

3

4

5

6

7

8
Table 4.-Oven&yweight in pounds for willow oak hole wood, bole wood plus bark, and complete trees-Continued

Dbh

in

inches

9

2 0

____..

10

11

12

13

14

1 5

1 6

1 7

18

19

2 0

2 1

2 2

2 3

2 4

2 5

Total height in feet

30 40 50 60 70 80 90 100 110 120 130

230 285

268 333

342 425

349

407

523

340 394

396 460

509 592

pounds

449

523

675

503 557

585 648

757 840

416 48<3 550 616 683

486 563 640 717 793

626 728 830 932 1033

420 501 581 661 741 821 900

489 583 676 769 861 953 1044

631 754 878 1001 1123 1246 1368

497 593 688 783 877 971 1065

579 689 799 909 1018 1127 1235

748 895 1041 1187 1332 1478 1623

580 692 803 914 1024 1134 1243

675 804 933 1060 1187 1314 1440

876 1047 1218 1389 1559 1729 1899

669 798 927 1054 1182 1308 1435

778 927 1075 1223 1369 Iii15 1661

1013 1211 1409 1607 1803 2000 2196

765 912 1059 1205 1350 1495 1640

889 1059 1228 1396 1563 1730 1896

1160 1387 1614 1840 2065 2290 2515

867 1034 1200 1365 1530 1694 1858 2021

1006 1199 1390 1581 1770 1959 2147 2334

1316 1574 1832 2088 2344 2600 2855 3109

1162 1349 1535 1720 1905 2089 2272

1347 1562 1776 1989 2201 2412 2623

1773 2063 2352 2640 2928 3215 3502

1298 1507 1714 1921 2127 2333 2538

1503 1743 1982 2220 2457 2692 2927

1984 2308 2631 2954 3276 3597 3918

1441 1673 1903 2133 2362 2590 2817

1668 1934 2199 246,3 2726 2987 3248

2206 2567 2926 3285 t3643 4000 4357

1591 1847 2102 2356 2608 2860 3111

1841 2135 2427 2718 3008 3297 3585

2440 2839 3236 3633 4029 4424 4819

1749 2030 2310 2589 2866 3143 3419 3694

2022 2345 2666 2986 3304 3621 3937 4252

2685 3124 3562 3998 4434 4869 5303 5737

1914 2221 2527 28*32 3136 3439 3741 4042

2211 2564 2916 3265 3613 3960 4306 4650

2942 3423 3902 4381 4858 5335 5810 6285

2085 2421 2754 3087 <3418 3748 4077 4405

2408 2793 3176 3557 3936 4313 4690 5065

3210 3735 42,58 4780 5301 5821 6340 6859

2264 2628 2991 3351 3711 4069 4426 4783

2614 3031 3447 3860 42 71 4681 5090 5497

3490 4061 4629 5197 5763 6328 6893 7456

2844 3236 3627 4016 4403 4790 5176

3279 3728 4175 4620 5064 5505 5946

4399 5016 5630 6244 6857 7468 8079

1 0
Table 4.-Ovendry weight in pounds for willow oak bole wood, bole wood plus bark, and complete trees-Continued

Dbh

in

inches

26

27

28

29

30

31

‘I&al height in feet

20 30 40 50 60 70 80 90 100 110 120 130

. .._.................~..~~.~~~~~~~~~~~~~~~~..~ -~----.---~pounds ..-.__-- ________________________________________

3068 3491 3913 4332 4750 5168 5583

3536 4020 4502 4982 5460 5937 6411

4752 5417 6081 6744 7405 8066 8725

3301 3756 4209 4660 5110 5559 6006

3802 4323 4841 5357 5871 6383 6894

5117 5834 6549 7263 7975 8686 9396

3541 4029 4516 5000 5483 5964 6444

4077 4636 5192 5745 6296 6846 7393

5496 6266 7034 7800 8565 9329 10092

3790 4312 4833 5351 5868 6383 6896

4362 4959 5554 6146 6736 7324 7910

5888 6713 7535 8357 9176 9995 10812

4047 4605 5160 5714 6265 6815 7364

4656 5293 5928 6560 7190 7817 8442

6293 7175 8054 8932 9808 10683 11556

4312 4906 5498 6088 6675 7261 7846

4959 5638 6314 6987 7658 8326 8992

6712 7652 8590 9526 10460 11393 12324

32

33

34

35

36

37

38

39

40

4585 5217 5846 6473 7098 7721 8343

5271 5993 6711 7427 8140 8850 9558

7143 8144 9142 10139 11133 12126 13117

4866 5537 6205 6870 7533 8195 8854

5592 6358 7121 7880 8636 9389 10140

7588 8651 9712 10770 11826 12881 13934

5866 6573 7278 7981 8682 9381

6734 7541 8345 9146 9944 10739

9173 10298 11420 12540 13659 14775

6204 6952 7698 8441 9182 9921

7120 7973 8823 9670 10514 11355

9711 10901 12089 13275 14459 15641

7342 8129 8914 9697 10477

8417 9315 10208 11099 11987

11521 12777 14030 15281 16530

7741 8572 9399 10224 11047

8873 9819 10761 11700 12636

12158 13483 14805 16125 17444

8151 9025 9897 10765 11632

9339 10335 11327 12315 13300

12811 14208 15601 16992 18382

8571 9490 10407 11320 12231

9818 10864 11907 12946 13982

13482 14951 16417 17882 19343

9001 9967 10929 11888 12845

10308 11406 12501 13592 14679

14169 15713 17254 18793 20329

‘Bole wood weight only, from a 1-ft stump to tip of tree.

‘Bole weight of wood plus bark from a 1-ft stump to tip of tree.

%omplete tree weight, including branches, from a l-ft stump to tip of tree

*Italicized numbers denote limits of the data.

11
‘Iable 5.-Willow oak ratio parameter estimates for calculating the

proportion of merchantable bole to total bole: RI = t y -t

PY””

Ratio n’ a B Y SYX

R2 62 0.999 - 0.426 0.654 0.00140

R4 62 0.995 - 1.251 0.732 0.00847

R6 61 0.979 -32.613 0.607 0.03062

R8 58 0.970 -- 22.975 0.694 0.03285

RlO 51 0.964 -43.915 0.718 0.04494

R12 44 0.944 -57.668 0.735 0.05016

*RI = (merchantable bole to outside bark diameter Ilitotal bole.

‘n = number ofobservations used to estimate equation parameters.

Table B.-Regression statistics forpredicting willow oak bole uolurnes and weights;’ Ln(Y) = Ln(a) + b Ln(D.D,/,H)

Component Average Ln(a1 b FI %,

C.V.

percent

Volume icubic feeti

Bole wood 54.7 - 5.901

Bole bark 7.3 -7.073

Total bole 62.0 -5.654

0.98709 0.992

0.90868 0.938

0.97561 0.990

Green weight (pounds)

5.03": 9.2

1.73 23.6

6.35* 10.2

Bole wood

Bole bark

Total bole

3634

464

4098

- 1.710

-2.774

-- 1.446

0.98764 0.989

0.89352 0.931

0.97395 0.987

Dry weight ipoundsi

402" 11.1

117 25.2

478" 11.7

Bole wood 1991 -2.235 0.98105 0.986 243”: 12.2

Bole bark 299 -3.733 0.94483 0.915 84 28.2

Total bole 2290 -2.034 0.97539 0.984 297" 13.0

‘All predictions from a I-ft stump to tree tip.

“Significantly more precise than D’H model; O L = 0.05

12
Table ‘I.-Regression statistics forpredicting willow oak bole volumes and weights;’ Ln(Y) = Ln(a) + b Ln[(D.Dvz +

D”,,JHl

Component Average Ln(a)

C.V.

b FI $YX percent

Volume (cubic feet)

Bole wood

Bole bark

Total bole

54.7

7.3

62.0

- 6.545 1.00359 0.998 2.38” 4.4

- 7.672 0.92423 0.959 1.41* 19.3

- 6.291 0.99196 0.998 3.02* 4.9

Green weight (pounds)

Bole wood 3634 - 2.354

Bole bark 464 - 3.364

Total bole 4098 -- 2.083

1.00410 0.995

0.90895 0.953

0.99026 0.995

Dry weight (pounds}

259* 7.1

97’i 20.8

284” 6.9

Bole wood 1991 - 2.875 0.99738 0.993 168* 8.4

Bole bark 299 - 4.356 0.96103 0.940 71-b 23.7

Total bole 2290 - 2.672 0.99169 0.993 191” 8.3

‘All predictions from a l-ft stump to tree tip.

*Significantly more precise than D.D,jz.H model; a = 0.05.

tsignificantly more precise than D”H model; 01 = 0.05.

APPENDIX

Examples of Equation and Table Use

In this section a few examples are given to illustrate

use of the equations and tables presented. The following tabulation presents data for one of the trees used in

constructing the equations; these data are used to

illustrate equation use:

D = 18.0 in

H = 107 ft

DI/, = 14.5 in

Dti3 = 14.1 in

Dl/, = 10.0 in

To calculate bole wood volume from D’H and the

coefficients from table 1:

LnCV) = Ln(a) + b Ln(D’H)

= -6.047 + 0.97301 Ln (180x 18.0x 107)

= -6.047 + 0.97301 Ln (34668)

= -6.047 + 0.97301 (10.454)

= -6.047 + 10.171

Ln(V) = 4.124

v = ,(4.124)

Bole wood volume = 61.8 ft3.

To calculate total bole green weight from X =

D*Dv;H and the coefficients given in table 6:

Ln(W) = Ln(a) + b Ln (D.D1/,*H)

= -1.446 + 0.97395 Ln(18.0x 14.1 x 107)

= -1.446 + 0.97395 Ln(27156.6)

= -1.446 + 0.97395(10.209)

= -1.446 + 9.943

Ln(W1 = 8.497

W = e(8.497)

Total bole green weight = 4,902 lb.

To2 calculate bole bark dry weight using X=(D*D1/,

+ D I/JH and the coefficients of table 7;

Ln(W) = Ln(a) + b Ln[(DxDvz+D I/,)H]

= -4.356 + 0.96103 Ln[(l8.0x 10.0 + 14.5

x 14.5) x 1071

= -4.356 + 0.96103 Ln[(180 + 210.25)

x 1071

= -4.356 + 0.96103 Ln[41756.75]

= -4.356 + 0.96103 (10.640)

= -4.356 + 10.225

Ln(W) = 5.869

13
w = ,(5.869)

Bole bark dry weight = 353.9 lb.

Merchantable bole values to a 6-inch top, for example, are calculated using table 5 to estimate the merchantable proportion of the total bole and then multiplying this proportion by the total bole estimate of

interest:

RI = a + l3.y”

R6 = 0.979 + (-32.613) (0.607)18.0

= 0.979 + (-32.613) (0.00012514)

= 0.979 - 0.00408

R6 = 0.97492.

Then bole wood volume to a 6-inch top can be calculated:

V6 = (R6) (total bole wood volume)

V6 = (0.97492) (61.8)

V6 = 60.3ft3.

And dry bark weight to the 6-inch top is:

W6 = (R6) (total bole dry bark weight)

W6 = (0.97492) (353.9)

W6 = 345 lb.

Total bole volumes or weights can be calculated by any

one of the three sets of coefficients given in tables 1,6,

or 7. Then, any of these total bole calculations can be

used with the ratio estimators to find merchantable

bole values. The choice of equations is left to the user

who must balance inventory precision against inventory cost.

14
SCHLAEGEL, BRYCE E.

1981. Willow oak volume and weight tables for the Mississippi

Delta. U.S. Dep. Agric. For. Serv. Res. Pap. SO-173 14 p.

South. For. Exp. Stn., New Orleans, La.

A sample of trees from the Mississippi Delta is used to construct

volume and weight tables for willow oak.

Additional keywords: Quercus phellos, merchantable bole

estimates, biomass, allometric regression.

*U.S. GOVERNMENT PRINTING OFFICE: 1981--771.081/3