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Official Journal of the Japan Wood Research Society

Table 1 The various regression relationships of the examined properties of oil palm wood, including both linear and nonlinear relationships

From: Property gradients in oil palm trunk (Elaeis guineensis)

Properties

In relationship

with density, ρ (kg/m3)

In relationship

with 1-r/R

In relationship with modulus of elasticity

Linear

Power law

Linear

Power law

Linear

Power law

ρ(kg/m3)

(n = 65)

Equation

\( \rho = - 153(1 - r/R) + 374 \)

\( \rho = 237(1 - r/R)^{ - 0.27} \)

R 2

0.60

0.66

SSE

60,648

47,890

\( {\text{WU}}(\% ) \)

(n = 59)

Equation

\( {\text{WU}} = 3 9 6 9 8\; ( 1 / { }\rho )+ 7 0 \)

\( {\text{WU}} = 9 0 3 4\; ( 1 / { }\rho )^{ 0. 6 7} \)

\( {\text{WU}} = 9 0\; ( 1- r/R )+ 1 5 9 \)

WU = 241(1 - r/R)0.22

R 2

0.50

0.47

0.50

0.49

SSE

32,813

34,727

33,521

33,100

SR(%)

(n = 59)

Equation

\( {\text{SR}} = 0. 0 6\;\rho \, - 4. 8 8 \)

\( {\text{SR}} = 0. 0 0 0 2\;\rho^{ 1. 8 9} \)

\( {\text{SR}} = - 3.96\, (1 - r/R )+ 13.77 \)

\( {\text{SR}} = 8. 6 9 ( 1 { - }r/R )^{{{ - 0} . 2 6}} \)

  

R 2

0.28

0.37

0.04

0.06

SSE

982

1328

1367

1446

MOR(MPa)(n = 65)

Equation

MOR = 0.08ρ - 15.2

\( {\text{MOR}} = 8 \times 10^{ - 7} \rho^{2.82} \)

\( {\text{MOR}} = - 13.51 (1 - r/R )+ 15.66 \)

\( {\text{MOR}} = 4. 0 1 ( 1- r/R )^{ - 0. 8 3} \)

\( {\text{MOR}} = 0. 0 0 6 ( {\text{MOE) }} + 0. 8 2 \)

\( {\text{MOR}} = 0. 0 0 6 4 ( {\text{MOE)}}^{ 1. 0 1} \)

R 2

0.86

0.86

0.62

0.69

0.82

0.81

SSE

162

168

430

376

199

212

MOE(MPa)

(n = 65)

Equation

\( {\text{MOE}} = 1 0. 3 2 { }\rho - 1 8 2 9 \)

\( {\text{MOE}} = 0.002\rho^{2.32} \)

\( {\text{MOE}} = - 153 (1 - r/R )+ 374 \)

\( {\text{MOE}} = 631.5\; (1 - r/R )^{ - 0.71} \)

  

R 2

0.66

0.73

0.48

0.64

SSE

8,127,401

8,344,221

12,597,622

10,336,166

\( \sigma_{//} ( {\text{MPa)}} \)

(n = 63)

Equation

\( \sigma_{ / /} = 0.039\rho - 7.19 \)

\( \sigma_{ / /} = 6 \times 10^{ - 7} \rho^{2.76} \)

\( \sigma_{ / /} = { - }6.86 (1{ - }r/R )+ 8.03 \)

\( \sigma_{ / /} = 2.1 (1 - r/R )^{ - 0.82} \)

\( \sigma_{ / /} = 0.0097 (E_{//} )+ 0.80 \)

\( \sigma_{ / /} = 0.029 (E_{//} )^{0.85} \)

R 2

0.80

0.78

0.63

0.66

0.82

0.82

SSE

55

70

104

84

50.3

48.8

\( E_{//} ( {\text{MPa)}} \)

(n = 63)

Equation

\( E_{ / /} = 3.13\rho - 569.44 \)

\( E_{ / /} = 8 \times 10^{ - 5} \rho^{2.67} \)

\( E_{ / /} { = } - 5 3 4 ( 1- r/R ) { + 644} \)

\( E_{ / /} = 176.9 (1 - r/R )^{ - 0.75} \)

R 2

0.60

0.64

0.44

0.49

SSE

991,353

1,136,873

1,379,713

1,138,552

\( \sigma_{ \bot } ( {\text{MPa)}} \)

(n = 59)

Equation

\( \sigma_{ \bot } = 0.0023\rho - 0.05 \)

\( \sigma_{ \bot } = 0.0036\rho^{0.91} \)

\( \sigma_{ \bot } { = } - 0. 4 4 5 ( 1- r/R ) { + 0} . 9 0 \)

\( \sigma_{ \bot } = 0.53 (1 - r/R )^{ - 0.27} \)

R 2

0.40

0.43

0.42

0.41

SSE

1.53

1.54

1.46

1.23

\( \tau_{//} ( {\text{MPa)}} \)

(n = 118)

Equation

\( \tau_{//} = 0.004\rho + 0.02 \)

\( \tau_{//} = 0.005\rho^{0.94} \)

\( \tau_{//} = - 0.48 (1 - r/R )+ 1.33 \)

\( \tau_{//} = 0.88 (1 - r/R )^{ - 0.22} \)

  

R 2

0.37

0.33

0.18

0.18

SSE

5.81

5.83

7.60

7.27

  1. n = number of the test specimens, SSE is error sum of squares