Table 2. Equations of tree height, crown shape, branch size and board strength given with parameterisation sample size and parameter values.

algorithm

equation

number

specification

sample size

a0

a1

a2

a3

a4

height

[m]

7

P = 1,000

866

–4.33

1.27

–4.21

–0.155

P = 2,000

1,579

–0.27

1.29

–2.80

–0.20

P = 4,000

865

2.65

1.34

–2.00

–0.24

crown base height

[m]

8

any

3,599

0.630

–0.944

–0.0122

crown diameter

[m]

9

any

594

0.597

0.0845

0.0340

–0.887

1.25

branch diameter

[mm]

10

any

991

4.78

8.68

1.2

wood density

[kg m–3]

11

any

802

162

39.9

494

–7.11

bending strength

[N mm–2]

12

≤ 20

606

–32.0

0.150

–18.3

0.504

–21.3

> 20

103

–45.0

0.175

–5.43

0

–3.64

wood density 1

[kg m–3]

13

any

802

515

–10.7

2.28

bending strength 1

[N mm–2]

14

any

709

–45.22

0.18

–10.69

0.53

–25.81

1 basic Version

h0 = breast height, const = 1.3 m

P = planting density

= tKAR (BS 4978, 2007)

d = diameter at breast height (DBH) [cm]

= mean cambial age of board

= distance from pith of board cross-sectional centre

dg = quadratic mean stem diameter (QMD) [cm]

= mean ring width of board

= top diameter of log

= branch length

= DEK of biggest branch in board (DIN 4074-1, DIN 2012)