Table 2 Fitted taper equations and their corresponding mathematical expression
From: Stem taper function for sweet chestnut (Castanea sativa Mill.) coppice stands in northwest Spain
Model | Expression | ||
|---|---|---|---|
Fang et al. (2000) | \( d={c}_1\sqrt{H^{\left(k-{b}_1\right)/{b}_1}{\left(1-q\right)}^{\left(k-\beta \right)/\beta }{\alpha}_1^{I_1+{I}_2}{\alpha}_2^{I_2}} \) \( {c}_1=\sqrt{\frac{a_0{D}^{a_1}{H}^{a_2-k/{b}_1}}{b_1\left({r}_0-{r}_1\right)+{b}_2\left({r}_1-{\alpha}_1{r}_2\right)+{b}_3{\alpha}_1{r}_2}} \) | ||
\( {r}_0={\left(1-{h}_{\mathrm{stump}}/H\right)}^{k/{b}_1} \) | \( {r}_1={\left(1-{p}_1\right)}^{k/{b}_1} \) | \( {r}_2={\left(1-{p}_2\right)}^{k/{b}_2} \) | |
\( \beta ={b}_1^{1-\left({I}_1+{I}_2\right)}{b}_2^{I_1}{b}_3^{I_2} \) | \( {\alpha}_1={\left(1-{p}_1\right)}^{\frac{\left({b}_2-{b}_1\right)k}{b_1{b}_2}} \) | \( {\alpha}_2={\left(1-{p}_2\right)}^{\frac{\left({b}_3-{b}_2\right)k}{b_2{b}_3}} \) | |
I 1 = 1 if p 1 ≤ q ≤ p 2, 0 in all other cases I 2 = 1 if p 2 < q ≤ 1, 0 in all other cases p 1 = h 1/H y p 2 = h 2/H | |||
Bi (2000) | \( d=D{\left[\frac{\mathrm{lnsin}\left(\frac{\pi }{2}q\right)}{\mathrm{lnsin}\left(\frac{1.3\pi }{2H}\right)}\right]}^{a_1+{a}_2 \sin \left(\frac{\pi }{2}q\right)+{a}_3 \cos \left(\frac{3\pi }{2}q\right)+\frac{a_4 \sin \left(\frac{\pi }{2}q\right)}{q}+{a}_5D+{a}_6q\sqrt{D}+{a}_7q\sqrt{H}} \) | ||
Kozak (2004) | \( d={a}_0{D}^{a_1}{H}^{a_2}{X}^{b_1{q}^4+{b}_2\left(1/{e}^{D/H}\right)+{b}_3{x}^{0.1}+{b}_5{H}^w+{b}_6x} \) | ||
Demaerschalk (1972) | \( {d}_i={b}_0{d}^{b_1}{\left(h-{h}_i\right)}^{b_2}{h}^{b_3} \) | ||
Thomas and Parresol (1991) | \( {\left(\frac{d_i}{d}\right)}^2={b}_1\left(q-1\right)+{b}_2 \sin \left({b}_4\pi q\right)+{b}_3\mathrm{cotan}\left(\frac{\pi q}{2}\right) \) | ||