deletions | additions       diff --git a/method.tex b/method.tex  index 18a46f5..398be8f 100644  --- a/method.tex  +++ b/method.tex 
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\boldsymbol{\Omega_1} = \Big\{(x,y,z) \in \boldsymbol{\Omega} : z > S_c \Big\}  \end{equation}  Where \(r_s\) is the radius of the stem (from Equation \ref{eq:slenderness}), \(r_{z_0}\) is the radius of the stem at height \(z_0\) , \(r_{z_1}\) is the radius of the stem at height \(z_1\) and \(g\) is gravity. \(\rho_c\) is the canopy density of \(5.6 kg/m^3\) estimated from data in Beets and Whitehead (1996) at a stocking of 741 stems per hectare. The canopy force due to gravity is only applied to the subdomain \(\boldsymbol{\Omega_1}\) , defined in Equation \ref{eq:)1}, where \(z\) is the vertical coordinate of any point. \(V_1\) s \(\frac{1}{V_s}\)  is needed in order transform the canopy’s gravitational force into a force per unit stem volume. In order to stress the stem a constant wind profile was applied to the canopy. The crown sail area was assumed to be the upper half of an ellipse attached to the stem on the surface Γ 1 (defined by Equation 3.20) a surface subregion of total surface Γ. The common drag model presented in Equation 3.19 has been used previously (Spatz and Bruechert, 2000; Rudnicki et al., 2004; Mayer et al., 1989) and is used to approximate the wind load. It should be noted that more complex models are available (Coutts and Grace, 1995). The drag coefficient ς in Equation 3.16 was produced from data reported by Mayhead (1973), for Scotts pine as no data was available for radiata. The use of the Mayhead (1973) Scotts pine data set has previously been suggested as a suitable substitute (Moore and Gardiner, 2001).