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Nicholas Davies added Restults.tex
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\section{results}
Two stem and crown profiles were investigated. An open grown stem, assumed to have no light competition, at a stocking rate of one stem per hectare and a stem under competition at a stocking rate of 741 stems per hectare. The dimensions of the open grown stem and crown for different ages are available in Table 3.1. Stems grown in the open tend to produce a lower taper and a wider crown which protrudes further to the base of the stem. The open grown stem and crown dimensions are extrapolated from measurements reported by Waghorn et al. (2007a). Table 3.2 presents the stem and crown dimensions used under considerable light competition. These dimensions represent architecture for a stem grown at a stocking rate of 741 stems per hectare. The stocking rate of 741 stems per hectare was chosen as it is the stocking rate used to estimate crown density and it falls within the bounds of the data from Waghorn et al. (2007a).
In order to ensure that the values being presented were realistic Equations 3.22 and 3.21 from Papesch et al. (1997) were solved with h = 15 resulting in a maximum bending moment of 42 M P a at a deflection of 13 degrees. Solving the equations presented in Section 3.2.5 with wind speed ω as the unknown, the wind speed at maximum bending moment (42 M P a) was calculated to be 15.5 m/s. From these equations and the assumption that the maximum bending moment will occur at the lowest wind speed needed to surpass the proportional limit it is seen that at a stocking rate of 741 stems per hectare the FEM model predicts the stem with the radial profile LW →HS will fail at approximately 16 m/s, however the deflection angle is approximately 21 degrees at this point. The radial profiles at a stocking rate of 741 stems per hectare fall on either side of the 13 degree deflection at 15.5 m/s wind speed from Papesch et al. (1997). Open grown stems withstand higher wind speeds, however they break at lower deflection angles than stems at a stocking of 741. Open grown stems also fail at higher and lower wind speeds and deflections than the predictions from Papesch et al. (1997), with the radial profiles performing in a similar order as for the higher stocking rate. If growth stresses are not considered a reduction in the wind speeds to below the predicted value of 15.5 m/s is observed, for both stocking rates. The deflection angle at first failure is also reduced with radial profile LW →HS to approximately 14 degrees (from 21 degrees). Radial profiles fall on either side of the prediction of 13 degrees from Papesch et al. (1997).
