## Appendix A.3. External Loads
### Hydrodynamic Pressure  
The wave pressure, \(P_{w}\), for OSA-1 load cases at any load point can be obtained from the following equation.  
\[P_{w}=\left\{\begin{array}{l}max(P_{OSA},\rho g(z-T_{LC}))\;\;for\;z\leq T_{ LC}\\ P_{W,WL}-\rho g(z-T_{LC})\;\;for\;T_{LC}<z\leq h_{W}+T_{LC}\\ 0\;\;for\;z>h_{W}+T_{LC}\end{array}\right.\] (A5)  
where  
\(P_{OSA}\;=0.81f_{corr}f_{nl}k_{a}k_{p}f_{yz}C_{w}\sqrt{\frac{L_{0}+\lambda-1 25}{L}}(1+0.5f_{T})\);  
\(\lambda\) = wave length of the dynamic load case, to be taken as: \(\lambda=0.7L\);  
\(L\) = rule length;  
\(L_{0}\) = rule length, but not to be taken less than 110 m;  
\(f_{T}\) = ratio between draught at a loading condition and scantling draught, shall be taken as: \(f_{T}=\frac{T_{LC}}{T_{SC}}\), but shall not be taken less than 0.5 and not more than 1.0;  
\(T_{SC}\) = scantling draught;  
\(f_{corr}\) = fullness and draft correction factor, to be taken as:  
\(f_{ml}\) = coefficient considering non-linear effect, to be taken as:  
\(f_{nl}\) = \(\left\{\begin{array}{l}0.5\;at\;f_{xL}=0\\ 0.8\;at\;f_{xL}=0.3\\ 0.8\;at\;f_{xL}=0.7\\ 0.6\;at\;f_{xL}=1\end{array}\right.\)  
\(f_{xL}\) = ratio between the X coordinate of the load point and L, to be taken as:  
\(f_{xL}=\frac{x}{L}\), but shall not be taken less than 0.0 or greater than 1.0;  
\(\alpha\) = parameter, in deg.  
\[\alpha=\frac{25T_{LC}}{L}.\frac{180}{\pi}\]  
\(C_{B}=\) block coefficient at draught \(T_{SC}\);  
\(f_{yz}=\) girth distribution coefficient, to be taken as:  
\[f_{yz}=\left\{\begin{array}{l}0.9\frac{z}{T_{LC}}+0.4f_{yB}+2.2\ for\ y\geq 0 \\ 5.5\frac{z}{T_{LC}}+5.3f_{yB}+2.2\ for\ y<0\end{array}\right.\]  
\(f_{yB}=\) ratio between Y coordinate of the load point and \(B_{x}\), to be taken as:  
\(f_{yB}=\frac{|2y|}{B_{x}}\), but not greater than 1.0;  
\(B_{x}=\) moulded breadth at the waterline at the considered cross-section;  
\(C_{w}=\) wave coefficient, to be taken as:  
\[C_{w}=\left\{\begin{array}{l}0.0856\ for\ L<90\\ 10.75-\left(\frac{300-L}{100}\right)^{1.5}\ for\ 90\leq L<300\\ 10.75\ for\ 300<L\leq 350\\ 10.75-\left(\frac{L-350}{150}\right)^{1.5}\ for\ 350<L\leq 500\end{array}\right.\]  
\(k_{a}=\) amplitude coefficient, to be taken as:  
\(k_{a}=\left\{\begin{array}{l}y\geq 0\left\{\begin{array}{l}1+4(f_{T}-0.75)f _{yB}+1.2f_{yB}\text{cos}\left[90(5f_{xL}-0.75)\right]\ for\ f_{xL}<0.35\\ k_{a2}\ for\ 0.35<f_{xL}\leq 0.65\\ k_{a2}+36(f_{xL}-0.65)^{2}f_{yB}\ for\ f_{xL}\leq 0.65\\ \end{array}\right.\\ \left.y<0\left\{\begin{array}{l}min\{k_{a3};1.05\}\ for\ f_{xL}<0.275\\ min\{k_{a1};1.05\}\ for\ 0.275<f_{xL}\leq 0.7\\ k_{a1}+(1.9f_{T}-2.05)f_{yB}\text{cos}\left[\frac{1800(f_{xL}-0.4)}{0.6} \right]\ for\ f_{xL}\leq 0.7\\ \end{array}\right.\\ \left.k_{a1}=1+0.2(2-f_{T})f_{yB}\text{\left\{sin}\left[180\left(0.5+\frac{f_ {xL}-0.275}{0.425}\right)\right]+0.09\right\}\\ k_{a2}=1+2(f_{T}-0.75)f_{yB}(3.75-5f_{xL})\text{sin}\left[60(10f_{xL}-5) \right]\\ k_{a3}=k_{a1}+(0.3f_{T}-1.15)f_{yB}\text{cos}\left[\frac{180(f_{xL}-0.05)}{ 0.45}\right]\end{array}\right.\end{array}\right.\)  
\(k_{p}=\) phase coefficient, to be taken as:  
\(k_{p}\) shall not be taken less than \(-1.0\) or greater than 1.0.  
\(k_{p}\) for other \(f_{xL}\) shall be linearly interpolated.