## 3 Results of CFD Simulation  
Figure 8a-c presents the results of the carried-out CFD simulations for different kinds of terrain and geometry configurations of the crane. It should be noted that \(\rm F_{Z}\) aerodynamic force components are one order of magnitude less in comparison with the \(\rm F_{Y}\) components. Therefore, they are not reported here. As can be observed in all investigated cases, the maximum of the \(\rm F_{X}\) component of the aerodynamic force and the overturning moment \(\rm C_{M}\) are observed for the angle \(\rm\Theta\) = 75\({}^{\circ}\). For larger values of the angle \(\rm\Theta\), these values decrease. The value of the \(\rm F_{Y}\) aerodynamic force is one order of magnitude less in comparison with the \(\rm F_{X}\) component. It is worth stressing here that for such defined wind profiles, the greatest values of the aerodynamic forces are obtained for urban terrain and the smallest ones for open terrain. Finally, in Table 3, the aerodynamic force coefficients are collected, which are computed according to Formula (3), where \(\rm\
u_{ref}\) is determined with the use of (1) and (2). \begin{table}
\begin{tabular}{c c c c} \hline
**Cell Size [m]** & **F\({}_{X}\) [N]** & **F\({}_{Y}\) [N]** & **M\({}_{tip}\) [Nm]** & **Number of Iter.** \\ \hline
0.030 & 2227.649 & \(-\)43.411 & 61,278.525 & 91 \\
0.028 & 2221.892 & \(-\)34.000 & 61,043.122 & 87 \\
0.020 & 2196.509 & \(-\)31.652 & 60,187.756 & 51 \\ \hline \end{tabular}
\end{table} 
Table 2: Results of the converged test. Figure 7: The location of the tipping line. Figure 8: The values of aerodynamic forces (**a**) \(\text{F}_{\text{X}}\) component, (**b**) \(\text{F}_{\text{Y}}\) component, (**c**) overturning moment M, estimated concerning the tipping line (Figure 7), for the wind speed \(\text{v}_{\text{g}}=6\) [m/s] measured at 10 m over the ground. From the obtained values of the F\({}_{\rm X}\) and F\({}_{\rm Y}\) forces, the aerodynamic coefficients C\({}_{\rm X}\) and C\({}_{\rm Y}\) were determined, which served as the basis for stability calculations of the 63 K crane. The appropriate values of the aerodynamic force and moment coefficients are determined with the use of the following formulas:  
\[C_{\rm X}=\frac{2F_{\rm X}}{\rho\ v_{ref}^{2}A_{ref}},\ C_{\rm Y}=\frac{2F_{Y}}{ \rho\ v_{ref}^{2}A_{ref}},\ C_{M}=\frac{2M}{\rho\ v_{ref}^{2}A_{ref}B_{ref}} \tag{3}\]  
where A\({}_{\rm ref}\) is the area of the shadow normally projected by the crane lattice members on a plane parallel to the wall; A\({}_{\rm ref}\) = 23.31 m\({}^{2}\); and B\({}_{\rm ref}\) is the conventionally accepted characteristic dimension. In our case, B\({}_{\rm ref}\) is assumed to be equal to the total height of the crane; B\({}_{\rm ref}\) = H\({}_{\rm Z}\). The convergence test is carried out for urban terrain, where v\({}_{\rm ref}\) = 7.0321 m/s. Other parameters are as discussed above. The values of the obtained aerodynamic coefficients are shown in Table 3.  
Validation of Numerical Results Obtained from CFD Simulation with Experimental Results for Sectional Models  
The results of the CFD simulations have been verified by comparing the overturning moments that act on the structure of the tower crane 63 K concerning one of the tipping edges for the two characteristic positions of the tower jib, namely for the angles \(\theta\) = 0\({}^{\circ}\) and \(\theta\) = \(\pm\)90\({}^{\circ}\). As a basis for the verification, it is assumed that the experimental results reported in [36]. These results concern the values of the aerodynamic forces F\({}_{\rm X}\) and F\({}_{\rm Y}\) obtained for the sectional models of the tower truss and jib truss of the tower crane 63 K. With the values of these forces, it is possible to estimate the overturning moment caused by the wind according to the appropriate standard [41]. In the case of standard, the most dangerous position of the crane jib concerning the wind direction is taken into consideration, namely, the jib position is perpendicular to the wind direction \(\theta\) = 90\({}^{\circ}\).