# Impact of Wind on the Movement of the Load Carried by Rotary Crane
## 4 Results and Discussion
### Movement of the Load as a Mathematical Pendulum  
In the case where a telescopic boom remains stationary, three movement variants were considered with various initial conditions. In all cases, the load sway lasted 20 s. The influence of the variable area inclusion on which wind force had an impact on the calculations was also checked in the simulation. The sample results of numerical simulations were presented in the form of a trajectory of the load suspension--point \(P\)--and its center of mass \(O_{3}\), as marked in Figure 2. The values of wind power acting on the load were also determined. The first variant pertained to load motion in only one plane, and the initial conditions were as follows:  
\[\left.\xi(t)\right|_{t=0}=0.5\;\mathrm{m},\quad\left.\dot{\xi}(t)\right|_{t=0} =0,\quad\left.\eta(t)\right|_{t=0}=0,\quad\left.\dot{\eta}(t)\right|_{t=0}=0, \quad\left.\dot{\zeta}(t)\right|_{t=0}=4.97494\;\mathrm{m},\quad\left.\dot{ \zeta}(t)\right|_{t=0}=0.\]  
Based on the obtained results (Figures 3-6), it can be stated that in one plane motion, the parameter of the variability of surface area influenced by wind power has a negligible effect on the trajectory \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Load Mass**} & \multirow{2}{*}{**Cable Length**} & \multirow{2}{*}{**Load Dimensions**} & \multirow{2}{*}{**Aerodynamic Resistance**} & \multirow{2}{*}{**Wind Velocity**} \\  & & & & **Coefficient** & \\ \hline \multirow{3}{*}{7000 kg} & \multirow{3}{*}{5 m} & a = 3.5 m & & 0 m/s \\  & & b = 1.5 m & & 10 m/s \\ \cline{1-1}  & & c = 2.0 m & & 20 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the calculation model. Figure 2: Forces acting on the load during the work cycle. In the second case, the rotational motion of the pendulum was analyzed by adopting the following initial conditions:  
\[\xi(t)\big{|}_{t=0}=0.5\;\text{m},\quad\dot{\xi}(t)\big{|}_{t=0}=0,\quad\eta(t) \big{|}_{t=0}=0,\quad\dot{\eta}(t)\big{|}_{t=0}=0.702119\;\text{m/s},\;\zeta(t) \big{|}_{t=0}=4.97494\;\text{m},\quad\dot{\zeta}(t)\big{|}_{t=0}=0.\]  
Based on obtained results for rotational motion (Figures 8-11), it can be noticed that the parameter of surface area variability, on which wind power impacts, has a strong effect on the analyzed points trajectory. The difference in the value of wind power for this case reached 200 N for a wind velocity of 10 m/s and 1000 N for 20 m/s (Figure 12). Comparing wind powers as a function of time (Figure 12), similarities in trends can be noticed. Figure 6: Projection of the trajectory of the carried load’s suspension point on one of the lifting planes for (**a**) the variable effective area and (**b**) fixed effective area. Figure 7: Value of the wind impact force with respect to wind velocity equal to (**a**) 10 m/s and (**b**) 20 m/s (continuous line—fixed area, dotted line—variable area). Figure 8: Projection of the trajectory of the carried load’s suspension point on the rotation plane for (**a**) the variable effective area and (**b**) fixed effective area. Figure 10: Projection of the trajectory of the carried load’s suspension point on the rotation plane for (**a**) the variable effective area and (**b**) fixed effective area. Figure 9: Projection of the trajectory of the carried load’s suspension point on one of the lifting planes for (**a**) the variable effective area and (**b**) fixed effective area. The final variant that was analyzed concerning the stationary boom depicts the spatial motion of the load:  
\[\xi(t)\big{|}_{t=0}=1\,\mathrm{m},\quad\dot{\xi}(t)\big{|}_{t=0}=0,\,\eta(t) \big{|}_{t=0}=0,\quad\dot{\eta}(t)\big{|}_{t=0}=2.83016\mathrm{m/s},\,\zeta(t) \big{|}_{t=0}=4.89898\,\mathrm{m},\quad\dot{\zeta}(t)\big{|}_{t=0}=0.\]  
Considering the results achieved with spatial motion (Figures 13-16), the criterion of surface area variability on which wind power acted affects the trajectory of analyzed points. The different values of wind power for this variant have reached 300 N for a wind velocity of 10 m/s and 1200 N for 20 m/s.