## 2 Materials and Methods
### Experimental Setup  
In order to compare the phenomena acting on model M on a much smaller scale in an aerodynamic tunnel (sectional models of the tower and jib) and the real object N (parts of the tower and jib), the appropriate scales of the investigated phenomena should be satisfied. The appropriate dimensions and parameters, such as velocity V\({}_{0}\), characteristic length L\({}_{0}\) and density \(\rho\), were chosen. Only three parameters were considered for scaling \begin{table}
\begin{tabular}{l c} \hline \hline
**Technical Data** & **Value** \\ \hline Maximum permissible lifting capacity (kg) & 1750 \\ Range of crane rotation angle around its own axis (\({}^{\circ}\)) & 360 \\ Distance between end point of the jib and the axis of rotation (m) & 35 \\ Maximum lifting angle of the entire jib (\({}^{\circ}\)) & 30 \\ Maximum lifting angle of the second part of the jib (\({}^{\circ}\)) & 45 \\ Total height of the tower crane (m) & 34.6 \\ Spacing of the stationary supports (m) & 4.4 \\ Total distance between the mobile platform and the axis of rotation (m) & 3.6 \\ Distance between the rope immobilizing the jib to the axis of rotation (m) & 1.85 \\ Height of the entire tower with chassis and stationary supports (m) & 31 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The technical parameters of the fast-erecting Turmdrehkran 63K crane. Figure 1: Fast-erecting Turmdrehkran 63K crane by Liebherr. (1) Stationary support, (2) tower crane chassis, (3) movable platform, (4) lifting mechanism, (5) rotation mechanism, (6) switch cabinet, (7) counterweight, (8) rope immobilizing the horizontal jib, (9) lower part of the tower, (10) upper part of the tower, (11) auxiliary drive, (12) lifting winch, (13), trolley-driving mechanism, (14) rear lashing, (15) guy support I, (16) crane jib—lashing rope II, (17) crane jib—lashing rope III, (18) crane jib—lashing rope I, (19) lifting rope, (20) jib—articulated element, (21) jib—assembly rope, (22) guy support II—head, (23) jib extension, (24) jib extension, (25) jib extension, (26) hook (2/4 strand). The dimensions of the crane are listed in Table 1.  
parameters; because of mechanical problems, only three quantities could be chosen to be dimension-independent, and the others should fulfill the appropriate relationships. Taking into consideration the spatial dimensions of the aerodynamic tunnel, the model scale was equal to 1:7. Next, the other scales were estimated for both sectional models, i.e., the tower and jib. The determined scales are listed in Table 2.  
There are only three independent scales. However, in this work, there were six scales. Therefore, the following criteria will not be fulfilled:  
* [PERSON]'s similarity criterion: \[\left(\frac{f_{0}L_{0}}{V_{0}}\right)_{M}=\left(\frac{f_{0}L_{0}}{V_{0}}\right) _{N},\] (1) where L0 is the characteristic dimension (e.g., the lateral dimension of the flowing body by the air), V0 is the characteristic velocity (e.g., the velocity of the non-disturbed airflow before a body), and f0 is the frequency. The frequency scale for all considered frequencies is equal to \[k_{f}=\frac{1}{k_{t}}=k_{V}{k_{L}}^{-1}=7,\] (2)  
It should be mentioned that this is the only criterion that can be satisfied under the assumed scales of the dimensions (if the subject of the investigations in the aerodynamic tunnel is the aeroelastic model). For the rigid models, this criterion is not fulfilled. In our work, the studied models are rigid, openwork structures made of structural steel. * [PERSON]'s similarity condition: \[k_{Re}=\frac{(Re)_{M}}{(Re)_{N}}=k_{\
u}k_{L}={k_{L}}^{3/2}\
eq 1,\] (3)  
The above discussion shows that in reality, the satisfaction of all the similarity conditions is not possible.