## 3 Discussion  
In the second half of the 20 th century, experimental research began on actual models of spherical shells. These studies were conducted at several independent research centers on shells composed of different types of material with different geometries. The results of the experimental studies made it possible to verify the correctness of the calculation formulas proposed at the time for determining the buckling capacity of spherical shells. The difference between the results of the experiments and those obtained from the theoretical \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Experimental** & \multicolumn{5}{c}{**Experimental/Prediction**} \\ \hline  & \(P_{\text{c},\,Exp}\) [MPa] & **Num** & **DNV** & **ABS** & **PD 5500** & **B\&M** \\ \hline HS-1 & 5.49 & 0.99 & 0.95 & 1.36 & 1.00 & 1.06 \\ \hline HS-2 & 9.81 & 1.06 & 0.94 & 1.31 & 0.97 & 1.03 \\ \hline HS-3 & 3.10 & 1.02 & 0.92 & 1.31 & 0.97 & 0.99 \\ \hline HS-4 & 4.30 & 0.92 & 0.89 & 1.28 & 0.94 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the test and prediction results. Figure 15: Schematic of the test stand and view of the two pressure chambers. approach also became apparent. In order to best reflect the actual behavior of spherical shells, and thus optimize the process of their design, computer techniques began to be increasingly used. Their continuous development has led to a situation in which an engineer can model a spherical shell, declare any of its materials, load it, and then perform any numerical analysis determining its critical, plastic, and ultimate load capacity. This paper compares the formula developed by [PERSON] and [PERSON] [1; 3] for estimating the buckling capacity of spherical shells with the experimental studies conducted in the last 70 years. Historical studies [9; 10; 11; 12] and studies conducted in recent years [6; 7; 8; 13; 14] were deliberately selected. Such a choice demonstrates very well the development of the testing and measurement techniques and, in parallel with them, the development of numerical studies that enable the development of computational formulas, which are increasingly accurate in estimating the actual buckling capacity of spherical shells. Several basic conclusions can be drawn from the comparison of the B&M procedure with the historical studies. Almost all the points corresponding to the various tests are above the buckling capacity curves. Hence, the conclusion is that the developed calculation formulas estimate the buckling capacity safely. In some cases, one receives the impression that they are even very conservative, as in the case of the comparison with the studies of [PERSON] [10]. It should be remembered, however, that the test methods of the time did not enable monitoring the shell loading pressure continuously or the numerical scanning of the surface to determine the exact geometric parameters of the shell. The material used to create the test specimens was also not insignificant. It can be noted that buckling load curves fit better with the results of tests conducted on steel or light alloy specimens rather than PVC. This is certainly related to the possibility of more accurate control of the geometry and easier determination of the material properties of the tested shells. The dynamic development of computer analysis and increasingly advanced and precise testing as well as measurement techniques have led to a situation where a manufactured spherical shell sample is scanned and transferred to a CAD environment at a scale of 1:1, taking into account all the geometric imperfections present on its surface. In such a way, following the numerical analysis, we obtain in most cases quite a high convergence with the experimental results, as shown in [7; 8; 14]. However, in order for an engineer to be able to design spherical shells based on standards using the computational algorithms contained in them to this extent, these algorithms should be developed to take into account as many variables as possible while keeping their use simple.