## 5 Process of Optimal Foil Width Determination and Results
### Results TP1
#### 5.1.3 Determination of the Optimal Foil Width for TP1  
In order to determine the optimum width, it is necessary to determine the limit value of \(U_{\text{Slimit}}\). Although this is not the subject of this article, the method for its determination is briefly outlined. Figure 16: Functions F1 to F5, determined on the basis of _fw_ being 2, 5, and 8 m.  
Figure 17: Functions F1 to F5, determined on the basis of _fw_ being 2, 6, and 8 m.  
The basis for the calculation of \(U_{\rm{Slimit}}\) was the SIST EN 50341-1 Standard (overhead power lines for alternating voltages above 1 kV--Part 1) [1] and depends on the specific resistance of the upper layer. The shutdown time is 100 ms, and based on this, the current through the human body is determined, which is IB = 750 mA. According to the SIST EN 50341-2-21:2023 Standard, the permissible touch voltage is UTP = 654 V at a frequency of 50 Hz, which drives an IB current through a body with an impedance of \(\rm{ZB}=\rm{UTP}/\rm{IB}=872~{}\Omega\). This voltage is set for the case wherein a person stands barefoot on the floor without any action. For this fault shutdown time, \(\rm{UTP}(t_{F}=0.1~{}{\rm s})=654\) V. If the top layer of the earth has a specific resistance, this contact voltage will be higher. According to the Standard, the limit voltage of the touch can be determined according to Equation (27). \[U_{\rm{D}}(t_{F}=0.1~{}{\rm s})=U_{\rm{TP}}(t_{F}=0.1~{}{\rm s})\cdot\left(1+ \frac{R_{\rm{a}}}{Z_{\rm{B}}}\right)\left[{\rm V}\right] \tag{27}\]  
whereby the resistance of \(R_{\rm{a}}\) depends on the specificity of the upper layer of the earth and the resistance of the footwear. It is calculated according to Equation (28). \[R_{\rm{a}}=R_{\rm{a1}}+1.5\cdot\rho_{\rm{layer,1}}\left[\Omega\right] \tag{28}\]  
UD1 is selected from the standard curve. To sum up, we are standing barefoot on the ground, which means that the resistance of the shoes is \(R_{\rm{a1}}=0~{}\Omega\). The specific resistance of the upper layer is obtained in Table 3. Thus, the resistance of the earth and the shoe, \(R_{\rm{a}}\), can be calculated using Equation (29). \[R_{\rm{a}}=0+1.5\times 45.5=68.25~{}\Omega \tag{29}\]  
According to Equation (27), we can calculate the contact voltage above the ground with the given specific resistance written in (30). \[U_{\rm{D}}(t_{\rm{F}}=0.1~{}{\rm s})=654\cdot\left(1+\frac{65.25}{872}\right) =705~{}{\rm V} \tag{30}\]  
We assume that the limit value of the step voltage \(U_{\rm{Slimit}}\) is equal to the limit value of the touch voltage \(U_{\rm{D}}\) written in (30), which is the worst case. The optimum value of the foil width \(fw_{\rm{optimal}}\) can be determined using the selected function F4 by expressing \(fw\) and inserting \(U_{\rm{Slimit}}\) for \(U_{\rm{Smax}}\) written in (31). \[fw_{\rm{optimal}}=\frac{a}{U_{\rm{Slimit}}-c}-b \tag{31}\]  
The calculated \(fw_{\rm{optimal}}\) using (31) and parameters \(a\), \(b\), and \(c\) for F4 from Table 13 are presented in Table 15.  
Based on Table 15, it can be seen that the difference between the calculated values based on different \(fw\) values was less than 5%. If we take into account some reserve, we could choose 6 m as the optimal \(fw_{\rm{optimal}}\). The step voltage for \(fw=6\) m is shown in Figure 12c in Section 5.1, and the \(U_{\rm{Smax}}\) was 683.6V, which is less than the \(U_{\rm{Slimit}}\), which was 705 V. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Function F4**} & \multicolumn{3}{c}{**Used Foil Width for Parameter Determination**} \\ \cline{2-4}  & **2 m, 4 m, 8 m** & **2 m, 5 m, 8 m** & **2 m, 6 m, 8 m** \\ \hline \(fw_{\rm{optimal}}\) (m) & 5.58 & 5.68 & 5.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 15: The calculated \(fw_{\rm{optimal}}\) for different used foil width. The \(U_{\text{Smax}}\) was changed in the case of the depth of burial of the protective foil.