## 4 Experiments and Analysis
### Measurement and Evaluation of Parameters of Leading and Trailing Edges  
The leading and trailing edges of the blade studied in this paper are constructed by circular arc, and its mathematical model is as follows:  
\[x^{2}+y^{2}+ax+by+c=0 \tag{6}\]  
where \(a,b,c\) are the model coefficients, which can be solved by the least squares fitting algorithm based on coordinates collected of the leading and trailing edges [27,28]. Then the parameters of leading and trailing edges can be determined by the following equations:  
\[\left\{ \begin{array}{c}x_{0}=-a/2\\ y_{0}=-b/2\\ r=\sqrt{a^{2}+b^{2}-4c}/2\end{array} \right. \tag{7}\]  
where \((x_{0},y_{0})\) are the center coordinates of the leading and trailing edges, and \(r\) is the radius. The test profiles I and II have been measured five times using the method of the a priori planning measurement, and the coordinates collected of blade profiles are used for the accuracy analysis of the leading and trailing edges. Based on the five sets of coordinates collected and the least squares circle fitting algorithm, the parameters and measurement standard deviations of the leading and trailing edges are solved as shown in Table 2. In Table 2, \(R_{q}\) is the leading edge radius, \((x_{1},y_{1})\) are the center coordinates of the leading edge, \(R_{h}\) is the trailing edge radius, \((x_{2},y_{2})\) are the center coordinates of the trailing edge, \(m_{1}\sim m_{5}\) represent five sets of parameters solved of blade edges, \(\mu\) represents the average value of measurements, and \(\sigma\) represents the standard deviation of measurements. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Test Profile I**} & \multicolumn{4}{c}{**Test Profile II**} \\ \cline{2-13}  & \multicolumn{4}{c}{**Leading Edge**} & \multicolumn{4}{c}{**Trailing Edge**} & \multicolumn{4}{c}{**Leading Edge**} & \multicolumn{4}{c}{**Trailing Edge**} \\ \cline{2-13}  & \(R_{q}\) & \(x_{1}\) & \(y_{1}\) & \(R_{h}\) & \(x_{2}\) & \(y_{2}\) & \(R_{q}\) & \(x_{1}\) & \(y_{1}\) & \(R_{h}\) & \(x_{2}\) & \(y_{2}\) \\ \hline \(m_{1}\) & 0.458 & \(-\)48.810 & 10.853 & 0.417 & 7.336 & \(-\)11.585 & 0.537 & \(-\)33.611 & 1.964 & 0.542 & 23.228 & \(-\)5.024 \\ \(m_{2}\) & 0.462 & \(-\)48.805 & 10.852 & 0.416 & 7.339 & \(-\)11.586 & 0.538 & \(-\)33.609 & 1.965 & 0.543 & 23.222 & \(-\)5.024 \\ \(m_{3}\) & 0.456 & \(-\)48.812 & 10.853 & 0.419 & 7.336 & \(-\)11.583 & 0.534 & \(-\)33.616 & 1.967 & 0.541 & 23.229 & \(-\)5.023 \\ \(m_{4}\) & 0.457 & \(-\)48.810 & 10.850 & 0.415 & 7.335 & \(-\)11.587 & 0.534 & \(-\)33.614 & 1.966 & 0.539 & 23.231 & \(-\)5.022 \\ \(m_{5}\) & 0.461 & \(-\)48.806 & 10.853 & 0.418 & 7.335 & \(-\)11.583 & 0.535 & \(-\)33.613 & 1.966 & 0.541 & 23.229 & \(-\)5.027 \\ \(\mu\) & 0.459 & \(-\)48.809 & 10.852 & 0.417 & 7.336 & \(-\)11.585 & 0.536 & \(-\)33.613 & 1.966 & 0.541 & 23.228 & \(-\)5.024 \\ \(\sigma\) & 0.003 & 0.003 & 0.002 & 0.002 & 0.002 & 0.002 & 0.003 & 0.002 & 0.002 & 0.003 & 0.002 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measurement results of the leading and trailing edges (unit: mm). Figure 9: Measurement curves of test profiles. The parameters of blade edges and their statistical uncertainties shown in Table 2 are brought into Equations (11) and (12), then the result of uncertainty evaluation of \(\theta\) is as follows:  
\[\left\{ \begin{array}{l}u_{C}(\theta_{1})=7.016\times 10^{-5}\ \mathrm{deg}\\ u_{C}(\theta_{2})=7.408\times 10^{-5}\ \mathrm{deg}\end{array} \right.