## 4 Results and Discussion  
The detailed parameters of the compound coaxial rotor used for CFD simulations in this paper are shown in Table 2. Figure 9 shows the schematic diagram of the compound coaxial helicopter.  
The aerodynamic performance of the rotor with different overlapping azimuths of blades is calculated. The calculation status of the different rotor overlapping azimuths of the upper and lower blades is shown in Table 3.  
State 1 shows an instance when the upper and lower blades are overlapped at 0\({}^{\circ}\)(U1) and 180\({}^{\circ}\) (U2) for the upper rotor and 180\({}^{\circ}\)(L1) and 0\({}^{\circ}\) (L2) for the lower rotor or at 90\({}^{\circ}\)(U1) and 270\({}^{\circ}\) (U2) for the upper rotor and 270\({}^{\circ}\)(L1) and 90\({}^{\circ}\) (L2) for the lower rotor. State 2 shows an instance when the upper and lower blades are overlapped at 45\({}^{\circ}\)(U1) and 225\({}^{\circ}\) (U2) for the upper rotor and 225\({}^{\circ}\)(L1) and 45\({}^{\circ}\) (L2) for the lower rotor or at 135\({}^{\circ}\)(U1) and 315\({}^{\circ}\) (U2) for the upper rotor and 315\({}^{\circ}\)(L1) and 135\({}^{\circ}\) (L2) for the lower rotor. where, L1 represents lower rotor blade one, L2 represents lower rotor blade two, U1 represents upper rotor blade one, U2 represents upper rotor blade two.  
The simple moving average (SMA), as a tool, is used to smooth the thrust coefficients curve. When new data is available, old data will be deleted, thus resulting in the average  
\begin{table}
\begin{tabular}{c c} Number of blades (N) & 2 \(\times\) 2 \\ Blade radius (\(R\)) & 1.5 m \\ Plane shape of blade & Sabre \\ Airfoil & NACA0012 \\ Rotor solidity (\(\sigma\)) & 0.09 \\ Undercut (\(R_{cut}\)) & 0.21R \\ Torsion angle & \(-8^{\circ}\) \\ Distance between upper and lower & 0.3 m \\ \end{tabular}
\end{table}
Table 2: Detailed parameters of compound coaxial helicopter rotor.  
\begin{table}
\begin{tabular}{c c c c c} \multirow{2}{*}{**Configuration**} & **Overlapping** & **Rotor Speed** & **Rotor Speed** & **Collective Pitch** \\  & **Azimuth** & **in Hover** & **in Forward** & **\(\Theta\)** \\ State 1 & 0/90/180/270\({}^{\circ}\) & 891 RPM & 365 RPM & 8\({}^{\circ}\) \\ State 2 & 45/135/225/315\({}^{\circ}\) & 891 RPM & 365 RPM & 8\({}^{\circ}\) \\ \end{tabular}
\end{table}
Table 3: Detailed parameters of coaxial helicopter rotor.  
Figure 9: Schematic diagram of the compound coaxial helicopter.  
to move along the time axis. The reason for this situation is that the monitoring results will fluctuate with the passage of physical time, which requires smoothing processing. This process is achieved by calculating the average of \(n\) data points contained in the SMA. By using this method, it will be easier to obtain the calculated results while suppressing the resulting fluctuations. The SMA formula is as follows:  
\[\text{SMA}=\frac{x_{M}+x_{M-1}+x_{M-2}+\cdots+x_{M-(n-1)}}{n}\]  
In this case, \(n\) is 60.  
It can be found from Figures 13-15 that the amplitude and peak values of the total thrust coefficients, total torque coefficients, and total power loads for the upper and lower rotors are consistent in the two states, but the phase difference between the two states is \(90^{\circ}\). After SMA processing, the total thrust coefficients, total torque coefficients, and total power loads in the two states are also very close, indicating that the rotor overlapping azimuth has little effect on the aerodynamic performance of the isolated rotors in hover.