## 2 Small-Scale Compound Helicopter (SCH) Illustration
### General Helicopter Components  
The FORZA 700 helicopter was used as the main component in SCH prototype model. This version is an electric type, motor powered. It does not have a stabilizer bar. To obtain all of the parameters needed for analysis, five steps can be used: direct measurement, ground experiment, aerodynamic coefficient gathering, flight testing and fine-tuning [20]. Now the first two steps will be expanded.  
The size parameters were directly measured and the blade moment of inertia was calculated. The center of gravity (CG) was measured using the suspension method. High-quality photos were captured at each suspension position and the intersection point (CG) of the suspension lines was found by photo post-processing. The measured parameters are shown in Table 1:  
Figure 1: Small-scale compound helicopter (SCH) prototype model. (**a**) Configuration D; (**b**) Configuration WD. (In the Figures: (1) Main rotor; (2) Tail rotor; (3) Onboard computer; (4) GPS antenna; (5) Main batteries (\(\times 2\)); (6) Ducted fan batteries (\(\times 2\)); (7) Ducted fan; (8) Wings).  
Figure 2: Diagram of SCH Configuration WDH. (**a**) Top view; (**b**) Side view.  
The swashplate of the helicopter was controlled by three servo actuators. The fourth servo controlled the tail rotor. \(\theta_{0}\), \(\theta_{1c}\) and \(\theta_{1s}\) (deg) are the main rotor pitch components, which represent collective pitch, lateral cyclic pitch and longitudinal cyclic pitch, respectively. \(\theta_{T}\) (deg) is the tail rotor collective pitch. The four control angles can be decided based on the pitch linkage and swashplate geometry as below:  
\[\left\{\begin{array}{c}\theta_{0}=K_{1}\Big{(}\frac{\theta_{A1}+\theta_{A2} +\theta_{A2}}{3}\Big{)}+\theta_{00}\\ \theta_{1c}=K_{2}\Big{(}\frac{\theta_{A1}-\theta_{A2}}{2}\Big{)}+\theta_{1c0} \\ \theta_{1s}=K_{3}\Big{(}\frac{\theta_{A1}+\theta_{A2}}{3}-\frac{2\theta_{A2}}{ 3}\Big{)}+\theta_{1s0}\\ \theta_{T}=K_{4}\theta_{A4}+\theta_{\text{T0}}\end{array}\right. \tag{1}\]  
where \((\theta_{00},\theta_{1c0},\theta_{1s0},\theta_{\text{T0}})\) correspond to the mid-point of the pitch angle ranges; \((\theta_{A1},\theta_{A2},\theta_{A2},\theta_{A2})\) are the control signals of the four servo actuators (normalized to [\(-\)0.5,0.5]). The three swashplate actuators are equispaced as shown in Figure 3. All the linkage gains can be obtained by identification tests on the ground, shown in Table 2. After \((\theta_{0},\theta_{1c},\theta_{1s},\theta_{T})\) were obtained, the variables were normalized to [\(-\)0.5,0.5], marked as \(\Big{(}\delta_{col},\delta_{lat},\delta_{lon},\delta_{ped}\Big{)}\), respectively denoting collective, lateral cyclic, longitudinal cyclic and pedal control inputs.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Meaning** \\ \hline \(l_{\text{mr}}\) & 0.0715 kg \(\cdot\) m\({}^{2}\) & Main rotor blade moment of inertia related to the hub \\ \(R_{\text{mr}}\) & 0.767 m & Main rotor disc radius \\ \(R_{tr}\) & 0.137 m & Tail rotor disc radius \\ \(c_{mr}\) & 0.065 m & Main rotor blade chord length \\ \(c_{tr}\) & 0.031 m & Tail rotor blade chord length \\ \(l_{f}\) & 1.332 m & Airframe length \\ \(D_{tr}\) & 0.963 m & Tail rotor hub location behind the CG \\ \(H_{tr}\) & 0.025 m & Tail rotor hub location above the CG \\ \(H_{mr}\) & 0.214 m & Main rotor hub location above the CG \\ \(g\) & 9.8015 N \(\cdot\) kg\({}^{-1}\) & Acceleration due to gravity \\ \(\rho\) & 1.225 kg/m\({}^{3}\) & Air density \\ \(\Omega_{mr}\) & 1700 rpm & Main rotor rotation speed \\ \(\Omega_{tr}\) & 360.2 rpm & Tail rotor rotation speed \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters from direct measurement.  
Figure 3: Swashplate structure.