## 6 Hydrolplane and Propulsion System Design
The coefficients are obtained adopting the following definitions:  
\[C_{L}=\frac{2F_{L}}{\rho U^{2}S},\ C_{D}=\frac{2F_{D}}{\rho U^{2}S} \tag{2}\]  
where \(\rho\) is the density of the water, \(U\) is the velocity of the robot, and \(S\) is the area of the hydrofoil equal to 0.36 m\({}^{2}\). Figure 9: Selected wing section. The results are reported in Figure 12 where \(C_{L}\) and \(C_{D}\) are plotted with the angle of attack ranging from 0 to 10 degrees for the free wing (diamond marker) and for the aft (round marker) and stern (cross marker) hydrofoil when they are located inside the vehicle. In the case of \(C_{L}\), the behavior of the aft hydrofoil is similar to the free flow configuration, while the stern rudder is less loaded. On the other hand, the value of \(C_{D}\) is close to 0 in the three cases and is higher for the aft hydrofoil. Figure 11: Mesh for fluid-dynamic simulations. (**a**) Whole vehicle in longitudinal cross section view (angle of attack: 10\({}^{\circ}\)). (**b**) Airfoil. Figure 10: Simplified model for fluid-dynamic analysis (angle of attack: 10\({}^{\circ}\)). (**a**) Isometric view. (**b**) Frontal view. (**c**) Lateral cross section view. The second part of the analysis is focused on the evaluation of the forces exerted on the whole vehicle. The results of the simulations are reported in Figure 13, where the lift (diamond marker), drag (round marker) and total resulting force (cross marker) are plotted with a velocity ranging from 1 to 5 m/s and in three cases of angle of attack: 0\({}^{\circ}\) (a), 5\({}^{\circ}\) (b), and 10\({}^{\circ}\) (c). The distribution of the pressure on the vehicle and on the cut-plot at the longitudinal symmetry plane is illustrated in Figure 14 in the case of 5 m/s and angle of attack equal to 10\({}^{\circ}\). It is evident that the pressure is more intense on the front part of the vehicle and it is confirmed that the stern hydrofoil is remarkably less loaded than the aft one. Figure 12: Lift (**a**) and drag (**b**) coefficients computed on the free wing (diamond marker), on the aft (round marker) and stern hydrofoil (cross marker). Figure 7:0 Resulting force. (**a**) Angle of attack: 0\({}^{\circ}\). (**b**) Angle of attack: 5\({}^{\circ}\). (**c**) Angle of attack: 10\({}^{\circ}\). Round marker: drag force. Diamond marker: lift force. Cross marker: total resulting force. The selected motors for the propulsion of the robot are two electric thrusters with nominal thrust \(F_{MAX}\) equal to 1650 N (nominal power: 1.5 kW, DC Voltage: 48 V, weight: 7.5 kg), the maximum propulsion force is thus equal to 3300 N. Therefore, the maximum velocity of 5 m/s can be reached when the angle of attack is 0\({}^{\circ}\). Increasing the angle of attack to 5\({}^{\circ}\) and 10\({}^{\circ}\), the velocity reduces to 4 m/s and 3.7 m/s respectively as indicated in Figure 7:1 High values of \(\alpha\) imply the reduction of the velocity but this does not represent a strong limitation since high angles of attack are required mainly during diving and emerging operations, thus at low velocity. Considering the characteristics of the propellers and a minimum time of 15 min for rescuing operations, the required capacity of the batteries to supply the electric motors is obtained by  
Figure 7:2  
where \(C_{BM}\) is the capacity of the battery in Ah required by the electric thrusters, \(P\) is the power of the electric loads in W, \(t\) is the working time in h, and \(V\) is the supply voltage in V. A further amount of energy has to be provided for hydroplane actuation \(C_{BH}\) (460 Wh at 48 V), the communication \(C_{BCom}\) (30 Wh at 24 V obtained and stabilized with a converter from eight series cells of the battery pack) and the control system \(C_{BContr}\) (6 Wh at 12 V obtained and stabilized with a converter from four series cells of the battery pack). Considering a safety factor of 1.25, the resulting total value of the battery capacity is  
Figure 7:3  
LiFePo04 is the selected battery technology.