2.2 Motion Control System
Pitching motion of the boat is controlled by changing attack angle of the fore foil using ultrasonic sensing system. The ultrasonic sensor installed at the stem of the boat measures the distance between water surface and the sensor. A microcomputer board (V25 CPU) processes this signal and outputs command for the stepping motor, which adjusts directly the attack angle of the fore foil. The PID control method is employed for the computer program. The pitching motion control system is shown in Figure 3.
On the other hand, for the rolling motion, the boat has no automatic control system. Therefore, the crew maintains lateral stability by controlling rudder angle and shifting his weight in the cockpit just such as controlling a bicycle. Figure 4 shows the boat at foil born cruising.
2.3 Measurement System
The attitude angles of the boat are measured by using inertia sensor of optical-fiber gyroscope. Moreover, the outputs of three ultrasonic sensors, installed at the stem and both sides of the stern, are used as assistance. The boat speed is measured with a paddle-wheel speedometer attached to the bottom of the main strut. Rudder angle is measured using a potentiometer. In order to take lateral balance of the boat, the crew inclines his body laterally in the cockpit. A VR sensor attached on the crew chest measures his incline angle. Trajectory of the boat is measured by using GPS. All these outputs are taken into a data logger, which works as an A/D converter and transfers the data to a personal computer. However, the data of VR sensor and GPS are not taken directly into the data logger. Therefore, these data are combined off-line with others by synchronizing recorded time. The measurement system is shown in Figure 5.
Fig.5 Block diagram of measurement system
3. NUMERICAL SIMULATION
3.1 Hydrodynamic Forces Acting on Hydrofoils and Struts
The coordinate system for the numerical simulation is the body axes system as shown in Figure 6. Suppose the coordinates of the acting point of hydrodynamic forces on the hydrofoils and struts in the body axes are (xi, yi, zi), where the suffix i means each part of hydrofoils and struts. When the boat moves with velocities U, V and W, angular velocities P, Q and R, the velocities at the acting points expressed in the body axes are described as follows:
Ui = U + Qzi - Ryi
Vi = V + Rxi - Pzi (1)
Wi = W + Pyi - Qxi
The acting points move with these velocities in still water. Then the attack angle in x-z plane ζi and leeway angle βi are obtained as follows:
Fig.6 Coordinate of body axes system
The hydrodynamic coefficients of hydrofoils and struts, CLi and CDi, are determined as the function of submerged depth, aspect ratio and attack angle derived from Equation (2). Then the hydrodynamic forces, Li and Di, are calculated as follows:
where Si means wing area of hydrofoil or strut. The components of these forces act in the direction of the flow axes, which is defined using angles of ζi and βi. Therefore we have to transform these forces to the body axes as follows:
where Γi means dihedral angle, and for the horizontal hydrofoils Γ = 0° and for the struts Γ = -90°.