## 3 Mechanical Design  
This section describes a robust mechanical design for a small autonomous sailboat intended to cross the Atlantic autonomously. To assess navigation ability in a wide range of conditions, the heel angle is predicted as a function of wind speed. Furthermore, the motor control system is described to minimize energy consumption. Finally, the boat fabrication process is summarized. In order to determine the vessel's angle of heel at sea, both the experienced wind and the boat's resistance to heeling must be known. Pilot charts with average monthly wind information are available for the Atlantic ([[https://msi.nga.mil/Publications/APC](https://msi.nga.mil/Publications/APC)]([https://msi.nga.mil/Publications/APC](https://msi.nga.mil/Publications/APC)), accessed on 29 August 2021), outlining the expected range of wind speeds for a given course over a reasonable time frame. However, almost all weather data are taken in freely moving air 10 m off the water surface. The height of the center of the sail plane (\(h_{CE}\)) for the SeaLeon, as drawn in Figure 1b, is only 65.5 cm above the surface. At this height, wind shear reduces the apparent wind from the free air speed. Using the ITTC standard power law [19] or a logarithmic wind shear model [20], the reduction in wind speed can be calculated. At this height, the reduction is reasonably approximated by taking, respectively, either 75 or 68% of the forecast speed. Next, for the modeled hull, the locations of the center of mass (\(CM\)) and center of buoyancy (\(CB\)) were found using SolidWorks for varying heeling angles equal to \(\phi=0,5,10,\cdots 180\). The horizontal distance, or Righting Arm (\(RA\)), between the center of mass and the center of buoyancy (for example, shown in Figure 1a) defines the righting moment along with the mass of the sailboat. The results using a spline fit are shown in Figure 1c. The hull of the final design predicted positive righting moment up to 171 degrees, with very little negative stability. This intersection was interpolated, but was so far beyond operational heeling angles that providing a more accurate estimate was not pursued. Using the calculated reduced wind speed as well as the necessary righting moment in Figure 1c allows the expected angle of heel to be found in Figure 1d. This model uses the area of the sails to obtain the maximum heeling combination for a given wind speed. The relationship between the wind speed and effective pressure used is  
\[P=0.5\rho_{air}V_{w}^{2}C_{SF}, \tag{1}\]  
where \(\rho_{air}\) is the air density, \(V_{w}\) the wind velocity and \(C_{SF}\) the side force coefficient. [PERSON] [21] and the ORC documentation [22] quote a maximum value of \(C_{SF}\) approximately equal to 1.3. Therefore, the relationship between \(U_{10}\), the standard reference wind, in m/s, at 10 m above the sea, and the heel \(\phi\) plotted in Figure 1d is given by:  
\[U_{10}=\left(\frac{100}{h_{CE}^{2}\cos^{7}(\phi)}\right)^{(\frac{1}{\Omega})} \sqrt{\frac{4\Delta\text{RA}}{\rho_{air}\text{SAC}_{SF}(T+2h_{CE})}}. \tag{2}\]  
The term in \(\cos^{7}(\phi)\) is due primarily to the classical aerodynamic assumption that the component in the span direction (i.e., mast direction) has no significant influence on the side force. To a lesser extent, it is due to the variation of the altitude of the sail's center with the heel. As can be seen in Figure 1d, the maximum heel angle remains below \(20^{\circ}\) in winds up to 20 knots and it remains under \(40^{\circ}\) up to 30 knots, which shows good dispositions for ocean voyages. The motor design took into consideration the operating conditions of the sailboat, and considerable power and construction savings were found by disabling the motors, particularly in extreme conditions. For this purpose, a set of clutches was designed into the rudder and sail winch drives. First, a worm gear transmission was used to eliminate static power draw when the position of the rudder or sails was not commanded to change.