Stability analysis of the equations of motion for the 2014 Delft Solar Boat

The TU Delft Solar Boat is a very efficient boat that sails on solar power. To reduce drag the boat lifts out of the water with the hull and "flies" on two hydrofoils. As a result the boat is likely to fall over and seems to be unstable. To analyse the stability we first made a mathematical model that describes the motion of the boat. Based on this model we calculate numerically whether the boat is stable under the given conditions. The stability analysis for our model indicates that the boat is not stable, as expected. Next we investigate how to improve the stability of the boat. To derive the model, the equations of motion of the Solar Boat have been derived using a force and torque balance. Most forces depend on drag and lift coefficients of parts of the boat. Those coefficients depend on the incident angle and have been approximated by polynomials as function of the angle. For rotational motion the inertia moments are important and those have also been approximated. The result is six non-linear differential equations of second order, which have been reduced to twelve first order differential equations, still non-linear. Euler forward time integration has been used to calculate how the boat moves in time for different initial conditions. We used the symmetry of the boat and the Newton Raphson method to calculate quasi-linear solutions of the system for all realistic velocities. The problem has been linearized around these points and the eigenvalues of the matrix have been determined. The real positive eigenvalues found indicate that the boat is not stable. A parametric study has been done to determine what possible changes on the boat have positive influence on the stability. This parametric study shows that, in order of priority, the following have this possible influence: -bring the struts closer together -make the front hydrofoil narrower -move the driver more to the front of the boat The largest eigenvalues does not drop below zero using any of those variations. Therefore, according to our model, it does not seem possible to make the boat stable by varying those parameters.

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