Prediction of the longitudinal stability and motions of a hydrofoil ship with a suspension system between the wings and the hull using a state-space model

Abstract

Hydrofoil ships with fully submerged wings offer great speed at a relatively low fuel cost. They are also unstable, which is why they require an active control system. Current hydrofoil ships are more limited in their operation by waves. A passive suspension system could reduce the motions of a hydrofoil ship in waves but it must remain controllable. This becomes more difficult when the ship is sailing in waves because the wave orbital velocities affect the lift of the wings. In this thesis, a state-space model is developed that predicts the stability and the motions in waves of a hydrofoil ship with a suspension system between the hull and the wings. A foiling ship experiences forces of different origins. To segment the model development, three levels of equations are created; physical level, component level and system level. The physical level consists of expressions that describe the forces like the lift, drag or added mass. All forces acting on a component are then combined into the component level equations. The effects of all components are then combined to find the system dynamics. The model development is split into two parts. The first part is the development of a fixed-wing model. The predictions of this model are compared to experiments of the Demonstrator of MARIN. The Demonstrator is a 3.5m long model and has a mass of 150kg. A subset of these tests is used to compare to the predictions of the developed model. The motions are predicted well for the lowest wave frequency, but the motions for higher frequency waves are not predicted sufficiently accurate. The suspected cause for the inaccuracies is a lag in the control signal in the experiments, which plays a greater role in the higher frequencies. It is recommended to implement this delay effect into the model to improve the range of frequencies the model can be validated for. The model is also compared to higher wave amplitudes for the lowest wave frequency. The predictions of the model for the higher wave amplitudes match the measurements from the experiment reasonably well. The state-space model is then extended to allow for a suspension at the forward wing, aft wing or both wings. No experiments were available to compare to the model predictions, which means the model is only verified. The verification is done by making the increasing the stiffness to sufficiently high values, that the fixed-wing limit is reached. In the analysis of the results, it was found that the suspension system can reduce the motions of the ship, but only in very specific circumstances. In all other circumstances, the motions are either larger than the fixed-wing model or the system becomes unstable. It is therefore recommended for future research to try rotational springs.