Modeling and dynamic analysis of a “flying” fully submerged hydrofoil craft for control

Hydrofoil boats are equipped with underwater lifting surfaces that raise the hull out of the water once a certain speed is reached. This reduces the vessel’s drag and can contribute to decarbonizing cargo transport via the oceans. However, a boat in foiling mode in general requires to be actively controlled because it is inherently unstable. This research provides an accessible and structured approach to identify and model the most relevant dynamic components required for control design and system analysis. A non-linear 6-degree of freedom (DoF) model for a tandem configuration fully submerged hydrofoil craft (FSHC) is developed, including kinematic relations specific to the operation of FSHC. The model incorporates changes in wetted surface area of drag-generating elements such as masts, as well as the influence of local flow conditions on the foils. Hydrodynamic force and moment coefficients are derived from flow simulations using open-source software. Propulsive forces and moments are identified experimentally, and the vessel’s inertia tensor is determined via IMU-based measurements using a simple test setup. An optimization problem is formulated to estimate the inertia. The resulting 6-DoF model is used to analyze the dynamic behavior of the vessel. Furthermore, the model is trimmed and linearized. It is shown that the longitudinal and lateral dynamics can be decoupled. The resulting linear models and the eigenmodes of the vessel are analyzed. The modeling framework, originally developed on the first prototype, is transferred to a second vessel of different geometry and validated against measurements from towing tests. The agreement between measured and predicted dynamics demonstrates the transferability of the proposed approach.