Dynamic Stability Analysis of a Hydrofoiling Sailing Boat using CFD

Abstract

Abstract. This paper describes the study of the dynamic stability of a hydrofoiling sailing boat called the “Goodall Design Foiling Viper”. The goal of Goodall Design is to make hydrofoiling accessible to a wider public, whereas it was previously reserved for professional sailors at the highest level of the sport. To allow for safe operation, stability is an essential characteristic of the boat. The aim of this work is to find a strategy to perform a dynamic stability analysis using computational fluid dynamics (CFD), which can be used in a preliminary design stage. This paper starts by establishing a theoretical framework to perform the dynamic stability analysis. A stability analysis has to be performed around an equilibrium state which depends on operating parameters such as speed, centre of gravity, etc. . A fluid-structure interaction strategy is applied to determine these equilibrium states. The last part discusses the stability characteristics of the Viper. The framework managed to assess the dynamic stability of the Viper and found 5 longitudinal eigenmodes: two complex conjugated pairs of eigenvalues and one real eigenvalue. It can be concluded that the boat was both statically and dynamically stable.

Split-Flaps – a Way to Improve the Heel Stability of T-Foil Supported Craft

“…During calculations of the stability derivatives, several assumptions were made to reduce the order of the equations, thereby reducing the accuracy of the method. Hence, Bagué et al (2021) used CFD to compute the stability derivatives for a foiling catamaran rather than the semi-empirical methods used by Masuyama. Though the stability derivatives provide data regarding the stability of the boat, dynamic simulations like disturbances and manoeuvring could not be studied.…”

Typhoon: A vortex-lattice code for assessing dynamic stability characteristics of hydrofoil crafts

“…( 1) the left hand side of the equation is the time derivative of the state-vector. The meaning of this state-vector is explained in more detail in the work by Bagué et al [1], but for this discussion it suffices to understand that it exists out of the change in forward speed u, change in fleight height z, change in trim angle θ , change in vertical speed…”

“…w and change in pitch velocity p. The longitudinal stability matrix [A] allows us to write this formula in a more convenient format, and it is this matrix which determines the dynamical behaviour. For a more thorough background on this particular case we refer to Bagué et al [1] and for a more general background to the dynamic stability analysis (of aeroplanes) we refer to Drela [2]. Apart from the mass and the mass-moment of inertia the stability matrix gets influenced by the so-called force and moment derivatives which originate from the afore mentioned substitution by the Taylor expansion of both the force and moment equations.…”

“…Therefore Typhoon is provided with a Newton-Rhapson algorithm which alters the position and orientation of the vessel iteratively and, provided a good initial guess, will end up in an approximate equilibrium point. This algorithm is also explained in the work by Bagué et al [1]. The basic idea of this algorithm is that it changes the position of the vessel making use of a linear extrapolation of the forces which it wants to be zero.…”

“…A more profound explanation of the DSA for aircrafts and the linearization of the system can be found in the work by Drela [2]. The DSA especially for hydrofoil crafts is explained in the work by Masuyama [4] or more recently by Bagué et al [1] where a framework is laid out to perform this DSA.…”