Development of a 6-DOF Dynamic Velocity Prediction Program for offshore racing yachts Paul Kerdraon, Boris Horel, Patrick Bot, Adrien Letourneur, David Le Touzé To cite this version: Paul Kerdraon, Boris Horel, Patrick Bot, Adrien Letourneur, David Le Touzé. Development of a 6-DOF Dynamic Velocity Prediction Program for offshore racing yachts. Ocean Engineering, Elsevier, 2020, 212, pp.107668. 10.1016/j.oceaneng.2020.107668. hal-02884999 HAL Id: hal-02884999 https://hal.archives-ouvertes.fr/hal-02884999 Submitted on 8 Oct 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution| 4.0 International License Development of a 6-DOF Dynamic Velocity Prediction Program for offshore racing yachts Paul Kerdraon a,b,<, Boris Horel b, Patrick Bot c, Adrien Letourneur a, David Le Touzé b a VPLP Design, 18 Allée Loïc Caradec, 56000 Vannes, France b Ecole Centrale Nantes, LHEEA Lab. (ECN and CNRS), 1 Rue de la Noë, 44300 Nantes, France c Naval Academy Research Institute - IRENAV CC600, 29240 Brest Cedex 9, France Thanks to high lift-to-drag ratios, hydrofoils are of great interest for high-speed vessels. Modern sailing yachts fitted with foils have thus reached impressively high speeds on the water. But this hydrodynamic efficiency is achieved at the expense of stability. Accurate tradeoffs are therefore needed to ensure both performance and safety. While usual Velocity Prediction Programs (VPPs) are inadequate to assess dynamic stability, the varying nature of the offshore racing environment further complicates the task. Dynamic simulation in the time-domain is thus necessary to help architects assess their designs. This paper presents a system-based numerical tool which aims at predicting the dynamic behavior of offshore sailing yachts. A 6 degrees of freedom (DOF) algorithm is used, calculating loads as a superposition of several components (hull, appendage, sails). Part of them are computed at runtime while the others use pre-computed dataset, allowing a good compromise between efficiency and flexibility. Three 6DOF simulations of an existing offshore trimaran (a maneuver, unsteady wind conditions and quartering seas) are presented. They underline the interest of dynamic studies, demonstrating how important the yacht state history is to the understanding of her instantaneous behavior and showing that dynamic simulations open a different field of optimization than VPPs. 1. Introduction measure of her racing efficiency and should be included in the design trade-offs. The need for dynamic simulation is growing in many fields of In addition, recent years have seen a substantial growth of foiling engineering, as it allows to test and compare prototypes and processes technologies, leading to fully flying yachts and introducing specific at much lower costs than actual full-scale tests. Naval architecture stability issues with direct impact on average speed. A better knowledge is no exception. Nowadays, it widely relies on Velocity Prediction of the dynamic response of flying yachts is paramount for safe and Programs (VPPs) to help architects and engineers in the design process sustained offshore flight. Non-linear couplings between the different of sailing yachts. However VPPs have proved inadequate to optimize degrees of freedom further complicate the study and traditional VPPs all of the design parameters. Originally introduced by Kerwin (1978), VPPs are constrained non-linear steady state optimizers which, based have proven inadequate to handle these matters with the accuracy on experimental, numerical or empirical data, enable boat settings required for high performance sailing. optimization to derive the reachable speeds in given steady conditions. In this context, numerical tools enabling time-domain analysis and Unlike inshore yachts such as the AC45 or the AC75 where class including unsteady environment – often called Dynamic Velocity Pre- rules limit the acceptable wind and waves conditions, offshore vessels diction Programs (DVPPs) – have become a major research topic. may encounter rough sea and wind conditions with short characteristic This paper is interested in such a simulation tool, handling variable time of evolution. In such unsteady environments, racing yachts may be wind and waves as well as mode transition between Archimedean and compelled to sail at much lower speed than the steady state optimized fully flying conditions. Section 2 presents a literature review on yacht values. Assessing the boat real performance and her ability to safely dynamic simulation. The mathematical modeling is given in Section 3. maintain high average speeds in varying conditions is therefore a key < Corresponding author at: VPLP Design, 18 Allée Loïc Caradec, 56000 Vannes, France. E-mail addresses: [email protected] (P. Kerdraon), [email protected] (B. Horel), [email protected] (P. Bot), [email protected] (A. Letourneur), [email protected] (D. Le Touzé). 1 Notations V Yacht linear velocity vector [m/s] V Apparent flow velocity vector at X [m/s] A Wave amplitude [m] X_f low V Wave orbital velocity [m/s] A Added mass coefficients matrix [kg, kg m, wave 훽 Leeway angle [◦] kg m2] 훿 Rudder angle [◦] A Infinite frequency added mass matrix [kg, R ∞ ◦ kg m, kg m2] 휃 Pitch angle [ ] B Damping coefficients matrix [kg/s, kg m/s, 휆 Wave length [m] ◦ kg m2/s] 휇 Ship-waves relative heading [ ] 흃 Ship perturbation vector [m, rad] B∞ Infinite frequency damping matrix [kg/s, 2 2 kg m/s, kg m /s] 훷i Potential of incoming waves [m /s] B Yacht breadth [m] ' Heel angle [◦] C Yacht center of effort 'd Diffraction force phase [rad] c Appendage characteristic chord length [m] 휌 Water density [kg/m3] 3 Cd Sail drag coefficient [–] 휌air Air density [kg/m ] ◦ Cl Sail lift coefficient [–] 훹 Yaw angle [ ] ◦ Cm Midship section coefficient [–] 훹T Autopilot target heading [ ] d Yacht draft [m] ! Frequency-domain variable [s*1] ̄ ù *1 F n Froude number [–], F n = U_ gLWL Wave frequency [s ] *1 F External linear forces vector [N] !e Frequency of encounter [s ] *1 Fi Force component i [N, Nm] ! Yacht angular velocity vector [s ] 3 |Fd| Diffraction force modulus [N/m, N] ( Displacement [m ] fR Reduced frequency [–], fR = c_VT AWA Apparent Wind Angle G Ship center of gravity AWS Apparent Wind Speed g Acceleration of gravity [m/s2] CFD Computational Fluid Dynamics I Yacht inertia matrix [kg, kg m, kg m2] DOF Degree(s) of Freedom ◦ ◦ KP Controller proportional coefficient [ / ] DSYHS Delft Systematic Yacht Hull Series k Wave number [m*1], k = 2휋_휆 DVPP Dynamic Velocity Prediction Program ki Unsteady wind intensity factor for compo- IMS International Measurement System nent i [–] QST Quasi-Steady Theory K Impulse response function matrix [kg/s2, RANS Reynolds-averaged Navier–Stokes kg m/s2, kg m2/s2] RAO Response Amplitude Operator kyy Yacht pitch radius of inertia [m] TWA True Wind Angle LWL Waterline length [m] TWD True Wind Direction (relative to North) m Yacht mass [kg] TWS True Wind Speed M External moments vector [Nm] VPP Velocity Prediction Program n Outgoing body's normal unit vector O Origin of the ship reference frame Rb 2 pi Pressure of incoming waves [N/m ] ( ) 2008). As match racing competitions are generally run inshore, shel- R0 = X0;Y0;Z0 Earth-fixed reference frame ( ) tered from the deep-water waves, and due to the complexity of waves Rb = Xb;Yb;Zb Ship-fixed reference frame effect, the first numerical tools considered flat water conditions. Most of S Total sail area [m2] Sails these works are based on the usual maneuvering approach (Abkowitz, S Yacht wetted area [m2] w 1964) in which loads are described using hydrodynamic derivatives: a T Appendage characteristic period of oscilla- Taylor-series expansion of the forces with respect to all the involved pa- tions [s] rameters (attitudes, sinkage, speed components). Such models allowed TD Controller derivative coefficient [s] the study of the three or four degrees of freedom (DOFs) boat motion Ti Unsteady wind period for component i [s] (surge, sway, yaw and sometimes roll). Nevertheless foiling greatly Ū Yacht mean speed [m/s] enhances the need to factor in the two other degrees of freedom as heave (flight height) and trim (appendages angles of attack) are now at the core of boat stability (Heppel, 2015). Full 6 degrees of freedom modeling is therefore needed. Section 4 presents and analyzes three examples of dynamic simulation Introduction of time-domain studies in the design of racing yachts performed with the developed numerical tool. occurred for the victorious 26th America's Cup challenger Stars and Stripes (see Oliver et al., 1987) using a quasi-steady approach. Velocity Prediction Program results were combined with wind statistics and 2. Sailing yacht dynamic simulation game theory to simulate match races between several candidates and isolate the best performing design. Based on the widely used steady The ability to simulate maneuvers and especially tacking has long state models of the IMS VPP (Claughton, 1999), the four degrees of been the main subject of sailing dynamic studies (Masuyama et al., freedom program of Larsson (1990) included a first account of wave 1995; Keuning et al., 2005; Gerhardt et al., 2009). In match racing, effects by computing added resistance through strip theory. Masuyama maneuvers are critical and simulations provide an efficient way for et al. (1993, 1995) developed a numerical tool based on hydrodynamic designers as well as crew to improve the on-water results (Binns et al., derivatives computed from tank tests and aerodynamic coefficients 2 Fig.