Wave-induced steady forces and yaw moment of a ship advancing in oblique waves

Abstract

Wave-induced added resistance, steady sway force, and steady yaw moment, which are of second order in the incident-wave amplitude, are studied for the forward-speed case using the far-field method based on the principles of momentum and energy conservation. The Kochin functions representing ship-disturbance waves, important input data in the far-field method, are evaluated by means of both enhanced unified theory (EUT) and new strip method (NSM) to see the difference due to bow wave diffraction, 3D and forward-speed effects in the final results of second-order steady forces and moment. Special attention is paid on the precise integration method to ensure convergence in semi-infinite integrals in the calculation formulae, introducing no artificial decaying factor unlike conventional strip-theory methods. Validation of the present calculation method is made through comparison with the experiment conducted with a bulk-carrier model advancing in regular oblique waves and motion-free condition. Good agreement between computed and measured results and also superiority of EUT to NSM are confirmed for all modes of ship motion and the steady forces and yaw moment in a wide range of wave frequency.

Ship to Ship Manoeuvring Simulation to Determine Elements of Tugboat Handling

“…The simulation used a non-dimensional time-averaged wave-induced steady forces and yaw moment (𝑅, ̅ 𝑌 ̅ and 𝑁 ̅ ) of a vessel having a block coefficient 𝐶 𝐵 of 0.84 published by Wicaksono [12]. Equations 19 to 21 express the disturbance forces and moment of the wave.…”

Added resistance using Salvesen–Tuck–Faltinsen strip theory and the Kochin function

“…In this paper we present an improved far-field method for calculation of added resistance in waves within STF strip theory. It is based on Maruo's approach [5], [6], and is essentially a simplified version of the method adopted in EUT as described for example by [29]. STF theory is used to convert the 3D body surface integrals of the associated Kochin functions to line integrals over the two-dimensional sections and then along the length of the vessel.…”

“…Thus, for convergence of the semi-infinite integrals, the Kochin function must decay at least as fast as 1/m, which generally requires a semianalytic treatment of the oscillatory terms, in particular for geometries with surface piercing sections. Following [26,29], we adopt a slender-body (or unified) theory approach and consider a far-field, 3D velocity potential of the form…”

Enhanced Unified Theory with Forward-Speed Effect Taken into Account in the Inner Free-Surface Condition

“…is the wave number of incident wave in deep water; j(k) and are defined in equations ( 8) and ( 9). There are a couple of points to be cautious in the numerical integration of equation ( 39), for which the readers are referred to Wicaksono and Kashiwagi (2018).…”