Fig. 3 Coordinate system and notation Fig. 1 The hydrodynamic force and wave measured system Fig. 2 Apparatus of model testing

The Hydrodynamic Force Acting on the Ship in a Following Sea (1 St Report) Summary by Yutaka Terao, Member Broaching phenomena are most likely to occur in a following sea to relative small and fast craft under the condition that the wavelength/the ship length ratio is about 1. 5 to 2. O. There are many studies and explanations about it, and it is thought that the forces acting on the ship are almost consist of the hydrostatic force and steady state lift. Towing flat plate model in following waves without attack angle it become obvious that side force and heading moment are of such magnitude as to a marked extend. These changed or additional disturbing forces depend upon the wave height and upon the relative position of the ship to waves. In this paper two attempt are made in order to investigate the hydrodynamic force. Firstly, transforming vortex core model is used under the assumption of the free surface is flat. Slender-rectangular thin wing in the constant stream, 3-dimensional separation occurs at the end of the side edges, which form a symmetrical spiral vortex sheet. In a following sea, these spiral vortex sheet may be affected by the wave orbital velocity. A simple flow model, consists of core vortices and feed vortex sheets which emerge from side edges to the core vortices, is used. And core vortices are transformed by the wave orbital velocity and the induced velocities of vortices. By the method, reasonable results are obtained for normal force coefficient, centre of pressure and location of the core vortex in the constant flow. But in a following sea, calculated normal force coefficient is not so good. Secondly, high speed slender body theory is used introducing the data of incident wave as free surface. These method, calculated normal force and heading moment coefficients show quite good agreement to the data obtained from towing flat plate model test.

Fig. 3 Coordinate system and notation Fig. 1 The hydrodynamic force and wave measured system Fig. 2 Apparatus of model testing

Fig. 4 Sway force and yaw moment in following sea Fig. 5 Coordinate system of wing

Fig. 6 Vortex system

Fig. 10 Transformed vortex core in the uniform stream (x-y plane) Fig. 7 Lift coefficient (A. R. =0. 2) Fig. 8 Centre of lateral resistance (A. R. =0.2) Fig. 9 Transformed vortex core in the uniform stream (x-z plane)

Fig. 11 Sway force and yaw moment in following sea Fig. 12 Transformed vortex core in following sea (x-z plane) Fig. 13 Kernel function

(y,z) on the boundary Fig. 14 Coordinate system Fig. 15 xn, section parallel to wave crest on the outer boundary on the outer boundary

Fig. 17 Wave elevation in following sea Fig. 18 Sway force and yaw moment in following sea (X=15 ) Fig. 16 Finite difference mesh Fig. 19 Sway force and yaw moment in following sea (X=30 )

1) R. Wahab and W. A. Swaan : Courcekeeping and broaching of ships in following seas. J. S. R., 7. 4, (1964), pp. 1-15. 4) W. Bolley : A nonlinear wing theory and its application to rectangular wing of small aspect ratio, Z. Angew. Math. Mech., Bd. 19, Nr. 1. pp. 21 `25, Feb. (1939). 6) R. B. Chapman : Free surface effects for yawed surface-piercing plate, J. S. R., 20. 3, (1976), Sep. pp. 125-136.