British Kinematography (1953)

October, 1953 HOULT I WATER EFFECTS 93 Fig. 1 1 . Wave-pattern produced by water flowing past a stationary body TRANSVERSE WAVES Fig. 12. Analysis of Fig. 11. Ship Waves Irrespective of any waves which may exist on the surface of a stretch of water, wave systems are produced by the passage of a floating body such as a ship. The system of waves produced by a ship is complex and can be divided into four separate wave-trains. Before defining these, we will establish the type of wave system produced by a small body moving through a fluid. The conditions are the same as obtain when the fluid moves past a stationary body, e.g. a river flowing past a fishing line. In Fig. 11 is shown a small (point) body P partly immersed in a moving mass of water. The dotted lines in the figure mark the envelope of the wave system. In general, a pattern of waves established of the form shown remains stationary relative to the body, that is they travel on the surface at the same velocity as the body itself in the direction of its motion. This pattern is composed of two parts — two rows of echelon waves and a system of transverse waves, shown separately in Fig. 12. This system is obtained when the velocity of the stream exceeds a certain minimum and when the water is deep. Under these conditions, the shape of the envelope remains constant at all speeds. The contained angle is twice 19° 28' (see Fig. 13). Accordingly the length of the waves increases with increase of body speed. If the velocity between P and the water is Vw and the velocity of the wave along the normal to its envelope is V\, then V\ sin 19° 28' (7) The velocity V-\ determines the value of A. If Kx falls below 23*2 cm./sec. the wave system cannot be maintained. Hence the lower limit for the velocity Vw is 23-2 sin 19° 28' =69*6 cm./sec 1-35 knots. .(8) The significance of this is that a model will Fig. 13. Angle of envelope of Fig. 1 1 , Fig. 14. Construction of angle shown in Fig. 13.