British Kinematography (1953)

October, 1953 HOULT I WATER EFFECTS 95 It should be realized that resistance to a ship's motion arises from the following three causes only : (1) Skin friction due to viscosity ; (2) Eddy resistance due to vorticity at the stern or behind any protrusion ; (3) Wave resistance, i.e. the loss of power in generating waves. A wholly submerged body, such as a fish, contends with (1) and (2) only and these are minimized by the provision of a smooth skin and a lack of unnecessary protrusions. When a ship passes into shallow water, different wave-systems may be produced. Consider again a point impulse moving relative to the surface in water of depth h, at a velocity c. Provided c < J g.h , a train Fig. 18. Wave-system produced in shallow water, is not constant (as in deep water) and can approach an angle zero as the velocity increases (Fig. 19). At the same time the shape of the waves has changed, these being concave to the ship. As the depth is decreased the group velocity approaches the phase velocity, and the tendency to form a train of waves is reduced. The waves formed when c= Jg.h are known as " long waves," because their length to height ratio is large and their slope gradual. The length of wave corresponding to a velocity J g.h is the longest free wave which can exist in water of depth h. Thus, when a vessel exceeds this velocity, the phase velocity must equal the velocity of the vessel but any train formed has a lesser velocity and cannot be maintained. So the system developed in Fig. 19 shows no train and the vessel travels on a single wave without forming any wash. The wave-pattern formed in deep water tends to change to the less oblique form when c = \ J g . h approximately. This provides a minimum value for h for any given c, if we wish to simulate deep-water will be generated as in Fig. 11. If the velocity is increased however, the lateral (echelon) waves become less oblique and when c = s^gTi [ we have a critical condition in I which the echelon waves disappear, leaving only the transverse waves (Fig. 18). This last system is simpler than c = the previous system and results in a decrease in wave-resistance. Consequently a vessel in shallow water can attain a critical velocity at which the resistance to motion falls to a minimum before rising again with increased velocity. This fact has been utilised in the movement of barges in canals, to achieve this economical speed ; further increase in c results in the lateral wave system becoming oblique again but without echelon waves. The obliquity g-h Fig. 19. c > gh c >> g.h Effect of increased velocity on the svstem shown in Fig. 18. effects by means of models. The minimum depth should therefore be obtained from Jg ■ h i.e. c2 =% g.h = ti ll (feet) c2 8 where c is in ft. /sec (9)