In Depth- Wave Making Resistance (Part One)

Today, let us learn in depth about an important component of a ship’s resistance. The component here which I speak of is the wave making resistance. Now, before trying to understand about Wave Making Resistance, we need to know one thing about waves which are basically gravity based phenomenon. The first thing necessary for wave generation would be a free surface between air and water. 

These interfaces would be what would give rise to waves owing to pressure differences. These pressure differences are a result of the interaction of the fluid streamlines with the ship shape at the fore peak which causes reduction in the velocity. This means a rise in pressure has occurred (Remember Bernoulli’s Theorem?) at this point. We will call them ‘Pressure Points’ from now on. Let us not consider flow circulation and vortices around these slopes for now.

Fig. 1:A pictorial representation of the various terms associated with the wave generated from passage of a ship across water (Courtesy: http://www.ifm.zmaw.de/ )

When a ship or for all normal purposes, a body moves in a fluid, the surrounding layer of fluid exerts pressure normal to the surface in contact with it. Now, assuming the situation to be an ideal one, where the fluid is non-viscous (remember, viscous to fluids is what friction is to solids), we observe that the pressure components hog the body from all directions and so their normal components cancel out eventually. However, this is not the case with viscous flow in real fluids as we will see now.

In a viscous medium, the pressure at the forward end and the aft end will be more than the middle body of the ship. This is because the water when flowing across the ship encounters the slope of the fore peak of your ship for the first time, causing the pressure at this point to rise. Now, the flow could have continued along this new path as shown below, no trouble here, but we shall ‘close’ the shape of our ship here and this calls for another slope around what we will now call the ‘forward shoulder’ of our ship.

Fig. 2: The wedge shaped model used to analyse the wave systems generated by the body when travelling in a fluid. These observations hold in the same way for a stationary body in a moving fluid too.

Actually, a more appropriate visualization would be to consider our ship half-breadth as having 4 distinct pressure points-2 at the fore and 2 aft of the middle body which is predominantly continuous without any steep slopes. Yes, two peaks and two shoulders. The pressures are positive at the peaks and negative at the shoulders. Remember this assertion.

Now waves are composed of crests (elevations) and troughs (depressions). The forward peak and the aft peak ‘wave systems’ originate from crests and the shoulders (fore and aft) from troughs. The ships waves are generated as a superposition of ‘wave systems’ generated at different pressure points on the ship’s water plane. A model used to describe this is the wedge-shaped boat model as schematically represented below. There is another symmetrical pressure disturbance which is often considered together with the wave systems in many texts is given separately below here.

Overall Wave Systems

The work of Lord Kelvin gave a better physical interpretation of wave making in ships. He considered these ‘pressure points’ moving on the flat free surface and gave a theoretical explanation for the wave systems generated. Two sets of wave systems are generated, one being the transverse wave system, the other being the divergent wave system. Take a look at the image below for the same body moving on the fluid from different perspectives to get a clearer idea.

When observing from a ship, what you would perceive would be the combination or superposition of the wave systems described above and so the most prominent bow wave system would be primarily perceived.

Fig. 3:Photo of a ship taken with the wake pattern clearly showing the turbulent component of wake in the middle. (Courtesy: www.bit-player.org)

The Divergent Wave System

Kelvin found that the divergent wave system would be contained by two straight lines originating from the pressure point which in this case is roughly our slender ship moving on a vast ocean. The angle which one of these straight lines would make with the centreline of the vessel was found to be around 19 degrees 28 minutes. This would continue to propagate way aft beyond the ship. We will talk a bit more about this divergent wave system the next time.

The Transverse Wave System

The transverse wave system would be perceived when viewed about the mean sea level. This wave system constitutes the major part of the wave making resistance. As it is left behind far aft of the vessel, the wave height becomes shorter and the wave length longer.

Both these systems move with the ship and might appear stationary to an observer aboard the ship.

What Next?

Fig. 4:The Kelvin Wake pattern clearly observed for a boat. (Courtesy: Wikipedia/Edmont)

The wave making component of a ship’s overall resistance adds to the power consumption. In simple words, we cannot afford to allow the ship’s power go into generating waves and this is difficult to avoid in ship design. However there has been extensive analysis and now Naval Architects can put the science behind the phenomenon to use in the design of the  propulsion based on certain features.

We shall talk a bit more about this component of the ship’s resistance next time in the sequel to this article.LSD

Article By: Sudripto Khasnabis