# Ship Resistance/Components of Resistance

A ship moves on the surface of water. Water is normally taken to be an incompressible fluid, with low viscosity. However, in order to study the components of resistance, let us begin by assuming that the ship is submerged in an ideal fluid. We then see what changes if the fluid is now viscous and finally look at what happens if we bring the ship to the surface.

#### Body in Ideal Fluid

Let us assume that the ship is submerged in an infinitely large ideal fluid, so that the ship is far away from the surface. The forces acting on the ship in static equilibrium are the weight of the ship acting at the centre of gravity, and the pressure forces acting all along the surface, normal to the surface. If the body is neutrally buoyant, then these forces will be equal and opposite. Therefore, the net effect of the hydrostatic forces is to oppose the weight of the body. In fact, this is what is known as the Archimedes' Principle.

If the body is in motion, we first change our frame of reference so that we move with the body and therefore see the fluid in motion in the opposite direction. Now, the pressure is not purely hydrostatic. Due to the motion of the fluid, and the relation between pressure and velocity as given by the Bernoulli's Equation, a hydrodynamic pressure is set up. This pressure varies along the body, and is maximum at the start and end of the body.

The forces acting on the body are everywhere normal to the body. We can split these forces into components along the direction of motion, and transverse to the direction of motion. Due to symmetry of the body, we can see that the transverse forces are in pairs, opposite and equal, and therefore will cancel out. There need not be symmetry in the longitudinal direction, but because the discontinuity in the flow, which was caused by the body, starts and ends with the body, the net opposing forces at the fore end will be the same as the net supporting forces at the aft. Therefore, the net force acting on the body will be zero.

This paradox, that a body moving in an ideal fluid in steady state, experiences no resistance, was first proposed by D'Alembert and is known as D'Alemberts paradox.

#### Body in Viscous Fluid

If we now relax our assumption about the viscosity of the fluid, we need to account for viscous forces. Due to viscosity, the tangential velocity of water relative to the ship is zero at all points on the surface. As we move away from the surface, the velocity gradually increases until it reaches the ideal fluid velocity at some distance away from the body. This layer of high velocity gradients is called the boundary layer.

Now the viscous force is directly proportional to the velocity gradients. Hence, a viscous force, opposite in direction to the velocity, acts on the body through the boundary layer. This force which acts on the surface of the body is called drag. Drag can be studied by decomposition. The mere presence of a surface leads to a drag, which is called the 2D drag. A ship also has a form, and the two ships with the same wetted surface area, but differing in form, will have different drag. This drag is called the form drag.

The formation of the boundary layer also has an effect on the hydrodynamic pressure forces. As we said, the velocity reaches the ideal fluid velocity at a distance away from the surface. This distance is called the boundary layer thickness. The thickness increases from the bow of the ship to the stern. The pressure forces now act on the effective body, which is the boundary layer. The net force acting on this body is zero, but because the boundary layer thickness is not uniform, the ship faces the same resisting force, but gets only a part of the supporting stern pressure forces. Hence, there is a net resisting pressure force on the ship because of the effect of viscosity. This is called the viscous pressure drag.

#### Body at the surface

In addition to the resistance in the ideal and viscous fluids, when the body is at the surface it will subjected to wind resistance, body waves which generates when the body moves and the fluid waves itself.

#### Other components of resistance

1. Induced Resistance: If a vessel moves with a leeway, like in turn or when there is a wind force component sidewards, a lift force (directed sidewards) is developed. Associated with the lift as an induced resistance, which can be considerable, especially for sailing yachts and vessels. When the hull moves slightly sidewards a high pressure is developed on one side (leeward) and a low pressure on the other (windward). The pressure difference gives rise to a flow from the high to the low pressure, normally under the bottom or tip of the keel and rudder, and longitudinal vortices are generated. These vortices contain energy left behind and are thus associated with a resistance component, the Induced Resistance.

2. Appendage Resistance: This resistance is mainly the viscous resistance, hence can be included in the viscous resistance. There are reasons, however, to treat this component separately. First, the Reynold's number, based on the chord length of brackets, struts, etc is considerably smaller than that of the hull herself and therefore a separate scaling is required. Second, the appendages are normally streamlined sections, for which separate empirical relations apply. For sailing yachts the correct shape of the appendage sections is of utmost importance for good performance, particularly since these appendages normally operate at an angle of attack.

3. Blockage Effect: In restricted waters the flow around the hull and the wave making are influenced by the presence of the confining surface. This could be the seabed in shallow water or the banks of a canal. All resistance components may be influenced. Often the effect is modeled as an additional resistance component due to the Blockage Effect of the confining wall.

4. Air Resistance: An additional resistance, which may be considerable, for instance for fully loaded container ships is the wind resistance. The frontal area facing the relative wind on board the ship can be large and the containers do not have an aerodynamic shape, so large forces may be generated in strong winds. Even in still air, there is in fact a resistance component, however small. This component, the Air Resistance, is considered in the model-ship extrapolation procedure.

5. Added Resistance: A seaway will cause an additional resistance on the vessel. This is mainly due to the generation of waves by the hull when set in motion by waves, but also due to wave reflection in short waves.