# Resistance Types

## Introduction

The objective of finding out the resistance of a ship is to find the speed-power relationship. I.e, to estimate the speed when the power is known or to estimate the power required for a desired speed long before the ship is actually built.

To move a ship, it is necessary to overcome resistance. This is dependent on various factors like speed, displacement, hull form, fluid property. Further the resistance can be treated as in an ideal case like Calm water resistance or case like Trial resistance or Service resistance, each of which are described below.

Tow rope resistance or Calm water resistance is the resistance of a ship at a given speed to tow the ship in smooth water, assuming no interference from the towing ship. It is represented as RT and conventionally estimated in Kilo Newton (KN).

PE = RT . V (in KW),

Where V is in m/s and RT is in KN

Fig.(i) - Ship towed by a tug

Fig.(ii) - Representation of Ship towed by a tug

Trial resistance is the resistance of the ship in trial conditions where the sea state is calm, ship surface and propeller surface are smooth.

 Fig.(iii) - Beaufort Scale 0. Still water Fig.(iv) - Beaufort Scale 4. Moderate breeze Fig.(v) - Smooth ship surface. A ship immediately after launching Fig.(vi) - Propeller smooth surface. A ship just before launching

Service resistance or Resistance in service add an allowance for fouling, corrosion, currents, waves to the trial resistance.

 Fig.(vii) - Corroded ship surface Fig.(viii) - Propeller surface fouled
 Fig.(ix) - Ship in rough sea

## Ideal Scenario

An ideal scenario of a streamline body submerged deep in a non-viscous fluid (perfect fluid) and moving in a constant velocity represents an ideal scenario. In the diagram the body is moving from left to right.

Fig.(x) - Ideal scenario fluid flow pressure distribution

At the forward and aft end of the body, the pressure increases because of discontinuity. Since the pressure acts perpendicular to the surface of the body, the aft and forward location can be split in to components – horizontal and vertical. The vertical components cancel each other.

As can be seen, in the forward region the pressure opposes the motion and in the aft region the pressure supports motion. It is also shown that the two horizontal components also cancel each other. This means that the resultant force is zero. This was first shown by the French mathematician d’Alembert in 1744, and is known as d’Alembert’s paradox. This is only valid for ideal fluid under ideal scenario.

Fig.(xi) - Ideal scenario fluid flow pressure forces

## Read Fluids in Idea Scenario

Real fluids have viscosity and hence there is resistance between the surface of the body and the fluid. As the fluid comes in contact with the forward of the body, some of the particles get stuck on the body and the relative velocity is zero. In that same region as we move vertically upwards, the relative velocity increases rapidly and equals the speed of the body.

When we move along the surface of the body towards aft, we can see that more and more particles get stuck at the same point, and it takes a much longer distance to move vertically to attain the speed of the body. Defining the boundary layer as the thickness of this fluid when it attains the speed of the body (precisely defined as 99%), we can see that the boundary layer increases as we go from forward end to aft.

Fig.(xii) - Real fluid in ideal scenario

On any give point the velocity profile from the surface of the body to the boundary layer increases from zero to the velocity as a parabolic curve and beyond that constant velocity equal to that of the body.

This boundary layer implies that lot of fluid is carried along with the body. One can see this on the aft region of a moving ship.

Fig.(xiii) - Flow around real ship

Beyond the boundary layer the fluid behaves as an ideal fluid and the body can be assumed to be modified to the new shape including the boundary layer. If we use the same method done in above, we can see that the aft pressure component horizontally is less than the forward component and hence there is a net opposing force or resistance. This resistance is called viscous pressure resistance. This is the pressure resistance coming due to viscosity.

There is a force required to push the water in the direction of the body, ie. to reduce its relative speed from velocity of the body. It is the frictional force between the various layers of the water in the boundary layer. This total force required is called frictional resistance.

## Blunt body

There would be a pressure drop and might go negative. This means that the flow will separate and cause formation of eddies. This is called Separation resistance or Eddy drag.

Fig.(xiv) - Flow around a blunt body

## Surface Ships

In case of a ship moving on the surface in addition to those resistances on a submerged body – viscous pressure resistance, frictional resistance and eddy drag, the presence of a free surface adds new components called the wave making and wave breaking resistance. This is because unlike a submerged body where it interacts with only one fluid, in the case of a surface ship, it interacts with two fluids and a free surface between them.

For any fluid surface interacting with the atmosphere, irrespective of the shape of the fluid, the pressure on the surface is same and equal to the atmospheric pressure.

Fig.(xv) - Pressure on Air-water interface

With reference to above, it was seen that the pressure at the forward end of the body is high. Because of this high pressure at the entry, ie., at bow the water is pushed up which creates the formation of waves. Similarly a wave will be generated at the aft end. Apart from this there maybe waves generated along the length of the ship because of the generation of high pressure.

There are two kinds of waves generated – divergent waves and transverse waves.

Fig.(xvi) - Divergent waves and transverse waves

Waves are a result of pressure phenomenon and a gravity phenomenon and not affected by friction, hence viscosity of the fluid has no bearing. Wave making is strictly a surface phenomenon and as you go down (from the water surface) there are no waves.

The location of the formation of the stern wave have a bearing on the resistance of the ship. If the stern wave is generated closed to the stern of the ship the component of the pressure in the longitudinal direction support the ship motion - see fig. However, if the stern wave is created at a distance from the stern of the ship, then the pressure on the surface of the stern is low and hence this horizontal component is low and therefore there is low support to ship motion – see fig below.

Fig.(xvii) - Stern shape on resistance of ship

Wave making is a very complicated phenomenon. It is dependent on the shape of the body primarily at the water level and curvature all along the length. Fore body is the major contributor of this.

## Wave breaking resistance

Take the case of a tanker or bulk carrier with full form, high block coefficient (CB). The fore body shape would have a blunt shape with large half-angle of entrance. This means that the discontinuity is very high and creates the formation of large wave. In addition these waves would be restricted by the shape of the fore body resulting in larger angle for divergent waves as well as higher amplitudes and large slope. This large slope in the gravity wave will cause it to break just like what is observed in the beaches or coast. This breaking dissipates the energy in form of sound energy and creation of eddies as foam. This means we cannot see large waves trailing a large full form ship like tankers.

Fig.(xviii) - Bow wave of an Oil Tanker

In such full form ships there is small wave making resistance but very large wave breaking resistance.

## Summary

Fig.(xix) - Summary of resistance types

The above divisions were based on a 2-D flow of water around the body. However, in case of a ship, the water particles do not move parallel to the surface; they dip down fast depending on the slope of the surface. This gives a complex 3-D effect to the viscous effect. This is tried to captured in three of the above components – viscous pressure drag, wave breaking resistance and separation / eddy making drag as a term called Form factor. This is a computed as a percentage of the 2-D viscous drag.

Fig.(xx) - Flow around forebody of ships

Fig.(xxi) - Flow around aftbody of ships