Powering estimation procedure for warships – Part 1: Resistance Components

Powering estimation procedure for warships – Part 1: Resistance Components

-Raghu Varier

This is a purely naval architecture article, so it is advisable that you have some idea of the terms used.

The main objective of the ship power-plant is to propel it by overcoming the resistances it encounters in its motion. The primary resistance of the ship is the hydrodynamic resistance i.e. resistance offered by the sea against the ship motion. When one talks of hydrodynamic resistance, essentially it refers to the resistance offered by the sea-waves.

Of course, the usual hydrostatic force also exists. But what is to be noted here is that the motion of a ship in calm water would produce waves. This means that wave generation requires energy; here it is supplied by the ship. So it means that the ship propulsion plant must be able to provide for this energy. Hence intuitively speaking, it is the resistance offered by wave that needs to be overcome by the ship.

The above discussion was about the waves created by ship in calm water (called as the Kelvin wave pattern that consists of two distinct wave systems – transverse and longitudinal). However a ship in sea encounters waves from the nature. And their influence on ships depends on the direction relative to ship motion.

Thus some additional factor needs to be accommodated for the added resistance due to the waves hitting on the ship, which in turn disturbs the Kelvin wave system developed by the ship. Hence it is conclusive that the ship propulsion plant must also provide for this additional resistance.

Kelvin wave pattern using Shipflow CFD software
Kelvin wave pattern – a bird’s eye view

What has been talked about so far is the resistance by waves without considering the viscosity of water. The influence of viscosity on the resistance aspects of ships is in various ways. First of all, we will look at the frictional aspect of water. It is well known that a viscous fluid will offer resistance and this has been well established by the famous ‘Boundary Layer concepts’ during the 19th and 20th centuries. (Read here about the Boundary Layer Theory).

By considering an equivalent flat plate to a ship and accounting a form factor to consider 3D nature of hull, the Boundary Layer theory has been well applied to ships and hence facilitated the estimation of frictional resistance through various empirical relations in the past, which was later modified by ITTC and stated as a model-ship correlation line. This resistance is known as viscous resistance (after accounting the 3D form of hull).

An illustration of the boundary layer

But the role of viscosity doesn’t stop there. The viscous nature of sea water causes the waves generated to be comparatively lower in height than the ones calculated using the potential flow theory. (Read here about the potential flow theory). Thus the wave resistance in actual would be slightly less than the one predicted. Also this viscosity retards the flow towards the aft end of the hull, thereby altering the pressure in that region. This results in an additional component of resistance known as ‘viscous-pressure resistance’.

The exact method for predicting this theoretically is not yet fully understood, however using CFD tools one can arrive at some ‘estimation’ based on various theories. Although the deviation would be small to observe, it cannot be said with absolute certainty that the theory is 100% correct. This still is a challenge when it comes to ship model resistance prediction using CFD and hence model testing still is needed.

In addition to it, any sudden changes in the hull form results in formation of eddies typically at the stern. Eddy formation results in additional resistance on the ship and hence eddy resistance needs to be overcome. Apart from that, when conditions of wave breaking occur, this phenomenon also results in an additional resistance component.

And finally, at high speeds (Fn>0.3) we need to also consider the air resistance which is due to the part of hull above the waterline and the superstructure.

The below chart summarizes the various components of ship resistance, in terms of pressure component and viscous component. A much detailed investigation into each of these components is dealt with in the subsequent parts. It is a long journey before one arrives at powering requirement considering even the onboard systems and weaponry. So please have patience while we go step by step so that you will have proper understanding of how the installed power is arrived at.

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