Chapter V. Ship Resistance

5.1 IntroductionWhen a ship moves forward through the water at a constant velocity, V. Its forward motion is going to generate:

a) dynamic pressure on the hull, producing a resultant force in the longitudinal direction and opposite to the advancing direction; andb) tangential stresses on the immersed (or wetted) surface due to the viscosity; their resultant force is also opposite to the ships moving direction.

The total force opposite to the motion is called the resistance of the ship or drag. The resistance components most concerned arise from one of the two forces; namely normal dynamic pressures or tangential stresses on the ship surface.

The ship actually moves at the same time through two fluids, water and air, with widely different density. While the lower part of the hull is moving through water, the upper part is moving through air. Like moving in the water, the upper part of the ship moving in the air is also subject to the same types of forces (dynamic pressures and tangential stresses).

Because , the air resistance is usually much smaller than the water resistance, except for those aerostatic support of hydrodynamic support crafts.

Summary: Water resistance (submerged part of a hull) Air resistance (upper part of hull & superstructure)

5.2 Types of Water Resistances

Wave-Making Resistance: belongs to the category of normal dynamic pressures. Due to these dynamic pressures waves are generated on the surface of water and spread away from a ship. Waves possess energy. Thus a ship making waves means a loss of its energy. Wave-making resistance is important to surface ships, especially those of high speeds, but may be negligible to submarines.

Frictional Resistance: arising due to the viscosity of water, i.e. tangential stresses. Because of viscosity & velocity gradient in the direction normal to the ship hull, there is a mass of fluid being dragged along with a ship. Energy necessary to drag the mass of fluid is the work done by the ship against the frictional resistance.

3. Eddy-making Resistance: contributed from normal pressure applied on a hull. Due to the viscosity of the fluid, the flow separates from the surface of a hull and eddies (vortices) are formed. These eddies induce the changes in the velocity field and thus change the normal pressures on a hull. The changes in the pressure field around a ship result in the eddy-making resistance. 4. Air resistance (mainly resulting from wind resistance).

5. Appendage resistances: are caused by the appendages of a ship, such as propellers, rudders and bilge keels.

5.3 Dimensional Analysis of Ship Resistance

The purpose of studying Dimensional Analysis (D.A)

D. A is helpful to classify and compute various types of resistances, by examining the basic laws governing the resistances of a body moving through a fluid.

Although CFD has made considerable progresses, the present practice still depends on ship model test to determine the resistances of the ship. D.A is especially useful in data analysis of ship model test, which may deduce the resistances of the corresponding prototype ship.

The foundation of dimensional analysis (review)

D. A is based on the principle that an equation which expresses a physical relationship must be dimensionally homogenous.

In other words, the physical units of all terms at both sides of an equation must be the same, e.g. In general, all physical units can be expressed by 3 fundamental units, such as mass-length-time or force-length-time.

Buckingham theory: if there are n dimensional variables in a physical equation, described by m fundamental dimensions, they may be grouped into n m dimensionless variables.

Dimensional Analysis of model test of resistance

When a model and its prototype are geometrically similar and their two dimensionless coefficients (Re, Fr) are the same, their resistance coefficients (CT) should be the same.

Dimensional analysis reduces the number of the related parameters involved in model tests. However, it can take the problem no further than the above conclusion.

5.4 Model Tests of Ship Resistance

Model tests are widely used in the design and study of large engineering constructions, such as harbor, breakwater, bridge constructions, and ship buildings.

A ship model is geometrically similar to its prototype. The size of the model is usually much smaller than that of the ship.

Ship model tests are employed to predict the resistance, the interaction between the hull and the propeller, seakeeping properties of a ship, etc. Therefore, model tests are very important in ship design and ship research. Here we focus on model resistance tests.

Ship Resistance and Model Test

Model resistance tests are usually carried out in a towing tank. A towing tank is a long and narrow basin. Small towing tanks are about 200-300 long, 15-30 wide, 5-9 deep. Large ones, e.g. U.S. Navy, the David Taylor Model Basin has a length of 2775, a width of 51 and a depth of 22.

A ship model (at a fixed displacement and a naked hull (no appendage, 4-7 for small towing tank, 12-30 for large one) is towed at a constant velocity by a mechanically propelled towing carriage (see website below). The resistance of the model at the constant velocity is recorded by the instruments on the carriage. Usually the test is carried at a number of constant velocities, and a resistance curve is thus obtained.

http://www.dt.navy.mil/hyd/fac/tow-bas/hig-spe-bas/index.html

A typical resistance curve in a model test

A Towing Carriage and A Ship Model

A Towing Carriage

Overview of MarinTeks Shop Model Tank (Norway)

Determining the Resistance of a ship based on its model test

When a ship and its model are geometrically (all characteristics & dimensions are in the same ratio) and dynamically similar, we may use Eq (5.1) to determine the resistance of a ship based on the measured data from its model test. Namely,

Geometrical similarity indicates the main characteristics of a model & its prototype are in the same ratio.

In order to overcome this fundamental difficulty to satisfy the similarity laws, a major (first) assumption was made by Froude that the frictional and the wave-making resistances are independent, and the frictional-resistance coeff. depends only on the Reynolds #. The wave-making or residual resistance coeff. depends only on the Froude # .

2. It is also assumed that the frictional resistance coeff. of a ship (or a model) is the same as that of a smooth flat plate with the same length and wetted surface area as the ship (or the model). Therefore, CF or RF of a ship (or a model) can be computed given the length according to the half-analytically & half-empirically friction formulas.

3. Based on these two assumptions, we may determine the resistance of a ship at a constant velocity given the results of model resistance test. The steps are detailed below.

In most cases, the total resistance of a ship can be determined accurately based on the model test results using the above method. However, the method is based on the 2 major assumptions (a. CF & CR are independent, b. CFS of a ship is equal to that of a flat plate with the same length). Sometimes the errors due to the approximations may be significant. We will study the frictional, wave-making and eddy-making resistances in detail, for understanding the computation using the method & its validity.

5.5 Frictional Resistance

Laminar and Turbulent Flow (review of CVEN 311)

Laminar flow: the fluid appears to move by the sliding of laminations of the infinitesimal thickness relative to adjacent layers. Turbulent flow: is characterized by fluctuations in velocity at all points of the flow field and these fluctuations with no definite frequency. Whether a flow is laminar or turbulent flow depends mainly on its Reynolds #. For a plate flow,

Friction formulas for a flat plateThe following formulas are commonly used.

It is noted that CF computed according to the Blasius formula (laminar) and CF according to turbulent flow formula, say Schoenherr formulas are quite different. For a small model there would be a laminar flow over the (at least) forward part which would develop into turbulent flow further afterwards. Then it would be inaccurate, if we either use Blasius formula or Scheonherr formula to compute the frictional coeff. of the model.

To overcome this problem, we have to set a lower limit on the size of model use turbulence stimulating devices at the bow of a model to stimulate an early transition from a laminar to turbulence flow, such as a trip wire at station after the forward perpendicular line. Therefore, the frictional coeff. of a model can be computed according to a turbulent flow formula.

Influence of Roughness of a plate on CF

The formulas for computing CF are applied to the flat plates with smooth surface. The rough surface (of a ship) will result in the increase of CF . Roughness (on the surface of a hull) may be classified into 3 types.

Structural roughness: caused by welded joints, warviness of shell plating on the hull. A newly-built ship will have (for Schoenherr formula).2. Corrosion3. Fouling: caused by the attachment of marine organisms such as seaweeds, shells and barnacles. Corrosion & fouling occur for ships having sailed for a certain period of time. They will decrease the velocity of the ship. Ship owner will decide when the ship should go to the dock for cleaning.

5.6 Wave-Making Resistance

Wave-making resistance is important to a surface ship (negligible for submarine); and its speed is high. Accurately speaking, its Froude # ,

or in U.S. the speed/length ratio, is high. It is noticed that the speed to length ratio is a dimensional coefficient, where V is in knots, L in feet. A nautical mile/hr (knot) = 0.5144 m/s.

Ways to study or determine wave-making resistance

Experiments with models in towing tank; At present, model test is still the most important tool for prediction of wave-making resistance. *Theoretical and numerical computations (CFD): help in interpreting model test results, reduce the range of model tests, and guide further research.

Ship Wave Pattern

Lord Kelvin (1887) considered a single pressure point traveling in a straight line over the surface of the water, sending out waves which combine to form a characteristic pattern. Transverse Waves

Divergence Waves

Description of the wave pattern of a moving pressure point

A system of transverse waves: the heights of successive crests diminish when T.W go afterwards w.r.t. the pressure point. A series of divergent waves: the whole pattern is roughly contained within two straight lines, which start from the pressure point and make angles of 19 28 on each side of the line of the motion.

Ship Wave Pattern

Kelvin wave pattern illustrates and explains many of the features of ship waves. Ship wave pattern is similar to the combination of two Kelvin wave systems generated by two pressure points, with one near the bow and the other near the stern.

Wave pattern of a ship

Wave pattern behind a moving duck

Wave Pattern of a small boat (divergence wave pattern)

Wave Pattern of a small boat (divergence wave pattern)

Interference Effects

At lower speed (Froude #), waves made by a ship are very small & wave-making resistance is insignificant.

At lower Froude #, divergent waves are the primary wave system. As the Froude # of a ship increases and the depth of water decreases, transverse waves are more important.

The wavelength of T.W. increases with the speed of a ship. Thus the position of the T.Ws crest (or trough) w.r.t. the ship changes.

4.If the trough of the T.W. generated by the bow coincides with that generated by the stern, then CW becomes very large. If the crest of T.W generated by the bow coincides with the trough of T.W generated by the stern, then CW becomes small. This phenomenon is called bow and stern wave interference, which accounts for the humps and valley in the CW curves.5. In order to reduce the resistance, a ship designer chooses appropriate L, V such that CW is at valley instead of at humps. (p149-151)