Chapter V. Ship Resistance

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Chapter V. Ship Resistance
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5.1 Introduction When 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 and b) 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.
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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)
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• 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.

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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.
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• 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.

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• 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.
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• Dimensional Analysis of model test of resistance

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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.
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• 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.

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• 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

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A typical resistance curve in a model test
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A Towing Carriage and A Ship Model
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A Towing Carriage
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Overview of MarinTeks Shop Model Tank (Norway)
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• 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,

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Geometrical similarity indicates the main
characteristics of a model its prototype are in
the same ratio.
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1. 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 .

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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.
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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.
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• 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,

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• Friction formulas for a flat plate
• The following formulas are commonly used.

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• 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 ½ station after the forward perpendicular
  line.
• Therefore, the frictional coeff. of a model can
  be computed according to a turbulent flow
  formula.

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• 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. Corrosion
• 3. 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.

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• 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.

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• 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.

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• 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
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• 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.

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• 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.

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Wave pattern of a ship
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Wave pattern behind a moving duck
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Wave Pattern of a small boat (divergence wave
pattern)
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Wave Pattern of a small boat (divergence wave
pattern)
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• 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.

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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)