Recall Static Equilibrium!

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Chap 7 Resistance and Powering of Ship

• Recall Static Equilibrium!
• What are the forces in the x-axis of the ship?
• Resistance or Drag
• Thrust (Propulsion)
• We will first look at propulsion, then drag in
  this chapter.

41 knots!
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Ship Drive Train and Power
7.2 Ship Drive Train System
Engine
Reduction Gear
Screw
Strut
Bearing
Seals
THP
Shaft
BHP
DHP
SHP
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Ship Drive Train and Power
Horse Power in Drive Train
Brake Horse Power (BHP) - Power output at the
shaft coming out of the engine before the
reduction gears Shaft Horse Power (SHP) -
Power output after the reduction gears (at
shaft) - SHPBHP - losses in reduction gear
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Ship Drive Train and Power
Delivered Horse Power (DHP) - Power delivered
to the propeller - DHPSHP losses in
shafting, shaft bearings and seals Thrust Horse
Power (THP) - Power created by the
screw/propeller (ie prop thrust) - THPDHP
Propeller losses
EHP
BHP
SHP
DHP
THP
Prop.
Hull
Shaft Bearing
E/G
R/G
Relative Magnitudes?
BHPgtSHPgtDHPgtTHP
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7.3 Effective Horse Power (EHP)

• EHP The power required to move the ship hull
  at a given
• speed in the absence of propeller action
  (related to resistance)
• (EHP is not related with Power Train
  System)
• EHP can be determined from the towing tank
  experiments at
• the various speeds of the model ship.
• EHP of the model ship is converted into EHP of
  the full scale
• ship by the Froudes Law.
• EHP is approximately equal to THP (usually
  slightly less)

Measured EHP
V
Towing carriage
Towing Tank
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Effective Horse Power (EHP)
Typical EHP Curve of YP
What EHP is required for the 12 knot YP cruise?
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Effective Horse Power (EHP)
Efficiencies

• Hull Efficiency

• Hull efficiency changes due to hull-propeller
  interactions.
• Well-designed ship
• Poorly-designed ship

• Flow is not smooth.
• THP is reduced.
• - High THP is needed
• to get designed speed.

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Effective Horse Power (EHP)
Efficiencies (contd)
EHP

• Propeller Efficiency

Screw
THP
DHP
SHP

• Propulsive Coefficient (PC) An overall measure
  of drive train efficiency

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7.5 Total Hull Resistance

• Total Hull Resistance (RT)
• The force that the ship experiences opposite
  to the motion of
• the ship as it moves.
• EHP Calculation

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Total Hull Resistance (cont)

• Coefficient of Total Hull Resistance
• - Non-dimensional value of total resistance

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Total Hull Resistance (cont)

• Coefficient of Total Hull Resistance (contd)

• Total Resistance of full scale ship can be
  determined using

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Total Hull Resistance (cont)

• Relation of Total Resistance Coefficient and
  Speed

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7.6 Components of Total Resistance

• Total Resistance

• Viscous Resistance
• - Resistance due to the viscous stresses that
  the fluid exerts
• on the hull.
• ( i.e. due to friction of the water against
  the surface of the ship)
• - Water viscosity, ships velocity, wetted
  surface area and roughness of the ship generally
  affect the viscous resistance.
• Characterized by the non-dimensional Reynolds
  Number, Rn

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Components of Total Resistance

• Wave-Making Resistance
• - Resistance caused by waves generated by the
  motion of the ship
• - Wave-making resistance is affected by beam
  to length ratio,
• displacement, shape of hull, (ship length
  speed)
• Characterized by the non-dimensional Froude
  Number, Fn
• Air Resistance
• - Resistance caused by the flow of air over
  the ship with no
• wind present
• - Air resistance is affected by projected
  area, shape of the ship
• above the water line, wind velocity and
  direction
• - Typically 4 8 of the total resistance

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Components of Total Hull Resistance

• Total Resistance and Relative Magnitude of
  Components

Air Resistance
Hollow
Wave-making
Hump
Resistance (lb)
Viscous
Speed (kts)

• Low speed Viscous R dominates
• Higher speed Wave-making R dominates
• Hump (Hollow) location is function of ship
  length and speed.

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Coefficient of Viscous Resistance

• Viscous Flow around a ship

Real ship Turbulent flow exists from near the
bow. Model ship Studs or sand strips are
attached at the bow to
create the turbulent flow.
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Coefficient of Viscous Resistance (cont)

• Coefficients of Viscous Resistance
• - Non-dimensional quantity of viscous
  resistance
• - It consists of tangential and normal
  components.

normal
tangential
flow
stern
ship
bow

• Tangential Component
• - Tangential stress is parallel to ships hull
  and causes
• a net force opposing the motion Skin
  Friction
• - It is assumed can be obtained
  from data of flat plates.

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Coefficient of Viscous Resistance (cont)
Semi-empirical equation
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Coefficient of Viscous Resistance (cont)

• Tangential Component (contd)
• - Relation between viscous flow and Reynolds
  number
• Laminar flow In laminar flow, the
  fluid flows in layers
• in an orderly fashion. The layers do not
  mix transversely
• but slide over one another.
• Turbulent flow In turbulent flow, the
  flow is chaotic and
• mixed transversely.

Flow over flat plate
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Coefficient of Viscous Resistance (cont)

• Normal Component
• - Normal component causes a pressure
  distribution along the
• underwater hull form of ship
• - A high pressure is formed in the forward
  direction opposing
• the motion and a lower pressure is formed
  aft.
• - Normal component generates the eddy behind
  the hull.
• - It is affected by hull shape.
• Fuller shape ship has larger normal
  component than slender
• ship.

large eddy
Full ship
Slender ship
small eddy
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Coefficient of Viscous Resistance (cont)

• Normal Component (contd)
• - It is calculated by the product of Skin
  Friction with Form Factor.

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Summary of Viscous Resistance Coefficient

• Reducing the Viscous Resistance Coefficient

• Method Increasing L with constant submerged
  volume
• 1) Form Factor K ? ? Normal component KCF ?
• ? Slender hull is favorable. ( Slender
  hull form will create
• a smaller pressure difference
  between bow and stern.)
• 2) Reynolds No. Rn ? ? CF ? ? KCF ?

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Wave-Making Resistance

• Definition refer to the previous note
• Typical Wave Pattern

Stern divergent wave
Bow divergent wave
Bow divergent wave
L
Transverse wave
Wave Length
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Wave-Making Resistance
Transverse wave system Waves perpendicular to
wake

• It travels at approximately the same speed as
  the ship.
• At slow speed, several crests exist along the
  ship length
• because the wave lengths are smaller than the
  ship length.
• As the ship speeds up, the length of the
  transverse wave
• increases.
• When the transverse wave length approaches the
  ship length,
• the wave making resistance increases very
  rapidly.
• This is the main reason for the dramatic
  increase in
• Total Resistance as speed increases.

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Wave-Making Resistance (cont)
Transverse wave System
Vs lt Hull Speed
Vs ? Hull Speed
Hull Speed speed at which the transverse wave
length equals the ship
length. (Wavemaking resistance drastically
increases above hull speed)

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Wave-Making Resistance (cont)
Divergent Wave System waves that angle out

• It consists of Bow and Stern Waves.
• Interaction of the bow and stern waves create
  the Hollow or
• Hump on the resistance curve.
• Hump When the bow and stern waves are in
  phase,
• the crests are added up so that larger
  divergent wave systems
• are generated.
• Hollow When the bow and stern waves are out
  of phase,
• the crests match the troughs so that smaller
  divergent wave
• systems are generated.

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Wave-Making Resistance (cont)
Calculation of Wave-Making Resistance Coeff.

• Wave-making resistance is influenced by
• - beam to length ratio
• - displacement
• - hull shape
• - Froude number
• The calculation of the coefficient is too
  complex for a simple theoretical or empirical
  equation.
• (Because mathematical modeling of the flow
  around ship
• is very complex since there exists fluid-air
  boundary,
• wave-body interaction)
• Therefore model test in the towing tank and
  Froude expansion
• are the best way to calculate the Cw of the
  real ship.

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Wave-Making Resistance (cont)
Reducing Wave Making Resistance
1) Increasing ship length to reduce the
transverse wave - Hull speed will increase.
- Therefore increment of wave-making resistance
of longer ship will be small until the
ship reaches to the hull speed.
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Wave-Making Resistance (cont)
Reducing Wave Making Resistance (contd)
2) Attaching Bulbous Bow to reduce the bow
divergent wave - Bulbous bow generates the
second bow waves . - Then the waves interact
with the bow wave resulting in ideally no
waves, practically smaller bow divergent waves.
- EX DDG 51 7 reduction
in fuel consumption at cruise speed
3 reduction at max speed.
design retrofit cost less
than 30 million
life cycle fuel cost saving for all the ship
250 mil. Tankers Containers
adopting the Bulbous bow 3) Stern flaps -
helps with launching small boats, too!
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Wave-Making Resistance (cont)
Bulbous Bow
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Coefficient of Total Resistance
Coefficient of total hull resistance the Cs
added
Correlation Allowance

• It accounts for hull resistance due to surface
  roughness,
• paint roughness, corrosion, and fouling of the
  hull surface.
• It is only used when a full-scale ship
  prediction of EHP is made
• from model test results.
• For model,
• For ship, empirical formulas can be used.

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Other Type of Resistances

• Appendage Resistance
• - Frictional resistance caused by the
  underwater appendages
• such as rudder, propeller shaft, bilge
  keels and struts
• - 2?24 of the total resistance in naval ship.
• Steering Resistance
• - Resistance caused by the rudder motion.
• - Small in warships but troublesome in sail
  boats
• Added Resistance
• - Resistance due to sea waves which will cause
  the ship
• motions (pitching, rolling, heaving,
  yawing).

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Other Resistances

• Increased Resistance in Shallow Water
• - Resistance caused by shallow water effect
• - Flow velocities under the hull increases in
  shallow water.
• Increment of frictional resistance due to
  the velocities
• Pressure drop, suction, increment of
  wetted surface area
• ? Increases frictional resistance
• - The waves created in shallow water take more
  energy from
• the ship than they do in deep water for the
  same speed.
• ? Increases wave making resistance

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7.7 Basic Theory Behind Ship Modeling

• Modeling a ship
• - Not possible to measure the resistance of
  the prototype ship
• - The ship needs to be scaled down to test
  in the tank but
• the scaled ship (model) must behave in
  exactly same way
• as the real ship.
• - How to scale the prototype ship ?
• How to make relationships between the
  prototype and model
• data?
• - Geometric and Dynamic similarity must be
  achieved.

prototype ship
model ship
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Basic Theory behind Ship Modeling

• Geometric Similarity
• - Geometric similarity exists between model
  and
• prototype if the ratios of all
  characteristic dimensions
• in model and prototype are equal.
• - The ratio of the ship length to the model
  length is typically
• used to define the scale factor.

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Basic Theory behind Ship Modeling

• Dynamic Similarity
• - Dynamic Similarity exists between model
  and prototype
• if the ratios of all forces in model and
  prototype are the
• same.
• - Total Resistance Frictional Resistance
  Wave MakingOthers

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Basic Theory behind Ship Modeling

• Dynamic Similarity (contd)
• - Both Geometric and Dynamic similarity
  cannot be achieved
• at same time in the model test because
  making both Rn and
• Fn the same for the model and ship is not
  physically possible.

Example
Ship Length100ft, Ship Speed10kts, Model
Length10ft Model speed to satisfy both geometric
and dynamic similitude?
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Basic Theory behind Ship Modeling

• Dynamic Similarity (contd)
• - Choice ?
• Make Fn the same for the model.
• Have Rn different
• ? Incomplete dynamic similarity
• - However partial dynamic similarity can be
  achieved by
• towing the model at the corresponding
  speed
• - Due to the partial dynamic similarity, the
  following
• relations in forces are established.

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Basic Theory behind Ship Modeling

• Corresponding Speeds

• Example
• Ship length 200 ft, Model length 10
  ft
• Ship speed 20 kts, Model speed towed ?
  

1kts1.688 ft/s
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Chap 7.7 Basic Theory Behind Ship Modeling

• Modeling Summary

1)
2)
3)
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7.9 The Screw Propeller
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7.9 Screw Propeller
Diameter Hub Blade Tip Blade Root
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Pitch Distance Pitch Angle Fixed Pitch
Variable Pitch Controllable Pitch (Constant Speed)
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7.9 Screw Propeller

• Variable Pitch (the standard prop)
• - The pitch varies at the radial distance
  from the hub.
• - Improves the propeller efficiency.
• - Blade may be designed to be adjusted to a
  different
• pitch setting when propeller is stopped.
• Controllable Pitch
• - The position of the blades relative to the
  hub can be
• changed while the propeller is rotating.
• - This will improve the control and ship
  handling.
• - Expensive and difficult to design and build

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Right and Left Hand Props
Right Hand
Left Hand
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Suction Face
Leading Edge
Trailing Edge
Pressure Face
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Propeller Walk

• Due to a difference in the pressure at the top
  and bottom of the prop (due to boundary layer),
  the lower part of the prop works harder.
• This leads to a slight turning moment.
• Right hand props cause turns to port when moving
  ahead.

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Prop Walk Solutions

• Twin Screws
• Counter rotating propellers (one shaft)
• Tunnels/shrouds (nozzle)

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Shrouded (nozzle) prop
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7.9 Skewed Screw Propeller
Highly Skewed Propeller
Advantages

• Reduce interaction between
• propeller and rudder wake.
• - Reduce vibration and noise

Disadvantages

• Expensive
• Less efficient operating in
• reverse

DDG51
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7.9. Propeller Theory
Propeller Theory

• Speed of Advance

• The ship drags the surrounding water so that the
  wake to
• follow the ship with a wake speed (Vw) is
  generated in the
• stern.
• The flow speed at the propeller is,

Speed of Advance
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7.9 Propeller Theory
Propeller Efficiency
70 for well-designed prop
Maximum
- For a given T (Thrust),
Ao
(Diameter ) CT Prop Eff
The larger the diameter of propeller, the better
the propeller efficiency
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Chap 7.9.3 Propeller Cavitation

• Cavitation Definition

• The formation and subsequent collapse of vapor
  bubbles
• on propeller blades where pressure has fallen
  below the
• vapor pressure of water.
• - Bernoullis Equation can be used to predict
  pressure.
• Cavitation occurs on propellers (or rudders)
  that are heavily loaded, or are experiencing a
  high thrust loading coefficient.

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1 atm101kpa 14.7psi
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Blade Tip Cavitation
Navy Model Propeller 5236
Flow velocities at the tip are fastest so that
pressure drop occurs at the tip first.
Sheet Cavitation
Large and stable region of cavitation covering
the suction face of propeller.
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Propeller Cavitation
Consequences of Cavitation
1) Low propeller efficiency (Thrust
reduction) 2) Propeller erosion (mechanical
erosion as bubbles collapse, up to 180 ton/in²
pressure) 3) Vibration due to uneven loading 4)
Cavitation noise due to impulsion by the bubble
collapse
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Propeller Cavitation

• Preventing Cavitation

• Remove fouling, nicks and scratch.
• Increase or decrease the engine RPM smoothly to
  avoid
• an abrupt change in thrust.
• rapid change of rpm ? high propeller
  thrust but small
• change in VA ? larger CT ? cavitation
• low propeller efficiency
• Keep appropriate pitch setting for controllable
  pitch propeller
• For submarines, diving to deeper depths will
  delay or prevent cavitation as hydrostatic
  pressure increases.

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Propeller Cavitation

• Ventilation

• If a propeller or rudder operates too close to
  the water surface, surface air or exhaust gases
  are drawn into the propeller blade due to the
  localized low pressure around propeller. The prop
  digs a hole in the water.
• The load on the propeller is reduced by the
  mixing of air or exhaust gases into the water
  causing effects similar to those for cavitation.
• Ventilation often occurs in ships in a very light
  condition(small draft), in rough seas, or during
  hard turns.

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Other forms of propulsion
A one horsepower cable-drawn ferry!