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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!. Ship Drive Train and Power. 7.2 Ship Drive Train System. Engine.

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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!


Ship Drive Train and Power

7.2 Ship Drive Train System














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)

- SHP=BHP - losses in reduction gear


Ship Drive Train and Power

Delivered Horse Power (DHP)

- Power delivered to the propeller

- DHP=SHP – losses in shafting, shaft bearings and seals

Thrust Horse Power (THP)

- Power created by the screw/propeller (ie prop thrust)

- THP=DHP – Propeller losses












Relative Magnitudes?



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.
  • EHPof the model ship is converted into EHP of the full scale
  • ship by the Froude’s Law.
  • EHP is approximately equal to THP (usually slightly less)

Measured EHP


Towing carriage

Towing Tank


Effective Horse Power (EHP)

Typical EHP Curve of YP

What EHP is required for the 12 knot YP cruise?




Effective Horse Power (EHP)


  • 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.

Effective Horse Power (EHP)

Efficiencies (cont’d)


  • Propeller Efficiency





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

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

Total Hull Resistance (cont)

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

Total Hull Resistance (cont)

  • Coefficient of Total Hull Resistance(cont’d)
  • Total Resistance of full scale ship can be determined using

Total Hull Resistance (cont)

  • Relation of Total Resistance Coefficient and Speed

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, ship’s velocity, wetted surface area and roughness of the ship generally affect the viscous resistance.
  • Characterized by the non-dimensional Reynold’s Number, Rn

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

Components of Total Hull Resistance

  • Total Resistance and Relative Magnitude of Components

Air Resistance




Resistance (lb)


Speed (kts)

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

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.


Coefficient of Viscous Resistance (cont)

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







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

Laminar Flow

Turbulent Flow

Coefficient of Viscous Resistance (cont)

  • Tangential Component(cont’d)
  • - 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


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


Coefficient of Viscous Resistance (cont)

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

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 

Wave-Making Resistance

  • Definition : refer to the previous note
  • Typical Wave Pattern

Stern divergent wave

Bow divergent wave

Bow divergent wave


Transverse wave

Wave Length


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.







Wave Length

Wave-Making Resistance (cont)

Transverse wave System

Vs < 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)


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.

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.

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.


Wave-Making Resistance (cont)

Reducing Wave Making Resistance (cont’d)

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!


Coefficient of Total Resistance

Coefficient of total hull resistance: the C’s 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.

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).

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







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


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.

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 Making+Others

Basic Theory behind Ship Modeling

  • Dynamic Similarity (cont’d)
  • - 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.


Ship Length=100ft, Ship Speed=10kts, Model Length=10ft

Model speed to satisfy both geometric and dynamic similitude?


Basic Theory behind Ship Modeling

  • Dynamic Similarity (cont’d)
  • - 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.

Basic Theory behind Ship Modeling

  • Corresponding Speeds
  • Example :
  • Ship length = 200 ft, Model length : 10 ft
  • Ship speed = 20 kts, Model speed towed ?

1kts=1.688 ft/s


Measured in tank



Chap 7.7 Basic Theory Behind Ship Modeling

  • Modeling Summary





7.9 Screw Propeller



Blade Tip

Blade Root


Pitch Distance

Pitch Angle

Fixed Pitch

Variable Pitch

Controllable Pitch

(Constant Speed)


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
right and left hand props

Right and Left Hand Props

Left Hand

Right Hand


Suction Face

Leading Edge

Trailing Edge

Pressure Face

propeller walk
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.
prop walk solutions
Prop Walk Solutions
  • Twin Screws
  • Counter rotating propellers (one shaft)
  • Tunnels/shrouds (nozzle)

7.9 Skewed Screw Propeller

Highly Skewed Propeller


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


  • Expensive
  • Less efficient operating in
  • reverse




Wake Region


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


7.9 Propeller Theory

Propeller Efficiency

~70 % for well-designed prop


- For a given T (Thrust),


(Diameter ) ; CT ; Prop Eff

The larger the diameter of propeller, the better the propeller efficiency


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.
  • - Bernoulli’s 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.

1 atm=101kpa



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.


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


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.

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.
other forms of propulsion
Other forms of propulsion

A one horsepower cable-drawn ferry!