Basics of Ship Resistance

2

Chap 7 Resistance and Powering of Ship

Objectives

• Prediction of Ship’s Power- Ship’s driving system and concept of power- Resistance of ship and its components

· frictional resistance· wave-making resistance· others

- Froude expansion- Effective horse power calculation

• Propeller Theory- Propeller components and definitions- Propeller theory- Cavitation

3

Ship Drive Train and Power

Ship Drive Train System

Engine ReductionGear Bearing Seals

ScrewStrut

BHP SHP DHP

THP

EHP

4

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

- SHP=BHP - losses in reduction gear

Horse Power in Drive Train


5

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- THP=DHP – Propeller losses

Relative Magnitudes

BHP>SHP>DHP>THP>EHP

E/G R/GBHP SHP Shaft

Bearing Prop.DHP THP EHP

Hull


6

Effective Horse Power (EHP)

• EHP : The power required to move the ship hull at a given speed in the absence of propeller action

(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 Froude’s Law.

VTowing Tank Towing carriage

Measured EHP

7


0

200

400

600

800

1000

Effe

ctiv

e H

orse

pow

er, E

HP

(HP

)

0 2 4 6 8 10 12 14 16 Ship Speed, Vs (Knots)

POWER CURVEYARD PATROL CRAFT

Typical EHP Curve of YP

8


Efficiencies• Hull Efficiency

THPEHP

H =η

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

1fHη1pHη

Well-designed

Poorly-designed- Flow is not smooth.- THP is reduced.- High THP is neededto get designed speed.

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Screw


Efficiencies (cont’d)

• Propeller Efficiency

DHPTHP

propeller =η

• Propulsive Coefficients (PC)

SHPEHP

p =η

propeller designed for well 6.0≈pη

SHP DHP

THP

EHP

10

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

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎠⎞

⎜⎝⎛⋅

=

P

ST

P

s Hft lb

sftV(lb) R

)EHP(H550 ship of speedV

resistance hull total

S ==TR

( )

P

ST

Hatts

WattssJ

sftlb

sftlbVR

550/1W 1

:

=

==⋅

=⎟⎠⎞

⎜⎝⎛⋅⇒⋅ Power

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Total Hull Resistance (cont)

• Coefficient of Total Hull Resistance

- Non-dimensional value of total resistance

5.0 2 SV

RCs

TT ρ=

hull submerged theon area surface wettedship of Speed

density Fluid resistance hull Total

watercalm in resistance hull totaloft Coefficien

=====

SV

RC

S

T

T

ρ

dimension-nonlb 2

2

4

2⇐

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅⇒

ftsft

ftslb

12


• Coefficient of Total Hull Resistance (cont’d)

-Total Resistance of full scale ship can be determined using

ST VSC , , andρ

TST CSVlbR ⋅= 25.0)( ρ

speed ship scale Fullform of Curves from obtained

table property water from availabletest model the by determined

: : : :

S

T

VS

Cρ

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• Relation of Total Resistance Coefficient and Speed

0

5000

10000

15000

20000

Tota

l Res

ista

nce,

Rt (

lb)

0 2 4 6 8 10 12 14 16 Ship Speed, Vs (knots)

TOTAL RESISTANCE CURVEYARD PATROL CRAFT

speed highat 5 o t speedlow at 2 from

2

=∝

⋅≈

nV

VCRn

S

STT

speed highat 6 to speedlow at 3 from

2

=∝

⋅⋅≈≈

nV

VVCVREHPn

S

SSTST

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Components of Total Resistance

• Total Resistance

AWVT RRRR ++=Resistance Viscous: RV

Resistance Making Wave: RWResistance Air: RA

• Viscous Resistance- Resistance due to the viscous stresses that the fluid exertson the hull.( due to friction of the water against the surface of the ship)

- Viscosity, ship’s velocity, wetted surface area of ship generally affect the viscous resistance.

15

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, Froude number (ship length & speed)

• Air Resistance- Resistance caused by the flow of air over the ship with nowind present

- Air resistance is affected by projected area, shape of the shipabove 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

Viscous

Air Resistance

Wave-making

Speed (kts)

Res

ista

nce

(lb)

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

HumpHollow

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Why is a Golf Ball Dimpled?

• Let’s look at a Baseball (because that’s what I have numbers for)– At the velocities of 50 to 130 mph dominant in baseball the air

passes over a smooth ball in a highly resistant flow.– Turbulent flow does not occur until nearly 200 mph for a smooth

ball– A rough ball (say one with raised stitches like a baseball) induces

turbulent flow

– A baseball batted 400 feet would only travel 300 feet if it was smooth.

– A non-dimpled golf ball would really hamper Tiger Woods’ long game

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Coefficient of Viscous Resistance

• Viscous Flow around a ship

Real ship : Turbulent flow exists 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.

FF KCC +=+= normaltangentialV CCC

• 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 the experimental data of flat plate.

FC

flow shipbow sterntangentialno

rmal

FC

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νS

n

nF

FV

LVR

RC

CC

=

−=

=

)2(log075.0

210

of Component Tangential

Semi-empiricalequation

watersalt for water freshfor

/sft101.2791/sft101.2260

/s)(ft ViscosityKinematic

)Speed(ft/s Ship(ft)L

Number Reynolds

25-

25-

2

pp

×=

×=

=

=

==

νS

n

VL R

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• 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 transverselybut slide over one another.

· Turbulent flow : In turbulent flow, the flow is chaotic and mixed transversely.

Laminar Flow Turbulent Flow5105×< about Rn

5105 ×> about Rn

Flow overflat plate

22

• 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 slendership.

Full shipSlender ship

large eddy

small eddy


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• Normal Component (cont’d)

- It is calculated by the product of Skin Friction with Form Factor.

23

)()(

)()()()(ft 19 K

K

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∇=

==

=

ftLftB

ftTftBftL

CCKC

F

Fv

Factor FormCoeff. Friction Skin

of Component Normal


24

23

)()(

)()()()(ft 19 K ⎟⎟

⎠

⎞⎜⎜⎝

⎛ ∇=

ftLftB

ftTftBftL

FF C KC +=+= normaltangentialV CCC

210 )2(log

075.0−

=n

F RC

Summary of Viscous Resistance Coefficient

watersalt for water freshfor

/sft101.2791/sft101.2260

/s)(ft ViscosityKinematic

)Speed(ft/s Ship(ft)L

Number Reynolds

25-

25-

2

pp

×=

×=

=

=

==

=

ν

ν

S

n

Sn

VL R

LVR K= Form Factor

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• Reducing the Viscous Resistance Coeff.

- Method : Increase L while keeping the submerged volume constant

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 ↓

Summary of Viscous Resistance Coefficient

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Wave-Making Resistance

Typical Wave Pattern

Bow divergent waveBow divergent wave

Transverse waveL

Wave Length

Stern divergent wave

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Wave-Making Resistance

Transverse wave System

• 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

Wave Length

WaveLength

SlowSpeed

HighSpeed

Vs < Hull Speed

Vs ≈ Hull Speed

Hull Speed : speed at which the transverse wave length equalsthe ship length.

(Wavemaking resistance drastically increases above hull speed)

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Divergent Wave System

• 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 matches the trough so that smaller divergent wave

systems are generated.


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Calculation of Wave-Making Resistance Coeff.• Wave-making resistance is affected by

- beam to length ratio- displacement- hull shape- Froude number

• The calculation of the coefficient is far difficult and inaccuratefrom any theoretical or empirical equation.(Because mathematical modeling of the flow around shipis very complex since there exists fluid-air boundary, wave-body interaction)

• Therefore model test in the towing tank and Froude expansionare needed to calculate the Cw of the real ship.


32

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. - EX :

FFG7 : ship length 408 ft Which ship requires morehull speed 27 KTS horse power at 35 KTS?

CVN65 : ship length 1040 fthull speed 43 KTS


33

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 speed3% 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


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Bulbous Bow


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Coefficient of Total Resistance

Allowancen Correlatio 1

: C CCK)(C

CCCC

A

AWF

AWVT

+++=++=

Coefficient of total hull resistance

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.

. 0 smooth is surface model Since=AC

36

Other Type of Resistances

• Appendage Resistance- Frictional resistance caused by the underwater appendagessuch 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).

37

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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Basic Theory Behind Ship Modeling• Modeling a ship

- It is not possible to measure the resistance of the full-scale ship- The ship needs to be scaled down to test in the tank but

the scaled ship (model) must behave in exactly same wayas the real ship.

- How do we scale the prototype ship ?- Geometric and Dynamic similarity must be achieved.

?Dimension

SpeedForce

prototype Model

prototype shipmodel 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 dimensionsin model and prototype are equal.

- The ratio of the ship length to the model length is typicallyused to define the scale factor.

Volume :

Area :

:

Factor Scale

3

33

2

22

)(ft)(ft

)(ftS)(ftS

(ft)L(ft)L

λ

M

S

M

S

M

S

∇∇

=

=

=

=

λ

λ

λ Length ModelM

shi scale fullS :

p:

40


• Dynamic Similarity- Dynamic Similarity exists between model and prototype

if the ratios of all forces in model and prototype are thesame.

- Total Resistance : Frictional Resistance+ Wave Making+Others

S

MSM

M

S

S

MSM

M

M

S

S

M

MM

S

SS

nMnSnMnS

nWnV

LLVV

LL

vvVV

gLV

gLV

vVL

vVL

FFRRFfCRfC

==

==

====

,

,

)( ),(

,

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• 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.

)(1 10010)(10

ktsftftkts

LLVV

S

MSM

=

=

=

)(100

) (assume 10

100)(10

kts

vvftftkts

LL

vvVV

SM

M

S

S

MSM

=

==

=

Example

Ship Length=100ft, Ship Speed=10kts, Model Length=10ftModel speed to satisfy both geometric and dynamic similitude?

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• 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.

WSWM CC =

VSVM CC ≠

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• Corresponding Speeds

M

M

S

SnMnS gL

VgLVFF == ,

- Example :Ship length = 200 ft, Model length : 10 ftShip speed = 20 kts, Model speed towed ?

ktsktsV

LLV

LLVV

S

MSS

S

MSM

47.4 201201

/1

===

==

λ

(ft)L(ft/s)V

(ft)L(ft/s)V

M

M

S

S =

1kt.=1.688 ft/s

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Basic Theory behind Ship Modeling• Modeling Summary

AWFAWVT CCKCCCCC +++=++= )1(

AMWMMFMTM CCKCC +++= )1(

)5.0*( 550

)(

)1(

2sSSTSTS

STS

ASWSSFSTS

VSCRVRhpEHP

CCKCC

ρ=⋅

=

+++=

AMFMTMWM CKCCC −+= − )1(FroudeExpansion

Measured in tank

)calculatedor (given, 0smooth) is Model( 0

)givenor Calculated .factor scale todue( d)(calculate ,

)//V ,( S

≠=

=

===

AS

AM

MS

FSFM

MMSnMnSWMWS

CC

KKCC

gLVgLFFCC

Q

Q

λ

1)

2)

3)

Basics of Ship Resistance

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