Chapter 7

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 ReductionGear

Bearing Seals

ScrewStrut

BHP SHP DHP

THP

Shaft

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

Horse Power in Drive Train


Delivered Horse Power (DHP) - Power delivered to the propeller - DHP=SHP – losses in shafting, shaft bearings and sealsThrust Horse Power (THP) - Power created by the screw/propeller (ie prop thrust) - THP=DHP – Propeller losses

Relative Magnitudes?

BHP>SHP>DHP>THP

E/G R/GBHP SHP Shaft

Bearing Prop.DHP THP EHP

Hull


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 Froude’s Law.EHP is approximately equal to THP (usually slightly less)

VTowing Tank Towing carriage

Measured EHP

Effective Horse Power (EHP)

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

What EHP is required for the 12 knot YP cruise?


Efficiencies

• Hull Efficiency

THPEHP

H

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

1H1H

Well-designed

Poorly-designed

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

Screw


Efficiencies (cont’d)

• Propeller Efficiency

DHPTHP

propeller

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

SHPEHP

p

propeller designed for well 6.0p

SHP DHPTHP

EHP

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

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

Total Hull Resistance (cont)

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

S V 5.0

RC 2s

TT

hull submerged theon area surface wettedship of Speed

density Fluid resistance hull Total

watercalm in resistance hull totaloft Coefficien

SV

RC

S

T

T

dimension-nonlb 2

2

4

2

ftsft

ftslb


• Coefficient of Total Hull Resistance (cont’d)

-Total Resistance of full scale ship can be determined using

ST VSC , , and

TST CSVlbR 25.0)(

speed ship scale Fullform of Curves from obtained

table propertywater from availabletest model the by determined

:V : S :

:C

S

T


• 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

7.6 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 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

Viscous

Air Resistance

Wave-making

Speed (kts)

Res

ista

nce

(lb)

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

Hump

Hollow

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.

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 data of flat plates.

FC

flow shipbow stern

FC

tangential

norm

al


S

n

nF

FV

LVR

RC

CC

)2(log075.0

210

of Component Tangential

Semi-empirical equation

watersalt for water freshfor

/sft101.2791/sft101.2260

/s)(ft ViscosityKinematic

)Speed(ft/s Ship(ft)L

Number Reynolds

25-

25-

2

pp

S

n

V

L R


• 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.

Laminar Flow Turbulent Flow

Flow overflat plate

5105about Rn5105 about Rn

• 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.

Full shipSlender ship

large eddy


small eddy

• 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


• 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

Summary of Viscous Resistance Coefficient

Wave-Making Resistance

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

Bow divergent waveBow divergent wave

Transverse wave

L

Wave Length

Stern divergent wave

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-Making Resistance (cont)

Transverse wave System

Wave Length

WaveLength

SlowSpeed

“Hull”Speed

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)

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.


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.


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.


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!


Bulbous Bow


Coefficient of Total Resistance

Allowancen Correlatio : C CCK)1(C

CCCC

A

AWF

AWVT

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.

. 0 smooth is surface model SinceAC

Other Type of Resistances

• Appendage Resistance - Frictional resistance caused by the underwater appendages such as rudder, propeller shaft, bilge keels and struts - 224% 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.

?Dimension

SpeedForce

prototype Model

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.

Volume :

Area :

:

Factor Scale

3

33

2

22

)(ft)(ft

)(ftS)(ftS

(ft)L(ft)L

λ

M

S

M

S

M

S

Length ModelM

shi scale fullS :

p:


• 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

S

MSM

M

S

S

MSM

M

M

S

S

M

MM

S

SS

nMnSnMnS

nWnV

LLVV

LL

vvVV

gLV

gLV

vVL

vVL

FFRRFfCRfC

,

,

)( ),(

,


• 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.

)kts(16.3 ft100

ft10)kts(10

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?


• 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


• Corresponding Speeds

M

M

S

SnMnS gL

VgLVFF ,

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

ktsktsV

LLV

LLVV

S

MSS

S

MSM

47.4 201201

/1

(ft)L(ft/s)V

(ft)L(ft/s)V

M

M

S

S

1kts=1.688 ft/s

Chap 7.7 Basic Theory Behind Ship Modeling• Modeling Summary

AWFAWVT CCKCCCCC )1(

AMWMMFMTM CCKCC )1(

)5.0*( 550

)(

)1(

2sSSTSTS

STS

ASWSSFSTS

VSCRVRhpEHP

CCKCC

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

1)

2)

3)

7.9 The Screw Propeller

7.9 Screw Propeller

DiameterHubBlade TipBlade Root

Pitch DistancePitch AngleFixed Pitch

Variable PitchControllable 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 HandLeft Hand

Pressure Face

Suction Face

Leading Edge

Trailing Edge

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

Shrouded (nozzle) prop

7.9 Skewed Screw PropellerHighly Skewed Propeller

DDG51

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

Advantages

Disadvantages- Expensive- Less efficient operating in reverse

7.9. Propeller Theory

Propeller Theory• Speed of Advance

Q

PWake Region

SV WV

0waterV

Swater VV

• 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,

WSA VVV Speed of Advance

7.9 Propeller Theory

Propeller Efficiency

tpropeller C

112

DHPTHP

propeller

~70 % for well-designed prop

oAT AV

TC 25.0

- For a given T (Thrust),Ao (Diameter ) ; CT ; Prop Eff

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

Maximumdiscpropeller projected theofArea :A r thrust Propelle:

tcoefficien loadingThrust :

o

TCT

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 =14.7psi

Blade Tip Cavitation

Sheet Cavitation

Navy Model Propeller 5236

Flow velocities at the tip are fastest so that pressure drop occurs at the tip first.

Large and stable region of cavitation covering the suction face of propeller.

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.


• 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

A one horsepower cable-drawn ferry!

Chapter 7

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Transcript of Chapter 7