Basics of Ship Resistance

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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

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Ship Drive Train and Power Ship Drive Train System EHP Engine

Reduction Gear

Bearing

Strut Screw Seals THP

BHP

SHP

DHP 3

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 - SHP=BHP - losses in reduction gear

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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 - THP=DHP – Propeller losses E/G

BHP

R/G

SHP

Shaft Bearing

DHP

Prop.

THP

Hull

EHP

Relative Magnitudes BHP>SHP>DHP>THP>EHP

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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. Towing Tank

Measured EHP V Towing carriage

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Effective Horsepower, EHP (HP)

Effective Horse Power (EHP) POWER CURVE YARD PATROL CRAFT

1000 800 600 400 200 0 0

2

4

6

8

10

12

14

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Ship Speed, Vs (Knots)

Typical EHP Curve of YP

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Effective Horse Power (EHP) Efficiencies • Hull Efficiency

EHP ηH = THP - Hull efficiency changes due to hull-propeller interactions. - Well-designed ship : η H  1 - Poorly-designed ship : η H 1 Well-designed

Poorly-designed

- Flow is not smooth. - THP is reduced. - High THP is needed 8 to get designed speed.

Effective Horse Power (EHP) Efficiencies (cont’d) EHP • Propeller Efficiency

η propeller

Screw

THP = DHP

• Propulsive Coefficients (PC)

THP SHP

DHP

EHP ηp = SHP

η p ≈ 0.6 for well designed propeller

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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

 ft  RT (lb) ⋅ VS   s EHP(H P ) =  ft lb   550  s HP 

RT = total hull resistance VS = speed of ship

 ft  lb ⋅ ft J RT ⋅V S ⇒ ( lb ) ⋅   = = = Watts : Power s s  s  1 Watts = 1 / 550 H P 10

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

RT lb ⇒ ⇐ non - dimension CT = 2 2  lb ⋅ s 2  ft  2 0.5ρ Vs S  4   ft  ft

 s 

CT = Coefficient of total hull resistance in calm water RT = Total hull resistance

ρ = Fluid density VS = Speed of ship S = wetted surface area on the submerged hull

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

CT , ρ , S and VS

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RT (lb) = 0.5ρSVS ⋅ CT CT : determined by the model test

ρ : available from water property table S : obtained from Curves of form VS : Full scale ship speed 12

Total Resistance, Rt (lb)

Total Hull Resistance (cont)

• Relation of Total Resistance Coefficient and Speed TOTAL RESISTANCE CURVE YARD PATROL CRAFT

20000

15000

10000

5000

0 0

RT ≈ CT ⋅ VS ∝ VS

2

4

6

8

10

12

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Ship Speed, Vs (knots)

2

n

n = from 2 at low speed to 5 at high speed

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2

EHP ≈ RTVS ≈ CT ⋅ VS ⋅ VS ∝ VS

n

n = from 3 at low speed to 6 at high speed 13

Components of Total Resistance • Total Resistance

RT = RV + RW + RA RV : Viscous Resistance RW : Wave Making Resistance RA : Air Resistance • Viscous Resistance - Resistance due to the viscous stresses that the fluid exerts on 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. 14

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 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

Resistance (lb)

• Total Resistance and Relative Magnitude of Components

Air Resistance Hollow Hump

Wave-making

Viscous Speed (kts)

- Low speed : Viscous R - Higher speed : Wave-making R 16 - Hump (Hollow) : location is function of ship length and speed.

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 17 game

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. 18

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

flow

al m r o n

CV = Ctangential+ Cnormal= CF + KCF bow

l

tan

g

ia t n e

ship

stern

• Tangential Component : CF - Tangential stress is parallel to ship’s hull and causes a net force opposing the motion ; Skin Friction - It is assumed CF can be obtained from the experimental data of flat plate. 19

Coefficient of Viscous Resistance (cont) Tangential Component of CV = CF 0.075 CF = (log10 Rn − 2) 2

Semi-empirical equation

LVS Rn = ν

Rn = Reynolds Number L = L pp (ft)

VS = Ship Speed(ft/s)

ν = Kinematic Viscosity (ft 2 /s) = 1.2260 × 10 -5 ft 2 /s forfresh water 20

= 1.2791 × 10 ft /s for saltwater -5

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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 Laminar Flow

Turbulent Flow

Rn < about 5 × 10

5

Rn > about 5 × 10215

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 22

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

Normal Component of Cv = K CF CF = Skin Friction Coeff. K = Form Factor  ∇(ft ) B ( ft )   K = 19   L( ft ) B ( ft )T ( ft ) L( ft )  3

2

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Summary of Viscous Resistance Coefficient

CV = Ctangential+ Cnormal= CF + K CF 2 3 0.075  ∇(ft ) B ( ft )  CF =  2 K = 19   (log10 Rn − 2)  L( ft ) B ( ft )T ( ft ) L( ft ) 

LVS ν Rn = Reynolds Number Rn =

K= Form Factor

L = L pp (ft) VS = Ship Speed(ft/s)

ν = Kinematic Viscosity (ft 2 /s) = 1.2260 × 10-5 ft 2 /s forfresh water = 1.2791 × 10-5 ft 2 /s for saltwater

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Summary of Viscous Resistance Coefficient • 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 ↓

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Wave-Making Resistance Typical Wave Pattern Stern divergent wave

Bow divergent wave

L Transverse wave

Wave Length 26

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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. 28

Wave-Making Resistance (cont) Transverse wave System Vs < Hull Speed

Vs ≈ Hull Speed

Slow Speed Wave Length High Speed Wave Length

Hull Speed : speed at which the transverse wave length equals the ship length. 29 (Wavemaking resistance drastically increases above hull speed)

Wave-Making Resistance (cont) 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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Wave-Making Resistance (cont) 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 inaccurate from any 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 31 are needed 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. - EX : FFG7 : ship length 408 ft Which ship requires more hull speed 27 KTS horse power at 35 KTS? CVN65 : ship length 1040 ft hull speed 43 KTS

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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

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Wave-Making Resistance (cont) Bulbous Bow

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Coefficient of Total Resistance Coefficient of total hull resistance CT = CV + CW + C A = C F ( 1 + K) + CW + C A C A: Correlation Allowance

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, C A = 0 Since model surface is smooth. • For ship, empirical formulas can be used. 35

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). 36

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 37

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

prototype ship

prototype

? Dimension Speed Force

model ship

Model 38

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. Scale Factor = λ LS (ft) λ= : Length LM (ft) S S (ft 2 ) λ = S M (ft 2 )

: Area

∇ S (ft 3 ) λ = ∇ M (ft 3 )

: Volume

2

3

S : full scale ship M : Model

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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 Making+Others

CV = f ( Rn ),

CW = f ( Fn )

RnS = RnM ,

FnS = FnM

LSVS LMVM = , vS vM vM LS VM = VS , vS LM

VS VM = gLS gLM VM = VS

LM LS 40

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. Example Ship Length=100ft, Ship Speed=10kts, Model Length=10ft Model speed to satisfy both geometric and dynamic similitude? VM = VS

LM LS

10 ft = 10( kts ) 100 ft = 1( kts )

vM LS VM = VS vS LM

100 ft = 10( kts ) (assume vM = vS ) 10 ft 41 = 100( kts )

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.

CWM = CWS

CVM ≠ CVS

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Basic Theory behind Ship Modeling • Corresponding Speeds FnS = FnM ,

VS VM = gLS gLM

VS (ft/s) VM (ft/s) = LS (ft) LM (ft) - Example : Ship length = 200 ft, Model length : 10 ft Ship speed = 20 kts, Model speed towed ?

VM = VS = VS

LM 1 = VS LS LS / LM 1 1 = 20kts = 4.47 kts λ 20

1kt.=1.688 ft/s

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Basic Theory behind Ship Modeling • Modeling Summary

CT = CV + CW + C A = CF (1 + K ) + CW + C A 1) CTM = CFM (1 + K M ) + CWM + C AM Froude Expansion

Measured in tank

CWM = CTM −CFM (1 + K ) − C AM

2) CTS = CFS (1 + K S ) + CWS + C AS 3)

RTS ⋅ VS EHP ( hp ) = 550

( RTS = CTS * 0.5ρ S S SVs 2 )

CWS = CWM ( FnS = FnM , VS / gLS = VM / gLM ) C FM , CFS

(calculate d)

KS = KM

( due to scale factor λ. Calculated or given )

C AM = 0

( Model is smooth)

C AS ≠ 0

(given, or calculated)

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