1

Chap 7 Resistance and Powering of ShipObjectives Prediction of Ships Power - Ships driving system and concept of power - Resistance of ship and its components frictional resistance wave-making resistance others - Froude expansion - Effective horse power calculation 2

Introduction When the hull form has been decided upon, it is necessary to determine the amount of engine power that will enable the ship to meet its operational requirements. Knowing the power required to propel a ship enables the naval architect to select a propulsion plant, determine the amount of fuel storage required, and refine the ships center of gravity estimate naval architects have endeavored to increase the speed of ships. wind was the force used to propel ships through the water and ships could only go as fast as the wind would propel them. wind was the force used to propel ships through the water and ships could only go as fast as the wind would propel them. Testing of full-scale ships and models determined that the power required to propel a ship through the water was directly related to the amount of resistance a hull experiences when moving through the water. the modern screw propeller was developed, replacing the paddle wheel as the prime mode of ship propulsion. The screw propeller, with many modifications to its original design, remains the principle method of ship propulsion to this day.3

Ship Drive Shaft and PowerShip Drive Shaft SystemEHP Engine Reduction Gear

Bearing

Strut Screw Seals THP

BHP

SHP

DHP4

Ship Drive shaft and PowerHorse 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

5

Ship Drive Train and PowerDelivered 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>EHP6

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 Froudes Law. Towing Tank Measured EHP V Towing carriage

7

Effective Horse Power (EHP)Effective Horsepower, EHP (HP)

P W RC R E O E U VYR PT O C AT A D AR L RF

10 00 80 0 60 0 40 0 20 0 0 0 2 4 6 8 1 0 1 2 1 4 1 6

S ip S e d V (K o ) h p e , s n ts

Typical EHP Curve of YP

8

Effective Horse Power (EHP)Efficiencies Hull Efficiency

EHP H = THP- Hull efficiency changes due to hull-propeller interactions. - Well-designed ship : H 1 - Poorly-designed ship : H 1 Well-designed - Flow is not smooth. - THP is reduced. - High THP is needed 9 to get designed speed.

Poorly-designed

Effective Horse Power (EHP)Efficiencies (contd)EHP Propeller Efficiency Screw THP SHP DHP

propeller

THP = DHP

Propulsive Coefficients (PC)

EHP p = SHP

p 0.6 for well designed propeller

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

ft RT (lb) VS s EHP(H P ) = ft lb 550 sH P

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 11

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 0.5 Vs S 4 ft ft s CT = Coefficient of total hull resistance in calm water RT = Total hull resistance

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

12

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

CT , , S and VS

RT (lb) = 0.5SVS CTCT : determined by the model test

2

: available from water property table S : obtained from Curves of form VS : Full scale ship speed13

Relation of Total Resistance Coefficient and SpeedT T L EI T NE UV OA R S A C C R E SY R P T O C AT A D AR L RF200 00

100 50

100 00

Total Resistance, Rt (lb)

Total Hull Resistance (cont)

50 00

0 0 2 4

Si Se d V ( n t ) h pe, s k o p s

6

8

1 0

1 2

1 4

1 6

RT CT VS VSn

2

EHP RTVS CT VS VS VSn

2

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

n = from 3 at low speed to 6 at high speed 14

Components of Total Resistance Total Resistance

R = R + R + RA T V WRV : 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, ships 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 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

16

Components of Total Hull Resistance Total Resistance and Relative Magnitude of Components

Resistance (lb)

Air Resistance Hollow Hump Wave-making

Viscous Speed (kts)

- Low speed : Viscous R - Higher speed : Wave-making R 17 - Hump (Hollow) : location is function of ship length and speed.

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.

CV = Ctangential Cnormal= CF + KCF +a norm l

flow

bow

ta n

g

a nt i e

l

ship

stern

Tangential Component : CF - Tangential stress is parallel to ships 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

Wave-Making ResistanceTypical Wave Pattern Stern divergent wave Bow divergent wave

L Transverse waveWave Length20

21

Wave-Making ResistanceTransverse 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.22

Wave-Making Resistance (cont)Transverse wave SystemVs < Hull Speed Wave Length High Speed Wave Length Hull Speed : speed at which the transverse wave length equals the ship length. 23 (Wavemaking resistance drastically increases above hull speed) Slow Speed

Vs Hull Speed

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 24 are needed to calculate the Cw of the real ship.

Wave-Making Resistance (cont)Bulbous Bow

25

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).26

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 resistance27

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

?Dimension Speed Force

model ship

prototype

Model28

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 = LS (ft) = : Length LM (ft) S S (ft 2 ) = S M (ft 2 )2

S : full scale ship M : Model

: Area : Volume29

S (ft 3 ) = M (ft 3 )3

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 ), RnS = RnM , LSVS LMVM = , vS vM vM LS VM = VS , vS LM

CW = f ( Fn ) FnS = FnM VS VM = gLS gLM VM = VS LM LS30

Basic Theory behind Ship Modeling Corresponding SpeedsFnS = 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 20

1kt.=1.688 ft/s

31