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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!

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Ship Drive Train and Power 7.2 Ship Drive Train System Engine Reduction Gear Bearing Seals Screw Strut BHP SHP DHP THP Shaft

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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 Ship Drive Train and Power

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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? BHP>SHP>DHP>THP E/GR/G BHPSHP Shaft Bearing Prop. DHPTHP EHP Hull Ship Drive Train and Power

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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) V Towing Tank Towing carriage Measured EHP

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Effective Horse Power (EHP) Typical EHP Curve of YP What EHP is required for the 12 knot YP cruise?

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Effective Horse Power (EHP) Efficiencies Hull Efficiency - Hull efficiency changes due to hull-propeller interactions. - Well-designed ship : - Poorly-designed ship : Well-designed Poorly-designed - Flow is not smooth. - THP is reduced. - High THP is needed to get designed speed.

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Screw Effective Horse Power (EHP) Efficiencies (cont’d) Propeller Efficiency Propulsive Coefficient (PC) ~ An overall measure of drive train efficiency SHP DHP THP EHP

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7.5 Total Hull Resistance Total Hull Resistance (R T ) The force that the ship experiences opposite to the motion of the ship as it moves. EHP Calculation

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

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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

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Total Hull Resistance (cont) Relation of Total Resistance Coefficient and Speed

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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

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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

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Components of Total Hull Resistance Total Resistance and Relative Magnitude of Components Viscous Air Resistance Wave-making Speed (kts) Resistance (lb) - Low speed : Viscous R dominates - Higher speed : Wave-making R dominates - Hump (Hollow) : location is function of ship length and speed. Hump Hollow

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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.

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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. 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. flow ship bow stern tangential normal

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Coefficient of Viscous Resistance (cont) Semi-empirical equation

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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. Laminar Flow Turbulent Flow Flow over flat plate

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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 ship Slender ship large eddy Coefficient of Viscous Resistance (cont) small eddy

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

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Reducing the Viscous Resistance Coefficient - Method : Increasing L with constant submerged volume 1) Form Factor K Normal component KC F Slender hull is favorable. ( Slender hull form will create a smaller pressure difference between bow and stern.) 2) Reynolds No. Rn CF KC F Summary of Viscous Resistance Coefficient

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Wave-Making Resistance Definition : refer to the previous note Typical Wave Pattern Bow divergent wave Transverse wave L Wave Length Stern divergent wave

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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.

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Wave-Making Resistance (cont) Transverse wave System Wave Length Wave Length Slow Speed “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)

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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)

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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)

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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)

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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! Wave-Making Resistance (cont)

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Bulbous Bow Wave-Making Resistance (cont)

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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.

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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).

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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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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 Speed Force prototype Model prototype ship model 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 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.

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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

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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?

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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.

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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

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Chap 7.7 Basic Theory Behind Ship Modeling Modeling Summary Froude Expansion Measured in tank 1) 2) 3)

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7.9 The Screw Propeller

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7.9 Screw Propeller Diameter Hub Blade Tip Blade Root

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Pitch Distance Pitch Angle Fixed Pitch Variable Pitch Controllable Pitch (Constant Speed)

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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

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Right and Left Hand Props Right HandLeft Hand

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Pressure Face Suction Face Leading Edge Trailing Edge

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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.

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Prop Walk Solutions Twin Screws Counter rotating propellers (one shaft) Tunnels/shrouds (nozzle)

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Shrouded (nozzle) prop

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7.9 Skewed Screw Propeller Highly Skewed Propeller DDG51 - Reduce interaction between propeller and rudder wake. - Reduce vibration and noise Advantages Disadvantages - Expensive - Less efficient operating in reverse

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7.9. Propeller Theory Propeller Theory Speed of Advance Q P Wake Region 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

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7.9 Propeller Theory Propeller Efficiency ~70 % for well-designed prop - For a given T (Thrust), Ao ( Diameter ) ; C T ; Prop Eff The larger the diameter of propeller, the better the propeller efficiency Maximum

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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.

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1 atm=101kpa =14.7psi

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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.

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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

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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.

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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.

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Other forms of propulsion A one horsepower cable-drawn ferry!

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