7.5 - 7.6RESISTANCE&RESISTANCE COEFFICIENTS

As a ship moves through the water, it experiences forces that workagainst its forward movement. The sum of all these forces is the

Resistance Values and CoefficientsResistance values, denoted by R, are dimensional valuesRT = Total hull resistance is the sum of all resistanceRT = RAA + RW + RV RAA = Resistance caused by calm air on the superstructure

RW = Resistance due to waves caused by the ship - A function of beam to length ratio, displacement, hull shape & Froude number (ship length & speed) RV = Viscous resistance (frictional resistance of water)- A function of viscosity of water, speed, and wetted surface area of ship

Total Resistance and Relative Magnitude of Components At low speeds Rv dominates At higher speeds Rw is dominates Hump (Hollow)- location is function of ship length and speedThe amount of each resistance component will vary depending on speed:

Total Hull Resistance & HP Total Hull Resistance (RT)- The sum of forces that the ship experiences opposite to the motion of the ship as it moves

Total Hull Resistance & EHP Calculation:

Similar to the resistance components are the- Resistance Coefficients, C, are dimensionless values of resistance- Allow the comparison of dissimilarly shaped vessels- Used extensively in modeling

CoefficientsCT = Coefficient of total hull resistance CT = CV + CW - CV = Coefficient of viscous resistance over the wetted area of the ship as it moves through the water - CF = Tangential component (skin resistance) - KCF = Normal component (viscous pressure drag) - CW = Coefficient of wave-making resistance

Coefficient of Viscous Resistance, CVLets look at the resistance due to the water, CV, first- Consists of tangential and normal components- Tangential resistance, CF, is parallel to ships hull and causes a net force Skin Friction opposing the motion by the water

- Normal resistance, KCF, is perpendicular to the ships hull. K is unique to the hull form flowshipbowsterntangentialnormal

Coefficient of Viscous Resistance, CVTangential Component, CFAlso called the hull frictional resistance, CF can be characterized by the fluid flow around the hull:

Normal Component, KCF - 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 - Is affected by hull shape Fuller shape ship has larger normal component than slender ship Coefficient of Viscous Resistance, CV

- The viscous resistance component CV can be related to another common dimensionless coefficient, the Reynolds NumberCoefficient of Viscous Resistance, CV

How to Reduce the Viscous Resistance Coefficient- For tangential component, increasing the length decreases the skin resistance

- For normal component, a more slender ship decreases the pressure drag on the hull

Very long, narrow, slender hull is favorable ( A slender hull form will create a smaller pressure difference between bow and stern) Increase L while keeping the submerged volume constant

Froude Number, FnThe Froude Number is another dimensionless value derived from model testing...Velocity is typically expressed in Knots (1 knot = 1.688ft/s)

Typical Wave Patterns are made up of TRANSVERSE and DIVERGENT wavesCoefficient of Wave Resistance, CW

Wave-Making ResistanceTransverse Wave System - Travel at approximately the same speed as the ship

- At slow speeds, several crests exist along the ship length because the wave lengths are smaller than the ship length

- As the ship increases speed, the length of the transverse wave increases- As the 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

Vs < Hull SpeedVs Hull SpeedWhen the transverse wave length equals the ships length the vessel has reached its HULL SPEED (Wave making resistance drastically increases above hull speed)Wave-Making Resistance

Divergent Wave System - Divergent waves consist of Bow and Stern Waves - Interaction of the bow and stern waves create the Hollow or Hump on the resistance curveWave-Making Resistance- Hump: The bow and stern waves are in phase, the crests are added up creating a larger divergent wave system- Hollow: 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

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 too difficult and inaccurate from any theoretical or empirical equation

- Model test in the towing tank and Froude expansion are needed to calculate the Cw of the real shipWave-Making Resistance

It takes energy to produce waves, and as speed increases, the energy required is a square function of velocity!The limiting speed, or hull speed, can be found as:V = 1.34 \/LsNote: Remember at the hull speed, Lwave and Ls are approximately equal!Wave-Making Resistance

Reducing Wave Making Resistance1) Increasing ship length to increase the wave length

- Hull speed will increase - The hull speed will be greater for the longer ship (the wave-making resistance of longer ship will be small until the ship reaches to the hull speed)Wave-Making Resistance2) Attaching Bulbous Bow to reduce the bow divergent wave - Bulbous bow generates the second bow waves - The waves interact with the bow wave resulting in smaller bow divergent waves

Bulbous BowWave-Making Resistance

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 a problem in sail boats)Added Resistance - Resistance due to sea waves which will cause the ship motions (pitching, rolling, heaving, yawing)

Increased Resistance in Shallow WaterResistance caused by shallow water effect - Water flow is restricted under the vessel,so water velocity under the hull increases - The faster moving water decreases pressure causing the ship to squat- Increases wetted surface- Increases surface friction- Waves tend to be larger compared to waves in deep water at the same speed

- Traveling through a canal can produce the same effect The bottom line is it will require more HP to travel at the same speed!Other Type of Resistances