Propulsion Chapter 9

Powering of Ships - Historical Oars Sails Jet (1661) Steam driven side wheeler (1801 - 1850) Fulton’s Clermont for passenger service on Hudson River Savannah (1819), first American steamer to cross Atlantic, full rigged auxiliary steam ship Scotia, built by Cunard, last side wheeler (1861) Propeller First proposed in England by Hooke in 1680 First steam driven boat in NY 1804, Colonel Stevens First successful application 1828 in Trieste, 60 ft boat, travelled at 6 knots First practical application 1836, Ericsson (American) and Smith (British) Great Britain, first screw-propeller steamer to cross the Atlantic (1845)

Power Definition Various types of marine engines are not rated on the same basis Internal Combustion Engines – Brake Horsepower PB Power measured at the crankshaft coupling by means of a mechanical, hydraulic or electrical brake. Determine by a shop test PB=2πQn/550 where Q=brake torque and n = revolutions per second Steam turbine – Shaft Horsepower PS Power transmitted through the shaft to the propeller Usually measured aboard ship as close to the propeller as possible by means of a torsionmeter. The instrument measures the angle of twist between the two sections of the shaft, which angle is directly proportional to the torque transmitted. Ps = (ds)4 * G * θ * n / (613,033 * Ls) , where ds = shaft diameter, G = shear modulus of elasticity, θ = measured angle of twist in degrees, n = revolutions per second, Ls = length of shaft over which θ is measured Delivered Horsepower – PD The power actually delivered to propeller is actually somewhat less than measured by the torsionmeter, as there is some power lost in the stern tube bearings and in any shaft tunnel bearings between the sterntube and site of the torsionmeter

Power Definition Effective Power = PE = RTV (power needed to overcome RT at velocity V)   Thrust Power = PT = TVA where T (thrust) is a measure of the useful output of the propeller which is located in water moving at an average velocity called the velocity of advance (VA­) Hull Efficiency = ηH = PE/PT = RTV / TVA PD = Delivered Power = 2 π n QD, where QD is torque delivered to the propeller

Theory of Propeller Action Propellers derive their propulsive thrust by accelerating the fluid in which they work. Momentum Theory – “disk” is capable of imparting a sudden increase of pressure to the fluid passing (axial direction) through it Impulse Theory – assumes that the disk propeller is capable of accelerating the fluid both axially and rotationally. Blade Element Theory – blade is considered to made up of a number of separate blades instead of a disk. These blades can then be divided into successive strips across the blade from leading to trailing edge. The forces on each strip can then be evaluated from a knowledge of the relative velocity of the strip to the water and the characteristics of the section shape ηo = TVA / 2 π 𝑛 𝑄 - open water efficiency (testing propeller in open water)

Nomenclature Blade extends from its “root” where it’s attached to the hub “tip” outmost extremity   When rotating, the blade edge cutting the water first is the “leading edge” “trailing edge” other edge “face” of the propeller is seen from behind or aft, also called “pressure face or driving face” “the back” the other blade surface

Other terms –   Cavitation – occurs when on the back or the suction side of the propeller blade, the pressure becomes so low, that the water vaporizes at the low pressure point and vapor filled bubbles form in the water locally “boiling” the water. Cavitation can cause erosion and pitting of the blades and noise, also causes propeller efficiency to drop. Wake – region of disturbed fluid behind a body that is moving through a fluid. Ship propellers are located within the wake of the ships that they propel and the propeller’s performance is influenced by the flow in which it operates. Wake = V – VA , where V is the ship speed and VA is the speed of advance Speed of Advance – is the velocity of the water passing through the propeller disk in the absence of any influences of the propeller. In most cases the speed of advance (VA) is less than the ship speed (V), because the ship hull forward of the propeller moves some water with it. Wake Fraction (w) – non dimensional expression of the wake or wake speed as a fraction of ship speed W = (V – VA) / V = (1 – VA) / V

Efficiencies Behind Efficiency ηB = PT/PD = TVA/2πnQD Open Water Efficiency ηo = TVA/2πnQo Relative Rotative Efficiency ηR = ηB/ηo Shaft Transmission Efficiency ηS = PD/PS Shaft power PS = 2πnQS Propulsive Efficiency (PC) ηP = PE / PS Overall efficiency of ship propulsion ηP = PE/PT = PT/PD = PD/PS ηP = ηH x ηB x ηS = ηH x ηo x ηR x ηS Quasi-propulsive efficiency ηD = PE/PD = ηH ηo ηR This efficiency represents how well the propeller is matched to the ship

Thrust Deduction – Resistance force measured with model being towed When self propelled, the thrust force produced must be sufficient to overcome the ship resistance at the corresponding speed Resistance of the self propelled ship greater then the towed vessel because the high pressure system caused at the stern. These pressures are normal to the hull and have components that act in the forward direction due to the shape of the stern. The propeller changes the flow of water around the stern by accelerating the water. This reduces the beneficial high pressure around the stern. Effect is defined as Thrust Deduction Fraction (t) t = T – RT / T = 1 – RT / T where t = Thrust deduction fraction, T = propeller thrust, RT = ship resistance or RT = T (1 – t) where (1 - t) is the Thrust deduction factor

Hull Interaction: Wake Region of disturbed fluid behind a body that’s moving through a fluid Ship propellers are located within this wake and must be defined by the designer The ship hull forward of the propeller carries along water within the boundary layer which helps to reduce the resistance, called positive wake wake = V – VA or w = (V – VA) (wake fraction 1– w)   w = (1 - VA) / V or rewritten VA = V (1 – w)

Hull Efficiency - ηH = PE / PT ratio of effective power to the thrust power Also written in terms of wake fraction and thrust deduction factor ηH = RTV / TVA = (1 – t) / (1 – w) Hull efficiency depends on the shape and fullness of the stern of the ship. Ship and Propeller Together Propellers must be designed for optimum performance considering the flow of water around the hull since the propeller change the pressure distribution around the stern thereby increasing the resistance of the propeller

Coefficients Thrust Coefficient Propeller must deliver a large thrust for it’s size, referred to as “heavily loaded” Non-dimensional way of expressing the propeller output KT = T / ρ n D4 Torque Coefficient Represents the input (torque) to the propeller KQ = Q / ρ n D4 Advance Coefficient Necessary to have kinematic similarity for testing model propellers and scaling to full size propellers J = VA / nD = (P/D) (1 – sR) Since the pitch ratio is the same for geometrically similar propellers, equivalence of their advance coefficients will assure equivalence of their slip ratios as well.

Potential Wake –   the pressure distribution around vessel moving through a fluid is always high around the stern where the flow lines close in after passing around the body. The velocity of the water in this region is slower than the velocity of the ship Called Potential Wake and always positive in the stern Frictional Wake Within the viscous boundary layer, some water is carried in the direction of motion of the ship Boundary layer thickness increases from bow to stern so most of the propeller (especially on single screw ships) will be within the boundary layer. Frictional wake is always positive and stronger close to hull (weaker with increased distance from hull). Strongest of the three components of wake. Wake strength is influenced by shape of the stern and can not be calculated. Experimental evidence is needed - “wake survey”