Chapter 9
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
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
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 great 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 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
Hull Interaction:
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
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 – w)
w = (1 - VA) / V or rewritten VA = V (1 – w)
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”

similar documents