propeller.cal

7/27/2019 Propeller.cal

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PROPELLER

Propeller Dimensions

The marine propeller is characterized by three fundamental measurements: number of

blades, diameter, and pitch.

Fig 1 Propeller definition diagram (three blade, right hand, constant-pitch propeller)

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Basic Nomenclature

Hub

The hub or boss of a propeller is the solid center disk that mates with the propeller shaft

and to which the blades are attached. Ideally the hub should be as small in diameter aspossible to obtain maximum thrust, however there is a trade-off between size and

strength. Too small a hub ultimately will not be strong enough.

Blades

Blades are twisted fins or foils that protrude from the propeller hub. The shape of the

blades and the speed at which they are driven dictates the torque a given propeller candeliver.

Blade Root and Blade Tip

The root of a propeller blade is where the blade attaches to the hub. The tip is the

outermost edge of the blade at a point furthest from the propeller shaft.

Blade Face and Back

The face of a blade is considered to be the high-pressure side, or pressure face of the

blade. This is the side that faces aft (backwards) and pushes the water when the vessel is

in forward motion. The back of the blade is the low pressure side or the suction face of

the blade. This is the side that faces upstream or towards the front of the vessel.

Leading and Trailing Edges

The leading edge of a propeller blade or any foil is the side that cuts through the fluid.

The trailing edge is the downstream edge of the foil.

Right Handed vs. Left Handed

A propellers handedness affects its shape. A right-handed propeller rotates clockwise

when propelling a vessel forward, as viewed from the stern of the ship. A left-handedpropeller rotates counter-clockwise, as viewed from the stern, when in a forward

propulsion mode. When viewing a propeller from astern, the leading edges of the blades

will always be farther away from you than the trailing edges.

The propeller rotates clockwise, and is right-handed, if the leading edges are on the right.

A propellers handedness is fixed. A right-handed propeller can never be exchanged witha left-handed propeller, and vice versa. Most single screw vessels (one engine, one

propeller) have right-handed propellers and clockwise rotating propeller shafts (as viewed

from astern). Single propellers tend to naturally push the vessel to one side when going

forward (and the opposite side when in reverse): a right-handed propeller will push the

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stern to starboard when in forward (and port when in reverse). Since Propellers are not

ideally designed for reverse propulsion, this effect is somewhat exaggerated when

operating a single-screw vessel in reverse. Twin screw vessels have counter rotatingpropellers with identical specifications. The port (left) side propeller is usually left-

handed and the starboard (right) side propeller is usually right-handed.

Diameter

The diameter (or radius) is a crucial geometric parameter in determining the amount ofpower that a propeller can absorb and deliver, and thus dictating the amount of thrust

available for propulsion. With the exception of high speed (above 35 Knots) vessels the

diameter is proportional to propeller efficiency (i.e. Higher diameter equates to higher

efficiency). In high speed vessels, however, larger diameter equates to high drag. Fortypical vessels a small increase in diameter translates into a dramatic increase in thrust

and torque load on the engine shaft, thus the larger the diameter the slower the propeller

will turn, limited by structural loading and engine rating.

Propeller (RPMs)

RPM is the number of full turns or rotations of a propeller in one minute. RPM is often

designated by the variable N. High values of RPM are typically not efficient except on

high speed vessels. For vessels operating under 35Knots speed, it is usual practice toreduce RPM, and increase diameter, to obtain higher torque from a reasonably sized

power plant. Achieving low RPM from a typical engine usually requires a reduction

gearbox.

Pitch

The pitch of a propeller is defined similarly to that of a wood or machine screw. Itindicates the distance the propeller would drive forward for each full rotation. If a

propeller moves forward 10inches for every complete turn it has a 10inch nominal pitch.

In reality since the propeller is attached to a shaft it will not actually move forward, butinstead propel the ship forward. The distance the ship is propelled forward in one

propeller rotation is actually less than the pitch. The difference between the nominal

pitch and the actualdistance travelled by the vessel in one rotation is calledslip.

Typically blades are twistedto guarantee constant pitch along the blades from root to tip.

Often apitch ratio will be supplied. This is simply the ratio of pitch to diameter, usually

in millimetres, and typically falls between 0.5 and 2.5 with an optimal value for mostvessels closer to 0.8 to 1.8. Pitch effectively converts torque of the propeller shaft to

thrust by deflecting or accelerating the water astern simple Newtons Second Law.

Different types of pitch are:

Constant (fixed) pitch - pitch is equal for each radius

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Progressive pitch - pitch increases along the radial line from the leading edge

(LE) to the trailing edge (TE).

Variable pitch - pitch is different at selected radii

Controllable pitch - blade angle is mechanically varied

Pitch Angle (Not to be confused with pitch)

Angle of the pressure face along the pitch line with respect to the plane of rotationmeasured in degrees. Pitch angle decreases from the blade root to the tip in order to

maintain constant pitch.

Relationship between Pitch & Pitch Angle

If R = radius from centre of shaft

And = pitch angle

Formula:

Tan a = Pitch / 2R

Where 2R = circumference

Therefore pitch = 2RTan

The following geometry definitions apply to the overall propeller geometry and are a

function of radius:

Pitch: The axial distance travelled by the section if rotated one revolution and translated

along the section nose-tail line (arc)

Mid-chord line: line produced from the mid-chords (i.e. Midpoint of section nose tail

line) of each section along a propeller blade.

Rake: Axial distance from the mid-chord point at the hub section and the section of

interest i.e. when the propeller blades lean or slope either forward or aft as viewed fromthe side they are said to have a rake. Blades that are sloped aft have a positive rake, while

blades that are sloped forward have a negative rake. Rake is indicated either as a slope in

degrees or by rake ratio.

Skew or Skew Angle: Tangential component of the angle formed on the propeller

between a radial line going through the hub section mid-chord point and a radial line

going through the mid-chord of the section of interest and projected

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Variable Pitch Propellers

The majority of propellers have blades with essentially constant pitch, but a few

specialized propellers have blades with pitch that changes substantially from the root totip. This means that the blade angles do not vary in such a way as to keep the pitch

constant. The principal reason for these variable-pitch propellers is to take advantage of

varying speeds of water flow to the propeller as measured radially out from the hub dueto the interference of the hull ahead.

This type of installation is called for only on large vessels with special need for ultimateefficiency. However, many modern propellers do have small amount of variable pitch

introduced near the blade root as a result of changing blade section. Frequently, they also

reduce the pitch near the tip of the blades slightly from that of a theoretical helix. This is

called pitch relief or tip unloading, and it has been found to reduce the tendency for

cavitations to start at the propeller tips.

Controllable Pitch Propellers

An alternative design is the controllable pitch propeller (CPP, or CRP for controllable-

reversible pitch), where the blades are rotated normal to the drive shaft by additionalmachinery (usually hydraulics) at the hub and control linkages running down the shaft.

This allows the drive machinery to operate at a constant speed while the propeller loading

is changed to match operating conditions. It also eliminates the need for a reversing gearand allows for more rapid change to thrust, as the revolutions are constant. This type of

propeller is most common on ships such as tugswhere there can be enormous differences

in propeller loading when towing compared to running free, a change which could causeconventional propellers to lock up as insufficient torque is generated. The downsides of a

CPP/CRP include: the large hub which decreases the torque required to cause cavitation,

the mechanical complexity which limits transmission power and the extra blade shaping

requirements forced upon the propeller designer.

The CPP consists of a flange mounted hub inside which a piston arrangement is moved

fore and aft to rotate the blades by a crank arrangement. The piston is moved byhydraulic oil applied at high pressure (typically 140 bars) via an Oil transfer tube (OT

tube). This tube has and inner and outer pipe through which aheadand astern oil passes.

The tube is ported at either end to allow oil flow and segregated by seals.

Oil is transferred to the tube via ports on the shaft circumference over which is mountedthe OT box. This sits on the shaft on bearings and is prevented from rotation by a peg.

The inner bore of the box is separated into three sections. The ahead and astern and also

an oil drain which is also attached to the hydraulic oil header to ensure that positivepressure exists in the hub and prevents oil or air ingress

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http://en.wikipedia.org/wiki/Controllable_pitch_propellerhttp://en.wikipedia.org/wiki/Surface_normalhttp://en.wikipedia.org/wiki/Hydraulicshttp://en.wikipedia.org/wiki/Tughttp://en.wikipedia.org/wiki/Tughttp://en.wikipedia.org/wiki/Cavitationhttp://en.wikipedia.org/wiki/Controllable_pitch_propellerhttp://en.wikipedia.org/wiki/Surface_normalhttp://en.wikipedia.org/wiki/Hydraulicshttp://en.wikipedia.org/wiki/Tughttp://en.wikipedia.org/wiki/Cavitation


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The OT tube is rigidly attached to the piston, as the piston moves fore and aft so the

entire length of the tube is moved in the same way. A feedback mechanism is attached to

the tube, this also allows for checking of blade pitch position from within the engineroom.

Fig 2 Controllable Pitch Propeller System

Advantages

Allow greater manoeuvrability

Allow engines to operate at optimum revs

Allow use of PTO alternators

Removes need for reversing engines

Reduced size of Air Start Compressors and receivers

Improves propulsion efficiency at lower loads

Disadvantages

Greater initial cost

Increased complexity and maintenance requirements

Increase stern tube loading due to increase weight of assembly, the stern

tube bearing diameter is larger to accept the larger diameter shaft required

to allow room for OT tube

Lower propulsive efficiency at maximum continuous rating

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Propeller shaft must be removed outboard requiring rudder to be removed

for all propeller maintenance.

Increased risk of pollution due to leak seals Operation Modes

There are two main methods of operation of a vessel with a CPP.

Combinator: For varying demand signals both the engine revs and the pitch are

adjusted to give optimum performance both in terms of maneuverability and

response, and also economy and emissions.

Constant speed: The engine operates at continuous revs (normally designed

for maximum working revs), demand signals vary CPP pitch only. This isparticularly seen in engines that are operating with power-take-off (PTO)

generator systems

Emergency running

In the event of CPP system hydraulic failure an arrangement is fitted to allow for

mechanical locking of the CPP into a fixed ahead pitch position. This generally takes the

form of a mechanical lock which secures the OT tube. Either hand or small auxiliaryelectric hydraulic pump is available for moving the pitch to the correct position.

Cavitation

Cavitation is the phenomenon of water vaporizing orboilingdue to the extreme decrease

in pressure on the forward or, suction side of the propeller blade. Cavitation can becaused by nicks in the leading edge, bent blades, too much cup, sharp corners at the

leading edge, incorrect matching of propeller style to the vessel and engine or, simply,

high vessel speed.

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Propeller Calculations

The pitch of a screw is the axial distance it will move forward, working in an unyieldingmedium, when turn through one revolution. As already outlined pitch = 2RTan

Measurement of Pitch

This can be done by measuring the pitch angle of the driving face of the blade and noting

the radius from the centre of the section at which the pitch angle is measured thenapplying the expression: Pitch = 2RTan . This should be done at a number of different

radii along the blade and the average taken as the propeller pitch.

Fig 3 Pitchometer

An instrument called a pitchometer is designed for measuring the pitch of a screw-

propeller. It consists of an arm normal to and pivoting around a shaft placed in the axial

line of the propeller, which carries a sliding pointer-arm with an adjustable point at rightangles to the first arm and parallel to the axis of the propeller. By bringing the point of

the pointer-arm in contact with a point on the surface of the propeller-blade, its distance

from the axis and from the plane of reference at right angles to the axis, formed by the

first arm, can be determined from suitable scales on the arm and the pointer. By revolvingthe system around its axis, a series of such points on the surface can be measured.

If such an instrument is not available a weighted cord may be hung over the blade when

horizontal measuring the distance AC and BC as well as the radius from the centre of the

boss. The tangent of the pitch angle is BC divided by AC

Therefore:

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Pitch = 2 x R tan

= 2 x R x BC

AC

Fig 4 Pitch Measurement

Example 1

The pitch angles of a propeller blade measured at radii 1, 1.5, 2, 2.5 and 3 metres are

respectively 44, 33, 26.5, 22.5 and 20 degrees. Calculate the pitch of the propeller.

Solution

At 1 metre radius,

Pitch = 2 X 1 X tan 44 = 6.067 m

At 1.5 metre radius,

Pitch = 2 X 1.5 X tan 33 = 6.12 m

At 2 metre radius,

Pitch = 2 X 2 X tan 26.5 = 6.265 m

At 2.5 metre radius,

Pitch = 2 X 2.5 X tan 22.5 = 6.506 m

At 3 metre radius,

Pitch = 2 X 3 X tan 20 = 6.861 m

Propeller Pitch = Mean Value

= 6.067 + 6.12 + 6.265 + 6.506 +6.861

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= 6.364 metres *

Propeller Slip

The pitch of a propeller is the distance (in metres) through which the propeller would

move forward in one revolution if it worked in a solid unyielding medium. If one knot is

equal to 1.852 Km/h, therefore:

Propeller Speed = pitch x rev/min metre/min

= pitch x rev/min x 60 metre/hour

= pitch x rev/min x 60 x 10-3 km/hour

= pitch x rev/min x 60 knots **

1.852 x 103

The actual distance the ship moves forward is less than the above because, as thepropeller works in water, there is always a certain amount of slip. The slip is the

difference between the speed of the propeller and the speed of the ship and is expressed

as a percentage of the propeller speed. Thus, if the propeller speed was equivalent to 16knots and the speed of the ship was 14 knots then,

Slip = 16 14 = 2 knots.

Slip = 2/16 = 0.125 or 12.5%

Slip = 12.5% of propeller speed

Example 2

The pitch of a propeller is 4.9m and the speed of the ship is 13.5 knots when the propeller

is turning at 95 rev/min. What is the percentage slip of the propeller?

Propeller Speed = pitch x rev/min X 60103 x 1.852

= 4.9 x 95 x 60

103

x 1.852

= 15.09 knots

Per cent slip = propeller speed ships speed x 100

propeller speed

= 15.09 13.5 x 100

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15.09

= 10.54% Ans***

Friction of a Ships Hull through the Water

The amount of friction between the hull of a ship and the water through which it is

moving is proportional to approximately the square of the speed, to the wetted surface

area, and to the density of the water: it also depends upon the roughness of the surface ofthe shell. It is independent of the water pressure, which means that there is the same

amount of friction per square metre at the bottom of the hull as there is near the water

surface.

From the rule that areas of similar figures vary as the square of their corresponding

dimensions, we have

Wetted surface area varies as (length)2

From the rule that volumes of similar objects vary as the cube of their correspondingdimensions, we have

Displacement varies (length)3

Therefore, Length varies as (displacement)1/3

Since friction varies as wetted surface area and (speed)2

Then friction varies as (displacement)2/3 and (speed)2

Power = Force x Speed

Therefore

Power varies as (displacement)2/3 x (speed)2 x speed

= (displacement)2/3 x (speed)3

The power of the engine is proportional to the power to propel the ship through the water,

therefore engine power varies as (displacement)2/3 x (speed)3

Hence, (displacement)2/3 x (speed)3 = a constant

Engine power

This constant is called the Admiralty Coefficient and may be used for estimating the

power of the ships engines under different conditions of displacement and speed, or forthe comparison of the engine power of similar ships.

If = displacement in tonneV = speed in knots

P = power

12/3 x V1

3 = 22/3 x V1

3

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P1 P2

Example 3

The power developed by a ships engine was 3200 KW when her displacement was10000 tonne and speed 14 knots. Estimate the power required to run at a speed of 16

knots when her displacement is 12,000 tonne.

Solution

12/3 x V1

3 = 22/3 x V1

3

P1 P2

100002/3 x 143 = 120002/3 x 163

3200 P2

P2 = 3200 x 120002/3 x 163

100002/3 x 143

P2 = 5394 KW

Many cases will arise when the power is required to be estimated for change of speed

only, that is, assuming that the displacement remains the same or such little change ofdisplacement that it can be neglected.

In such cases (displacement)2/3 cancels from both sides to leave

V13

= V13

P1 P2

Fuel Consumption

The mass of fuel burned in a given time (per hour or per day) is proportional to the powerdeveloped by the engines, therefore

(displacement)2/3 x (speed)2 = a constant

Daily consumption of fuel

This constant is termed the fuel coefficient and by the use of this expression the quantity

of fuel required under different conditions of displacement and speed can be estimated,thus:1

2/3 x V13 = 2

2/3 x V1 Equation (1)

Daily consumption1 daily consumption2

This may be written in the form:

New daily cons. = {new displ.} 2/3 x {new speed}3

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Old daily cons. {Old displ. } {old speed}

Daily consumption = consumption over the whole voyageNumber of days on voyage

Number of days on voyage = distanceSpeed in knots x 24

Daily consumption = Voyage consumption x speed x 24Distance

Substituting for daily consumption, new and old into equation (1) we get

12/3 x V1

3 x distance = 22/3 x V1 x distance

Voyage cons1 x V1 x 24 Voyage cons2 x V2 x 24

V1 cancels into V13 leaving V1

2

V2 cancels into V2

3

leaving V22

24 cancels each other

The equation may now be written:

New voyage cons. = {new displ.} 2/3 x {new speed}2 x new distance

Old voyage cons. {Old displ. } {old speed} old distance

The above equation can be taken as the general formula for solving most fuel

consumption problems.

The voyage can be taken as the days run where the consumption of fuel per day is given,

thus the daily fuel consumption can be put down as the voyage consumption if the

corresponding distance be taken as speed (in knots) x 24.

If there is no change in displacement, this term will cancel out. If the distance is the same,this term will also cancel.

The worked examples to follow will clarify these few points

Example 4

A vessel uses 300 tonne of fuel on a voyage of 3000 nautical miles travelling at a speed

of 12 knots when her displacement is 10000 tonne. Estimate the fuel required for avoyage of 1500 nautical miles at a speed of 15 knots when her displacement is 14000

tonne.

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Solution

Known formula

New voyage cons. = {new displ.} 2/3 x {new speed}2 x new distanceOld voyage cons. {Old displ. } {old speed} old distance

New voyage cons. = {14000} 2/3 x {15}2 x 1500

300 {10000} {12} 3000

New voyage cons = 300 x 1.42/3 x 1.252 x 0.5

New voyage cons = 293.3 tonne Ans***

Example 5

A vessel of 10000 tonne displacement burns 25 tonne of fuel per day when her speed is

12 knots. Calculate the probably consumption of fuel over a voyage of 3000 nauticalmiles at a speed of 11 knots when the displacement is 11000 tonne.

Solution

The original fuel consumption is given as 25 tonne per day; therefore assume the original

voyage to be one days run which is 12 x 24 nautical miles and the consumption of fuelfor the voyage is 25 tonne.

New voyage cons. = {new displ.} 2/3 x {new speed}2 x new distance

Old voyage cons. {Old displ. } {old speed} old distance

New voyage cons. = {11000} 2/3 x {11}2 x 3000

25 {10000} {13} 12 x 24

New voyage cons. = 25 x 1.12/3 x 0.922 x 10.42

New voyage cons. = 234 tonne

Example 6

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A ship travels 900 nautical miles at a speed of 12.5 knots and burns 150 tonne of fuel

over the voyage. Estimate the distance the ship could travel at a speed of 13.5 knots on

250 tonne of fuel.

Solution

Assuming the displacement to be the same in each case:

New voyage cons. = {new speed}2 x new distance

Old voyage cons. {Old speed} old distance

250 = 13.52 x New distance

150 12.52 900

New distance = 900 x 12.52 x 250

150 x 13.52

New distance = 1286 Nautical Miles Ans****

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