basic principles of ship propulsion -...

Contents:

Basic Principles of Ship Propulsion

Page

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Scope of this Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Chapter 1Ship Definitions and Hull Resistance . . . . . . . . . . . . . . . . . . 4

• Ship types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

• A ship’s load lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

• Indication of a ship’s size . . . . . . . . . . . . . . . . . . . . . . . . 5

• Description of hull forms . . . . . . . . . . . . . . . . . . . . . . . . 5

• Ship’s resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Chapter 2Propeller Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

• Propeller types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

• Flow conditions around the propeller . . . . . . . . . . . . . . . . . . 11

• Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . · · · · 11

• Propeller dimensions . . . . . . . . . . . . . . . . . . . . . . · · · · 13

• Operating conditions of a propeller . . . . . . . . . . . . . . . . . . . 15

Chapter 3Engine Layout and Load Diagrams . . . . . . . . . . . . . . . . . . 20

• Power functions and logarithmic scales . . . . . . . . . . . . . . . . . 20

• Propulsion and engine running points . . . . . . . . . . . . . . . . . . 20

• Engine layout diagram . . . . . . . . . . . . . . . . . . . . . . . . . 22

• Load diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

• Use of layout and load diagrams – examples . . . . . . . . . . . . . . 25

• Influence on engine running ofdifferent types of ship resistance – summary . . . . . . . . . . . . . . 27

Closing Remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Introduction

For the purpose of this paper, the term“ship” is used to denote a vehicle em-ployed to transport goods and personsfrom one point to another over water.Ship propulsion normally occurs withthe help of a propeller, which is theterm most widely used in English,although the word “screw” is some-times seen, inter alia in combinationssuch as a “twin-screw” propulsion plant.

Today, the primary source of propellerpower is the diesel engine, and the powerrequirement and rate of revolution verymuch depend on the ship’s hull formand the propeller design. Therefore, inorder to arrive at a solution that is asoptimal as possible, some generalknowledge is essential as to the princi-pal ship and diesel engine parametersthat influence the propulsion system.

This paper will, in particular, attempt toexplain some of the most elementaryterms used regarding ship types,ship’s dimensions and hull forms andclarify some of the parameters pertain-ing to hull resistance, propeller condi-tions and the diesel engine’s loaddiagram.

On the other hand, it is considered be-yond the scope of this publication togive an explanation of how propulsioncalculations as such are carried out, asthe calculation procedure is extremelycomplex. The reader is referred to thespecialised literature on this subject, forexample as stated in “References”.

Scope of this Paper

This paper is divided into three chapterswhich, in principle, may be considered asthree separate papers but which also,with advantage, may be read in closeconnection to each other. Therefore,some important information mentioned inone chapter may well appear in anotherchapter, too.

Chapter 1, describes the most elemen-tary terms used to define ship sizesand hull forms such as, for example,the ship’s displacement, deadweight,design draught, length between per-pendiculars, block coefficient, etc.Other ship terms described include theeffective towing resistance, consistingof frictional, residual and air resistance,and the influence of these resistancesin service.

Chapter 2, deals with ship propulsionand the flow conditions around the pro-peller(s). In this connection, the wakefraction coefficient and thrust deduc-tion coefficient, etc. are mentioned.

The total power needed for the propel-ler is found based on the above effec-tive towing resistance and variouspropeller and hull dependent efficien-cies which are also described. A sum-mary of the propulsion theory is shownin Fig. 6.

The operating conditions of a propelleraccording to the propeller law valid fora propeller with fixed pitch are describedfor free sailing in calm weather, and

followed up by the relative heavy/lightrunning conditions which apply whenthe ship is sailing and subject to differenttypes of extra resistance, like fouling,heavy sea against, etc.

Chapter 3, elucidates the importanceof choosing the correct specified MCRand optimising point of the main engine,and thereby the engine’s load diagramin consideration to the propeller’s designpoint. The construction of the relevantload diagram lines is described in detailby means of several examples. Fig. 24shows, for a ship with fixed pitch pro-peller, by means of a load diagram, theimportant influence of different types ofship resistance on the engine’s contin-uous service rating.

3

Basic Principles of Ship Propulsion

Ship Definitions and HullResistance

Ship types

Depending on the nature of their cargo,and sometimes also the way the cargois loaded/unloaded, ships can be dividedinto different categories, classes, andtypes, some of which are mentioned inTable 1.

The three largest categories of shipsare container ships, bulk carriers (forbulk goods such as grain, coal, ores,etc.) and tankers, which again can bedivided into more precisely definedclasses and types. Thus, tankers canbe divided into oil tankers, gas tankersand chemical tankers, but there arealso combinations, e.g. oil/chemicaltankers.

Table 1 provides only a rough outline.In reality there are many other combi-nations, such as “Multi-purpose bulkcontainer carriers”, to mention just oneexample.

A ship’s load lines

Painted halfway along the ship’s sideis the “Plimsoll Mark”, see Fig. 1. Thelines and letters of the Plimsoll Mark,which conform to the freeboard ruleslaid down by the IMO (InternationalMaritime Organisation) and local au-thorities, indicate the depth to whichthe vessel may be safely loaded (thedepth varies according to the seasonand the salinity of the water).

There are, e.g. load lines for sailing infreshwater and seawater, respectively,with further divisions for tropical condi-tions and summer and winter sailing.According to the international freeboardrules, the summer freeboard draughtfor seawater is equal to the “Scantlingdraught”, which is the term applied tothe ship’s draught when dimensioningthe hull.

The winter freeboard draught is lessthan that valid for summer because of

the risk of bad weather whereas, on theother hand, the freeboard draught for

tropical seas is somewhat higher thanthe summer freeboard draught.

4

Category Class Type

TankerOil tanker

Gas tankerChemical tanker

OBO

Crude (oil) CarrierVery Large Crude CarrierUltra Large Crude CarrierProduct Tanker

Liquefied Natural Gas carrierLiquefied Petroleum Gas carrier

Oil/Bulk/Ore carrier

CCVLCCULCC

LNGLPG

OBO

Bulk carrier Bulk carrier

Container ship Container shipContainer carrierRoll On-Roll Off Ro-Ro

General cargo shipGeneral cargoCoaster

Reefer Reefer Refigerated cargo vessel

Passenger shipFerryCruise vessel

Table 1: Examples of ship types

T TropicalS SummerW WinterWNA Winter - the North Atlantic

D L

D: Freeboard draught

SeawaterFreshwater

Danish load mark

TF

F

D

Freeboard deck

Fig. 1: Load lines – freeboard draught

Indication of a ship’s size

Displacement and deadweightWhen a ship in loaded condition floats atan arbitrary water line, its displacement isequal to the relevant mass of water dis-placed by the ship. Displacement is thusequal to the total weight, all told, of therelevant loaded ship, normally in seawa-ter with a mass density of 1.025 t/m3.

Displacement comprises the ship’slight weight and its deadweight, wherethe deadweight is equal to the ship’sloaded capacity, including bunkers andother supplies necessary for the ship’spropulsion. The deadweight at any timethus represents the difference betweenthe actual displacement and the ship’slight weight, all given in tons:

deadweight = displacement – light weight.

Incidentally, the word “ton” does notalways express the same amount ofweight. Besides the metric ton (1,000kg), there is the English ton (1,016 kg),which is also called the “long ton”. A“short ton” is approx. 907 kg.

The light weight of a ship is not normallyused to indicate the size of a ship,whereas the deadweight tonnage(dwt), based on the ship’s loading ca-pacity, including fuel and lube oils etc.for operation of the ship, measured intons at scantling draught, often is.

Sometimes, the deadweight tonnagemay also refer to the design draught ofthe ship but, if so, this will be mentioned.Table 2 indicates the rule-of-thumb rela-tionship between the ship’s displacement,deadweight tonnage (summer freeboard/scantling draught) and light weight.

A ship’s displacement can also be ex-pressed as the volume of displacedwater ∇, i.e. in m3.

Gross register tonsWithout going into detail, it should bementioned that there are also suchmeasurements as Gross Register Tons(GRT), and Net Register Tons (NRT)where 1 register ton = 100 English cubicfeet, or 2.83 m3.

These measurements express the sizeof the internal volume of the ship in ac-cordance with the given rules for suchmeasurements, and are extensivelyused for calculating harbour and canaldues/charges.

Description of hull forms

It is evident that the part of the shipwhich is of significance for its propulsion

is the part of the ship’s hull which isunder the water line. The dimensionsbelow describing the hull form referto the design draught, which is lessthan, or equal to, the scantlingdraught. The choice of the designdraught depends on the degree ofload, i.e. whether, in service, the shipwill be lightly or heavily loaded. Gen-erally, the most frequently occurringdraught between the fully-loaded andthe ballast draught is used.

Ship’s lengths LOA, LWL, and LPP

The overall length of the ship LOA isnormally of no consequence whencalculating the hull’s water resistance.The factors used are the length of thewaterline LWL and the so-called lengthbetween perpendiculars LPP. The di-mensions referred to are shown inFig. 2.

5

Ship type dwt/lightweight ratio

Displ./dwtratio

Tanker andBulk carrier 6 1.17

Container ship 2.5-3.0 1.33-1.4

Table 2: Examples of relationship between dis-placement, deadweight tonnage and light weight

L

L

L

PP

WL

OA

AM

DA

BWL

DF

D

Length between perpendiculars: LLength on waterline: LLength o : LBreadth on waterline: BDraught: D = 1/2 (D +D )Midship section area: A

PP

WL

OA

WL

m

F A

verall

Fig. 2: Hull dimensions

The length between perpendiculars isthe length between the foremost per-pendicular, i.e. usually a vertical linethrough the stem’s intersection withthe waterline, and the aftmost perpen-dicular which, normally, coincides withthe rudder axis. Generally, this length isslightly less than the waterline length,and is often expressed as:

LPP = 0.97 × LWL

Draught DThe ship’s draught D (often T is used inliterature) is defined as the vertical dis-tance from the waterline to that point ofthe hull which is deepest in the water,see Figs. 2 and 3. The foremost draughtDF and aftmost draught DA are normallythe same when the ship is in the loadedcondition.

Breadth on waterline BWLAnother important factor is the hull’slargest breadth on the waterline BWL,see Figs. 2 and 3.

Block coefficient CB

Various form coefficients are used toexpress the shape of the hull. The mostimportant of these coefficients is theblock coefficient CB, which is definedas the ratio between the displacementvolume ∇ and the volume of a box withdimensions LWL × BWL × D, see Fig. 3, i.e.:

CL B D

B

WL WL

=∇

× ×

In the case cited above, the block co-efficient refers to the length on water-line LWL. However, shipbuilders often useblock coefficient CB, PP based on thelength between perpendiculars, LPP, inwhich case the block coefficient will, as arule, be slightly larger because, as previ-ously mentioned, LPP is normally slightlyless than LWL.

CL B D

B PP

PP WL

, =∇

× ×

A small block coefficient means less re-sistance and, consequently, the possibil-ity of attaining higher speeds.

Table 3 shows some examples of blockcoefficient sizes, and the pertaining

service speeds, on different types ofships. It shows that large block coeffi-cients correspond to low speeds andvice versa.

Ship typeBlock

coefficientCB

Approxi-mate shipspeed Vin knots

Lighter 0.90 5 – 10

Bulk carrier 0.80 – 0.85 12 – 17

Tanker 0.80 – 0.85 12 –16

General cargo 0.55 – 0.75 13 – 22

Container ship 0.50 – 0.70 14 – 26

Ferry boat 0.50 – 0.70 15 – 26

Table 3: Examples of block coefficients

Water plane area coefficient CWL

The water plane area coefficient CWL

expresses the ratio between the ves-sel’s waterline area AWL and the productof the length LWL and the breadth BWL ofthe ship on the waterline, see Fig. 3, i.e.:

CA

L BWL

WL

WL WL

=×

Generally, the waterplane area coeffi-cient is some 0.10 higher than the blockcoefficient, i.e.:

CWL ≅ CB + 0.10.

This difference will be slightly larger onfast vessels with small block coefficientswhere the stern is also partly immersedin the water and thus becomes part ofthe ”waterplane” area.

Midship section coefficient CM

A further description of the hull form isprovided by the midship section coeffi-cient CM, which expresses the ratio be-tween the immersed midship sectionarea AM (midway between the foremostand the aftmost perpendiculars) and theproduct of the ship’s breadth BWL anddraught D, see Fig. 3, i.e.:

CA

B DM

M

WL

=×

6

LWL

AWL

BWL

DAMWaterline plane

LPP

,

Midship section coefficient

Volume of displacement

Waterline area

Block coefficient L based

Waterplane area coefficient

WL

Longitudinal prismatic coefficient

:

:

: =

: =

: =

: =

A

C

C

C

C

WL

B

WL

M

P

L BWL x x DWL

B x DWL

A x LM WL

L BWL WLxAWL

AM

Fig. 3: Hull coefficients of a ship

For bulkers and tankers, this coefficientis in the order of 0.98-0.99, and forcontainer ships in the order of 0.97-0.98.

Longitudinal prismatic coefficient CP

The longitudinal prismatic coefficientCP expresses the ratio between dis-placement volume ∇ and the productof the midship frame section area AM

and the length of the waterline LWL,see also Fig. 3, i.e.:

CA L C B D L

C

Cp

M WL M WL WL

B

M

=∇×

=∇

× × ×=

As can be seen, CP is not an independ-ent form coefficient, but is entirely de-pendent on the block coefficient CB

and the midship section coefficient CM.

Longitudinal Centre of Buoyancy LCBThe Longitudinal Centre of Buoyancy(LCB) expresses the position of thecentre of buoyancy and is defined asthe distance between the centre ofbuoyancy and the mid-point betweenthe ship’s foremost and aftmost perpen-diculars. The distance is normally statedas a percentage of the length betweenthe perpendiculars, and is positive ifthe centre of buoyancy is located tothe fore of the mid-point between theperpendiculars, and negative if locatedto the aft of the mid-point. For a shipdesigned for high speeds, e.g. containerships, the LCB will, normally, be nega-tive, whereas for slow-speed ships,such as tankers and bulk carriers, it willnormally be positive. The LCB is gener-ally between -3% and +3%.

Fineness ratio CLD

The length/displacement ratio or fine-ness ratio, CLD, is defined as the ratiobetween the ship’s waterline length LWL,and the length of a cube with a volumeequal to the displacement volume, i.e.:

CL

LD

WL=∇3

Ship’s resistance

To move a ship, it is first necessary toovercome resistance, i.e. the force work-ing against its propulsion. The calculationof this resistance R plays a significant role

in the selection of the correct propeller andin the subsequent choice of main engine.

GeneralA ship’s resistance is particularly influ-enced by its speed, displacement, andhull form. The total resistance RT, con-sists of many source-resistances Rwhich can be divided into three maingroups, viz.:

1) Frictional resistance2) Residual resistance3) Air resistance

The influence of frictional and residualresistances depends on how much ofthe hull is below the waterline, while theinfluence of air resistance depends onhow much of the ship is above the wa-terline. In view of this, air resistance willhave a certain effect on container shipswhich carry a large number of contain-ers on the deck.

Water with a speed of V and a densityof r has a dynamic pressure of:

½ × r × V 2 (Bernoulli’s law)

Thus, if water is being completelystopped by a body, the water will reacton the surface of the body with the dy-namic pressure, resulting in a dynamicforce on the body.

This relationship is used as a basiswhen calculating or measuring thesource-resistances R of a ship’s hull,by means of dimensionless resistancecoefficients C. Thus C are related tothe reference force K, defined as theforce which the dynamic pressure ofwater with the ship’s speed V exerts ona surface which is equal to the hull’swetted area AS. The rudder’s surface isalso included in the wetted area. Thegeneral data for resistance calculationsis thus:

Reference force: K = ½ × r × V 2 × AS

and source resistances: R = C × K

On the basis of many experimentaltank tests, and with the help of pertain-ing dimensionless hull parameters,some of which have already been dis-cussed, methods have been estab-lished for calculating all the necessary

resistance coefficients C and, thus, thepertaining source-resistances R. Inpractice, the calculation of a particularship’s resistance can be verified bytesting a model of the relevant ship ina towing tank.

Frictional resistance RF

The frictional resistance RF of the hulldepends on the size of the hull’s wet-ted area AS, and on the specific fric-tional resistance coefficient CF. Thefriction increases with fouling of thehull, i.e. by the growth of, i.a. algae,sea grass and barnacles.

An attempt to avoid fouling is made bythe use of anti-fouling hull paints toprevent the hull from becoming“long-haired”, i.e. these paints reducethe possibility of the hull becomingfouled by living organisms. The paintscontaining TBT (tributyl tin) as theirprincipal biocide, which is very toxic,have dominated the market for decades,but the IMO ban of TBT for new appli-cations from 1 January, 2003, and afull ban from 1 January, 2008, may in-volve the use of new (and maybe notas effective) alternatives, probably cop-per-based anti-fouling paints.

When the ship is propelled through thewater, the frictional resistance increasesat a rate that is virtually equal to thesquare of the vessel’s speed.

Frictional resistance represents a con-siderable part of the ship’s resistance,often some 70-90% of the ship’s totalresistance for low-speed ships (bulkcarriers and tankers), and sometimesless than 40% for high-speed ships(cruise liners and passenger ships) [4]. Thefrictional resistance is found as follows:

RF = CF × K

Residual resistance RR

Residual resistance RR comprises waveresistance and eddy resistance. Waveresistance refers to the energy losscaused by waves created by the vesselduring its propulsion through the water,while eddy resistance refers to the losscaused by flow separation which cre-ates eddies, particularly at the aft endof the ship.

7

Wave resistance at low speeds is pro-portional to the square of the speed,but increases much faster at higherspeeds. In principle, this means that aspeed barrier is imposed, so that a fur-ther increase of the ship’s propulsionpower will not result in a higher speedas all the power will be converted intowave energy. The residual resistancenormally represents 8-25% of the totalresistance for low-speed ships, and upto 40-60% for high-speed ships [4].

Incidentally, shallow waters can alsohave great influence on the residualresistance, as the displaced water un-der the ship will have greater difficultyin moving aftwards.

The procedure for calculating the spe-cific residual resistance coefficient CR isdescribed in specialised literature [2]and the residual resistance is found asfollows:

RR = CR × K

Air resistance RA

In calm weather, air resistance is, in prin-ciple, proportional to the square of theship’s speed, and proportional to thecross-sectional area of the ship above thewaterline. Air resistance normally repre-sents about 2% of the total resistance.

For container ships in head wind, theair resistance can be as much as 10%.The air resistance can, similar to theforegoing resistances, be expressed asRA = CA × K, but is sometimes basedon 90% of the dynamic pressure of airwith a speed of V, i.e.:

RA = 0.90 × ½ × rair × V 2 × Aair

where rair is the density of the air, andAair is the cross-sectional area of thevessel above the water [4].

Towing resistance RT

and effective (towing) power PE

The ship’s total towing resistance RT isthus found as:

RT = RF + RR + RA

The corresponding effective (towing)power, PE, necessary to move the ship

through the water, i.e. to tow the shipat the speed V, is then:

PE = V × RT

The power delivered to the propeller,PD, in order to move the ship at speedV is, however, somewhat larger. This isdue, in particular, to the flow conditionsaround the propeller and the propellerefficiency itself, the influences of whichare discussed in the next chapterwhich deals with Propeller Propulsion.

Total ship resistance in generalWhen dividing the residual resistanceinto wave and eddy resistance, as earlierdescribed, the distribution of the total shiptowing resistance RT could also, as aguideline, be stated as shown in Fig. 4.

The right column is valid for low-speedships like bulk carriers and tankers, andthe left column is valid for very high-speedships like cruise liners and ferries. Con-tainer ships may be placed in betweenthe two columns.

The main reason for the differencebetween the two columns is, as earliermentioned, the wave resistance. Thus,in general all the resistances are pro-portional to the square of the speed,but for higher speeds the wave resis-tance increases much faster, involvinga higher part of the total resistance.

This tendency is also shown in Fig. 5for a 600 teu container ship, originallydesigned for the ship speed of 15 knots.Without any change to the hull design,

8

RF

V

RA

V

RW

RE

Ship speed V

% of RTType of resistance

RA

RW

RE

RF = Friction= Wave= Eddy= Air

Highspeed

ship

Lowspeedship

45 - 9040 - 55 - 3

10 - 2

Fig. 4: Total ship towing resistance RT = RF + RW + RE + RA

the ship speed for a sister ship was re-quested to be increased to about 17.6knots. However, this would lead to arelatively high wave resistance, requir-ing a doubling of the necessary propul-sion power.

A further increase of the propulsionpower may only result in a minor shipspeed increase, as most of the extrapower will be converted into wave en-ergy, i.e. a ship speed barrier valid forthe given hull design is imposed bywhat we could call a “wave wall”, seeFig. 5. A modification of the hull lines,suiting the higher ship speed, is neces-sary.

Increase of ship resistance in service,Ref. [1], page 244During the operation of the ship, thepaint film on the hull will break down.Erosion will start, and marine plantsand barnacles, etc. will grow on thesurface of the hull. Bad weather, per-haps in connection with an inappropri-ate distribution of the cargo, can be areason for buckled bottom plates. Thehull has been fouled and will no longerhave a “technically smooth” surface,

which means that the frictional resist-ance will be greater. It must also beconsidered that the propeller surfacecan become rough and fouled. The to-tal resistance, caused by fouling, mayincrease by 25-50% throughout thelifetime of a ship.

Resistance will also increase becauseof sea, wind, and current. The resis-tance when navigating in head-on seacould, in general, increase by as muchas 50-100% of the total ship resistancein calm weather.

Estimates of average increase inresistance for ships navigating themain routes:

North Atlantic route,navigation westward 25-35%

North Atlantic route,navigation eastward 20-25%

Europe-Australia 20-25%

Europe-East Asia 20-25%

The Pacific routes 20-30%

On the North Atlantic routes, the firstpercentage corresponds to summernavigation and the second percentageto winter navigation.

However, analysis of trading conditionsfor a typical 140,000 dwt bulk carriershows that on some routes, especiallyJapan-Canada when loaded, the in-creased resistance (sea margin) canreach extreme values up to 220%, withan average of about 100%.

Unfortunately, no data have been pub-lished on increased resistance as afunction of type and size of vessel. Thelarger the ship, the less the relative in-crease of resistance due to the sea.On the other hand, the frictional resis-tance of the large, full-bodied ships willvery easily be changed in the course oftime because of fouling.

In practice, the increase of resistancecaused by heavy weather depends onthe current, the wind, as well as thewave size, where the latter factor mayhave great influence. Thus, if the wavesize is relatively high, the ship speedwill be somewhat reduced even whensailing in fair seas.

In principle, the increased resistancecaused by heavy weather could berelated to:

a) wind and current against, andb) heavy waves,

but in practice it will be difficult to dis-tinguish between these factors.

9

Power and speed relationship for a 600 TEU container ship

20 knots

6,000

Normal service point

Ship speed

Propulsion power

10 15

4,000

2,000

0

8,000"Wave wall"

New service point

kW

Fig. 5: The “wave wall” ship speed barrier

Chapter 2

Propeller Propulsion

The traditional agent employed tomove a ship is a propeller, sometimestwo and, in very rare cases, more thantwo. The necessary propeller thrust Trequired to move the ship at speed Vis normally greater than the pertainingtowing resistance RT, and the flow-relatedreasons are, amongst other reasons,explained in this chapter. See also Fig. 6,where all relevant velocity, force, powerand efficiency parameters are shown.

Propeller types

Propellers may be divided into the follow-ing two main groups, see also Fig. 7:

• Fixed pitch propeller (FP-propeller)

• Controllable pitch propeller(CP-propeller)

Propellers of the FP-type are cast inone block and normally made of a copperalloy. The position of the blades, andthereby the propeller pitch, is once andfor all fixed, with a given pitch that can-not be changed in operation. Thismeans that when operating in, for ex-ample, heavy weather conditions, thepropeller performance curves, i.e. thecombination of power and speed(r/min) points, will change according tothe physical laws, and the actual pro-peller curve cannot be changed by thecrew. Most ships which do not need aparticularly good manoeuvrability areequipped with an FP-propeller.

Propellers of the CP-type have a rela-tively larger hub compared with theFP-propellers because the hub has tohave space for a hydraulically activatedmechanism for control of the pitch (an-gle) of the blades. The CP-propeller isrelatively expensive, maybe up to 3-4times as expensive as a correspondingFP-propeller. Furthermore, because ofthe relatively larger hub, the propellerefficiency is slightly lower.

CP-propellers are mostly used forRo-Ro ships, shuttle tankers and simi-lar ships that require a high degree of

10

Efficiencies1 t1 w

Relative rotative efficiency :Propeller efficiency - open water :Propeller efficiency - behind hull : =Propulsive efficiency : =Shaft efficiency :Total efficiency :

__

x

x

VelocitiesShip’s speed : VArriving water velocity to propeller : V

Effective wake velocity : V = V _ V

A

W A

ForcesTowing resistance : R

Thrust force : TThrust deduction fraction : F = T _ R

T _ RT

T

T

T

PowerEffective (Towing) power : P = R V

by the propeller to water : P = P /

Power delivered to propeller : P = P /

Brake power of main engine : P = P /

E T

T E

D T

B D

x

Thrust deduction coefficient : t =

Hull efficiency : =

Thrust power delivered

H

H

B

D

S

T B

S

B

0 R

T

---- ---- x ---- x ---- x x x x x= = = =P P P PB T D B

P P P PE E T D

H

S H 0 R SH

VA

V

VW

PD PEPT PB

V

TRT

F

Wake fraction coefficient : w =

R

0

B

(Speed of advance of propeller)

V _ V

VA

Fig. 6: The propulsion of a ship – theory

Controllable pitch propeller (CP-Propeller)Fixed pitch propeller (FP-Propeller)

Monobloc with fixedpropeller blades(copper alloy)

Hub with a mechanismfor control of the pitchof the blades(hydraulically activated)

Fig. 7: Propeller types

manoeuvrability. For ordinary ships likecontainer ships, bulk carriers and crudeoil tankers sailing for a long time in nor-mal sea service at a given ship speed,it will, in general, be a waste of moneyto install an expensive CP-propeller in-stead of an FP-propeller. Furthermore, aCP-propeller is more complicated, invol-ving a higher risk of problems in service.

Flow conditions around the propeller

Wake fraction coefficient wWhen the ship is moving, the friction ofthe hull will create a so-called frictionbelt or boundary layer of water aroundthe hull. In this friction belt the velocityof the water on the surface of the hull isequal to that of the ship, but is reducedwith its distance from the surface of thehull. At a certain distance from the hulland, per definition, equal to the outer“surface” of the friction belt, the watervelocity is equal to zero.

The thickness of the friction belt increaseswith its distance from the fore end ofthe hull. The friction belt is thereforethickest at the aft end of the hull andthis thickness is nearly proportional tothe length of the ship, Ref. [3]. Thismeans that there will be a certain wakevelocity caused by the friction along thesides of the hull. Additionally, the ship’sdisplacement of water will also causewake waves both fore and aft. All thisinvolves that the propeller behind thehull will be working in a wake field.

Therefore, and mainly originating fromthe friction wake, the water at the pro-peller will have an effective wake veloc-ity Vw which has the same direction asthe ship’s speed V, see Fig. 6. Thismeans that the velocity of arriving waterVA at the propeller, (equal to the speedof advance of the propeller) given asthe average velocity over the propeller’sdisk area is Vw lower than the ship’sspeed V.

The effective wake velocity at the pro-peller is therefore equal to Vw = V – VA

and may be expressed in dimensionlessform by means of the wake fractioncoefficient w. The normally used wakefraction coefficient w given by Taylor isdefined as:

wV

V

V V

V

you getV

Vw

W A

A

= =−

= −( )1

The value of the wake fraction coefficientdepends largely on the shape of thehull, but also on the propeller’s locationand size, and has great influence onthe propeller’s efficiency.

The propeller diameter or, even better,the ratio between the propeller diameterd and the ship’s length LWL has someinfluence on the wake fraction coeffi-cient, as d/LWL gives a rough indicationof the degree to which the propellerworks in the hull’s wake field. Thus, thelarger the ratio d/LWL, the lower w willbe. The wake fraction coefficient w in-creases when the hull is fouled.

For ships with one propeller, the wakefraction coefficient w is normally in theregion of 0.20 to 0.45, correspondingto a flow velocity to the propeller VA of0.80 to 0.55 of the ship’s speed V. Thelarger the block coefficient, the larger isthe wake fraction coefficient. On shipswith two propellers and a conventionalaftbody form of the hull, the propellerswill normally be positioned outside thefriction belt, for which reason the wakefraction coefficient w will, in this case,be a great deal lower. However, for atwin-skeg ship with two propellers, thecoefficient w will be almost unchanged(or maybe slightly lower) comparedwith the single-propeller case.

Incidentally, a large wake fraction co-efficient increases the risk of propellercavitation, as the distribution of thewater velocity around the propeller isgenerally very inhomogeneous undersuch conditions.

A more homogeneous wake field forthe propeller, also involving a higherspeed of advance VA of the propeller,may sometimes be needed and can beobtained in several ways, e.g. by hav-ing the propellers arranged in nozzles,below shields, etc. Obviously, the bestmethod is to ensure, already at the de-sign stage, that the aft end of the hull isshaped in such a way that the opti-mum wake field is obtained.

Thrust deduction coefficient tThe rotation of the propeller causes thewater in front of it to be “sucked” backtowards the propeller. This results in anextra resistance on the hull normallycalled “augment of resistance” or, if re-lated to the total required thrust force Ton the propeller, “thrust deduction frac-tion” F, see Fig. 6. This means that thethrust force T on the propeller has toovercome both the ship’s resistance RT

and this “loss of thrust” F.

The thrust deduction fraction F may beexpressed in dimensionless form bymeans of the thrust deduction coeffi-cient t, which is defined as:

tFT

T R

T

you getR

Tt

T

T

= =−

= −( )1

The thrust deduction coefficient t canbe calculated by using calculationmodels set up on the basis of researchcarried out on different models.

In general, the size of the thrust deduc-tion coefficient t increases when thewake fraction coefficient w increases.The shape of the hull may have a sig-nificant influence, e.g. a bulbous stemcan, under certain circumstances (lowship speeds), reduce t.

The size of the thrust deduction coeffi-cient t for a ship with one propeller is,normally, in the range of 0.12 to 0.30,as a ship with a large block coefficienthas a large thrust deduction coefficient.For ships with two propellers and aconventional aftbody form of the hull,the thrust deduction coefficient t will bemuch less as the propellers’ “sucking”occurs further away from the hull.However, for a twin-skeg ship with twopropellers, the coefficient t will be almostunchanged (or maybe slightly lower)compared with the single-propeller case.

Efficiencies

Hull efficiency hH

The hull efficiency hH is defined as theratio between the effective (towing)power PE = RT × V, and the thrust power

11

which the propeller delivers to the waterPT = T × VA, i.e.:

hH = =××

= =−

−

P

P

R V

T V

R T

V Vt

w

E

T

T

A

T

A

//

1

1

For a ship with one propeller, the hullefficiency hH is usually in the range of1.1 to 1.4, with the high value for shipswith high block coefficients. For shipswith two propellers and a conventionalaftbody form of the hull, the hull effi-ciency hH is approx. 0.95 to 1.05, againwith the high value for a high block co-efficient. However, for a twin-skeg shipwith two propellers, the hull coefficienthH will be almost unchanged comparedwith the single-propeller case.

Open water propeller efficiency hO

Propeller efficiency hO is related toworking in open water, i.e. the propel-ler works in a homogeneous wake fieldwith no hull in front of it.

The propeller efficiency depends, es-pecially, on the speed of advance VA,thrust force T, rate of revolution n, di-ameter d and, moreover, i.a. on the de-sign of the propeller, i.e. the number ofblades, disk area ratio, and pitch/diam-eter ratio – which will be discussedlater in this chapter. The propeller effi-ciency hO can vary between approx.0.35 and 0.75, with the high value be-ing valid for propellers with a highspeed of advance VA, Ref. [1].

Fig. 8 shows the obtainable propellerefficiency hO shown as a function of thespeed of advance VA, which is given indimensionless form as:

JV

n dA=

×

where J is the advance number of thepropeller.

Relative rotative efficiency hR

The actual velocity of the water flowingto the propeller behind the hull is nei-ther constant nor at right angles to thepropeller’s disk area, but has a kind ofrotational flow. Therefore, comparedwith when the propeller is working inopen water, the propeller’s efficiency is

affected by the hR factor – called thepropeller’s relative rotative efficiency.

On ships with a single propeller therotative efficiency hR is, normally, around1.0 to 1.07, in other words, the rotationof the water has a beneficial effect. Therotative efficiency hR on a ship with aconventional hull shape and with twopropellers will normally be less, approx.0.98, whereas for a twin-skeg ship withtwo propellers, the rotative efficiency hR

will be almost unchanged.

In combination with w and t, hR is prob-ably often being used to adjust the re-sults of model tank tests to the theory.

Propeller efficiency hB working behindthe shipThe ratio between the thrust power PT,which the propeller delivers to the wa-

ter, and the power PD, which is deliv-ered to the propeller, i.e. the propellerefficiency hB for a propeller workingbehind the ship, is defined as:

h h hB

T

Do R

P

P= = ×

Propulsive efficiency hD

The propulsive efficiency hD, whichmust not be confused with the openwater propeller efficiency hO, is equal tothe ratio between the effective (towing)power PE and the necessary powerdelivered to the propeller PD, i.e.:

hD

E

D

E

T

T

D

P

P

P

P

P

P= = ×

= hH × hB = hH × hO × hR

12

0.3

0.2

0.4

00.6

0.1

0.6

0.5

Vn x d

AAdvance number J =

0.4 0.50.2 0.30 0.1

o

0.7

Propellerefficiency

ReefersContainer ships

Small tankers20,000 DWT

Large tankers>150,000 DWT

n ( revs./s )1.66

2.00

0.7

Fig. 8: Obtainable propeller efficiency – open water, Ref. [1], page 213

As can be seen, the propulsive efficiencyhD is equal to the product of the hullefficiency hH, the open water propellerefficiency hO, and the relative rotativeefficiency hR, although the latter hasless significance.

In this connection, one can be led tobelieve that a hull form giving a highwake fraction coefficient w, and hencea high hull efficiency hH, will also providethe best propulsive efficiency hD.

However, as the open water propellerefficiency hO is also greatly dependenton the speed of advance VA, cf. Fig. 8,that is decreasing with increased w,the propulsive efficiency hD will not,generally, improve with increasing w,quite often the opposite effect is obtained.

Generally, the best propulsive efficiencyis achieved when the propeller works ina homogeneous wake field.

Shaft efficiency hS

The shaft efficiency hS depends, i.a. onthe alignment and lubrication of theshaft bearings, and on the reductiongear, if installed.

Shaft efficiency is equal to the ratio be-tween the power PD delivered to thepropeller and the brake power PB deliv-ered by the main engine, i.e.

h =S

D

B

P

P

The shaft efficiency is normally around0.985, but can vary between 0.96 and0.995.

Total efficiency hT

The total efficiency hT, which is equal tothe ratio between the effective (towing)power PE, and the necessary brakepower PB delivered by the main engine,can be expressed thus:

hT

P

P

P

P

P

PE

B

E

D

D

B

= = ×

= hD´ h

S= h

H´ h

O´ h

R´ h

S

Propeller dimensions

Propeller diameter dWith a view to obtaining the highestpossible propulsive efficiency hD, thelargest possible propeller diameter dwill, normally, be preferred. There are,however, special conditions to be con-sidered. For one thing, the aftbody formof the hull can vary greatly depending ontype of ship and ship design, for another,the necessary clearance between thetip of the propeller and the hull will de-pend on the type of propeller.

For bulkers and tankers, which are oftensailing in ballast condition, there arefrequent demands that the propellershall be fully immersed also in this con-dition, giving some limitation to the pro-peller size. This propeller size limitationis not particularly valid for containerships as they rarely sail in ballast condi-tion. All the above factors mean that anexact propeller diameter/design draughtratio d/D cannot be given here but, asa rule-of-thumb, the below mentionedapproximations of the diameter/designdraught ratio d/D can be presented,and a large diameter d will, normally,result in a low rate of revolution n.

Bulk carrier and tanker:

d/D < approximately 0.65

Container ship:

d/D < approximately 0.74

For strength and production reasons,the propeller diameter will generally notexceed 10.0 metres and a power out-put of about 90,000 kW. The largest-diameter propeller manufactured so faris of 11.0 metres and has four propellerblades.

Number of propeller bladesPropellers can be manufactured with 2,3, 4, 5 or 6 blades. The fewer the num-ber of blades, the higher the propellerefficiency will be. However, for reasonsof strength, propellers which are to besubjected to heavy loads cannot bemanufactured with only two or threeblades.

Two-bladed propellers are used onsmall ships, and 4, 5 and 6-bladedpropellers are used on large ships.Ships using the MAN B&W two-strokeengines are normally large-type vesselswhich use 4-bladed propellers. Shipswith a relatively large power requirementand heavily loaded propellers, e.g. con-tainer ships, may need 5 or 6-bladedpropellers. For vibrational reasons, pro-pellers with certain numbers of bladesmay be avoided in individual cases inorder not to give rise to the excitationof natural frequencies in the ship’s hullor superstructure, Ref. [3].

Disk area coefficientThe disk area coefficient – referred to inolder literature as expanded blade arearatio – defines the developed surfacearea of the propeller in relation to itsdisk area. A factor of 0.55 is consideredas being good. The disk area coefficientof traditional 4-bladed propellers is oflittle significance, as a higher value willonly lead to extra resistance on thepropeller itself and, thus, have little ef-fect on the final result.

For ships with particularly heavy-loadedpropellers, often 5 and 6-bladed pro-pellers, the coefficient may have ahigher value. On warships it can be ashigh as 1.2.

Pitch diameter ratio p/dThe pitch diameter ratio p/d, expressesthe ratio between the propeller’s pitchp and its diameter d, see Fig. 10. Thepitch p is the distance the propeller“screws” itself forward through the wa-ter per revolution, providing that thereis no slip – see also the next sectionand Fig. 10. As the pitch can varyalong the blade’s radius, the ratio isnormally related to the pitch at 0.7 × r,where r = d/2 is the propeller’s radius.

To achieve the best propulsive efficiencyfor a given propeller diameter, an optimumpitch/diameter ratio is to be found,which again corresponds to a particu-lar design rate of revolution. If, forinstance, a lower design rate of revolutionis desired, the pitch/diameter ratio hasto be increased, and vice versa, at thecost of efficiency. On the other hand, ifa lower design rate of revolution is de-sired, and the ship’s draught permits,the choice of a larger propeller diame-

13

ter may permit such a lower design rateof revolution and even, at the same time,increase the propulsive efficiency.

Propeller coefficients J, KT and KQ

Propeller theory is based on modelsbut, to facilitate the general use of thistheory, certain dimensionless propellercoefficients have been introduced in re-lation to the diameter d, the rate of rev-olution n, and the water’s mass densityr. The three most important of thesecoefficients are mentioned below.

The advance number of the propeller Jis, as earlier mentioned, a dimensionlessexpression of the propeller’s speed ofadvance VA.

JV

n dA=

×

The thrust force T, is expresseddimensionless, with the help of thethrust coefficient KT, as

KT

n dT =× ×r 2 4

and the propeller torque

QP

nD=×2p

is expressed dimensionless with thehelp of the torque coefficient KQ, as

KQ

n dQ =× ×r 2 5

The propeller efficiency hO can be cal-culated with the help of the above-men-tioned coefficients, because, as previouslymentioned, the propeller efficiency hO isdefined as:

hp pO

= =×

× ×= ×

P

P

T V

Q n

K

KJT

D

A T

Q2 2

With the help of special and very com-plicated propeller diagrams, whichcontain, i.a. J, KT and KQ curves, it ispossible to find/calculate the propeller’sdimensions, efficiency, thrust, power, etc.

Manufacturing accuracy of the propellerBefore the manufacturing of the propeller,the desired accuracy class standard ofthe propeller must be chosen by thecustomer. Such a standard is, for ex-ample, ISO 484/1 – 1981 (CE), whichhas four different “Accuracy classes”,see Table 4.

Each of the classes, among other de-tails, specifies the maximum allowabletolerance on the mean design pitch ofthe manufactured propeller, andthereby the tolerance on the correspond-ing propeller speed (rate of revolution).

The price of the propeller, of course,depends on the selected accuracyclass, with the lowest price for class III.However, it is not recommended touse class III, as this class has a toohigh tolerance. This again means thatthe mean pitch tolerance should nor-mally be less than +/– 1.0 %.

The manufacturing accuracy tolerancecorresponds to a propeller speed toler-ance of max. +/– 1.0 %. When also in-corporating the influence of the toleranceon the wake field of the hull, the totalpropeller tolerance on the rate of revo-lution can be up to +/– 2.0 %. This tol-erance has also to be borne in mindwhen considering the operating condi-tions of the propeller in heavy weather.

Influence of propeller diameter andpitch/diameter ratio on propulsiveefficiency D.As already mentioned, the highest pos-sible propulsive efficiency required toprovide a given ship speed is obtainedwith the largest possible propeller dia-meter d, in combination with the corre-sponding, optimum pitch/diameter ra-tio p/d.

14

ISO 484/1 – 1981 (CE)

ClassManufacturing

accuracy

Mean pitchfor propel-

ler

SIIIIII

Very high accuracyHigh accuracyMedium accuracyWide tolerances

+/– 0.5 %+/– 0.75 %+/– 1.00 %+/– 3.00 %

Table 4: Manufacturing accuracy classesof a propeller

110 120100 r/min130

Shaft power

80 90

8,800

70

8,700

8,900

9,100

8,600

8,500

9,400

0.95

9,200

9,300

9,000

d = Propeller diameterp/d = Pitch/diameter ratio

Power and speed curvefor various propellerdiameters d withoptimum p/d Propeller speed

Power and speed curvefor the given propellerdiameter d = 7.2 m withdifferent p/d

80,000 dwt crude oil tankerDesign draught = 12.2 mShip speed = 14.5 kn9,500

0.90

0.850.80

0.71

1.00

0.60

0.75

d

0.65

0.55

6.8 m

p/d0.67

7.2 m

6.6 m

7.4 m

7.0 m

0.70

p/d

0.68

0.69

0.50

p/d

p/dd

kW

Fig. 9: Propeller design – influence of diameter and pitch

As an example for an 80,000 dwt crudeoil tanker, with a service ship speed of14.5 knots and a maximum possiblepropeller diameter of 7.2 m, this influenceis shown in Fig. 9.

According to the blue curve, the maxi-mum possible propeller diameter of 7.2m may have the optimum pitch/diame-ter ratio of 0.70, and the lowest possi-ble shaft power of 8,820 kW at 100r/min. If the pitch for this diameter ischanged, the propulsive efficiency willbe reduced, i.e. the necessary shaftpower will increase, see the red curve.

The blue curve shows that if a biggerpropeller diameter of 7.4 m is possible,the necessary shaft power will be re-duced to 8,690 kW at 94 r/min, i.e. thebigger the propeller, the lower the opti-mum propeller speed.

The red curve also shows that propul-sion-wise it will always be an advan-tage to choose the largest possiblepropeller diameter, even though theoptimum pitch/diameter ratio wouldinvolve a too low propeller speed (in rela-tion to the required main engine speed).Thus, when using a somewhat lowerpitch/diameter ratio, compared with theoptimum ratio, the propeller/ enginespeed may be increased and will onlycause a minor extra power increase.

Operating conditions of a propeller

Slip ratio SIf the propeller had no slip, i.e. if thewater which the propeller “screws”itself through did not yield (i.e. if thewater did not accelerate aft), the pro-peller would move forward at a speedof V = p × n, where n is the propeller’srate of revolution, see Fig. 10.

The similar situation is shown in Fig. 11for a cork screw, and because the corkis a solid material, the slip is zero and,therefore, the cork screw always movesforward at a speed of V = p × n. How-ever, as the water is a fluid and doesyield (i.e. accelerate aft), the propeller’sapparent speed forward decreaseswith its slip and becomes equal to theship’s speed V, and its apparent slipcan thus be expressed as p × n – V.

The apparent slip ratio SA, which isdimensionless, is defined as:

Sp n V

p nV

p nA =× −

×= −

×1

The apparent slip ratio SA, which is cal-culated by the crew, provides usefulknowledge as it gives an impression ofthe loads applied to the propeller underdifferent operating conditions. The ap-parent slip ratio increases when the

15

S x p x nV or VA

Pitch p

n

0.7 x r

r

d

p x n

Slip

The apparent slip ratio : S = = 1A_

The real slip ratio : S = = 1R_p x n _ V V

p x n p x nA A

p x n _ V Vp x n p x n

Fig. 10: Movement of a ship´s propeller, with pitch p and slip ratio S

Velocity of corkscrew: V = p x n Pitch p

Wine bottleCorkscrew Cork

V

n

Fig. 11: Movement of a corkscrew, without slip

vessel sails against the wind or waves,in shallow waters, when the hull isfouled, and when the ship accelerates.Under increased resistance, this in-volves that the propeller speed (rate ofrevolution) has to be increased in orderto maintain the required ship speed.

The real slip ratio will be greater thanthe apparent slip ratio because the realspeed of advance VA of the propeller is,as previously mentioned, less than theship’s speed V.

The real slip ratio SR, which gives a truerpicture of the propeller’s function, is:

SV

p nV w

p nR

A= −×

= −× −

×1 1

1( )

At quay trials where the ship’s speed isV = 0, both slip ratios are 1.0. Incidentally,slip ratios are often given in percentages.

Propeller law in generalAs discussed in Chapter 1, the resis-tance R for lower ship speeds is pro-portional to the square of the ship’sspeed V, i.e.:

R = c × V2

where c is a constant. The necessarypower requirement P is thus propor-tional to the speed V to the power ofthree, thus:

P = R × V = c × V3

For a ship equipped with a fixed pitchpropeller, i.e. a propeller with unchange-able pitch, the ship speed V will be pro-portional to the rate of revolution n, thus:

P = c × n3

which precisely expresses the propellerlaw, which states that “the necessarypower delivered to the propeller is pro-portional to the rate of revolution to thepower of three”.

Actual measurements show that thepower and engine speed relationshipfor a given weather condition is fairlyreasonable, whereas the power andship speed relationship is often seenwith a higher power than three. A rea-

sonable relationship to be used for esti-mations in the normal ship speed rangecould be as follows:

• For large high-speed ships like con-tainer vessels: P = c × V 4.5

• For medium-sized, medium-speedships like feeder container ships,reefers, RoRo ships, etc.: P = c × V 4.0

• For low-speed ships like tankers andbulk carriers, and small feeder con-tainer ships, etc.: P = c × V 3.5

Propeller law for heavy running propellerThe propeller law, of course, can onlybe applied to identical ship runningconditions. When, for example, theship’s hull after some time in servicehas become fouled and thus becomemore rough, the wake field will be differentfrom that of the smooth ship (clean hull)valid at trial trip conditions.

A ship with a fouled hull will, conse-quently, be subject to extra resistancewhich will give rise to a “heavy propellercondition”, i.e. at the same propellerpower, the rate of revolution will be lower.

The propeller law now applies to an-other and “heavier” propeller curvethan that applying to the clean hull,propeller curve, Ref. [1], page 243.

The same relative considerations applywhen the ship is sailing in a heavy seaagainst the current, a strong wind, andheavy waves, where also the heavywaves in tail wind may give rise to aheavier propeller running than whenrunning in calm weather. On the otherhand, if the ship is sailing in ballastcondition, i.e. with a lower displace-ment, the propeller law now applies toa “lighter” propeller curve, i.e. at thesame propeller power, the propellerrate of revolution will be higher.

As mentioned previously, for ships witha fixed pitch propeller, the propeller lawis extensively used at part load running.It is therefore also used in MAN B&WDiesel’s engine layout and load diagramsto specify the engine’s operationalcurves for light running conditions (i.e.clean hull and calm weather) and heavyrunning conditions (i.e. for fouled hull

and heavy weather). These diagrams us-ing logarithmic scales and straight linesare described in detail in Chapter 3.

Propeller performance in general atincreased ship resistanceThe difference between the above-men-tioned light and heavy running propellercurves may be explained by an exam-ple, see Fig. 12, for a ship using, as ref-erence, 15 knots and 100% propulsionpower when running with a clean hull incalm weather conditions. With 15% morepower, the corresponding ship speedmay increase from 15.0 to 15.6 knots.

As described in Chapter 3, and com-pared with the calm weather conditions,it is normal to incorporate an extrapower margin, the so-called sea mar-gin, which is often chosen to be 15%.This power margin corresponds to ex-tra resistance on the ship caused bythe weather conditions. However, forvery rough weather conditions the influ-ence may be much greater, as de-scribed in Chapter 1.

In Fig. 12a, the propulsion power isshown as a function of the ship speed.When the resistance increases to alevel which requires 15% extra powerto maintain a ship speed of 15 knots,the operating point A will move towardspoint B.

In Fig. 12b the propulsion power isnow shown as a function of the propellerspeed. As a first guess it will often be as-sumed that point A will move towards B’because an unchanged propeller speedimplies that, with unchanged pitch, thepropeller will move through the waterat an unchanged speed.

If the propeller was a corkscrew movingthrough cork, this assumption wouldbe correct. However, water is not solidas cork but will yield, and the propellerwill have a slip that will increase with in-creased thrust caused by increasedhull resistance. Therefore, point A willmove towards B which, in fact, is veryclose to the propeller curve through A.Point B will now be positioned on apropeller curve which is slightly heavyrunning compared with the clean hulland calm weather propeller curve.

16

Sometimes, for instance when the hullis fouled and the ship is sailing in heavyseas in a head wind, the increase inresistance may be much greater, cor-responding to an extra power demandof the magnitude of 100% or even higher.An example is shown in Fig. 12c.

In this example, where 100% powerwill give a ship speed of 15.0 knots,point A, a ship speed of, for instance,12.3 knots at clean hull and in calmweather conditions, point C, will requireabout 50% propulsion power but, atthe above-mentioned heavy runningconditions, it might only be possible toobtain the 12.3 knots by 100% propulsionpower, i.e. for 100% power going frompoint A to D. Running point D may nowbe placed relatively far to the left of pointA, i.e. very heavy running. Such a situ-ation must be considered when laying-out the main engine in relation to thelayout of the propeller, as described inChapter 3.

A scewed propeller (with bent bladetips) is more sensitive to heavy runningthan a normal propeller, because thepropeller is able to absorb a highertorque in heavy running conditions. For

a ducted propeller, the opposite effectis obtained.

Heavy waves and sea and wind againstWhen sailing in heavy sea against, withheavy wave resistance, the propeller

can be up to 7-8% heavier runningthan in calm weather, i.e. at the samepropeller power, the rate of revolutionmay be 7-8% lower. An example validfor a smaller container ship is shown inFig. 13. The service data is measured

17

(Logarithmic scales)

Power

Propeller speed

15.0 knots100% power

Propeller curvefor clean hull andcalm weather

Propellercurve forfouled hulland heavyseas

LR

Slip

HR HR = Heavy runningLR = Light running

D´ A

C


12.3 knots50% power

10.0 knots50% power

D

Fig. 12c: Propeller speed performance atlarge extra ship resistance


Power

Propeller speed



15%Seamargin

Slip

Propeller curve for cleanhull and calm weather


B´

A

B

Fig. 12b: Propeller speed performance at15% sea margin

BHP21,000

18,000

15,000

12,000

9,000

6,00076 80 9284 9688 100

Ship speedknots

Shaft power

Clean hull and draught DD = 6.50 mD = 5.25 mD = 7.75 m

Source: Lloyd's Register

MEAN

F

A

Average weather 3%

Extremely good weather 0%

Extremely bad weather 6%

Propeller speed

Apparent slip

10%6%

Heavyrunning

2%-2%

1316

19

22

CB

A

C

B

A

r/min

Fig. 13: Service data over a period of a year returned from a single screw container ship




15%Seamargin

Power

Ship speed

Propeller curve for cleanhull and calm weather


B

A

Fig. 12a: Ship speed performance at 15%sea margin

over a period of one year and onlyincludes the influence of weather con-ditions! The measuring points havebeen reduced to three average weatherconditions, and show an averageheavy running of 6%, and therefore, inpractice, the heavy running has provedto be even greater.

In order to avoid slamming of the ship,and thereby damage to the stem andracing of the propeller, the ship speedwill normally be reduced by the navigat-ing officer on watch.

Another measured example is shownin Fig. 14, and is valid for a reefer shipduring its sea trial. Even though thewind velocity is relatively low, only 2.5m/s, and the wave height is 4 m, themeasurements indicate approx. 1.5%

heavy running when sailing in headwind out, compared with when sailingin tail wind on return.

Ship accelerationWhen the ship accelerates, the propel-ler will be subjected to an even largerload than during free sailing. The powerrequired for the propeller, therefore, willbe relatively higher than for free sailing,and the engine’s operating point will beheavy running, as it takes some timebefore the propeller speed has reachedits new and higher level. An examplewith two different accelerations isshown in Fig. 15. The load diagram isdescribed in Chapter 3.

Shallow watersWhen sailing in shallow waters, the re-sidual resistance of the ship may be in-

creased and, in the same way as whenthe ship accelerates, the propeller willbe subjected to a larger load than dur-ing free sailing, and the propeller will beheavy running.

Influence of displacementWhen the ship is sailing in the loadedcondition, the ship’s displacement vol-ume may, for example, be 10% higheror lower than for the displacement validfor the average loaded condition. This,of course, has an influence on the ship’sresistance, and the required propellerpower, but only a minor influence onthe propeller curve.

On the other hand, when the ship issailing in the ballast condition, the dis-placement volume, compared to theloaded condition, can be much lower,and the corresponding propeller curvemay apply to, for example, a 2% “lighter”propeller curve, i.e. for the same powerto the propeller, the rate of revolutionwill be 2% higher.

Parameters causing heavy runningpropellerTogether with the previously describedoperating parameters which cause aheavy running propeller, the parame-ters summarised below may give an in-dication of the risk/sensitivity of gettinga heavy running propeller when sailingin heavy weather and rough seas:

1 Relatively small ships (<70,000 dwt)such as reefers and small containerships are sensitive whereas large ships,such as large tankers and containerships, are less sensitive because thewaves are relatively small comparedto the ship size.

2 Small ships (Lpp < 135 m≈ 20,000 dwt)have low directional stability and,therefore, require frequent ruddercorrections, which increase the shipresistance (a self-controlled rudderwill reduce such resistance).

3 High-speed shipsare more sensitive than low-speedships because the waves will act onthe fast-going ship with a relativelylarger force than on the slow-goingship.

18

Propell

er cu

rve

SMCR: 13,000 kW x 105 r/minWind velocity : 2.5 m/sWave height : 4 m

Propeller/engine speed

100

90

105

85

100

95

80

10199 103 105 % SMCR10297 9896 104

Heavyrunning

Engine

"pro

peller

curve

"

Propell

er cu

rve

Propeller designlight running

* 20.521.5

*

20.5*

*20.8

*21.2

*22.0

21.1 *

7

51

3

4

Shaft power% SMCR

22.3 *

21.8*

SMCR

* 21.1

Head wind

Tail wind


Fig. 14: Measured relationship between power, propeller and ship speed during seatrial ofa reefer ship

4 Ships with a “flat” stemmay be slowed down faster by wavesthan a ship with a “sharp” stem.Thus an axe-shaped upper bow maybetter cut the waves and therebyreduce the heavy running tendency.

5 Fouling of the hull and propellerwill increase both hull resistance andpropeller torque. Polishing the pro-peller (especially the tips) as often aspossible (also when in water) has apositive effect. The use of effectiveanti-fouling paints will prevent foulingcaused by living organisms.

6 Ship accelerationwill increase the propeller torque,and thus give a temporarily heavyrunning propeller.

7 Sailing in shallow watersincreases the hull resistance and re-duces the ship’s directional stability.

8 Ships with scewed propellerare able to absorb a higher torqueunder heavy running conditions.

Manoeuvring speedBelow a certain ship speed, called themanoeuvring speed, the manoeuvra-bility of the rudder is insufficient be-cause of a too low velocity of the waterarriving at the rudder. It is rather difficultto give an exact figure for an adequatemanoeuvring speed of the ship as thevelocity of the water arriving at the rud-der depends on the propeller’s slipstream.

Often a manoeuvring speed of themagnitude of 3.5-4.5 knots is men-tioned. According to the propeller law,a correspondingly low propulsionpower will be needed but, of course,this will be higher for running in heavyweather with increased resistance onthe ship.

Direction of propeller rotation (side thrust)When a ship is sailing, the propellerblades bite more in their lowermost po-sition than in their uppermost position.The resulting side-thrust effect is largerthe more shallow the water is as, forexample, during harbour manoeuvres.

Therefore, a clockwise (looking from aftto fore) rotating propeller will tend topush the ship’s stern in the starboarddirection, i.e. pushing the ship’s stemto port, during normal ahead running.This has to be counteracted by therudder.

When reversing the propeller to asternrunning as, for example, when berthingalongside the quay, the side-thrust ef-fect is also reversed and becomes fur-ther pronounced as the ship’s speeddecreases. Awareness of this behav-iour is very important in critical situa-tions and during harbour manoeuvres.

According to Ref. [3], page 15-3, thereal reason for the appearance of theside thrust during reversing of the pro-peller is that the upper part of the pro-peller’s slip stream, which is rotative,strikes the aftbody of the ship.

Thus, also the pilot has to know pre-cisely how the ship reacts in a givensituation. It is therefore an unwrittenlaw that on a ship fitted with a fixedpitch propeller, the propeller is alwaysdesigned for clockwise rotation whensailing ahead. A direct coupled mainengine, of course, will have the samerotation.

In order to obtain the same side-thrusteffect, when reversing to astern, onships fitted with a controllable pitchpropeller, CP-propellers are designedfor anti-clockwise rotation when sailingahead.

19

80 100 10585

50

7565 90 9560

60

70

80

90

mep110%

Engine speed, % A

40

A=M100

Engine shaft power, % A

100%

90%

80%

70%

60%

O

A 100% reference pointM Specified engine MCRO Optimising point

110


70

Fig. 15: Load diagram – acceleration

Engine Layout andLoad Diagrams

Power functions and logarithmicscales

As is well-known, the effective brakepower PB of a diesel engine is propor-tional to the mean effective pressure(mep) pe and engine speed (rate of rev-olution) n. When using c as a constant,PB may then be expressed as follows:

PB = c × pe × n

or, in other words, for constant mepthe power is proportional to the speed:

PB = c × n1 (for constant mep)

As already mentioned – when runningwith a fixed pitch propeller – the powermay, according to the propeller law, beexpressed as:

PB = c × n3 (propeller law)

Thus, for the above examples, the brakepower PB may be expressed as a func-tion of the speed n to the power of i, i.e.

PB = c × ni

Fig. 16 shows the relationship betweenthe linear functions, y = ax + b, see (A),using linear scales and the power func-tions PB = c × ni, see (B), using logarith-mic scales.

The power functions will be linear whenusing logarithmic scales, as:

log (PB) = i × log (n) + log (c)

which is equivalent to: y = ax + b

Thus, propeller curves will be parallel tolines having the inclination i = 3, andlines with constant mep will be parallelto lines with the inclination i = 1.

Therefore, in the layout and load diagramsfor diesel engines, as described in thefollowing, logarithmic scales are used,making simple diagrams with straightlines.

Propulsion and engine runningpoints

Propeller design point PDNormally, estimations of the necessarypropeller power and speed are basedon theoretical calculations for loadedship, and often experimental tank tests,both assuming optimum operatingconditions, i.e. a clean hull and goodweather. The combination of speedand power obtained may be called theship’s propeller design point PD placedon the light running propeller curve 6,

see Fig. 17. On the other hand, someshipyards and/or propeller manufactur-ers sometimes use a propeller designpoint PD‘ that incorporates all or partof the so-called sea margin describedbelow.

Fouled hullWhen the ship has been sailing forsome time, the hull and propeller be-come fouled and the hull’s resistancewill increase. Consequently, the shipspeed will be reduced unless the enginedelivers more power to the propeller, i.e.the propeller will be further loaded andwill become heavy running HR.

Furthermore, newer high-efficiency shiptypes have a relatively high ship speed,and a very smooth hull and propellersurface (at sea trial) when the ship isdelivered. This means that the inevitablebuild-up of the surface roughness onthe hull and propeller during sea serviceafter seatrial may result in a relativelyheavier running propeller, comparedwith older ships born with a more roughhull surface.

Heavy weather and sea margin usedfor layout of engineIf, at the same time, the weather isbad, with head winds, the ship’s resis-tance may increase much more, andlead to even heavier running.

When determining the necessary en-gine power, it is normal practice to addan extra power margin, the so-calledsea margin, which is traditionally about15% of the propeller design PD power.However, for large container ships,20-30% may sometimes be used.

When determining the necessary en-gine speed, for layout of the engine, itis recommended – compared with theclean hull and calm weather propellercurve 6 – to choose the heavier propel-ler curve 2, see Fig. 17, correspondingto curve 6 having a 3-7% higher rate ofrevolution than curve 2, and in generalwith 5% as a good choice.

Note that the chosen sea power mar-gin does not equalise the chosenheavy engine propeller curve.

20

A. Straight lines in linear scales

a

2

X1 20

1

0

b

y = ax + b

B. Power function curvesin logarithmic scales

P

P

B

B

= engine brake powerc = constantn = engine speed

log( ) = i x log(n) + log(c)

y = ax + bP = c x ni

i = 1

i = 2

i = 3

y = log (P )B

i = 0

x = log (n)

y = log (P ) = log (c x n )Bi

y

Fig. 16: Relationship between linear functionsusing linear scales and power functionsusing logarithmic scales

Continuous service propulsion point SPThe resulting speed and power combi-nation – when including heavy propellerrunning and sea margin – is called the“continuous service rating for propulsion”SP for fouled hull and heavy weather.The heavy propeller curve, curve 2, forfouled hull and heavy weather will nor-mally be used as the basis for the en-gine operating curve in service, and thepropeller curve for clean hull and calmweather, curve 6, is said to represent a“light running” LR propeller.

Continuous service rating SThe continuous service rating is thepower at which the engine, includingthe sea margin, is assumed to operate,and point S is identical to the servicepropulsion point SP unless a main en-gine driven shaft generator is installed.

Light running factor fLR

The heavy propeller curve for a fouledhull and heavy weather, and if no shaftgenerator is installed may, as mentionedabove be used as the design basis for

the engine operating curve in service,curve 2, whereas the light propellercurve for clean hull and calm weather,curve 6, may be valid for running con-ditions with new ships, and equal tothe layout/design curve of the propel-ler. Therefore, the light propeller curvefor clean hull and calm weather is saidto represent a “light running” LR pro-peller and will be related to the heavypropeller curve for fouled hull andheavy weather condition by means of alight running factor fLR, which, for thesame power to the propeller, is definedas the percentage increase of the rateof revolution n, compared to the rate ofrevolution for heavy running, i.e.

fn n

nLR

light heavy

heavy

=−

×100%

Engine marginBesides the sea margin, a so-called“engine margin” of some 10-15% isfrequently added as an operationalmargin for the engine. The correspond-ing point is called the “specified MCRfor propulsion” MP, see Fig. 17, andrefers to the fact that the power forpoint SP is 10-15% lower than forpoint MP, i.e. equal to 90-85% of MP.

Specified MCR MThe engine’s specified MCR point M isthe maximum rating required by theyard or owner for continuous operationof the engine. Point M is identical to thespecified propulsion MCR point MP un-less a main engine driven shaft genera-tor is installed. In such a case, the extrapower demand of the shaft generatormust also be considered.

Note:Light/heavy running, fouling and seamargin are overlapping terms.Light/heavy running of the propeller re-fers to hull and propeller deterioration,and bad weather, and sea margin, i.e.extra power to the propeller, refers tothe influence of the wind and the sea.

Based on feedback from service, itseems reasonable to design the pro-peller for 3-7% light running. The de-gree of light running must be decidedupon, based on experience from theactual trade and hull design, but 5%is often a good choice.

21

LR(5%)

Engine speed

Power

MP

Sea margin(15% of PD)

2 6

SP

2 Heavy propeller curve fouled hull and heavy weather6 Light propeller curve clean hull and calm weather

MP: Specified propulsion pointSP: Service propulsion pointPD: Propeller design pointPD`: Alternative propeller design pointLR: Light running factorHR: Heavy running

_

_

HR

PD´

PD

Engine margin(10% of MP)

Fig. 17: Ship propulsion running points and engine layout

Engine layout diagram

An engine’s layout diagram is limited bytwo constant mean effective pressure(mep) lines L1-L3 and L2-L4, and by twoconstant engine speed lines L1-L2 andL3-L4, see Fig. 17. The L1 point refers tothe engine’s nominal maximum contin-uous rating. Within the layout areathere is full freedom to select the en-gines specified MCR point M and rele-vant optimising point O, see below,

which is optimum for the ship and theoperating profile. Please note that thelowest specific fuel oil consumption fora given optimising point O will be ob-tained at 80% of point O’s power.

Based on the propulsion and enginerunning points, as previously found, thelayout diagram of a relevant main en-gine may be drawn-in. The specifiedMCR point M must be inside the limita-tion lines of the layout diagram; if it is

not, the propeller speed will have to bechanged or another main engine typemust be chosen. Yet, in special cases,point M may be located to the right ofline L1-L2, see “Optimising Point” below.

Optimising point OThe “Optimising point” O – or, better,the layout point of the engine – is therating at which the turbocharger ismatched, and at which the engine tim-ing and compression ratio are adjusted.

As mentioned below, under “Load dia-gram”, the optimising point O is placedon line 1 (layout curve of engine) of theload diagram, and the optimised powercan be from 85 to 100% of point M‘spower, when turbocharger(s) and en-gine timing are taken into consideration.When optimising between 93.5% and85% of point M‘s power, overload run-ning will still be possible (110% of M‘spower), as long as consideration to thescavenge air pressure has been taken.

The optimising point O is to be placedinside the layout diagram. In fact, thespecified MCR point M can be placedoutside the layout diagram, but only byexceeding line L1-L2, and, of course,only provided that the optimising pointO is located inside the layout diagram.

It should be noted that engines withoutVIT (variable injection timing) fuel pumpscannot be optimised at part-load. There-fore, these engines are always optimisedin point A, i.e. having point M‘s power.

Load diagram

DefinitionsThe load diagram (Fig. 18) defines thepower and speed limits for continuousas well as overload operation of an in-stalled engine which has an optimisingpoint O and a specified MCR point Mthat conforms to the ship’s specification.

Point A is a 100% speed and powerreference point of the load diagram,and is defined as the point on the pro-peller curve (line 1) – the layout curve ofthe engine – through the optimising pointO, having the specified MCR power.

Normally, point M is equal to point A,but in special cases, for example if a

22

Line 1: Propeller curve through optimising point (O) layout curve for engine

Line 2: Heavy propeller curve fouled hull and heavy seasLine 3: Speed limitLine 4: Torque/speed limitLine 5: Mean effective pressure limit

Line 6: Light propeller curve clean hull and calm weather layout curve for propellerLine 7: Power limit for continuous runningLine 8: Overload limitLine 9: Sea trial speed limitLine 10: Constant mean effective pressure (mep) lines

__

_ _

80 100 10585

50

70 7565 90 9560

60

70

80

90

mep110%

Engine speed, % A

40

2

4

A=M

9

7

8

5100

Engine shaft power, % A

6100%

90%

80%

70%

60%

1

10

3

O

A 100% reference pointM Specified engine MCRO Optimising point

110

Fig. 18: Engine load diagram

shaft generator is installed, point Mmay be placed to the right of point Aon line 7. The service points of the in-stalled engine incorporate the enginepower required for ship propulsion andfor the shaft generator, if installed.

During shoptest running, the engine willalways operate along curve 1, withpoint A as 100% MCR. If CP-propellerand constant speed operation is re-quired, the delivery test may be fin-ished with a constant speed test.

Limits to continuous operationThe continuous service range is limitedby the four lines 4, 5, 7 and 3 (9), seeFig. 18:

Line 3 and line 9Line 3 represents the maximum accept-able speed for continuous operation, i.e.105% of A, however, maximum 105% ofL1. During sea trial conditions the maxi-mum speed may be extended to 107%of A, see line 9.

The above limits may, in general, beextended to 105% and, during sea trialconditions, to 107% of the nominal L1

speed of the engine, provided the tor-sional vibration conditions permit.

The overspeed set-point is 109% ofthe speed in A, however, it may bemoved to 109% of the nominal speedin L1, provided that torsional vibrationconditions permit.

Running at low load above 100% ofthe nominal L1 speed of the engine is,however, to be avoided for extendedperiods.

Line 4:Represents the limit at which an ampleair supply is available for combustion andimposes a limitation on the maximumcombination of torque and speed.

Line 5:Represents the maximum mean effec-tive pressure level (mep) which can beaccepted for continuous operation.

Line 7:Represents the maximum power forcontinuous operation.

Line 10:Represents the mean effective pressure(mep) lines. Line 5 is equal to the 100%mep-line. The mep-lines are also anexpression of the corresponding fuelindex of the engine.

Limits for overload operationThe overload service range is limited asfollows, see Fig. 18:

Line 8:Represents the overload operation limi-tations.

The area between lines 4, 5, 7 and thedashed line 8 in Fig. 18 is available foroverload running for limited periodsonly (1 hour per 12 hours).

23

Point A of load diagram

Line 1: Propeller curve through optimising point (O)

Line 7: Constant power line through specified MCR (M)

Point A: Intersection between lines 1 and 7

Engine speed

Power

M: Specified MCR of engineS: Continuous service rating of engineO: Optimising point of engineA: Reference point of load diagram

A=M=MP

Propulsion andengine service curvefor heavy running

7

S=SPO

2

16

Fig. 19a: Example 1 with FPP – engine layout without SG (normal case)


Engine speed

A=M

Propulsion and engine servicecurve for heavy running

3.3% A5

62

4

Power 1

S

7

O5

6

3

4 1

7

2

5% A

5% L1

Fig. 19b: Example 1 with FPP – load diagram without SG (normal case)

Electronic governor with load limitationIn order to safeguard the diesel engineagainst thermal and mechanical overload,the approved electronic governors includethe following two limiter functions:

• Torque limiterThe purpose of the torque limiter isto ensure that the limitation lines ofthe load diagram are always observed.The torque limiter algorithm comparesthe calculated fuel pump index (fuelamount) and the actually measuredengine speed with a reference limitercurve giving the maximum allowablefuel pump index at a given enginespeed. If the calculated fuel pumpindex is above this curve, the result-ing fuel pump index will be reducedcorrespondingly.

The reference limiter curve is to beadjusted so that it corresponds to thelimitation lines of the load diagram.

• Scavenge air pressure limiterThe purpose of the scavenge air

pressure limiter is to ensure that theengine is not being overfuelled duringacceleration, as for example duringmanoeuvring.

The scavenge air pressure limiteralgorithm compares the calculatedfuel pump index and measuredscavenge air pressure with a refer-ence limiter curve giving the maxi-mum allowable fuel pump index at agiven scavenge air pressure. If thecalculated fuel pump index is abovethis curve, the resulting fuel pumpindex will be reduced correspondingly.

The reference limiter curve is to beadjusted to ensure that sufficient airwill always be available for a goodcombustion process.

RecommendationContinuous operation without a timelimitation is allowed only within the arealimited by lines 4, 5, 7 and 3 of theload diagram. For fixed pitch propelleroperation in calm weather with loaded

ship and clean hull, the propeller/enginemay run along or close to the propellerdesign curve 6.

After some time in operation, the ship’shull and propeller will become fouled,resulting in heavier running of the pro-peller, i.e. the propeller curve will moveto the left from line 6 towards line 2, andextra power will be required for propulsionin order to maintain the ship speed.

At calm weather conditions the extentof heavy running of the propeller willindicate the need for cleaning the hulland, possibly, polishing the propeller.

The area between lines 4 and 1 is avail-able for operation in shallow water,heavy weather and during acceleration,i.e. for non-steady operation withoutany actual time limitation.

24





Engine speed

M=MP

Propulsion andengine service curvefor heavy running

7

S=SP

621

O

Power

A


Fig. 20a: Example 2 with FPP – engine layout without SG (special case)

M

Propulsion and engine servicecurve for heavy running

3.3% A5

62

4

1

S

7

5

6

3

4 1

7

2

5% A

5% L1

A

O

Engine speed

Power


Fig. 20b: Example 2 with FPP – load diagram without SG (special case)

The recommended use of a relativelyhigh light running factor for design ofthe propeller will involve that a relativelyhigher propeller speed will be used forlayout design of the propeller. This, inturn, may involve a minor reduction ofthe propeller efficiency, and may possi-bly cause the propeller manufacturer toabstain from using a large light runningmargin. However, this reduction of thepropeller efficiency caused by the largelight running factor is actually relativelyinsignificant compared with the improvedengine performance obtained whensailing in heavy weather and/or withfouled hull and propeller.

Use of layout and loaddiagrams - examples

In the following, four different examplesbased on fixed pitch propeller (FPP)and one example based on controllablepitch propeller (CPP) are given in orderto illustrate the flexibility of the layoutand load diagrams.

In this respect the choice of the optimi-sing point O has a significant influence.

Examples with fixed pitch propeller

Example 1:Normal running conditions, withoutshaft generator

Normally, the optimising point O, andthereby the engine layout curve 1, willbe selected on the engine servicecurve 2 (for heavy running), as shownin Fig. 19a.

Point A is then found at the intersectionbetween propeller curve 1 (2) and theconstant power curve through M, line7. In this case, point A will be equal topoint M.

Once point A has been found in thelayout diagram, the load diagram canbe drawn, as shown in Fig. 19b, andhence the actual load limitation linesof the diesel engine may be found.

Example 2:Special running conditions, withoutshaft generator

When the ship accelerates, the propel-ler will be subjected to an even largerload than during free sailing. The sameapplies when the ship is subjected toan extra resistance as, for example,when sailing against heavy wind andsea with large wave resistance.

In both cases, the engine’s operatingpoint will be to the left of the normaloperating curve, as the propeller willrun heavily.

In order to avoid exceeding theleft-hand limitation line 4 of the loaddiagram, it may, in certain cases, benecessary to limit the accelerationand/or the propulsion power.

If the expected trade pattern of theship is to be in an area with frequentlyappearing heavy wind and sea and

25

Shaf

t gen

erat

or

Propulsion curvefor heavy running

O7

1 2

Engine service curvefor heavy running

MP

SG

6

SSG

SP

Engine speed

Power A=M






Fig. 21a: Example 3 with FPP – engine layout with SG (normal case)

Shaf

t gen

erat

or


3.3% A

S

5

62

4

1

7

O5

6

3

4 1

7

2

5% A

5% L1

A=M


MP

SP

Engine speed

Power


Fig. 21b: Example 3 with FPP – load diagram with SG (normal case)

large wave resistance, it can, therefore,be an advantage to design/move theload diagram more towards the left.

The latter can be done by moving theengine’s optimising point O – and thusthe propeller curve 1 through the opti-mising point – towards the left. How-ever, this will be at the expense of aslightly increased specific fuel oil con-sumption.

An example is shown in Figs. 20a and20b. As will be seen in Fig. 20b, andcompared with the normal case shownin Example 1 (Fig. 19b), the left-handlimitation line 4 is moved to the left, giv-ing a wider margin between lines 2 and4, i.e. a larger light running factor hasbeen used in this example.

Example 3:Normal case, with shaft generator

In this example a shaft generator (SG)is installed, and therefore the servicepower of the engine also has to incor-porate the extra shaft power required

for the shaft generator’s electricalpower production.

In Fig. 21a, the engine service curveshown for heavy running incorporatesthis extra power.

The optimising point O, and thereby theengine layout curve 1, will normally bechosen on the propeller curve (~ en-gine service curve) through point M.

Point A is then found in the same wayas in example 1, and the load diagramcan be drawn as shown in Fig. 21b.

Example 4:Special case, with shaft generator

Also in this special case, a shaft gener-ator is installed but, unlike in Example3, now the specified MCR for propul-sion MP is placed at the top of the lay-out diagram, see Fig. 22a. This involvesthat the intended specified MCR of theengine (Point M’) will be placed outsidethe top of the layout diagram.

One solution could be to choose adiesel engine with an extra cylinder,but another and cheaper solution is toreduce the electrical power productionof the shaft generator when running inthe upper propulsion power range.

If choosing the latter solution, the re-quired specified MCR power of the en-gine can be reduced from point M’ topoint M as shown in Fig. 22a. Therefore,when running in the upper propulsionpower range, a diesel generator has totake over all or part of the electricalpower production.

However, such a situation will seldomoccur, as ships rather infrequently op-erate in the upper propulsion powerrange. In the example, the optimisingpoint O has been chosen equal topoint S, and line 1 may be found.

Point A, having the highest possiblepower, is then found at the intersectionof line L1-L3 with line 1, see Fig. 22a,and the corresponding load diagram is

26

Shaf

t gen

erat

or

Propulsion curve for heavy running

SG

O=S

61

7

2

M


MP

SP

AM´

Engine speed

Power


Point A and M of load diagramLine 1: Propeller curve through optimising point (O)

M: Located on constant power line 7 through point Aand at MP’s speed

Point A: Intersection between line 1 and line L - LPoint

1 3

Fig. 22a: Example 4 with FPP – engine layout with SG (special case)


Shaf

t gen

erat

or


3.3% A

SG

5

62

4

1

7

O=S

6

3

1

7

2

5% A

5% L1

M


MP

SP

AM´

5

4

Engine speed

Power

Fig. 22b: Example 4 with FPP – load diagram with SG (special case)

drawn in Fig. 22b. Point M is found online 7 at MP’s speed.

Example with controllable pitch propeller

Example 5:With or without shaft generator

Layout diagram – without shaft generatorIf a controllable pitch propeller (CPP)is applied, the combinator curve (ofthe propeller with optimum propellerefficiency) will normally be selected forloaded ship including sea margin.

For a given propeller speed, the com-binator curve may have a given propellerpitch, and this means that, like for a fixedpitch propeller, the propeller may beheavy running in heavy weather.

Therefore, it is recommended to use alight running combinator curve (the dottedcurve), as shown in Fig. 23, to obtain anincreased operating margin for the dieselengine in heavy weather to the load limitsindicated by curves 4 and 5.

Layout diagram – with shaft generatorThe hatched area in Fig. 23 shows therecommended speed range between100% and 96.7% of the specified MCRspeed for an engine with shaft generatorrunning at constant speed.

The service point S can be located atany point within the hatched area.

The procedure shown in Examples 3and 4 for engines with FPP can also be

applied for engines with CPP runningon a combinator curve.

The optimising point O for engines withVIT can be chosen on the propeller curve1 through point A = M with an optimisedpower from 85 to 100% of the specifiedMCR as mentioned before in the sectiondealing with optimising point O.

Load diagramTherefore, when the engine’s specifiedMCR point M has been chosen includingengine margin, sea margin and thepower for a shaft generator, if installed,point M can be used as point A of theload diagram, which can then be drawn.

The position of the combinator curveensures the maximum load rangewithin the permitted speed range forengine operation, and it still leaves areasonable margin to the load limitsindicated by curves 4 and 5.

Influence on engine running ofdifferent types of ship resistance -summary

In order to give a brief summary regard-ing the influence on the fixed pitchpropeller running and main engine opera-tion of different types of ship resistance,an arbitrary example has been chosen,see the load diagram in Fig. 24.

The influence of the different types ofresistance is illustrated by means ofcorresponding service points for propul-sion having the same propulsion power,using as basis the propeller designpoint PD, plus 15% extra power.

Propeller design point PDThe propeller will, as previously described,normally be designed according to aspecified ship speed V valid for loadedship with clean hull and calm weatherconditions. The corresponding enginespeed and power combination isshown as point PD on propeller curve6 in the load diagram, Fig. 24.

Increased ship speed, point S0If the engine power is increased by, forexample, 15%, and the loaded ship isstill operating with a clean hull and incalm weather, point S0, the ship speed

27

Minspeed

A=M

S

3.3%A

5

4

1

75%A

5%L

Recommended rangefor shaft generatoroperation withconstant speed

3

15

1

O

7

Combinator curvefor loaded shipand incl. sea margin

Maxspeed


Engine speed

Power

4

Fig. 23: Example 5 with CPP – with or without shaft generator

V and engine speed n will increase inaccordance with the propeller law (moreor less valid for the normal speed range):

V V V

n n nS

S

03 5

03 0

115 1041

115 1048

= × = ×= × = ×

. .

. .

.

.

Point S0 will be placed on the samepropeller curve as point PD.

Sea running with clean hull and 15%sea margin, point S2Conversely, if still operating with loadedship and clean hull, but now with extra

resistance from heavy seas, an extrapower of, for example, 15% is neededin order to maintain the ship speed V(15% sea margin).

As the ship speed VS2 = V, and if thepropeller had no slip, it would be expectedthat the engine (propeller) speed wouldalso be constant. However, as the waterdoes yield, i.e. the propeller has a slip,the engine speed will increase and therunning point S2 will be placed on apropeller curve 6.2 very close to S0, onpropeller curve 6. Propeller curve 6.2will possibly represent an approximate0.5% heavier running propeller thancurve 6. Ref. [1], page 242.

Depending on the ship type and size,the heavy running factor of 0.5% maybe slightly higher or lower.

For a resistance corresponding toabout 30% extra power (30% sea mar-gin), the corresponding relative heavyrunning factor will be about 1%, Ref.[1], page 242.

Sea running with fouled hull, andheavy weather, point SPWhen, after some time in service, theship’s hull has been fouled, and thusbecomes more rough, the wake fieldwill be different from that of a smoothship (clean hull).

A ship with a fouled hull will, conse-quently, be subject to an extra resis-tance which, due to the changedwake field, will give rise to a heavierrunning propeller than experiencedduring bad weather conditions alone.When also incorporating some aver-age influence of heavy weather, thepropeller curve for loaded ship willmove to the left, see propeller curve2 in the load diagram in Fig. 24. Thispropeller curve, denoted fouled hulland heavy weather for a loaded ship,is about 5% heavy running comparedto the clean hull and calm weatherpropeller curve 6.

In order to maintain an ample airsupply for the diesel engine’s com-bustion, which imposes a limitationon the maximum combination oftorque and speed, see curve 4 of theload diagram, it is normal practice to

28

8

5

932

1

7

4

90

85

95

75

7085

105

100

110

6.3

80

90 95 100 105

S3

80 110

SP

100% ref. point (A)Specified MCR (M)

6

6.2 6.1

S2S1S0

PD

Engine speed, % of A

A=M

Engine shaft power % of A

PD: Propeller design point, clean hull and calm weather

Continuous service rating for propulsion witha power equal to 90% specified MCR, based on:

S0: Clean hull and calm weather, loaded ship

S1: Clean hull and calm weather, ballast (trial)

S2: Clean hull and 15% sea margin, loaded ship

SP: Fouled hull and heavy weather, loaded ship

S3: Very heavy sea and wave resistance

Line 1: Propeller curve through point A=M, layout curve for engine

Line 2: Heavy propeller curve, fouled hull and heavy weather, loaded ship

Line 6: Light propeller curve, clean hull and calm weather,loaded ship, layout curve for propeller

Line 6.1: Propeller curve, clean hull and calm weather, ballast (trial)

Line 6.2: Propeller curve, clean hull and 15% sea margin, loaded ship

Line 6.3: Propeller curve, very heavy sea and wave resistance

Fig. 24: Influence of different types of ship resistance on the continuous service rating

match the diesel engine and turbo-charger etc. according to a propellercurve 1 of the load diagram, equal tothe heavy propeller curve 2.

Instead of point S2, therefore, point SPwill normally be used for the engine lay-out by referring this service propulsionrating to, for example, 90% of the engine’sspecified MCR, which corresponds tochoosing a 10% engine margin.

In other words, in the example the pro-peller’s design curve is about 5% lightrunning compared with the propellercurve used for layout of the main engine.

Running in very heavy seas withheavy waves, point S3When sailing in very heavy sea against,with heavy waves, the propeller can be7-8% heavier running (and even more)than in calm weather, i.e. at the samepropeller power, the rate of revolutionmay be 7-8% lower.

For a propeller power equal to 90% ofspecified MCR, point S3 in the loaddiagram in Fig. 24 shows an exampleof such a running condition.

In some cases in practice with strongwind against, the heavy running hasproved to be even greater and even tobe found to the left of the limitation line4 of the load diagram.

In such situations, to avoid slamming ofthe ship and thus damage to the stemand racing of the propeller, the shipspeed will normally be reduced by thenavigating officers on watch.

Ship acceleration and operation inshallow watersWhen the ship accelerates and thepropeller is being subjected to a largerload than during free sailing, the effecton the propeller may be similar to thatillustrated by means of point S3 in theload diagram, Fig. 24. In some cases inpractice, the influence of accelerationon the heavy running has proved to beeven greater. The same conditions arevalid for running in shallow waters.

Sea running at trial conditions, point S1Normally, the clean hull propeller curve6 will be referred to as the trial trip pro-

peller curve. However, as the ship isseldom loaded during sea trials andmore often is sailing in ballast, the ac-tual propeller curve 6.1 will be morelight running than curve 6.

For a power to the propeller equal to90% specified MCR, point S1 on theload diagram, in Fig. 24, indicates anexample of such a running condition. Inorder to be able to demonstrate opera-tion at 100% power, if required, duringsea trial conditions, it may in somecases be necessary to exceed the pro-peller speed restriction, line 3, whichduring trial conditions may be allowedto be extended to 107%, i.e. to line 9of the load diagram.

Closing Remarks

In practice, the ship’s resistance willfrequently be checked against the resultsobtained by testing a model of the shipin a towing tank. The experimental tanktest measurements are also used foroptimising the propeller and hull design.

When the ship’s necessary power re-quirement, including margins, and thepropeller’s speed (rate of revolution)have been determined, the correctmain engine can then be selected, e.g.with the help of MAN B&W Diesel’scomputer-based engine selectionprogramme.

In this connection the interaction betweenship and main engine is extremely im-portant, and the placing of the engine’sload diagram, i.e. the choice of enginelayout in relation to the engine’s (ship’s)operational curve, must be made care-fully in order to achieve the optimumpropulsion plant. In order to avoid over-loading of the main engine for excessiverunning conditions, the installation of anelectronic governor with load control maybe useful.

If a main engine driven shaft generator –producing electricity for the ship – is in-stalled, the interaction between ship andmain engine will be even more complex.However, due to the flexibility of the lay-out and load diagrams for the MAN B&Wengines, a suitable solution will nearly al-ways be readily at hand.

References

[1] Resistance and Propulsion of Ships,Sv. Aa. Harvald, 1983

[2] Ship ResistanceH.E. Guldhammer andSv. Aa. Harvald, 1974

[3] Fartygspropellrar och Fartygs Framdrift,Jan Tornblad, KaMeWa Publication,1985

[4] Technical discussion withKeld Kofoed Nielsen,Burmeister & Wain Shipyard,Copenhagen

Furthermore, we recommend:

[5] Prediction of Power of ShipsSv. Aa. Harvald, 1977 and 1986

[6] Propulsion of Single-Screw ShipsSv. Aa. Harvald & J.M. Hee, 1981

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basic principles of ship propulsion -...

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