Chapter VI. Propulsion of Ships
The propulsion system of a ship is to provide the
thrust to the ship to overcome the resistance.
6.1 Introduction
•
Propulsive Devices (reading p205-209)
Paddle-Wheels: While the draft varying with ship displacement,
the immersion of wheels also varies. The wheels may come out
of water when the ship is rolling, causing erratic course-keeping,
& they are likely to damage from rough seas.
Propellers: Its first use was in a steam-driven boat at N.Y. in
1804. Advantages over paddle-wheels are,
1) not substantially affected by normal changes in draft;
2) not easily damaged;
3) decreasing the width of the ship, &
4) good efficiency driven by lighter engine.
Since then, propellers have dominated in use of marine
propulsion.
Paddle Wheels Propulsion (Stern)
Paddle Wheels Propulsion (Midship)
Propeller (5-blade)
Propeller (5-blade) & Rudder
Jet type: Water is drawn by a pump & delivered sternwards as a
jet at a high velocity. The reaction providing the thrust. It’s use
has been restricted to special types of ships.
Other propulsion Devices:
1. Nozzles (Duct) Propellers: main purpose is to increase the
thrust at low ship speed (tug, large oil tanker)
2. Vertical-Axis Propellers: Advantage is to control the direction
of thrust. Therefore, the ship has good maneuverability.
3. Controllable-Pitch Propellers (CCP): The pitch of screw can
be changed so that it will satisfy all working conditions.
4. Tandem and Contra-rotating Propellers: It is used because
the diameter of a propeller is restricted due to limit of the draft
or other reasons (torpedo). The efficiency of the propeller
usually decreases.
Jet Propulsion
Nozzle Propellers
Vertical-Axis Propellers
Vertical-Axis Propellers
Controllable Pitch Propellers (CPP)
Contra-rotating Propellers
• Type of Ship Machinery
1. Steam Engine (no longer used in common)
Advantages: 1) good controllability at all loads, 2) to be
reversed easily, & 3) rpm (rotations per minute) matches
that of propellers
Disadvantages: 1.) very heavy 2.) occupy more space
3.) the output of power per cylinder is limited
4.) fuel consumption is high
2. Steam Turbine
Advantages:
1.) deliver a uniform turning torque, good performance for large
unit power output, 2.) thermal efficiency is high.
Disadvantages:
1.) is nonreversible; 2.) rpm is too high, need a gear box to
reduce its rotating speed
3. Internal combustion engines (Diesel engine)
Advantages: 1.) are built in all sizes, fitted in ships ranging from
small boats to large super tankers, (less 100 hp ~ >30,000 hp);
2.) High thermal efficiency.
Disadvantages: 1.) Heavy cf. gas turbines;
4. Gas Turbines (developed for aeronautical applications)
Advantages: 1.) Do not need boiler, very light; 2.) Offer continuous
smooth driving, & need very short “warm” time.
Disadvantages: 1.) expensive in cost and maintenance 2.) need a
gear unit to reduce rpm.
5. Nuclear reactors – turbine
Advantages 1.) do not need boiler, fuel weight is very small
2.) operate full load for very long time (submarine)
Disadvantages 1.) weight of reactor and protection shield are heavy;
2) Environment problem, potential pollution.
• Definition of Power
Indicated horsepower (PI): is measured in the cylinders (Steam
reciprocating engines) by means of an instrument (an
“indicator”) which continuously records the gas or steam
pressure throughout the length of the piston travel.
PI  pm  L  A  n / 550
pm - mean effective pressure (psi)
L – Length of piston stroke (ft)
n – number of working strokes per second
A – effective piston area (in2)
n – number of cylinders
Brake Horsepower (PB): is the power measured at the crankshaft
coupling by means of a mechanical hydraulic or electrical brake.
PB  2 nQ / 550
where Q – brake torque (lb-ft) & n – revolutions per second.
Shaft horsepower (PS): is the power transmitted through the shaft
to the propeller. It is usually measured aboard ship as close to the
propeller as possible by means of a torsion meter .
d S  G n


4
PS
13, 033bLS
where dS – shaft diameter (in), G – shear modulus of elasticity of
shaft material (psi), θ – measured angle of twist (degree),
LS – length of shaft over which θ is measured & n – revolution per
second
Delivered horsepower (PD): the power delivered to the propeller.
Thrust horsepower (PT):
PT  T VA / 550
T – Thrust delivered by propeller (lb)
VA – advance velocity of propeller (ft/s)
Effective horsepower (PE , or EHP):
RT – total resistance (lb)
Vs – advance velocity of ship (ft/s)
PE  RT Vs / 550
• Propulsion Efficiency
Total propulsion efficiency
T 
PE
PS
PS can also be replaced by PB or PI
A more meaningful measure of hydrodynamic performance
of a propeller is: a quasi-propulsive coefficient,  D
PE
D  ,
PD
S 
PD
,
PS
where S is the shaft transmission efficiency
and thus, T   DS .
S - 98% for ships with main engine aft
- 97% for ships with main engine amidship
- smaller if a gear box is used.
6.2 Propeller Geometry and Terminology
Face
Back
Hubcap
Boss
Number of Blades: 2, 3, 4, 5 ,6
Boss
Hubcap
Shaft
• The face surface of a blade is a portion of a holicoidal surface
• The helicoidal surface: Considering a line AB perpendicular to a
line AA’ and supposing that AB rotates with uniform velocity
about AA’ and at the same time moves along AA’ with uniform
velocity, the surface swept out by AB is a helicoidal surface.
Pitch: P when the line AB makes one complete revolution
and arrives at A’B’. It traveled an axial distance AA’,
which represents the pitch of the surface. The propeller
blade is part of that surface and the pitch is also called the
pitch of the blade.
Pitch angle   tan 1  P  or tan   P
2 r
 2 r 
Pitch ratio: PR 
P
D
tan  
PR

A
P
o

2 r
p180
Expended Area AE
Developed Area AD
Boss: (aka, Hub)
Boss diameter – The blades at their lower ends or roots are
attached to a boss which in turn is attached to the propeller
shaft. The maximum diameter of this boss is called the
boss diameter . The boss diameter is usually made as small
as possible and should be no larger than the size sufficient
to accommodate the blades and satisfying the
requirement of strength. It is usually expressed as a
fraction of the propeller diameter.
At one time propeller blades were manufactured separately
from the boss, but modern fixed pitch propellers have the
boss and blades cast together. However, in controllable
pitch propellers it is of course necessary for blades and
boss to be manufactured separately.
• Blade outline: it is decided by propeller series diagrams.
• “Expanded blade outline”
• Blade sections: they are radial sections through the blade.
The shape of these sections is then shaped when laid out flat.
•Blade thickness
•Blade width (Chord)
•Leading edge
•Trailing edge
P181 figure 10.5
• Rake
(a blade is perpendicular or titled w.r.t the boss )
• Skew
(the skewness of a blade w.r.t. the center line)
• Pitch ratio
P
PR 
D
In case that the pitch, P, is not constant, then the pitch is
defined as P = Ptip (the pitch at the tip of a propeller).
• Blade area ratio = AD /A0
AD - Total (developed) blade area clear of that of the boss
A0   D 2 / 4
6.3 Theory of Propeller Action
• Assumptions:
1) replacing the propeller with a stationary actuating disk across
which the pressure is made to rise;
2) neglecting the rotational effect of propeller
3) neglecting vortices shed from the blade tip, & frictional loss.
VA
D
VA(1+a)
VA(1+b)
• Momentum Conservation
Force = net momentum flux
(horizontal)
T   Q VA 1  b   VA 
Q  1  a VA A0 = VA Af = 1  b VA Aa
(mass conservation)
T   QVAb   A0VA2 1  a  b
• Energy Equation
V
P V 1  b 


2g 
2g
2
A
2
A
2
A0 P  T ,
b  2  b  VA
T
1

, T  A0  b  2  b VA2
A0
2g
2
1 a  1 b
or a  b
2
2
2
Ideal Efficiency of a propeller
(no friction & no rotationary velo. considered)
VA A0
TVA
TVA
1
I 



QP TQ
1  a VA A0 1  a
A0
1
1

1 a 1 b / 2
Defining the thrust loading coeff., CT , as
I 
 A0VA2 1  a  b
T
CT  1

 4 1  a  a
2
2
1
2 VA A0
2 VA A0
1  1  CT
Thus, a 
2
2
& I 
1  1  CT
With the increase in CT , the ideal efficiency decreases.
CT
0
1
2
3
4
I
1.00 0.827 0.732 0.667 0.618
• Extension of momentum theory
Consider the rotation of the flow passing through the propeller
disc., the reduced ideal efficiency becomes,
1 a '
I 
& a '  0.
1 a
2 

  
2
2 

1 a ' 
 1

2
where  2 is the rotation velocity of flow after the propeller,
&  is the rotation velocity of the propeller.
• Blade Element Theory
In the momentum conservation of a propeller, no detailed
information can be obtained with regard to the effects of the
blade section shape on propeller thrust and efficiency.
The total velo. at radius r , Vr  VA  VT ,
Thrust:
VT  2 rN .
dT  d L cos   d D sin 
Resistance: d F  d L sin   d D cos 
Moment:
q  dF  r
& d L and d D  f  
f   is a function depending on section shape (wing
section theory). For a propeller, the relative advance velocity
of the fluid at the disc, is VA 1  a  & the rotation velocity is
r 1  a ' .
a & a’ are determined by experiments
aVA
VA
α
α’
Vr   r
r 1  a '
a ' r
6.4 Similarity Law for Propellers
Although theoretical studies and CFD on propellers are very
important and provides valuable guideline for designing propeller,
a great deal of knowledge concerning the performance of propellers
has been obtained from propeller model tests. Hence, it is
necessary to examine the relation between model and full-scale
results as the case of resistance. In open water (not behind a ship),
T  f   , D,VA , g , n, p,  
n - rotational speed, D - diameter of propeller
p - pressure in water,  - dynamic viscosity
VA - speed of advancing, T - Thrust
Using D.A, the non-dimensinal formula is given by,

VA D 
T
p
 VA VA


f
,
,
,


2
1
 n2 D 4
nD

V



A
2
 gD

VA
VA D
p
Froude #:
, Euler #: 1
, Reynolds #:
2

gD
2 VA
Advanced ratio: J 
VA
, Thrust coeff. :
nD
KT 
T
 n2 D 4
 V 
The Advanced ratio is related to the slip ratio 1  A  .
 nP 
Define Q as the Torque to drive a propeller
Q
The torque coeff .: K Q 
 n2 D5
In open water, the propeller efficiency coeff.:
TVA
K VA
J KT
o 
 T

.
2 nQ K Q 2 nD 2 K Q
When all the dimensionless parameters are the same for the
two geometrically similar propellers, the two propellers
will be dynamically similar.
Ds
Scale ratio:  
Dm
For the same Froude #:
VAs

VAm
Ds
 
Dm
For the same advance ratio (most important)
1
ns VAs Dm



  2 indicating the model rotating faster.
nm VAm Ds

 p 
 p 
For the same Euler # :  1
 1
2 
2 
 2 VA  m  2 VA  s
If the cavitation performance is not an issue, this number is not
of importance & may be neglected in the dynamical similarity.
ps  pos  H s   w
pos - water surface pressure, H s is the depth of a propeller.
VA m
pm 
2
VA s
2
In general,  m   s ,
Because   1,
ps 
ps

.
pm  ps and pm  pom  H m   w .
pom has to be negative, thus the model test is carried out in a
vacuum (cavitation) tunnel.
VAs
Dm vs 1
For the same Re:

 ,
VAm Ds vm 
which is contradict to the similarity of Fr. Therefore, it is almost
impossible to satisfy the Fr & Re similarity laws simutanously.
Similar to the assumption made in model resisrtance tests, we
assume viscous force is independent of other dynamic forces.
Hence, it may be computed separately. In reality, viscous force
is usually a small portion of the total force. The smilarity of
Re is neglected in propeller model tests.
Therefore, propeller model tests follows Fr & J (advance
ratio) similarity laws. If the cavitation is relevant, then the
Euler number should be the same as well.
6.5 Propeller Model Test
A test on a model propeller is run either in a towing tank or a
running flow in a water tunnel (cavitation tunnel) without a model
hull in front of it, which is called “open water” tests.
1) VA – velo.of flow
2.) n - rotation of
motor
3.) po - pressure can
be controlled
Measure VA , Q, T,
and n.
Development
of cavitations
of a propeller
in a
cavitation
tunnel
T
Q
Trust coeff. KT 
, Toeque coeff. K Q 
,
2 4
2 5
n D
n D
TVA
KT J
Open - water efficient o 

.
2 nQ K Q 2
Testing results
0
KQ
KT
J
VA
nD
VA
P
Slip ratio  1 
, Pitch ratio  , section types & # of blades.
nP
D
Purpose of open-water tests
• It is usually to carry out open water tests on standard series of
propellers. Their features (such as # of blades, blade outline
shape, blade area ratio, blade section shape, blade thickness
fraction, boss diameter & pitch-diameter ratio) are systematically
varied. The result data are summarized in a set of particular
diagrams, which can be used for design purposes. We will study
how to use these diagrams later for designing a propeller.
•Studying the efficiency of a propeller and find a propeller with
better efficiency
•Studying the extent and development of cavitations over a
propeller.