Screw Propellers
13
The projections of the leading and trailing edges of a blade section on a
plane tangential to the helix at the point C in Fig.2.3(d), Le. L' and T',
are also associated '.'lith what is called the developed blade outline. If these
tange
Propeller Theory
37
where a' = wl/w and a = vl/VA are the rotational and axial inflow factors,
VI and V2 are the axial, induced velocities at the propeller and far down
stream, Wl and W2 being the corresponding angular induced velocities. It
may be seen b
16
Basic Ship Propulsion
-~_ ~ _ -l~:=_.L1~-".L- _<E.:-'O-=O".:_"-"-Jte.-_":?>o:-"-:.-_
(0) SEGMENTAL
(c) LENTICULAR
(b) AEROFOIL
SECTION
SECTIONS
SECTION"
Figure 2.5: Propeller Blade Sections.
'mayor may not be flat, the maximum thickness is usually nea
Basic Ship Propulsion
30
FLUID COLUMN
ACTUATOR DISC
AREA . Ao
-r-'
'-._.-.'-'_.-i=-'-'-'-'-'
FAR ASTERN
FAR AHEAD
I
PRESSURES
VELOCITIES
-p.'
1
PRESSURE VARIATION
Figure 3.1 : Action of an Actuator Disc in the Axial Momentum Theory.
.\
(3.1)
where p is th
44
Basic Ship Propulsion
dQ
dr = r Z C L ~ P c V~ cos f3 (tan f3 + tan')')
Substituting the numerical values calculated:
dT
dr
1]
(b)
= 185.333 k.l~ m- 1
=
dQ = 66.148kNmm:"1
dr
tanf3
= 0.8918
tan(3+:)
a = 0.2000
Given:
v~
:
[(1
+ a)
. a' ~ 0.0225
\'A]2
"-Jr-
J.-!l!t
Propeller Tbeory
/.
~
/~
~
c
f<
41
at an angle of attack a, ~ shown in Fig. 3.4(a). The blade element will then
produce a lift d!,:-and a drag eyh where:
(3.26)
If the thrust and torque produced by the elements between rand r
for all the Z b
Screw PropeIlers
2.6
21
Non-dinlensional Geometrical Parameters
As will be seen in subsequent chapters, the study of propellers is greatly
dependent upon the use of scale models. It is therefore convenient to define
the geometrical and hydrodynamic charac
45
Propeller Theory
one obtains:
dT
dr
=
113.640kNm- 1
dQ
dr
=
48.991 kNmm- 1
1-
1]
3.5
a'
= 1 +a
tan(3r
tan(3r + "Y)
=
1- 0.0225 0.3722
x-1 + 0.2000 0.4104
= 0.7383
Circulation Theory
The circulation theory or vortex theory provides a more satisfactory
.
50
Basic Ship Propulsion
TRAILING
VORTEX
AT RADIUS r
U
Q
BOUND
TRAILING
VORTEX
SHEET
.1/ VORTEX
r
\
'~-=/:.~=iW-\:t=\=~=l
l'
-~-.r-~A
1.
n
FAR
AHEAD
FAR
ASTERN
Z
I
=
4
!
V
.cbr
I
I
I
cPr
i
r
Ut
9.
0
2JTr
I
cbr
v
I
\
Figure 3.10: Vortex System of a Prope
!
!
I
Propeller Theory
53
From the blade section velocity diagram in Fig. 3.11, it can be shown that:
VR
VA
=
cos (f3J - (3)
sincfw_3
=
tancfw_3J - tancfw_3
tancfw_3 (1 + tan2 (31)
=
tancfw_3J (tancfw_31 - tan(3)
tanf3 (1 + tan 2 (31)
1
2 Ua
VA
!
Ut
VA
(3
Basic Ship Propulsion
38
D = 4.0m
r
n = 180rpm
=
3.05- 1
VA
= 6.0ms- 1
dT = 200kNm- 1
dr
= 0.7R'= 0.7x2.0 = 104m
w = 211" n = 611" radians per sec
so that,
411" x 1025 x 1.4
X
6.0 2 a(l + a) = 200 x 1000
which gives,
a
= 0.2470
a' (1 -a') w 2 r 2 = a (1 +
CHAPTER
4
The Propeller in "Open" Water
4.1
Introduction
A propeller is normally fitted to the stern of a ship where it operates in water
that has been disturbed by the ship as it moves ahead. The performance of
the propeller is thus affected by the ship
Propeller Theory
43
Example 4
A four bladed propeller of 3.0 m diameter and 1.0 constant pitch ratio has a speed of
advance of 4.0 m per sec when running at 120 rpm. The blade section at 0.7R has a
chord of 0.5 m, a no-lift angle of 2 degrees, a lift-drag
PropeIIer Theory
59
in an inviscid fluid of density 1025 kg per m3 and has an efficiency of 0.750.
Determine the axial and rotational inflow factors a and a' at the different
radii, and calculate the propeller thrust and torque if the propeller operates
a
Basic Ship Propulsion
34
This relation between thrust and delivered power at zero velocity of ad
vance for a propeller in ideal conditions thus has a value of y'2. In actual
practice, the value 'of this relation is considerably less.
Example 2
A propeller
Propeller Theory .
55
Example 5
A propeller of 5.0 m diameter has an rpm of 120 and a speed of advance of 6.0 m
per sec when operating with minimum energy loss at an ideal efficiency of 0.750.
The root section is at 0.2 R. Determine the thrust and torque
Screw Propellers
27
10. A three-bladed propeller of diameter 4.0m has blades whose expanded blade
widths and thicknesses at the different radii are as follows:
r/R
Width, mm
Thickness, mm ;
0.2
1000
163.0
0.3
1400
144.5
0.4
1700
126.0
0.5
1920
107.5
0.6
Basic Ship Propulsion
20
,
Consider a propel~er of diameter D and pitch P operating at a revolution
rate n and advancing at a speed VA. If the propeller were operating in an
unyielding medium, like a screw in a nut, it would be forced to move an
axial dis
Propeller Theory
3.4
39
Blade Element Theory
The blade element theory, in contrast to the momentum theory, is concerned
with how the propeller generates its thrust and how this thrust depends upon
the shape of the propeller blades. A propeller blade is re
46
Basic Ship Propulsion
no force because of the symmetry of the velocity and pressure distributions
around the cylinder (D'Alembert's paradox). If, however, a vortex flow is
superposed on the uniform flow, there will be an asymmetry in the flow, the
resu
I
47
Propeller Tbeory
v
x _-\- .:;.
-'1.-.10
_~x
'-_dX
y
.
t
.
.- V
v
Figure 3.6: Circulation around an Aerofoil.
If the x-coordinate of the trailing edge lis
aerofoil per unit length (span) is:
L
Xl,
the lift produced by the
=
l['t>.PdX = pV['2VdX = pLC~
Propeller Theory
33
which gives:
VI
a
= 0.9425ms- 1
=
V2
= 1.8850ms- 1
7Ji
1
- =
=1+a
PD =
CTL
1,
0.2356
=
TVA
7Ji
=
0.8093
30.0 X 4.0
0.8093
T
~pAOVA2
=
~
X
= 148.27kW
30.0 X 1000
1025 X 3.1416 X 4.02
=
1.1645
If GT L r~duces to zero, i.e. T = 0, the ide
Propeller Theory
49
In the vortex system shown in Fig. 3.8, the circulation along the span of
the wing has been taken to be constant. Actually, however, the circulation
in a wing of finite span decreases from a maximum at mid-span to zero at
the ends, and
Basic Ship Propulsion
x
6. Mr. K. Neelakantan, Administrative Manager for India and Sri Lanka,
Lloyd's Register of Shipping.
7. Mr. Trevor Blakeley, Chief Executive, The Royal Institution of Naval
Architects.
8. Ms. Susan Grove Evans, Publications Mana
Nomenclature
I
I
J
Pc
Roughness peak count per nun
Pressure due to cavitation
PV
Vapour pressure
Po .
Pressure without cavitation
P
Pitch of the propeller
p
Mean pitch of propeller
PB
Brake power
PD
Delivered power
PDO
Delivered power in open water
P
xxix
Nomenclature
6R
Resistance augment
6T
Thrust deduction
6.
Displacement of the ship
Change in drag coefficient due to roughness
Roughness allowance
Correlation allowance for frictional resistance coefficient
Change in lift coefficient due to roughness
Physical Constants
The following standard values have been used in the examples and problems:
Density of sea water
= 1025 kg per m3
Density of fresh water
= 1000 kg per m3
Kinematic viscosity of sea water
= 1.188
Kinematic viscosity of fr~sh water
= 1.139