The Wageningen C- and D-Series Propellers
J. Dang, MARIN, The Netherlands
H. J. J. van den Boom, MARIN, The Netherlands
J. Th. Ligtelijn, MARIN, The Netherlands
SUMMARY
The Maritime Research Institute Netherlands (MARIN) has recently started a Joint Industry Project (JIP) on developing
two new propeller series for Controllable Pitch Propellers (CPPs). Following the well known Wageningen B-series and
Ka-series, the new C-series comprise open CPPs whereas the new D-series concern ducted CPP’s. The primary objective
of developing the new CPP series is to help the shipbuilding and offshore industries in understanding the off-design performance of the CPPs, for which systematic information was lacking.
CPP blades have been generated for 4- and 5-bladed open propellers and for 4-bladed ducted propellers in two ducts,
representing the most contemporary propeller design practice. Systematic measurements of the propeller and duct
thrusts, the torque and also the blade spindle torque have been carried out for the entire range of operational conditions
and pitch-settings of each propeller. The results of the C4-40 series are presented in this paper as an example case.
1.
INTRODUCTION
The Maritime Research Institute Netherlands (MARIN),
former Netherlands Ship Model Basin (N.S.M.B.),
started to develop the well-known Wageningen B-series
Propellers right from the establishment of this institute in
1932 [1]. The first series were published by van Lammeren [2] and Troost [3,4], followed by further developments and expansions of the series over more than 40
years. A major review of the available data was given by
van Lammeren et al [5,6]. The B-series had been further
extended to 6 and 7 bladed propellers in the 1970’s. Totally, 20 series with more than 120 propellers were tested
over that period.
Systematic series have also been developed for ducted
propellers since 1954 [7]. A major amount of data of the
Ka-series were published by Oosterveld [8]. In the meantime, other systematic propeller series were also developed worldwide, such as the Taylor- [9], Gawn- [10],
(M)AU- [11] and SSPA- [12,13] series. However, in practise the B-series data are among the most widely used in
the industry.
Besides that most of the propeller characteristics (the
thrust and the torque) of the series in design operation
condition have been made available by model tests between J=0 and KT=0, four-quadrant open water characteristics of some of the propellers in the B-series and the
ducted propellers in the Ka-series were also made available in the 1980’s [14] for off-design conditions. Table 1
provides an overview of the propellers in the B-series, of
which 4-quadrant open water characteristics are available. For the Ka-series, only Ka 4-70 propellers in 19A
and 37 ducts have been published [1].
Different from Fixed Pitch Propellers (FPPs), Controllable Pitch Propellers (CPPs) are well-known for their ad-
vantage for full power utilization at any circumstances:
accelerating and stopping, rapid manoeuvring, dynamic
positioning (DP), etc. For these reasons, CPPs are widely
used for multi-purpose vessels where their propulsors are
often used in off-design conditions.
Table 1 Overview of B-series with four-quadrant open
water characteristics (pitch ratio P/D of the propellers are
listed in the table).
AE/A0 [%] 40
Z=3
Z=4
Z=5
Z=6
Z=7
1.0
55
1.0
65
1.0
70
75
80
0.5, 0.6, 0.8
1.0, 1.2, 1.4
85 100
1.0 1.0
1.0
1.0
1.0
In order to predict the performance of a CPP in offdesign conditions, people have to either carry out dedicated and expensive measurements for a specific propeller design, such as often done for navy vessels [15,16], or
rely on the estimated values from the existing fourquadrant open water data from the B-series [17], which
were primarily designed for merchant ships with FPP
blade forms. Information for the complete two-quadrant
open water characteristics of CPPs in the public domain
is scarce, especially when the propeller blades are deflected away from their design pitch [18,19]. In the
Wageningen series book [1], off-design information is
only available for two CPPs in ahead and astern conditions, one with a design pitch ratio of zero and the other
of one.
With the deployment of more and more vessels with DPcapability, accurate prediction of the off-design performance of a propulsor becomes more important than ever.
Dedicated tests for each propeller design is unaffordable
for most of the projects, while the existing limited infor-
mation is far from enough. For this reason there is a
strong demand for systematic data on the performance of
CPP’s in off-design conditions.
In addition to these, a CPP blade has a completely different blade form than an FPP. This is because more practical issues need to be considered for a CPP, such as: the
blades must be able to pass each other from positive
pitch to negative pitch, the blade has to be positioned
properly between the bolt holes on the blade foot, the
cavitation performance must be acceptable for a wide
range of operational pitch settings, the blade overhang at
the blade foot should preferably be avoided to prevent
stress concentration; the blade tips must not touch the
inner side of a duct at any deflected pitch angles for the
ducted CPPs. Besides all these constraints, one of the
important and unique issues is the blade spindle torque of
CPPs [20], where very limited information can be found
[19,21,22]. To the knowledge of the authors, there is also
no CPP series with systematic information on the propeller blade spindle torque at all possible blade pitch settings (from full positive pitch to full negative pitch and
over the complete two quadrants). Also no systematic
information is available on blade feathering performance.
In close co-operation with industry and universities
MARIN started to explore the possibilities for developing new systematic series for both open and ducted
CPPs. In September 2011, a Jointed Industry Project
(JIP) was officially launched, which is called the Wageningen C- and D-series Propellers for CPPs and ducted
CPPs, respectively. Here the C stands for controllable
and the D stands for ducted.
Conducting conventional open water tests for an extensive propeller series in two quadrants is not economically
feasible as each propeller has to be tested at more than 10
pitch settings between full positive and full negative
pitch. New test technology had to be developed in order
to reduce the test time significantly. This leads to the idea
of a quasi-steady test technique for propeller open water
characteristics which is enabled by the new sensor technology that allows high frequent dynamic measurement
with rapid response.
Under support of the Wageningen C-series and D-series
JIP, a pilot study has been successfully carried out to
explore the possibility of using this technique. The study
proved that the quasi-steady test results are as accurate as
the conventional steady test results, while reducing the
test time by a factor of 8 to 10 [23]. This technology development enabled the JIP to test large systematic series
within reasonable budget.
The propeller series, the blade design methodology, the
parameterization of the propeller geometry, the test procedures, the data analyses and the presentation of the
results are discussed in the following sections. At the end
of the paper, the complete test results of the C4-40 series
are presented and discussed.
2.
DESIGN METHODOLOGY, THE PROPELLER SERIES AND THE TEST MATRIX
In order to obtain systematic information on propeller
open water characteristics, the Wageningen B-series Propellers were designed in such a way that the number of
blades, the blade area ratio and the pitch-diameter ratio
were systematically varied, while the blade contour, the
skew distribution, the pitch distribution (constant, except
for the 4-bladed), the rake angle (15o), the hub-propeller
diameter ratio (1/6, except for the 3-bladed propellers
which has a ratio of 18%) and the section profiles are all
kept the same for the whole series [1].
While designing the Wageningen C- and D-series propellers, an extensive propeller database search has been carried out first. A large number of practical propeller designs, made with up-to-date hydrodynamic knowledge
was gathered. Studies have been carried out to relate the
propeller main dimensions to the typical applications, so
that each design of the blades reflects a certain scenario
of a typical application. For instance, a 4-bladed CPP
with large blade area and high pitch ratio’s is often used
for the fast ferries and cruise ships where the comfort is
weighted more than the efficiency; a 4-bladed CPP with
small blade area and low pitch ratio’s is typically used by
transport ships with a large amount of harbour activities,
such a shuttle tanker, where the propulsive efficiency is
essentially important, rather than the comfort. The 5bladed CPP designs are aimed at applications for the
navies.
The statistics from the database also showed that the CPP
hub size changes noticeably with the blade area ratio and
the blade design pitch ratio for open propellers. This is
because these main parameters of a propeller are closely
related to the power density on the blade, which determines how strong a hub should be and how large the
pitch actuating system should be. However, this tendency
is not found for the ducted CPPs. These findings are applied to the present series designs where the C-series has
different hub-propeller diameter ratio’s for each propeller
design; while the D-series propellers have the same hubpropeller diameter ratio for all designs.
Thereafter, each propeller in the series was designed individually with the best present design practice with the
compromise between efficiency, comfort and mechanical
requirements, which comprise the blade strength requirements, minimum blade passing distance when going
from positive to negative pitch, fitting the blade root between the bolt holes, blade root over-hang, tip clearance
in a duct while the pitch is actuated through the whole
stroke, blade spindle torque at all operation conditions,
etc. The compromise has given more weight on:
-
propulsive efficiency for low pitch and blade
area ratio’s;
comfort (better cavitation performance) for high
pitch and large blade area ratio’s.
The design methodology and philosophy discussed above
for these C- and D-series propellers can be summarized
in one sentence: these series represent contemporary and
practical CPP designs.
and represents the present best practice on hub design
with smallest achievable hub size. The ratio is
determined by the following quadratic polynomial:
The whole series consist of 20 open propellers and 15
ducted propellers, as listed in Table 2, which were tested
for 604 complete two-quadrant open water characteristics
at various pitch settings and duct combinations (Table 3).
with a hub consisting of a basic spherical form contour
connected to two cylinders on the two sides (Figure 1).
Table 2 Overview of the C-series and D-series propeller
models (design pitch ratio P0.7R/D of the propellers are
listed in the table), in total 35 propeller models.
The radial distribution of the main parameters of the propellers (blade chord length ratio C/D, pitch ratio P/D,
skew ratio S/D, rake ratio X/D, maximum thickness ratio
tmax/D and maximum camber ratio fmax/D of the blade
sections) are all given in polynomials in the form of:
AE/A0 [%]
40
55
C4 series
0.8, 1.0,
1.2, 1.4
0.8, 1.0,
1.2, 1.4
70
0.0, 0.8,
1.0, 1.2,
1.4
75
0.8, 1.0,
1.2, 1.4
1.0, 1.2,
1.4, 1.6
C5 series
D4 series
60
0.0, 0.8,
1.0, 1.2,
1.4
0.0, 0.8,
1.0, 1.2,
1.4
tested pitch
settings P0.7R/D
Propeller design pitch ratio P0.7R/D
D4-40
D4-40
D4-55
D4-55
D4-70
D4-70
in No.19A duct in No. 37 duct
0.8 1.0 1.2 1.4 1.0 1.2 1.4 1.6 0.0 0.8 1.0 1.2 1.4 0.0 0.8 1.0 1.2 1.4
× ×
× × × × × ×
× ×
× ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × × × × × × × × × × × × ×
× × × × × × ×
× × ×
× × ×
× ×
× × ×
× ×
× ×
×
× ×
×
×
×
× × × ×
C5-60
C5-75
-1.4
-1.2
-1.0
-0.7
-0.4
-0.1
0.0
0.1
0.2
0.5
0.8
1.0
1.2
1.4
1.6
1.8
*
∞
*
blade feathering tests, in both positive & negative advance directions.
3.
BLADE PARAMETRIC DESCRIPTIONS
1.0, 1.2,
1.4, 1.6
Table 3 Overview of the test matrix, in total 604 complete two-quadrant propeller open water tests.
C4-40
C4-55
C4-70*
3.2
PROPELLER GEOMETRY
where s is the non-dimensional radius defined as:
and r is the radius. At the blade tip when r=D/2, s=0. At
the blade root when r=d/2, s=1. The coefficients a
depend on the design pitch of the propeller p by
quadratic polynomials defined as:
By integrating the chord length of the propeller blades
from the blade root to the tip, as given in Equation (3)
and (4), the blade area can be easily derived and
expressed also in parametric formula.
3.3
BLADE SECTION PROFILES
The NACA 66 (MOD) thickness distribution and the
NACA a=0.8 meanline have been used for all of the propeller blades for the present propeller series. The thickness distribution is, however, applied perpendicular to
the nose-tail line of the section profile.
In order to prevent very thin blade trailing edges in
model scale, the trailing edges of the propeller model
blades are thickened to minimal 0.4 mm, starting gradually from the maximum thickness of the profile to the
trailing edges by a parabolic distribution.
After the initial design of each propeller of the series, the
main parameters of every propeller were fitted with
polynomials and the propeller models were manufactured
according to the parametric descriptions. In order to
reduce the influence of the blade weight on the
measurements, all propeller blades and hubs were made
of aluminium with anodized final surface treatment.
3.4
3.1
3.5
TIP FORM, BLADE ROOT FILLETS AND
ANTI-SINGING EDGE
HUB-PROPELLER DIAMETER RATIO
The hub-propeller diameter ratio is determined first,
which varies with the design pitch ratio at 0.7R of the
propeller, defined as:
PITCH DEFINITION
The design pitch is defined based on the nose-tail line of
the blade section profile. At off-design condition, the
pitch setting refers to the pitch of the blade at 0.7R which
is based on the nose-tail line of the section profile at that
pitch setting (R is the propeller radius at design pitch).
A non-ice-strengthened tip form and composite blade
root fillets are applied to all of the model propellers. The
composite blade root fillets consist of two fillet radii, the
larger one has a radius of 3Tmax and the small one has a
radius of Tmax/3, where Tmax is the blade maximum thickness at the blade root. Due to the fact that the propeller
model blades are too thin to make anti-singing edges, no
anti-singing edges are applied.
4.
4.1
TEST SET-UP AND PROCEDURES
TEST SET-UP
The test set-up is the same as used and discussed in Reference [23] with a dummy test hub and force transducers
as shown in Figure 1. The thrust and torque are measured
on the shaft next to the propeller and the blade spindle
torque is measured inside the test hub.
C- and D-series two-quadrant tests, the following four
test runs have been used, as listed in Table 4.
Table 4 Quasi-steady test runs for the complete 2quadrant open water characteristics of a controllable
pitch propeller.
run
1
2
3
4
shaft rotational rate
constant +900RPM
0 to +900RPM to 0
constant +900RPM
0 to +900RPM to 0
advance speed
0 to +4m/s to 0
constant +4m/s
0 to 4m/s to 0
constant 4m/s
 range
0 o to ~+30o to 0 o
+90o to ~+30o to +90o
0 o to ~ 30o to 0 o
90o to ~ 30o to 90o
This makes it possible to test the complete two-quadrant
open water characteristics of a propeller in only 4 test
runs, using 2 runs by varying the towing speed of the
carriage and 2 runs by varying the shaft rotational rate.
From the first two runs - No. 1 and No. 2, the results in
the first quadrant for  from 0 to +90 degrees can be obtained. From the last two runs - No. 3 and No. 4, the results in the fourth quadrant for  from 0 to -90 degrees
can be obtained.
Figure 1 Test set-up and propeller shaft thrust and torque
sensors and blade spindle torque sensor.
4.2
A sinusoidal variation as sketched in Figure 2 has been
used for the variations of the carriage (advance) speed
and the propeller rotational rate during the tests.
TEST PROCEDURES
In a conventional propeller open water test from J=0 to
KT=0, the propeller shaft rotational rate is often kept constant while the advance speed of the propeller varies.
During propeller four-quadrant open water tests, like
done for FPP’s, both the advance speed and the shaft
rotational rate have to vary and change directions, because only a finite towing speed of the carriage can be
achieved. However, most controllable pitch propellers
will never rotate reversely. This practice has been also
used here during the model tests, where only one rotational direction (positive rotational direction) has been
tested. Therefore, only two-quadrant (the first and the
fourth quadrant) open water characteristics have been
measured.
At propeller off-design conditions, the propeller hydrodynamic pitch angle  is often used, instead of the advance ratio J, to define the operation condition of the
blades,
Figure 2 Sketch of the sinusoidal variations for towing
speed and propeller shaft rotational rate.
For the first quadrant (test runs No. 1 and No. 2), the
towing carriage is travelling in the normal towing direction, which we call the ‘positive’ direction as shown in
the sketch in Figure 3.
+n
+Va
Figure 3 Sketch of test set-up for the first quadrant tests.
Under this definition, a complete set of two-quadrant
open water characteristics of a controllable pitch propeller covers the range -90o ≤  ≤ +90o.
A quasi-steady open water test is, in principle, an unsteady model test by continuously varying the advance
speed and/or the rotational rate in such a way that the
steady state performance of the propeller for the complete range of conditions can be derived. For the whole
For the fourth quadrant (test runs No. 3 and No. 4), the
same set-up used for the first quadrant test but towed by
the carriage in the reverse direction, see Figure 4. The
advantage of this method is that the whole set-up remains
the same as for the first quadrant, except for the towing
direction of the carriage. The drawback is that the flow
goes first over the open water test POD housing and strut
before it reaches the propeller. The influence of the wake
from the strut was found to be very limited and has been
carefully corrected for.
+n
-Va
Figure 4 Sketch of test set-up for the fourth quadrant
tests.
(11)
More details of the quasi-steady propeller open water test
procedures are given by Dang et al [23].
5.
PRESENTATION OF RESULTS
The measured propeller shaft thrust and torque, and the
blade spindle torque, are non-dimensionalized by the
relative velocity to the blade at 0.7R radius defined as,
with the propeller thrust coefficient defined as,
6.
C4-40 SERIES
As an example case, the test results of the C4-40 series
are presented in this section.
The C4-40 series propeller model are shown in Figure 6
with MARIN’s propeller numbers and their design pitch
noted in the figure. The propeller diameters vary between
230.37mm to 242.81mm with hub diameter of 58.0mm.
the propeller torque coefficient defined as,
and the blade spindle torque coefficient defined as,
where, the positive directions of the propeller shaft
thrust, torque and the blade spindle torque are shown in
Figure 5. The positive blade spindle torque is defined as
the direction that tends to drive the propeller to a larger
pitch.
Model No. 7189 (P0.7R/D = 0.8)
Model No. 7190 (P0.7R/D = 1.0)
Model No. 7191 (P0.7R/D = 1.2)
Model No. 7192 (P0.7R/D = 1.4)
Figure 6 C4-40 series propeller models with aluminium
blades on the dummy hubs at design pitch settings.
All coefficients provided above are hydrodynamic coefficients. The spindle torque induced by the centrifugal
force of the model blade has been subtracted.
During the test runs, the blade Reynolds number varies
with the variation of the propeller advance speed and the
shaft rotational rate, which depends on the chord length
of the propeller blades. Table 5 provides the range of the
Reynolds numbers based on 0.7R chord length and local
inflow velocity during the tests for the C4-40 series,
where the Reynolds number is defined as,
Each set of data - the propeller thrust coefficients, the
propeller torque coefficients and the blade spindle torque
coefficients - was fitted with one of the following Fourier
series respectively. The Fourier series coefficients were
determined up to the order of 40, truncated from the 31st
harmonic gradually (linearly) until completely at the 40th
harmonic.
The open water characteristics of these series propellers
in the first quadrant are plotted in Figure 7 in KT, 10KQ, 
~ J diagram. Their two-quadrant open water characteristics are plotted into diagrams on Figure 9 through Figure
Figure 5 Definition of positive directions for the thrust,
torque and the blade spindle torque.
20. These values are all in model scale without any corrections for the Reynolds numbers, which varies during
the quasi-steady open water tests.
Table 5 Blade chord Reynolds numbers during test runs.
Blade chord Reynolds number Re × 10-5
Propeller Nos.
Runs
7189R
7190R
7191R
min.
4.4003
4.2608
4.1291
Run No. 1, 3
max.
4.9185
4.7799
4.6490
min.
2.1975
2.1663
2.1364
Run No. 2, 4
max.
5.0062
4.8645
4.7307
1.00
THRUST COEFFICIENT KT, TORQUE COEFFICIENT 10KQ, EFFICIENCY 
1.1
1.0
0.9
P0.7R/D=1.2
Ideal Efficiency
0.95
B4-40 P/D=0.8
B4-40 P/D=1.0
0.90
B4-40 P/D=1.2
0.85
PROPELLER OPEN WATER EFFICIENCY 
7192R
4.0043
4.5252
2.1078
4.6041
1.2
0.8
losses of a real propeller (such as the rotational losses,
friction losses, non-uniform losses due to finite number
of blades, vortex losses, etc.). An offset of the efficiency
of about 0.15 has been found for the C4-40 series, which
is regarded as excellent designs. The same results are
also found for the other C-Series Propellers.
P0.7R/D=1.4
B4-40 P/D=1.4
C4-40 P/D=0.8
0.80
C4-40 P/D=1.0
0.75
C4-40 P/D=1.2
C4-40 P/D=1.4
0.70
0.65
0.60
0.55
0.50
0.45
P0.7R/D=1.0
0.40
P0.7R/D=0.8
0.7
0.35
0.6
0.30
0.0
0.5
1.0
2.0
3.0
4.0
PROPELLER THRUST LOADING COEFFICIENT C T=8/p KT/J2
5.0
Figure 8 Comparison of open water efficiency with the
ideal efficiency.
0.4
7.
0.3
0.2
0.1
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
ADVANCE COEFFICIENT J
Figure 7 Open water characteristics of C4-40 series.
To make an assessment on the C4-40 series propeller
blade designs, a comparison has been made for the open
water efficiency to the propeller ideal efficiency, together
with the B-series for the same blade area ratio and the
same pitch ratio. The comparison is based on the propeller thrust loading coefficient CT, as shown in Figure 8.
It should be noted that the present series were carried out
at a shaft rotational rate of 900 RPM with a chord Reynolds number Re at 0.7R radius between 0.4×106 and
0.5×106 (Table 5) for C4-40 series, while the B-series
were tested at much lower shaft rotational rate and the
results were later corrected to a standard chord Reynolds
number of 2.00×106 on 0.75R chord [5]. A direct, quantitative and fair comparison of these two series is therefore
difficult.
However, for a qualitative assessment on C4-40 series,
Figure 8 can be used. The offsets between the ideal efficiency and the measured open water efficiency is often
used to evaluate a propeller design, which contains all
CONCLUSIONS AND FUTURE WORK
Two new propeller series – The Wageningen C- and DSeries Propellers have been developed within a Joined
Industry Project (JIP), with both industry and government funding. The series represent the most contemporary controllable pitch propeller design practice, both for
open and ducted propellers, with balanced compromise
between efficiency and comfort, while also observing
practical and mechanical constraints. Compared to the
ideal efficiency, the C-series propellers show good efficiency values.
The complete two-quadrant open water characteristics of
those propellers at all practically-used pitch settings have
been tested, which provide a huge database with complete information on the off-design performance of controllable pitch propellers. They are the first and the only
series with blade spindle torque information for a complete range of operational conditions and pitch settings.
All results are shared with the participating organisations
in this JIP. Furthermore, the data will be implemented in
software for practical use by all participants.
In addition, it has been also planned to test the C4-70 and
C5-75 series for blade spindle torque in cavitating conditions, the C4-70 and C5-75 series for cavitation inception
characteristics at one pitch ratio, and the D4-70 series in
No. 37 duct for thrust breakdown due to excessive cavitation in bollard pull and free running conditions.
90
90
P/D = -1.0
75
75
P/D = -1.2
P/D = -0.7
P/D = -1.0
P/D = -0.4
P/D = -0.7
P/D = -0.1
60
P/D = -0.4
60
P/D = 0.0
P/D = -0.1
P/D = 0.1
P/D = 0.2
30
P/D = 0.5
P/D = 0.8
15
P/D = 1.0
P/D = 1.2
-60
PROPELLER THRUST COEFFICIENT CT
P/D = -0.4
60
P/D = -0.7
P/D = -0.1
P/D = 0.1
45
P/D = 0.0
P/D = 0.2
30
P/D = 0.8
P/D = 1.0
15
P/D = 1.2
P/D = 1.4
-15
0
P/D = 1.6
Figure 10 Thrust coefficient CT at various pitch settings
for propeller C4-40 with design pitch ratio P0.7R/D=1.0.
-60
-75
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-0.8
-90
PROPELLER THRUST COEFFICIENT CT
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
-75
-60
-45
-30
-15
0
15
P/D = 1.2
P/D = 0.5
-30
30
P/D = 1.0
P/D = 0.2
-45
P/D = 0.8
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = 0.5
45
P/D = -0.1
P/D = 0.1
-0.8
-90
P/D = 0.0
60
P/D = -1.0
P/D = -0.4
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = -1.2
P/D = -0.7
75
P/D = -1.0
75
90
Figure 11 Thrust coefficient CT at various pitch settings
for propeller C4-40 with design pitch ratio P0.7R/D=1.2.
90
Figure 9 Thrust coefficient CT at various pitch settings
for propeller C4-40 with design pitch ratio P0.7R/D=0.8.
0.8
-0.8
-90
-0.6
-0.4
-0.2
0.0
-75
PROPELLER THRUST COEFFICIENT CT
0.2
0.4
0.6
0.8
-0.8
-90
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-75
-60
-45
-30
-15
0
P/D = 1.4
-45
-30
-15
0
15
30
P/D = 1.0
P/D = 0.1
HYDRODYNAMIC PITCH ANGLE  [degrees]
45
P/D = 0.8
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = 0.5
45
P/D = 0.0
P/D = 0.2
PROPELLER THRUST COEFFICIENT CT
Figure 12 Thrust coefficient CT at various pitch settings
for propeller C4-40 with design pitch ratio P0.7R/D=1.4.
90
90
P/D = -0.1
P/D = 0.1
P/D = 0.0
45
P/D = 0.0
30
P/D = 0.5
P/D = 0.8
15
P/D = 1.0
P/D = 1.2
-30
-15
0
P/D = 1.4
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-0.8
-90
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-75
-75
-60
-60
-45
-30
-15
0
15
P/D = 1.0
P/D = 0.2
-45
30
P/D = 0.8
P/D = 0.1
-0.8
-90
P/D = 0.5
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = 0.2
45
P/D = -0.4
60
P/D = -0.7
P/D = -0.1
60
P/D = -1.0
P/D = -0.4
HYDRODYNAMIC PITCH ANGLE  [degrees]
75
P/D = -0.7
75
P/D = -1.2
P/D = -1.0
PROPELLER TORQUE COEFFICIENT 10CQ
Figure 15 Torque coefficient CQ at various pitch settings
for propeller C4-40 with design pitch ratio P0.7R/D=1.2.
P/D = -0.4
60
P/D = -0.7
P/D = -0.1
P/D = 0.1
45
P/D = 0.0
P/D = 0.2
30
P/D = 0.8
P/D = 1.0
15
P/D = 1.2
P/D = 1.4
-15
0
P/D = 1.6
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-0.8
-90
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
-75
-75
-60
-60
-45
-30
-15
0
15
P/D = 1.2
P/D = 0.5
-30
30
P/D = 1.0
P/D = 0.2
-45
P/D = 0.8
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = 0.5
45
P/D = -0.1
P/D = 0.1
-0.8
-90
P/D = 0.0
60
P/D = -1.0
P/D = -0.4
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = -1.2
P/D = -0.7
75
P/D = -1.0
75
90
90
PROPELLER TORQUE COEFFICIENT 10CQ
Figure 13 Torque coefficient CQ at various pitch settings
for propeller C4-40 with design pitch ratio P0.7R/D=0.8.
PROPELLER TORQUE COEFFICIENT 10CQ
PROPELLER TORQUE COEFFICIENT 10CQ
Figure 14 Torque coefficient CQ at various pitch settings
for propeller C4-40 with design pitch ratio P0.7R/D=1.0.
Figure 16 Torque coefficient CQ at various pitch settings
for propeller C4-40 with design pitch ratio P0.7R/D=1.4.
90
90
P/D = -0.1
P/D = 0.1
P/D = 0.0
45
P/D = 0.0
30
P/D = 0.5
P/D = 0.8
15
P/D = 1.0
P/D = 1.2
-30
-15
0
P/D = 1.4
-60
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
-75
PROPELLER BLADE SPINDLE TORQUE COEFFICIENT 100CQblade
0.6
0.8
-1.0
-90
PROPELLER BLADE SPINDLE TORQUE COEFFICIENT 100CQblade
P/D = -0.4
60
P/D = -0.7
P/D = -0.1
P/D = 0.1
45
P/D = 0.0
P/D = 0.2
30
P/D = 0.8
P/D = 1.0
P/D = 1.2
P/D = 1.4
-15
0
P/D = 1.6
PROPELLER BLADE SPINDLE TORQUE COEFFICIENT 100CQblade
Figure 18 Blade spindle torque coefficient CQblade at various pitch settings for propeller C4-40 with design pitch
ratio P0.7R/D=1.0.
-60
-75
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-1.0
-90
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-75
-60
-45
-30
-15
0
15
P/D = 1.2
P/D = 0.5
-30
30
P/D = 1.0
P/D = 0.2
-45
P/D = 0.8
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = 0.5
45
P/D = -0.1
P/D = 0.1
15
P/D = 0.0
60
P/D = -1.0
P/D = -0.4
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = -1.2
P/D = -0.7
75
P/D = -1.0
75
90
Figure 19 Blade spindle torque coefficient CQblade at various pitch settings for propeller C4-40 with design pitch
ratio P0.7R/D=1.2.
90
Figure 17 Blade spindle torque coefficient CQblade at various pitch settings for propeller C4-40 with design pitch
ratio P0.7R/D=0.8.
-1.0
-90
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
-75
-60
-45
-30
-15
0
15
P/D = 1.0
P/D = 0.2
-45
30
P/D = 0.8
P/D = 0.1
-1.0
-90
P/D = 0.5
HYDRODYNAMIC PITCH ANGLE  [degrees]
P/D = 0.2
45
P/D = -0.4
60
P/D = -0.7
P/D = -0.1
60
P/D = -1.0
P/D = -0.4
HYDRODYNAMIC PITCH ANGLE  [degrees]
75
P/D = -0.7
75
P/D = -1.2
P/D = -1.0
PROPELLER BLADE SPINDLE TORQUE COEFFICIENT 100CQblade
Figure 20 Blade spindle torque coefficient CQblade at various pitch settings for propeller C4-40 with design pitch
ratio P0.7R/D=1.4.
8.
ACKNOWLEDGEMENTS
The authors thank all participants in The Wageningen Cand D-Series Propellers JIP: Advance Gearbox, Andritz
(Escher Wyss), Bluewater, Bruntons Propellers (Stone
Marine), Brunvoll, Caterpillar (Berg Propulsion),
CSDDC, CSSRC, Damen, DNV, DSME, GL-Group (FutureShip), Hundested, Hyundai, Kamome, Kawasaki,
MAN, MARIN, Nakashima, NGC, Niigata, Rolls-Royce,
Royal Netherlands Navy, Scana Volda, SMERI, SMMC,
TU Delft, Wärtsilä and ZF Marine. In addition, this JIP is
also supported by UDP-JIP, SPA-JIP and STA-JIP.
12.
13.
14.
15.
9.
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