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1 INTRODUCTION
The design and safe operation of port areas depend on
an accurate understanding of ship manoeuvrability. As
maritime traffic continues to grow [9] and port
environments become more constrained, the ability to
predict ship behaviour in complex navigation
scenarios becomes increasingly critical. Reduced-scale
physical modelling, based on Froude similitude,
remains one of the most reliable and widely adopted
techniques for evaluating manoeuvring performance
in port planning and design [1]. These models support
assessments of passing ship effects [5], confined water
navigation [4], mooring line dynamics [2], and berthing
or unberthing operations.
To ensure the validity of these simulations, it is
essential that the displacement response of the ship
model to rudder inputs closely replicates that of the
full-scale vessel. Guidelines such as those from the
IMO [7] provide recommendations for the physical
representation of ships in model tests. Validating the
model’s response typically involves conducting
standardized manoeuvring trials—such as turning
circle, zig-zag, and stopping tests—whose results
should closely match those observed in the prototype.
This validation approach is widely adopted and
applied not only in physical model testing but also in
computational simulations [6,8].
Although Froude scaling ensures similarity in
gravitational and inertial forces between a model and
its full-scale counterpart, it does not capture all
hydrodynamic effects—particularly those related to
viscosity. In physical modelling, rudders are typically
constructed by applying a geometric scale reduction of
the full-size design. However, this approach can lead
to discrepancies in manoeuvring behaviour, especially
Experimental Validation of Rudder Representation
in Reduced-scale Physical Model Tests
R. de Oliveira Bezerra & J.C. de Melo Bernardino
University of Sao Paulo, Sao Paulo, Brazil
ABSTRACT: Froude-based reduced-scale modelling of port areas is widely used to assess manoeuvring safety,
including passing ship effects, confined navigation, and berthing operations. For reliable results, ship models
must reproduce full-scale displacement responses to rudder inputs, particularly for turning performance.
Variations in rudder geometry influence flow patterns and the resulting hydrodynamic forces that govern
manoeuvrability. This study experimentally investigates the impact of rudder shape and aspect ratio on
manoeuvring performance by testing eighteen NACA rudder profiles with a free-running scale model. Standard
manoeuvring tests, such as turning circle trials, were conducted. The results revealed that strict geometric scaling
of the rudder leads to significant discrepancies in model behaviour, while modifications to rudder geometry
improve dynamic similarity. This research provides practical data showing how rudder design adjustments affect
manoeuvring responses and highlights that adapting rudder geometry for scale models is an effective strategy to
enhance the similarity between model and prototype ship behaviour.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 3
September 2025
DOI: 10.12716/1001.19.03.34
996
in free-running tests intended to replicate realistic ship
movements. These inconsistencies arise because the
scaled rudder may not generate forces in proportion to
those of the prototype. One way to mitigate this issue,
as demonstrated in previous computational studies, is
by adjusting the rudder’s shape and aspect ratio—key
factors that significantly influence the hydrodynamic
forces acting on the ship [6,8]
This study aims to contribute to this field by
presenting a comprehensive experimental
investigation into the effects of rudder shape and
aspect ratio on the manoeuvrability of a free-running
ship model. Eighteen different rudder configurations
derived from the NACA series were tested under
controlled conditions. Standard manoeuvring trials,
such as turning circle tests, were used to evaluate
dynamic responses.
The main objective is to assess whether adjustments
to rudder geometry can improve the similarity of
manoeuvring behaviour between the model and the
prototype. By identifying configurations that yield
more accurate displacement responses, this research
seeks to provide practical guidelines for rudder design
in physical models. Ultimately, enhancing the fidelity
of rudder representation in scale models contributes to
more reliable simulations of ship behaviour, better-
informed engineering decisions, and safer port
operations.
2 MATERIAL AND METHODS
2.1 Model Tank and Test Setup
The tests were conducted in a model tank located at the
University of Sao Paulo (USP), Brazil. This model is 40
meters long, 18 meters wide and 1.2 meters deep
(Figure 1). To simulate deep-water conditions and
avoid bottom interference during manoeuvring trials,
the water level was set at 1 meter.
Figure 1. Physical model at the USP used for reduced-scale
manoeuvring tests.
To track the ship's position over time, a set of four
overhead cameras was installed along the tank at a
height of 10 meters, covering the entire testing area.
The system uses bottom-mounted reference markers
and correlates pixel positions to real-world
coordinates. This tracking algorithm was developed by
USP and has been applied in various experimental
studies over the years [1,3,5]. The system provides a
spatial resolution of 0.1 meters and operates at a
sampling frequency of 30 Hz.
All tests were conducted in still water and inside a
closed environment, ensuring that external factors (like
wind) did not influence the results.
2.2 Ship Model Description
The scale model represents a VLOC (Very Large Ore
Carrier) with a capacity of 400,000 DWT, built at a non-
distorted geometric scale of 1:170, in accordance with
Froude similitude criteria. Table 1 presents the main
geometric dimensions of both the prototype and the
scale model.
Table 1. Main geometric characteristics of the prototype and
the scale model of the VLOC (Very Large Ore Carrier).
VLOC
Prototype (m)
LOA
362.00
LPP
350.00
Breadth
65.00
Depth
30.40
Draft
23.00
The ship model was built in fiberglass, faithfully
reproducing the lines of the full-scale vessel at the
corresponding scale. Figure 2 shows the body plan of
the prototype alongside an image of the constructed
scale model. The weight distribution was carefully
adjusted to ensure that the center of mass and moments
of inertia were properly calibrated. As a result, the
model's behavior in water accurately corresponds to
that of the full-scale ship.
Figure 2. Body plan of the full-scale ship (left) and the
corresponding scale model built in fiberglass (right).
The propulsion system consists of a DC motor
connected to a scaled propeller, controlled by a PWM
system that regulates speed while maintaining torque.
All velocity settings were based on the sea trial report
of the full-scale ship, ensuring that each propulsion
stage drives the model at the corresponding scaled
velocity. Rudder control is provided by a servomotor
connected to the rudder’s rotation axis through a gear
mechanism. Each rudder is mounted with the same
standardized axis to allow easy interchangeability
during tests. Communication between the computer
and the ship is established via a radio frequency
transmitter, and commands are issued using a joystick.
This system is described in greater detail in [1].
2.3 Rudder Configurations
Two geometric variables of the rudder were tested: the
thickness profile, defined by different NACA airfoil
sections, and the aspect ratio, a parameter representing
the ratio between the rudder's span (height) and chord
(width). All rudders used in the tests were of the spade
type, with a fixed height of 16.3 meters in the prototype
(corresponding to 9.6 cm in the scale model). This
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height was maintained to reflect the dimensions of the
reference ship, as increasing it could render the rudder
ineffective in shallow water conditions. Therefore,
variations were applied only to the profile shape and
width, ensuring compatibility with port operational
constraints.
Figure 3 presents an example of a rudder design,
illustrating the key variables used to define the
geometric variations tested in this study. Based on
these parameters, a total of 18 rudders were produced
using 3D printing technology: one corresponding to
the geometric scale of the prototype and 17 others
representing variations in thickness profile and aspect
ratio. All rudders were scaled to match the model
dimensions. Table 2 summarizes the values of each
geometric variable of the rudders used in the tests,
presented in millimeters.
Figure 3. Illustration of the rudder geometry, highlighting
the variables considered in the study: thickness profile
(NACA series) and aspect ratio (span-to-chord ratio).
Table 2. Geometric parameters of the 18 rudder
configurations tested, including chord length, thickness
(based on NACA profiles), and aspect ratio, in millimeters.
N°
Profile
Aspect
Ratio
a
B
e1
e2
1
Naca 12
1.00
93,81
65,60
11,26
7,87
2
1.25
75,05
52,48
9,01
6,30
3
1.5
62,54
43,73
7,51
5,26
4
1.65
56,85
39,76
6,82
4,78
5
1.75
53,60
37,49
6,43
4,51
6
2.0
46,90
32,80
5,63
3,94
7
Naca 18
1.00
93,81
65,60
16,88
11,81
8
1.25
75,05
52,48
13,51
9,44
9
1.5
62,54
43,73
11,25
7,88
10
1.65
56,85
39,76
10,23
7,16
11
1.75
53,60
37,49
9,65
6,75
12
2.0
46,90
32,80
8,44
5,91
13
Naca 25
1.00
93,81
65,60
23,46
16,40
14
1.25
75,05
52,48
18,76
13,12
15
1.5
62,54
43,73
15,64
10,93
16
1.65
56,85
39,76
14,21
9,94
17
1.75
53,60
37,49
13,40
9,37
18
2.0
46,90
32,80
11,73
8,20
The rudder that has geometric similarity with the
prototype corresponds to the configuration number 4
in Table 2, with a NACA 12 profile and an aspect ratio
of 1.65. Figure 4 illustrates all the rudders fabricated
using 3D printing. It can be observed that as the aspect
ratio increases, the rudder’s chord length decreases,
and as the NACA number increases, the profiles
become progressively thinner.
Figure 4. Set of 3D-printed rudders used in the experiments.
2.4 Experimental Procedures
To evaluate the performance of the rudders, turning
circle trials were conducted at full-speed ahead,
corresponding to approximately 15 knots in full scale,
with manoeuvres executed to both port and starboard
sides. A turning circle is a standard manoeuvring test
in which a ship continuously turns to one side with a
constant rudder angle—in this case, 35°—to assess its
turning characteristics.
To allow for an objective comparison between
different test repetitions and rudder profiles—beyond
visual inspection—three key manoeuvring parameters
defined by the IMO [7] were used. These parameters
are also illustrated in Figure 5.
1. Advance – the distance the ship travels in its
original heading direction from the point the
rudder is applied until it reaches a 90° heading
change.
2. Tactical Diameter – The perpendicular distance
between the original course and the ship’s position
when it has turned through 180°.
3. Transfer – The lateral distance the ship moves in the
direction perpendicular to its original course during
the turning manoeuvre.
Figure 5. Illustration of turning circle geometry used to
determine manoeuvring parameters.
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To enable comparison, a real-world trial was used
as a reference. Figure 6 shows the turning test results
from the full-scale VLOC trials, with all values
normalized by the ship’s length.
Figure 6. Turning circle results from full-scale VLOC trials,
used as a reference for model-scale comparisons. All values
are normalized by the ship’s length.
Each rudder underwent four repeated tests on both
port and starboard sides to ensure validation and
improve repeatability. In total, 144 manoeuvring tests
were conducted for this study. This approach improves
the repeatability of the model and ensures robust and
reliable data. In the end, the final values of the
manoeuvring parameters were calculated as the
arithmetic mean of the results from the four repetitions.
To determine the manoeuvring parameters, a
custom software was developed to calculate the ship’s
position, velocity, and heading angle over time. Based
on this data, the software automatically computes the
turning circle parameters using the ship's trajectory
and angular displacement. Figure 7 shows the initial
position in red, the ship’s path in black, and blue
markers indicating the points at which the ship reaches
±90° and ±180° relative to its initial heading (considered
as 0°). The sign of the angle depends on the turning
direction (port or starboard). These reference points are
used to calculate the advance, tactical diameter, and
turning radius.
Figure 7. Ship trajectory used for manoeuvring parameter
calculation. The red dot indicates the initial position, the
black line represents the ship’s path over time, and the blue
dots show the points where the ship reaches ±90° and ±180°
relative to the initial heading. All values are expressed in
meters in real-world scale.
3 RESULTS AND DISCUSSION
First, the results compare the performance of the
geometrically similar scaled-down rudder (Rudder
number 4 from Table 2), which maintains the same
configuration as the full-scale rudder in terms of height
(h), length (a), thickness (b), and profile shape (NACA
12). The objective is to evaluate how a simple geometric
scaling diverges from full-scale manoeuvring
behaviour. Figure 8 presents a comparison between the
scale model equipped with Rudder 4 and the full-scale
ship trials, illustrating both starboard and port turning
manoeuvres. All values shown have been converted
and are presented in meters, corresponding to the
dimensions of the full-scale vessel. It is worth noting
that the turning plot in Figure 8 represents only one of
the four repetitions performed, which may introduce
slight visual discrepancies in the manoeuvring
parameters compared to the averaged results.
Figure 8. Comparison of turning circle trajectories between
the scale model with rudder No. 4 and the full-scale ship
trials for both starboard and port turns. All values are
presented in real-world meters (full-scale dimensions).
For the analysis, Table 3 presents the values of the
three key parameters, advance, tactical diameter, and
turning radius—for each trial, providing a numerical
comparison between the scale model equipped with
Rudder No. 4 and the full-scale ship.
Table 3. Advance, tactical diameter, and turning radius for
each trial conducted with the scale model (Rudder No. 4)
and the full-scale ship. All values are presented in real-
world meters for direct comparison.
Parameters
PORT
STARBOARD
Prototype
Scale Model
Prototype
Scale Model
Advance (m)
1144,50
1162,11
1084,3
1191,93
Transfer (m)
237,3
426,02
188,3
570,46
T. Diameter (m)
949,9
1054,88
875,7
1331,01
Using the manoeuvring parameters to compare the
results, it becomes evident that the geometrically
similar scaled-down rudder does not accurately
replicate the real ship's turning behaviour. Among the
parameters, advance shows the closest agreement with
the full-scale values, with a percentage difference of
approximately 4% for the port side. This suggests that
the initial response to the rudder input occurs at a
similar point in both the model and the full-scale
vessel. However, the significantly larger values of
tactical diameter and turning radius in the model
highlight a reduced turning capability overall,
indicating that the scale model turns less effectively
than the real ship.
This discrepancy can be mitigated by adjusting the
rudder profile configuration. Among the tested
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designs, Rudder number 1 from Table 2 (NACA 12
profile with an aspect ratio of 1) provided the closest
match to the full-scale manoeuvring parameters.
Figure 9 and Table 4 present a comparison between the
turning trajectories of the scale model equipped with
Rudder 1 and the full-scale ship trials, illustrating both
starboard and port turning manoeuvres.
Figure 9. Comparison of turning trajectories between the
scale model equipped with Rudder No.1 (NACA 12, aspect
ratio 1) and the full-scale ship trials, for both starboard and
port manoeuvres. All values are converted and presented in
meters corresponding to the full-scale vessel.
Table 4. Advance, tactical diameter, and turning radius for
each trial conducted with the scale model (Rudder No. 1)
and the full-scale ship. All values are presented in real-
world meters for direct comparison.
Parameters
PORT
STARBOARD
Prototype
Scale Model
Prototype
Scale Model
Advance (m)
1144,50
1069,97
1084,3
1105,24
Transfer (m)
237,3
327,86
188,3
369,17
T. Diameter (m)
949,9
833,83
875,7
963,01
This rudder maintains a similar proximity to
Rudder No. 4 in terms of advance, but shows a closer
match to the full-scale values for transfer and tactical
diameter. Since both rudders share the same thickness
profile (NACA 12), we can infer that the increased
area—resulting from the higher aspect ratio—enhances
the turning capability. This is physically
understandable, as a larger rudder area generates
greater hydrodynamic force, leading to improved
manoeuvring performance.
Advance, Tactical Diameter, and Turning Radius
values for each rudder configuration tested. Table 5
presents data for port turning manoeuvres, while Table
6 presents data for starboard turning manoeuvres.
Each table includes the results of all four repetitions
performed for every rudder configuration. All values
are given in real-world meters.
Table 5. Advance, Tactical Diameter, and Turning Radius
for All Rudder Trials (Port Turning)
N°
Profile
Aspect
Ratio
Advance
Transfer
Tactical
PORT
Naca 12
1.00
1069,97
327,856
833,83
1.25
1103,12
406,564
1084,79
1.5
1148,44
531,777
1151,41
1.65
1191,93
570,491
1331,01
1.75
1158,2
523,408
1155,61
2.0
1125,1
570,656
1293,39
Naca 18
1.00
1099,78
447,763
994,635
1.25
1046,3
462,564
1053,34
1.5
1108,46
499,622
1169,72
1.65
1104,63
526,711
1146,11
1.75
1142,28
544,347
1227,27
2.0
1330,52
585,218
1360,79
Naca 25
1.00
1154,71
434,151
976,551
1.25
1102,73
451,362
1149,45
1.5
1169,41
507,72
1102,92
1.65
1191,84
544,972
1210,4
1.75
1168,91
650,592
1321,51
2.0
1136,98
645,91
1389,87
Table 6. Advance, Tactical Diameter, and Turning Radius
for All Rudder Trials (Starboard Turning)
N°
Profile
Aspect
Ratio
Advance
Transfer
Tactical
STARBOARD
Naca 12
1.00
1105,24
369,17
963,009
1.25
1125,63
419,852
1051,29
1.5
1141,93
468,505
1177,37
1.65
1162,11
426,019
1054,88
1.75
1151,94
476,096
1183,66
2.0
1119,46
484,711
1164,5
Naca 18
1.00
1081,57
406,046
1130,05
1.25
1191,17
449,668
1085,97
1.5
1112,82
449,003
1035,72
1.65
1117,97
469,042
1171,66
1.75
1061,23
471,554
1120,86
2.0
1149,63
554,564
1385,87
Naca 25
1.00
1202,56
390,489
1019,01
1.25
1086,4
387,065
978,90
1.5
1124,94
451,211
1104,80
1.65
1123,73
409,366
1061,32
1.75
1154,85
465,684
1128,00
2.0
1112,61
486,12
1185,25
Analyzing Tables 5 and 6, we can conclude that
advance is not significantly affected by changes in
rudder profile or aspect ratio, as all values remain
within the same order of magnitude across different
configurations. However, for tactical diameter and
turning radius, a consistent pattern is observed: when
maintaining the same profile, an increase in aspect
ratio—which implies a reduction in rudder area—leads
to higher values for these parameters. This indicates a
decrease in turning capability, as smaller rudder areas
generate less hydrodynamic force, reducing the
model's ability to execute tighter turns.
When comparing the NACA profiles with the same
aspect ratio, no consistent pattern is observed, which
suggests that in this test scenario, rudder thickness
plays a minor role in manoeuvring performance.
4 CONCLUSION
This study evaluated the influence of rudder shape and
aspect ratio on the turning manoeuvrability of a ship
using scale model tests. The results clearly indicate that
a geometrically similar scaled-down rudder of the full-
scale rudder does not accurately replicate the
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manoeuvring behaviour of the real ship. Among the
tested rudders, a configuration with increased area—
achieved by raising the aspect ratio while maintaining
the same NACA 12 profile—proved to be more
effective, offering better alignment with the full-scale
turning parameters.
The analysis showed that advance is the parameter
least affected by rudder geometry, while tactical
diameter and turning radius were significantly
improved with larger rudder areas. In contrast,
variations in the NACA profile had minimal impact,
suggesting that rudder area plays a more decisive role
in manoeuvring effectiveness than profile shape in this
scenario.
For future studies, it is recommended to test
rudders with intermediate aspect ratios between 1.0
and 1.25, as these may offer a better compromise. By
slightly increasing the turning effectiveness on port
side and slightly reducing it on starboard, this
configuration could bring the results of both turning
directions closer to the full-scale behaviour, potentially
leading to an even more accurate representation in
physical modelling.
These findings are important for physical
modelling practices, especially in manoeuvring
studies, as they highlight the need to optimize rudder
configurations rather than rely solely on geometric
scaling. By adjusting the rudder dimensions
appropriately, it is possible to improve the dynamic
similarity between the model and the full-scale ship,
leading to more accurate and reliable experimental
outcomes.
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