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1 INTRODUCTION
Limitations of shallow water areas relate to seaside and
canal effects and refer to the vertical and horizontal
plane of the waterway. The dimensions of the
hydrotechnical infrastructure in the rivers and canals
determine the maximum length, width, and draught of
inland waterway vessels [1,2,3]. These values are
implemented in local laws. A safe under-keel clearance
(UKC) is required to ensure adequate manoeuvrability,
sufficient stopping distance and space for
sedimentation, suitable accounting of errors in
bathymetry, economical fuel consumption, protection
of the ship's hull and also waterway and environment,
and adequate accounting of vessel pitch, roll and squat
so that the vessel does not strike the waterway
bottom[4].
Ferry crossing were operated from time
immemorial, enabled people transport cross the rivers
and lakes. One of the most important problems on
restricted areas including shallow rivers is to
determine hydrodynamic forces acting on moving
ship’s hull on restricted water areas. The
hydrodynamic behaviour of a vessel changes when
sailing in shallow or confined water. The restricted
space underneath and alongside a vessel has a
noticeable influence on both the sinkage and trim of a
vessel, also known as squat[5]. Ship squat is the
reduction in UKC that happens when a vessel moves
forward, caused by changes in pressure and flow of
water beneath the hull. So, prediction of squat depends
on the following parameters [6,5,1]:
− ship’s speed
− ship position (proximity to channel bank)
− ship geometry (length, beam, draft, shape, etc.)
− type of water area (the underwater cross-section
area of ship, the cross-section area of the canal or
river).
The water depth (H) and the mean draught (T) of
the static ship are broadly used as the parameters to
characterize shallow water. Figure 1 presents the squat
phenomenon in restricted waters, caused by the
Analysis of Squat Effect in Shallow River for Inland
Ferry
J. Jachowski & M. Schoeneich
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: The squat determination during ships movement on restricted water areas is one of the most
important problems affecting navigational safety. Precise squat prediction is essential to minimize the risk of
grounding for ships. In Poland we have about 60 operated ferry crossing, part of them are base of transport
infrastructure. The Lower Vistula River in Poland is a clear example of a shallow river. Zones of active sediment
transport of sandy material are big problem in navigation conditions maintenance on this river. The paper
presents an analysis of squat phenomena of ferry “Flisak” by empirical method and fluid dynamic in different
conditions. The results of this research could be helpful for inland transport management, risk assessment of ferry
crossing the Vistula River, and analysis for a new waterway project.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 19
Number 4
December 2025
DOI: 10.12716/1001.19.04.30
1316
acceleration of flow between the ship’s hull and the
bottom.
A)
B)
Figure 1. Squat phenomena on restricted water depending on
depth and draught A) H/T=2,5; B) H/T=,5
An area of particular concern is the prediction of
ship squat in shallow or restricted waters at different
speeds. Squat may cause grounding of the ship which
result in severe damage to the ship, and consequently
higher repair bills and off hire losses. In shallow water,
the effect of squat is much greater because the water
has less space to move around the hull, forcing it to
accelerate even more [5]. Ferry “Flisak” crossing was
opened in 2023 and less than a year of operation was
closed and cruises have been suspended, so research
were conducted for precise determination of squat,
which could be helpful for possibility of ferry
operational.
2 STUDY AREA
The aim of this work is squat assessment of ferry at
763,56 km on Vistula River. “Flisak” is newly built
ferry (2023) which operates between Solec Kujawski
and Czarnowo, but it has problem with good
functioning. About 90% of river ferries have
parameters similar to length 12 m, breadth 5 m and
engine power about 50-150 kW. Figure 2 presents new
buildings of infrastructure and a river.
Figure 2. “Flisak” ferry during crossing Vistula river [7]
An analysed ferry is bigger than typical values.
Figure 3 presented schedule of “Flisak” ferry and his
main parameters.
L
B
T
D
Cb
Vs
Vs
Engine: 89-120 kW
Figure 3. Main parameters and schedule of “Flisak” ferry [8]
The hydrological conditions in the Vistula basin
display a high seasonal variation, with a tendency to
occur in extremely high-water stages and long periods
of low water levels. The breadth of the shipping lane
equates to 320-420 m and has curved stretches, with the
radii equating to 250-300 m. For safety navigation ferry
level on gauging station should be between 175 – 375
cm but for carrying cars water level should be on 200
cm level on the other hand the big problem for
navigation conditions are sandbars. In research the
own data from depth measurements Vistula River in
cross-sections and in the longitudinal profile of the
shipping lane were used for determination of mean
actual depth in given sections. Figure 4 presents cross
profiles in reviewed area.
Figure 4. Example of longitudinal profile at cross section
Vistula River, taking into account route of the ferry [7]
3 SQUAT ANALYSIS
In research the own data from depth measurements
Vistula River in cross-sections and in the longitudinal
profile of the shipping lane were used for
determination of mean actual depth in given sections,
next step the values for squat were calculated. Ship
squat can be calculated by various strategies such as
analytical method [9], numerical and experimental
methods [10,11].
3.1 Empirical methods
Many scientific centres specializing in hydrodynamics
and ship theory conduct research on ship squat. As a
result of these studies, numerous methods have been
developed for determining the ship’s squat under way.
On the other hand, each study leads to the formulation
of empirical equations, the use of which allows the
calculation of squat values under various conditions.
Several empirical formulae have been developed for
estimating maximum ship squats, most of them based
on statistical analysis of experimental data. The
following methods were used in the research [1,5,6]:
Tuck:
2
2
2
1
nh
z
pp
nh
F
SC
L
F
=
−
1317
Huuska:
2
2
2
1
nh
zs
pp
nh
F
S C K
L
F
=
−
Millward 2:
2
2
61,7 0,6
100
1
pp
nh
b
pp
nh
L
F
T
SC
L
F

=−


−

Turner:
2
100
b
vT
SC
h
=
Barras 1:
1
3
2
2
4
2
3,75
2
ss
b
e
vv
S C S
vg

=


Barras 2:
2
2,08
3
2
30
b
C S v
S =
Barras 3:
2
100
b
v
SC=
Simard:
2
2
1,01
0,80
21
s
v
S
gS


=−


−



Eryuzlu:
2,298
2,972
2
0,298
s
b
v
hh
SK
TT
gT
−


=





Yoshimura 2:
3
2
11
0,7 1,5 15
e
BB
pp pp
V
CC
S
h L h L
g
TT
BB





= + +








Norbin:
15
B
Cv
S
Lh
BT
=



where:
S – squat,
Cz – squat factor,
– displacement [m
3
],
Lpp – lenght between perpendiculars [m],
T – draught [m],
Fnh – Froude number:
s
nh
v
F
gh
=
h – depth [m],
v – vessel speed [kn],
vs – vessel speed [m/s],
ve – vessel speed of exploatation [m/s],
g – acceleration due to gravity [m/s
2
],
Ks – correction factor for channel width:
1
1
1
0,03
7,45 0,76
for
0,03
1
s
S
s
K
S
+
=
S1 – corrected blockage factor,
S2 – velocity return factor,
1
1
s
w
A
A
S
K
=
2
s
ws
A
S
AA
=
−
As – ship’s underwater amidships cross section [m
2
],
Aw – net cross section area of waterway [m
2
],
K1 – correction factor on blockage (Huuska),
Kb – correction factor for channel:
3,1
9,61
if
9,61
1
b
D
D
B
K
D
B
B
=
D – distance between ship hull and toe of the bank,
B – ship’s beam.
The results obtained using these formulae should be
regarded as approximate, as they are limited and valid
only for selected conditions [1].
3.2 Numerical approach
Carrying out of numerical simulations requires
appropriate preparation of the ship hull and water area
geometry. For the simulations, the shape of the
“Flisak” ferry model was used. Based on the geometry
of the ship model, hydrostatic data were determined,
and subsequently, the mass and coordinates of the
center of gravity were calculated and implemented in
the numerical simulation. The moments of inertia of
the hull were estimated using the results obtained from
the RhinoCeros software, assuming an exemplary
distribution of cargo weight on the ferry.
The CFD technique requires the modeling of a space
surrounding the ferry divided into cells. The Reynolds-
averaged Navier–Stokes (RANS) equations applied
give the approximate time-averaged solutions in each
cell. The CFD software utilized in the presented
research was Flow3D, which code is based on the finite
volume method (FVM) and uses the volume of fluid
(VOF) method for the free surface problems solutions
[12].
The simulations were performed using the
overlapping mesh technique. The assumption of this
approach is that one of the meshes is stationary in the
whole computational domain, related to the global
reference system. The high accuracy of computation is
achieved by solving the governing equations in the
'free surface' cells (the cells partly filled with liquid).
The simulations of turbulent flows were based on the
Large Eddy Simulation (LES) turbulence model was
applied. The practical application of the Flow3D
software is based on the consecutive steps performance
(creation 3D geometry, importing geometry and
numerical mesh creation, setting Solver options,
calculations and results).
The assumptions accepted in CFD modelling of the
ferry movement are as follows:
− 3-dimensional flow simulations are used,
− simulations are performed in full scale,
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− calculations are based on model 6DOf for ferry over
variable bottom profile,
− simulations are performed using overlapping
meshes, enabling ferry pitch and roll motions,
draught,
− simulations are performed using overlapping
meshes, enabling ferry roll, pitch and vertical (Z)
motions – three degrees of freedom,
− the LES (Large Eddy Simulation) turbulence model
was applied,
− the VOF method was applied for the free surface
problems.
The CFD technique was verified in [13], which
showed that the CFD method could be used in the
future for squat determination and practical
applications. Figure 5 shows the computational
domain and the applied boundary conditions for
“Flisak” squat simulation.
Figure 5. The computational domain of ferry crossing Vistula
river
The computational mesh used in Flow3D consisted
of approximately 5 million finite volume cells (FV). A
high-resolution 3D block with refined cell size was
placed around the ferry hull to accurately capture flow
gradients and free surface effects, while it was
surrounded by a coarser shallow-water block to
optimize computational efficiency – Fig.6.
Figure 6. Structural mesh applied for ferry squat simulation
4 RESULTS
The analysed case concerns the squat phenomenon at a
small under-keel clearance, with a depth-to-draught
ratio (h/T) of 1,26. At such a small clearance, the
boundary layer effects from both the riverbed and the
ship’s hull significantly influence the squat results.
Figure 6 presents the results of bow and stern squat, as
well as the port and starboard side sinkage at midship
for the “Flisak” ferry. On the other hand non typical is
navigation crossed the river so simulations checked the
influence of river current additionally.
The simulations were carried out both without river
current and with a river current of 1 m/s. For the case
including the river current, the ferry was assumed to
move at an angle to the ground track, resulting from
the combination of the vessel’s velocity vector and the
transverse current vector. Based on the simulations, a
heel of the ferry due to the river current is clearly
visible. In addition, simulations were conducted to
assess the influence of the river current on the squat
behaviour. The results are shown in Figure 7.
A)
B)
Figure 7. Results of the squat changes for the Flisak ferry
during river crossing at a speed of 3 m/s – CFD simulation
results. A) without current B) with 1 m/s river current (SB-
starboard PS-port side)
The wave pattern generated during the squat
phenomenon can be visualized with Flow 3D. The red
area indicates the elevation of the bow wave, whereas
the blue area shows the water surface depression at the
stern. Figure 8 shows an example of the wave pattern
generated by the ferry moving at a speed of 3 m/s on
the river surface.
Figure 8. Example of the wave pattern generated by the ferry
moving at 3 m/s on the river surface
The results of the numerical and empirical analyses
are presented and next compared the squat values
obtained from CFD simulations with those calculated
using selected empirical methods (Figure 9). The
comparison allows for the evaluation of the accuracy
and applicability of these methods under shallow
water conditions of the Vistula River.
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Figure 9. Comparison of squat values for the Flisak ferry over
an irregular riverbed calculated using CFD and 12
approximate empirical methods for a ferry speed of 3 m/s.
It should be noted that most empirical squat
prediction methods show variability of results, as they
are generally formulated for larger under-keel
clearances and do not account for river currents.
Selected methods indicate a probability of grounding,
however the CFD simulation results do not confirm
this.
Based on the data comparison (Fig. 9), the mean
deviation and standard deviation of squat values
relative to CFD results are presented in Figure 10.
Figure 10. Comparison of mean deviation and standard
deviation of squat values obtained from 12 approximate
empirical methods relative to CFD results.
Analysing the results presented in Figures 9 and 10,
it can be concluded that at small under-keel clearances
(UKC) — for example, when h/T ≈ 1,3 — the
difference in squat estimation as a component of the
safe under-keel clearance becomes more significant.
Differences of results between empirical methods
become significant when navigation takes place in
shallow waters with irregular bottom geometry, such
as the Vistula River.
5 CONCLUSIONS
Newly built ferry “Flisak” which operates on Vistula
river from the last year can’t operate in navigational
season due to hydrologic situation and sandbars. The
study aimed to compare empirical methods with CFD
results. The CFD technique shows higher value of
squat with river current. The results indicate that the
squat accounting for the river current increased by
nearly 30% in the section with the minimum depth. The
study showed that the lowest coefficient of variation
was obtained using the Yoshimura 2 method, while the
highest was observed for the Barras 2 method. The
wave pattern formed during the ferry’s movement is
responsible for the squat effect, which is more
significant at the stern. This comparison allows for an
evaluation of the methods’ accuracy and applicability
in the shallow water of the Vistula River. Results of this
analysis can be used for further research connected
with minimal safety depth determination and risk
analysis in reviewed area. The research results provide
the foundation for further potential analysis of Lower
Vistula transport possibilities.
REFERENCES
[1] Gucma S., Jagniszczak I., Nawigacja morska dla
kapitanów, Poland, Szczecin, 2006
[2] Gucma S. Morskie drogi wodne Projektowanie i
eksploatacja w ujęciu inżynierii ruchu, Gdańsk, 2015
[3] Marta Schoeneich, Michał Habel, Dawid Szatten, Damian
Absalon and Jakub Montewka An Integrated Approach
to an Assessment of Bottlenecks for Navigation
Schoeneich M., Habel M., Szatten D., Limitation for
Inland Ships in the Area of Planned Multimodal Port on
Vistula River International Journal on Marine Navigation
and Safety of Sea Transportation 2019, DOI:
10.12716/1001.14.03.05
[4] Michaud S., Morse B., Santerre R., Tashereau A., Siles J.
(2002) Precise Determination of Vessel Squat and Under-
keel Clearance. 4th Transportation Specialty Conference
of the Canadian Society for Civil Engineering, Montréal,
Québec.
[5] Moustafa M. M. ,Yehia W. Squat assessment for safe
navigation of river Nile cruisers,
Brodogradnja/Shipbilding/Open access Volume 68
Number 2, 2017 http://dx.doi.org/10.21278/
[6] PIANC 2014, Harbour Approach channel design
Guidelines, Report n° 121-2014, Belgique, Bruxelles 2014
[7] Fot. G. Olkowski
[8] Schoeneich M, Jachowski J, Soszyńska-BudnyJ., Babiński
Z., Semrau M., Risk assessment of ferry crossing on river
with sandy bedforms, Book of abstracts of the XXth
International Scientific and Technical Conference on
Marine Traffic Engineering MTE 2024, Szczecin2024
[9] T. Gourlay, Mathematical and Computational Techniques
for Predicting the Squat of Ships, The University of
Adelaide, Department of Applied Mathematics, PhD
thesis, 2000.
[10] A. Olivieri, F. Pistani, A. Avanzini, F.Stern and R. Penna,
Towing Tank Experiments of Resistance, Sinkage and
Trim, Wake, and Free Surface Flow Around a Naval
Combatant, SEAN 2340 Model, Iowa Institute of
Hydraulic Research, Technical Report No. 421, Iowa,
2001.
[11] H. Zeraatgar, K. A. Vakilabadi and R. Yousefnejad,
Parametric Analysis of Ship Squat in Shallow Water by
Model Test, Brodogradnja, Vol. 62, No.1, Zegrab, 2011.
[12] https://fv-tech.com Flow Vision HPC, assessed on 27-09-
2023.
[13] Gucma L., Jachowski J., Schoeneich M. CFD Ship squat
determination method Validation by GPS-RTK
Measurements. Annual of Navigation No. 13. Gdynia,
2008