279
1 INTRODUCTION
Ship stability is undoubtedly a subject of paramount
importance in the field of Naval Architecture, its
fundamentals having wider implications for the design
and operation of ships and floating units ss is argued
by Bačkalov et el [2]. Ship stability assessment remains
an active and evolving area of maritime research, with
recent studies highlighting significant gaps and
challenges in current approaches. As per Zyczkowski
et al [39] the existing IMO Intact Stability Code has
been criticized for relying on outdated statistical
approaches that do not adequately account for
dynamic stability issues and the stochastic nature of
environmental conditions. According to Vidić et al [35]
in research about inland passenger ship stability
requirements, significant discrepancies in stability
assessments performed according to different
regulations have been identified, bringing into focus
the question of reliability of the present regulatory
framework for ship stability. According to recent
research [31], intact stability rules from IMO and
classification societies typically do not address
operational aspects, creating a gap between design
requirements and actual ship operations. Recent
developments in probabilistic damage stability
assessment have revealed that ships with identical
safety indices may have significantly different actual
safety levels, indicating fundamental limitations in
current evaluation methods [24].
Furthermore, the introduction of second-generation
intact stability criteria [25,27,34] represents a
recognition that traditional prescriptive regulations are
insufficient, with researchers advocating for
comprehensive risk analysis approaches that can
account for all relevant hazards during both design
and operational stages [19]. These ongoing research
Limitations and Practical Applicability of SEMIS
Methodology in Intact Stability Assessment
P. Kacprzak
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: This paper applies the SEMIS (Simple Evaluation Methodology for Intact Stability) approach to a
13593 DWT general cargo vessel for stability assessment using only metacentric height (GM). SEMIS estimate key
stability parameters through regression models and compares them with IMO Intact Stability Code criteria.
Analysis of 1314 loading conditions of investigated ship shows that SEMIS method provides quick and generally
accurate evaluations of stability for typical GM ranges (GM>0.30 m). However, results reveal notable
discrepancies for low-GM states (GM<0.30 m) especially in context of weather-related criteria. SEMIS in low GM
condition may incorrectly classify compliance and may underestimate critical stability parameters. These findings
indicate that while SEMIS is a practical supplementary tool, its application should be limited to preliminary
checks rather than final compliance verification. Additionally, we can determine the GM value associated with
the critical weather criterion. At this point, the b/a ratio reaches its peak, while for lower GM values it decreases
significantly, remaining a nonlinear function alongside other stability parameters.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 20
Number 2
June 2026
DOI: 10.12716/1001.20.02.04
280
efforts underscore the continued need for improved
stability assessment methodologies that can bridge the
gap between regulatory requirements and practical
operational safety. The IMO Intact Stability Code
requires ships to meet multiple stability criteria [11]
and still there is a need of extension of stability
assessment methods, as introducing simple ways of
assessment apart from complicated and numerical
methods. One of them is SEMIS concept [37] (Simple
Evaluation Methodology for Intact Stability) furtherly
described in section methodology, and IMSISA
concept [10] (Index for Marine Ship Intact Stability
Assessment) model which provides the ability to assess
the intact stability of ships based on the index of ship
stability performance, called the Ship Stability Index.
This study aims to comprehensively evaluate the
Simple Evaluation Methodology for Intact Stability
(SEMIS) as a novel approach to ship stability
assessment. The specific research objectives include:
1. Assess the effectiveness of SEMIS in providing
rapid, preliminary intact stability evaluation using
metacentric height (GM) as the primary input
parameter,
2. Validate the SEMIS methodology through
implementation on a specific vessel model,
3. Conduct a comparative analysis between vessel-
specific and literature-based SEMIS regression
models to determine accuracy and predictive
reliability,
4. Evaluate SEMIS's capability in predicting
compliance with IMO Intact Stability Code.
The research addresses a critical need in maritime
safety assessment through the implementation of a
simplified methodology for intact stability evaluation.
While previous studies [10,37] have implemented this
approach for many types of ships, this study focuses on
a specific 13593 DWT general cargo vessel, creating a
model tailored exactly for that ship.
SEMIS offers a practical solution by enabling rapid
preliminary stability checks using a single input
parameter - metacentric height (GM). This approach
can be particularly valuable in operational scenarios
where conventional stability assessment tools are
unavailable or when quick decision-making is
required.
By comparing vessel-specific and generic models,
this study provides evidence-based insights into the
potential and limitations of simplified stability
assessment approaches. The findings contribute to
understanding how such methodologies can support
maritime safety, offering practical recommendations
for their implementation. The research also highlights
the need for further development of rapid, accessible
stability evaluation techniques that maintain accuracy
while reducing complexity.
2 METHODOLOGY
2.1 Simple Evaluation Methodology for Intact Stability
SEMIS (Simple Evaluation Methodology for Intact
Stability) was developed to provide a straightforward
assessment of a ship’s intact stability parameters based
on the metacentric height (GM).
The purpose of SEMIS is to offer a simple
supplementary method for evaluating stability to
captains, officers, and crew members, particularly in
situations where loading software or specialized
equipment is unavailable, as calculating all intact
stability parameters is usually complex.
According to [37] SEMIS effectively assess a ship’s
stability using only GM. In the study [37] the regression
models of ship stability parameters was developed
based on 336 loading conditions of 19 model ships,
including mainly cargo ships like bulk carriers,
container ships, general cargo vessels and tankers. The
main particulars of model cargo ships are shown in
Table 1. and the mentioned regression models are
presented in Table 2.
Table 1. Model ships and loading conditions, based on Woo
et al. [37], p. 3
Model Ship
Number of
Scenarios
Range of
displacement [t]
Range of CB
[-]
Bulk carrier
ship
46
3640.5¬–233118.5
0.731–0.841
Container ship
93
8276.2–84257.0
0.545–0.662
Tanker ship
65
13589.2–364896.0
0.728–0.813
General cargo
ship
4
3498.5–6580.2
0.731–0.785
Table 2. Empirical formulas related to GM, based on Woo et
al. [37], p. 6
No.
Stability
parameter
Empirical Formula According to GM
[37],
R
2
1
A0°-30°
y1=0.1341GM+0.0216
0.9942
2
A0°-40°
y2=0.2214GM+0.0470
0.9870
3
A30°-40°
y3=0.0873GM+0.0253
0.9676
4
GZ
30
y4=0.5261GM+0.1145
0.9611
5
GZmax
y5=0.4775GM+37.043
0.0972
6
b/a
y6=-0.0121GM+4.4431
0.0009
7
Area\ "a"
y7=0.0766GM
0.9680
8
Area\ "b"
y8=0.307GM
0.9741
9
0
y9=1/(0.15689GM+0.05209)
0.58029
In general, the SEMIS procedure consists of four
phases aimed at evaluating seven intact stability
parameters based on GM, followed by determining
whether the criteria are met or not. The SEMIS
procedure of ship stability assessment is shown in
Figure 1.
Figure 1. Concept of SEMIS [37] p. 7
Phase 1 – Calculation of the ship’s GM. The
metacentric height (GM) can be calculated based on the
known distribution of masses on board [3,13,33,36]. It
can also be estimated from the ship’s roll period [8],
Phase 2 – Stability parameters are calculated
according to the empirical models presented in [37]. A
281
summary of these empirical models is provided in
Table 3.
Phase 3 – Each stability parameter is evaluated and
compared with the corresponding criterion values.
These values, derived from stability criteria, are
presented in Table 3.
Phase 4 – The overall stability of the ship is assessed,
including whether the stability criteria are met or not.
2.2 Intact Stability Assessment
The assessment of stability is fundamental to ensuring
safety of ship [9,18,23]. The biggest challenge in this
process is developing a loading plan, which directly
affects the ship’s stability, as the number of possible
loading conditions during operation is theoretically
unlimited due to continuous variations in parameters
such as ships center of gravity being and resultant of
mass distribution on board [32]. Problems related to
ship stability are widely researched [1,5,14–16,19,31],
which indicates that the issue is still not fully resolves.
Currently, the Intact Stability code (IS code) represents
the international mandatory regulation applicable to
all types of ships [28]. This is a formal assessment
method, an extract of stability criteria that present
specific inequalities shown in Table 3. In this study,
ship stability will be evaluated in accordance with the
Intact Stability Code (IS Code).
Table 3. IMO intact stability parameters and criteria found
from [11] and arranged according to interpretations in
[18,33,37]
Stability parameter
Criteria
Area (A) under the righting arm curve
([11], §2.2.1)
A0°-30° 0.055 m∙rad
A0°-40° 0.095 m∙rad
A30°-40° 0.030 m∙rad
(1)
(2)
(3)
Righting arm (GZ) ([11], §2.2.2)
GZ
30
0.20 m
(4)
Angle corresponding to the maximum of
the righting arms ([11], §2.2.3)
GZmax 25°
(5)
Initial metacentric height (GM) ([11], §2.2.1)
GM 0.15 m
(6)
Weather criterion. ([11], §2.3.1.4)
b/a 1
(7)
List of the ship under static wind pressure
perpendicular to the plane of symmetry.
([11], §2.3.1.2)
0 16°
0 0.8∙
zP
(8)
(9)
3 RESULTS
This analysis concerns the 13593 DWT ship of B–354
series type [22] which is a multipurpose vessel for
carrying bulk cargo and general cargo as well
containers. The B-354 vessel has been used as a case of
study in various maritime scientific research,
particularly focusing on its stability and dynamic
behavior, as documented in publications [12,20,21].
The main particulars of the B-354, including the
analyzed displacement and block coefficient (CB), are
presented in Table 4. When compared to the models
analyzed in [37], this vessel generally falls within the
displacement and CB ranges shown in Table 1.
Therefore, the SEMIS model can be applied to this ship.
Table 4. Particulars of B-354 ship
Model Ship
Range of displacement [t]
Range of CB [-]
B-354
8159–20767
0.644–0.718
The present research work flow is as follows:
1. Calculation of stability parameters for a set of
loading conditions of B–354 ship,
2. Preparation of regression lines with R² tests and
formulation of equations as per concept described
in [37],
3. Stability assessment and comparison based on
degree of compliance,
4. Error analysis between models derived by [37] and
those derived for B-354 ship.
Calculations of stability parameters were
performed using a custom spreadsheet developed with
VBA programming in Microsoft Excel, a widely
adopted tool for automating data processing and
implementing computational models in scientific
research [4,17,26,29,40].
Stability parameters were computed for 1314
distinct loading conditions, starting from displacement
and corresponding drafts ranging from 8.50 m to 9.14
m (the maximum permissible summer load draft of the
investigated ship) and transverse metacentric heights
between 0.08 m and 3.00 m. All data presented are the
author’s elaboration and are assumed to represent
realistic operational scenarios that may occur during
exploitation. Figures 2–10 present a comprehensive set
of stability parameters, defined by Equations (1–9), for
all 1314 loading conditions, illustrating their variation
as functions of the ship’s metacentric height.
Each graph includes the calculated stability
parameters, the regression line, and the coefficient of
determination (R²) as a measure of fit quality. The use
of R² was chosen because it provides an interpretable
and standardized metric for assessing the
compatibility of regression models with observed data
as argued by Chicco et al [7].
Figure 2. GM versus A(0-30)
Figure 3. GM versus A(0-40)
282
Figure 4. GM versus A(30-40)
Figure 5. GM versus GZ
30
Figure 6. GM versus (GZmax)
Figure 7. GM versus b/a
Figure 8. GM versus area „a”
Figure 9. GM versus area „b”
Figure 10. GM versus 0
Table 5 presents the regression models derived
from the data shown in Figure 2–10. The high value of
R
2
indicates good agreement between the calculated
values and the regression model, as values of R
2
close
to 1 [30], reveals to best fit, however, a low R
2
is
observed for the b/a ratio parameter (Figure 7). To
address this, the approach used in previous studies
[37,38] was used in which we separately calculated
area “a” under the GZ curve (Figure 8) and area “b”
under the GZ curve (Figure 9). Such an approach
shows good agreement with the R2 value. Later, the b/a
ratio for the weather criterion will be calculated
according to the derived models of area “a” and “b”
expressed as their quotient.
Table 5. Empirical formulas according to GM, B–354 ship.
Author elaboration.
No.
Stability parameter
Empirical Formula According to GM
R
2
1
A0°-30°
y1=0.1336GM+0.0230
0.9948
2
A0°-40°
y2=0.2334GM+0.0453
0.9926
3
A30°-40°
y3=0.0997GM+0.0224
0.9891
4
GZ
30
y4=0.5000GM+0.1042
0.9931
5
GZmax
y5=5.3776GM+41.746
0.9753
6
b/a
y6=-0.4005GM+5.8894
0.1816
7
Area\ "a"
y7=0.0724GM-0.0019
0.9943
8
Area\ "b"
y8=0.3550GM+0.0090
0.9931
9
0
y9=2.2499GM
-0.869
0.9841
Table 6 presents the results of 15 loading scenarios
evaluated for compliance with the IMO Intact Stability
Criteria. It was decided to examine full load condition
of the ship at design draught T = 9.14 m, and different
GM which may appear during exploitation.
Additionally, there were included 2 loading scenarios
with primary non-compliance with criteria GM < 0.15
m (6). The second column in Table 6 indicates overall
compliance, where “0” denotes non-compliance with
stability requirements and “1” denotes full compliance.
The remaining columns list stability parameters
calculated and compared to the stability standards
specified in Table 3.
Each parameter is referenced to the corresponding
criterion or formula, as indicated by the numbering in
parentheses (e.g., (1), (2), (3)). Cells highlighted in red
283
indicate non-compliance with the respective criterion.
Values listed in Table 6 stands for reference purposes
as exact values.
Table 6. Ship stability parameters and compliance
evaluation under IMO Intact Stability Code.
Loading
scenario
Compliance
with IMO
A₍₀₋₃₀) [m
⋅rad]
A₍₀₋₄₀) [m⋅rad]
A₍₃₀₋₄₀)
[m⋅rad]
φGZ(30°) [m]
φGZ
ₘₐₓ
[°]
GM [m]
b/a [-]
φ₀≤ 16° [°]
φ₀≤ 0.8⋅φzP
[°]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
1
0
0.027
0.048
0.022
0.11
38.1
0.1
2.1
12.4
12
2
0
0.032
0.058
0.026
0.13
38.8
0.14
2.8
10.1
12
3
0
0.033
0.060
0.027
0.14
39.0
0.15
3.0
9.6
12
4
0
0.040
0.072
0.032
0.16
39.8
0.2
3.8
7.9
12
5
0
0.051
0.090
0.040
0.20
41.0
0.28
4.9
6.2
12
6
1
0.079
0.140
0.061
0.31
44.1
0.49
5.7
4.0
12
7
1
0.080
0.142
0.062
0.31
44.3
0.5
5.6
3.9
12
8
1
0.119
0.210
0.091
0.46
46.4
0.79
5.0
2.6
12
9
1
0.154
0.270
0.117
0.59
47.9
1.05
4.8
2.0
12
10
1
0.179
0.315
0.135
0.68
48.9
1.24
4.7
1.7
12
11
1
0.186
0.326
0.140
0.71
49.2
1.29
4.7
1.7
12
12
1
0.212
0.373
0.160
0.81
50.2
1.49
4.6
1.5
12
13
1
0.247
0.434
0.186
0.94
51.5
1.75
4.7
1.3
12
14
1
0.266
0.466
0.200
1.01
52.2
1.89
4.7
1.2
12
15
1
0.283
0.497
0.213
1.07
52.7
2.02
4.7
1.1
12
where: φzP ¬– angle of deck innmersion see ([11], §2.3.1.2).
Stability parameters were calculated for each
criterion for the loading scenarios listed in Table 6
using the empirical model from Table 2 and the
empirical model derived for the investigated ship, as
shown in Table 5. The values in Table 7 present the
percentage of fulfillment of stability criteria, calculated
using Equation (1) for each model:
n
i
i1
δ
η 100%
n
=
=
(1)
where:
– percentage of criteria passed, n – total
number of criteria (see Eqs. (1–9)),
i – indicator
function equals 1 if criterion i is satisfied, and 0
otherwise.
Table 7. Degree of compliance with IMO stability criteria:
Comparison of exact method vs model [37], and current
study model.
Loading
scenario
Exact
assessment
Empirical model
(from [37])
Empirical model
(Current study)
1
33 %
44 %
33 %
2
44 %
56 %
44 %
3
44 %
67 %
67 %
4
67 %
89 %
89 %
5
89 %
100 %
89 %
6
100 %
100 %
100 %
7
100 %
100 %
100 %
8
100 %
100 %
100 %
9
100 %
100 %
100 %
10
100 %
100 %
100 %
11
100 %
100 %
100 %
12
100 %
100 %
100 %
13
100 %
100 %
100 %
14
100 %
100 %
100 %
15
100 %
100 %
100 %
Table 7 shows that the dedicated model for the B–
354 ship closely matches the overall stability
assessment in identifying compliance with IMO
criteria. Minor discrepancies occur for loading
conditions 3 and 4, where the dedicated model slightly
overestimates compliance. In contrast, the literature-
based model exhibits significant deviations and, for
loading condition 5, incorrectly predicts full
compliance within stability criteria.
Based on definition of relative errors (RE) [6], they
were calculated to show the differences between the
selected methods. Figure 11¬–19 illustrate RE values
for key stability parameters across different loading
scenarios. Orange points correspond to the vessel-
specific model from this study (Table 5), while blue
points represent the literature-based model (Table 2).
This comparison allows for assessing the impact of
model adaptation to a specific vessel on the accuracy of
the results. Calculating RE enables a quantitative
evaluation of how much the results of both models
deviate from the exact stability calculations and in
which loading scenarios the differences are most
significant.
Figure 11. RE for parameter A(0-30)
Figure 12. RE for parameter A(0-40)
Figure 13. RE for parameter A(30-40)
284
Figure 14. RE for parameter GZ
30
Figure 15. RE for parameter (GZmax)
Figure 16. RE for parameter b/a
Figure 17. RE for parameter area ”a”
Figure 18. RE for parameter area “b”
Figure 19. RE for parameter 0
Analysis of Figure 11¬–19 shows that the dedicated
model (orange points) achieves consistently lower
relative error (RE) values across most loading
conditions, particularly for weather criterion
parameters illustrated in Figure 16¬–19 In contrast, the
literature-based model (blue points) exhibits
substantially larger deviations, limiting its
applicability for precise stability assessments.
Both models demonstrate a pronounced increase in
discrepancies for loading scenarios 1 to 5, where RE
values differ substantially compared to scenarios 6 to
15. This pattern suggests that both models are less
reliable under conditions where the metacentric height
falls below approximately 0.30 m. The analysis
identifies GM ≈ 0.30 m as a critical threshold below
which prediction errors increase sharply.
The largest errors are observed for stability
parameters related to weather criteria, where both
models show significant deviations from exact
calculations. Despite the differences in absolute RE
values between the models, a similar trend in error
variation with respect to loading condition is observed.
In both cases, errors are largest at low GM levels
(scenarios 1–5) and decrease progressively as GM
increases (scenarios 6–15). This consistency in error
trends indicates that both models correctly capture the
general influence of loading condition on stability
parameters, although they differ significantly in the
magnitude of deviation from reference values.
4 DISSCUSSION
The comparative analysis between the SEMIS-based
empirical models and exact stability calculations
reveals significant insights into the methodology's
practical applicability. The dedicated model developed
specifically for the B-354 vessel (Table 5) demonstrates
markedly superior performance compared to the
literature-based model from Woo et al. [37]. This
superiority is particularly evident in the relative error
(RE) analysis presented in Figures 11-19, where the
dedicated model (orange points) consistently achieves
lower RE values across most loading conditions. The
high R² values obtained for the vessel-specific model
validate the fundamental SEMIS approach, with
coefficients ranging from 0.9753 to 0.9948 for most
stability parameters.
Notably, the R² value for the angle corresponding to
maximum GZ reaches 0.9753, while area parameters
A₀₋₃₀ and A₀₋₄₀ achieve exceptional correlations of
0.9948 and 0.9926, respectively. These values
significantly exceed those reported in the original
285
SEMIS study [37], where corresponding R² values were
0.0972, 0.9942, and 0.9870, demonstrating the clear
benefits of vessel-specific calibration.
The analysis of Figures 11-19 reveals a pronounced
pattern in model accuracy that correlates directly with
loading conditions. Both the dedicated model (orange
points) and literature-based model (blue points)
exhibit substantially increased relative errors for
loading scenarios 1-5, corresponding to metacentric
heights below approximately 0.30 m. This critical
threshold is consistently observed across all stability
parameters, as demonstrated in the RE plots. For the
area under the righting arm curve from 0° to 30°
(Figure 11), the dedicated model shows RE values
exceeding 20% for loading conditions 1-3, while
maintaining errors below 10% for loading scenarios 6–
15. Similarly, Figure 12 illustrates that the A₀₋₄₀
parameter exhibits comparable behavior, with the
literature model showing even more pronounced
deviations, reaching RE values above 40% in critical
loading conditions.
The weather criterion parameters present the most
challenging assessment scenario within the SEMIS
framework. Figure 16 demonstrates that the b/a ratio
exhibits the highest relative errors among all
parameters, with both models showing substantial
deviations that exceed 50% for low-GM conditions.
This finding is particularly concerning given that the
direct b/a regression yielded an unacceptably low R²
value of 0.1816 (Table 5), necessitating the separate
modeling approach for areas "a" and "b" illustrated in
Figures 8-9. Despite the improved individual
correlations achieved for areas "a" and "b" (R² = 0.9943
and 0.9931, respectively), the calculated b/a ratio
continues to exhibit substantial errors, suggesting that
weather criterion assessment requires more
conservative approach.
The compliance analysis presented in Table 6
illustrates the practical implications of these findings.
Loading scenarios 1-5, characterized by GM values
below 0.30 m, consistently fail to meet multiple IMO
criteria (highlighted in red), particularly criteria (1), (2),
and (3) related to area under the righting arm curve.
The transition to full compliance occurs at loading
scenario 6 (GM = 0.49 m), establishing a clear
operational threshold for safe loading conditions.
Table 7 provides compelling evidence of the
dedicated model's superior performance in compliance
assessment accuracy. The vessel-specific model
demonstrates remarkable agreement with exact
assessments, correctly identifying compliance status in
13 out of 15 loading scenarios. The minor discrepancies
occur in loading conditions 3 and 4, where the
dedicated model slightly overestimates compliance
(56% vs. 44% and 89% vs. 67%, respectively). In stark
contrast, the literature-based model exhibits significant
deviations, most notably in loading condition 5, where
it incorrectly predicts 100% compliance when the exact
assessment indicates only 89% compliance. This false
positive represents a critical safety concern, as it could
lead to operational decisions based on incorrect
stability assessments.
According to the histogram of metacentric heights
presented in Jachowski et al. [8] (p. 179), the most
frequently occurring GM values in operational practice
range from 0.25 to 2.2 m. This operational range
corresponds to loading scenarios 5-15 in the current
study, where the dedicated model demonstrates
acceptable accuracy with errors generally remaining
within ±20%. Figure 19, showing RE values for the
initial list angle φ₀, illustrates this operational
reliability, with the dedicated model maintaining
errors below 15% for the typical operational range.
However, the sharp increase in errors below GM = 0.30
m (loading scenarios 1-5) coincides with the lower
boundary of typical operational conditions,
highlighting the critical importance of accurate
assessment.
The comparison between vessel-specific and
literature-based models clearly demonstrates the
substantial benefits of model adaptation. While the
original SEMIS model was developed using 336
loading conditions from 19 different vessel types
(Table 1), the current study's approach using 1314
conditions specific to the B-354 vessel yields
substantially improved accuracy across all assessed
parameters. However, this improvement comes with
practical limitations, as the vessel-specific approach
requires extensive computational effort to generate the
necessary database of loading conditions, potentially
limiting widespread implementation.
The findings presented in Table 6 and Table 7,
combined with the RE analysis in Figure 11¬–19, have
significant implications for maritime safety. The SEMIS
methodology's tendency to overestimate compliance in
critical loading conditions poses potential safety risks
if used as a primary assessment tool.
The consistent pattern of increased errors in low-
GM conditions across all parameters indicates that
SEMIS reliability deteriorates precisely when accurate
stability assessment is most critical for safety. This
limitation necessitates careful consideration of the
methodology's appropriate application scope and the
implementation of safeguards to prevent misuse in
critical stability scenarios.
The regression-based approach underlying SEMIS
assumes linear relationships between GM and various
stability parameters. While this assumption holds
reasonably well for most parameters within typical
operational ranges (as evidenced by high R² values in
Table 5), the deteriorating accuracy at low GM values
suggests that non-linear effects become significant in
critical stability states. The particularly poor
performance of weather criterion assessment (Figure 7)
indicates that the b/a ratio may be influenced by factors
beyond GM alone. According to Figure 20–21 the GZ
curve range changes rapidly in function of GM (from
55 degrees to 60, as well GZmax 0.14 m up to 0.26 m).
Figure 20. GZ curve of B-354, T=9.14 m, GM = 0.10 m. Author
elaboration
286
Figure 21. GZ curve of B-354, T=9.14 m, GM = 0.30 m. Author
elaboration
As well angle of roll to windward due to wave
action φ₁ changes rapidly in function of GM as shown
on Figure 22. According to Figure 7, derived using the
SEMIS method, it can be observed that with respect to
the weather criterion, when the b/a ratio over the GM
value is less than 0.30 m, the b/a ratio decreases rapidly
going towards b/a going to zero.
This is an important consideration for vessel
operation, as it may justify introducing additional
regulatory criteria related to the weather criterion for a
particular vessel. Furthermore, the angle of roll to
windward due to wave action φ₁ determined by the
ISC also has an impact: at low GM values, the
amplitudes are small, whereas an increase in GM tends
to make the roll amplitude more stable which briefly
gives an explanation of nonlinearity of b/a ratio as well
its peak value.
Figure 22. Angle of roll to windward due to wave action of a
ship B–354 with T = 9.14 m for various values of transverse
GM
5 CONCLUSSIONS
The SEMIS methodology provides a practical and
rapid approach for preliminary intact stability
assessment based solely on metacentric height (GM),
offering potential benefits in operational scenarios
where conventional stability software is unavailable.
For the analyzed 13593 DWT general cargo vessel,
SEMIS demonstrated strong correlation with IMO
Intact Stability Code criteria within typical operational
GM ranges, confirming its usefulness for quick checks
under normal loading conditions.
However, significant limitations were identified in
low-GM states, which may occur due to atypical
loading or emergency situations. In such cases, SEMIS
can produce misleading results, overestimating
compliance and underestimating critical stability risks,
thereby creating a false sense of safety. This behavior is
linked to the nonlinear nature of stability parameters at
low GM values and cannot be fully corrected by vessel-
specific linear regression models. Consequently,
SEMIS should never be considered a substitute for
comprehensive stability calculations or as a design or
emergency assessment tool; its application must
remain restricted to preliminary evaluations in intact
conditions with GM above safe thresholds.
REFERENCES
[1] Andrei, C. A proposed new generation of intact stability
criteria for assessment of ship stability in longitudinal
waves. IOP Conference Series: Materials Science and
Engineering, 2017, 227 ,DOI: 10.1088/1757-
899X/227/1/012005.
[2] Bačkalov, I.; Bulian, G.; Cichowicz, J.; Eliopoulou, E.;
Konovessis, D.; Leguen, J.-F.; Rosén, A.; Themelis, N. Ship
stability, dynamics and safety: Status and perspectives
from a review of recent STAB conferences and ISSW
events. Ocean Engineering 2016, pp. 312–349 ,DOI:
10.1016/j.oceaneng.2016.02.016.
[3] Barrass , C.B. and Derrett, D.R. Ship Stability For Masters
And Mates 6th edition. Elsevier; 2006; ISBN 0-7506-6784-
2.
[4] Bauzon, J.; Murphy, C.; Wahi-Gururaj, S. Using macros in
microsoft excel to facilitate cleaning of research data.
Journal of Community Hospital Internal Medicine
Perspectives 2021, 11, pp. 653–657 ,DOI:
10.1080/20009666.2021.1954282.
[5] Bulian, G.; Francescutto, A. Level 1 vulnerability criterion
for the dead ship condition: A practical methodology for
embedding operational limitations. Ocean Engineering
2023, 113868 ,DOI: 10.1016/j.oceaneng.2023.113868.
[6] Burden, R.L.; Faires, J.D. Numerical analysis; 9. ed.,
International ed.; Brooks/Cole, Cengage Learning:
Boston, 2011; ISBN 978-0-538-73564-3.
[7] Chicco, D.; Warrens, M.J.; Jurman, G. The coefficient of
determination R-squared is more informative than
SMAPE, MAE, MAPE, MSE and RMSE in regression
analysis evaluation. PeerJ Computer Science 2021,DOI:
10.7717/peerj-cs.623.
[8] Dudziak, J. Teoria okrętu; Wyd. 2. popr. i uzup.; Fundacja
Promocji Przemysłu Okrętowego i Gospodarki Morskiej:
Gdańsk, 2008; ISBN 978-83-60584-09-5.
[9] Hanzu-Pazara, R.; Duse; Varsami, C.; Andrei, C.;
Dumitrache, R. The influence of ship’s stability on safety
of navigation. IOP Conference Series: Materials Science
and Engineering 2016 ,DOI: 10.1088/1757-
899X/145/8/082019.
[10] Im, N.-K.; Choe, H. A quantitative methodology for
evaluating the ship stability using the index for marine
ship intact stability assessment model. International
Journal of Naval Architecture and Ocean Engineering
2021, pp. 246–259 ,DOI: 10.1016/j.ijnaoe.2021.01.005.
[11] IMO Res. MSC.267(85). Adoption of the international
code on intact stability, 2008 (2008 IS CODE); 2008; Vol.
267
[12] Jachowski, J.; Krata, P.; Wawrzyński, W.; Więckiewicz,
W. Analysis of dynamic heeling moment due to liquid
sloshing in partly filled ship’s tanks for realistic range of
rolling periods – a case study. Journal of KONES.
Powertrain and Transport 2015, pp. 177–184 ,DOI:
10.5604/12314005.1138117.
[13] Kabaciński, J. Stateczność i niezatapialność statku;
Szczecin, 1993
[14] Kacprzak, P. Application of 2nd generation stability code
for 7600DWT bulk carrier with high value of GM , being
in dead ship condition in irregular waves. Scientific
Journals of the Maritime University of Szczecin 2023, pp.
14–19 ,DOI: 10.17402/569.
287
[15] Kacprzak, P. Stability Analysis of a Bulk Carrier under
Damage Scenarios during the Loading of Polymetallic
Nodules in the Clarion–Clipperton Zone. TransNav, the
International Journal on Marine Navigation and Safety of
Sea Transportation 2025, pp. 431–438 ,DOI:
10.12716/1001.19.02.12.
[16] Kacprzak, P. Stability evaluation during loading
simulation of bulk carriers in the Clarion-Clipperton
Zone using a modified weather criterion. Scientific
Journals of the Maritime University of Szczecin 2024, pp.
14–22 ,DOI: 10.17402/620.
[17] Kalwar, M.A.; Wassan, A.N.; Phul, Z.; Wadho, M.H.;
Malik, T.S.; Khan, M.A. Automation of material cost
comparative analysis report using VBA Excel: a case of
footwear company of Lahore. Journal of Applied
Research in Technology & Engineering 2023, pp. 13–23
,DOI: 10.4995/jarte.2023.18776.
[18] Kaup, M.; Łozowicka, D.; Baszak, K.; Ślączka, W. An
Assessment of Stability and Strength of a Container Ship
for Safety Compliance in Cargo Loading Plans. Applied
Sciences 2023 ,DOI: 10.3390/app14010345.
[19] Kobyliński, L. Stability of ships: risk assessment due
hazards created by forces of the sea. Archives of Civil and
Mechanical Engineering 2008, pp. 37–45 ,DOI:
10.1016/S1644-9665(12)60265-9.
[20] Krata, P. Variations of Ship’s Deck Elevation Due to
Stochastic Process of Containers Loading. TransNav, the
International Journal on Marine Navigation and Safety of
Sea Transportation 2015, pp. 467–473 ,DOI:
10.12716/1001.09.04.02.
[21] Krata, P.; Szpytko, J.; Weintrit, A. Computing of
momentary ship’s deck elevation for the purpose of
gantry control during cargo handling operations in sea
ports. Scientific Journals of the Maritime University of
Szczecin 2012, 29, 81–87.
[22] Kucharski, S. Semikontenerowiec B-354; Szkoła Morska
w Gdyni SP. Z O. O, 2008; ISBN 978-83-916956-5-4.
[23] Lapa, K. Assessment of the Stability of Passenger Ships
in Coastal Navigation in Case of Lacking Ship Geometry
Data. Transactions on Maritime Science 2020 ,DOI:
10.7225/toms.v09.n02.002.
[24] Mentes, A.; Akyildiz, H. Criticality analysis of
probabilistic damage stability of ships with aggregation
operators and additive ratio assessment. Ocean
Engineering 2023 ,DOI: 10.1016/j.oceaneng.2022.113577.
[25] Munakata, S.; Takagaki, K.; Umeda, N.; Koike, H.; Sakai,
M.; Maki, A.; Manabe, K.; Matsuda, A. An investigation
into false-negative cases for low-freeboard ships in the
vulnerability criteria of dead ship stability. Ocean
Engineering 2022 ,DOI: 10.1016/j.oceaneng.2022.113130.
[26] Naim, N. Application of Excel VBA in Physics
Education: A Case Study of Vector Field Simulation. In
Proceedings of the 3rd International Conference on
Mathematics and Science Education 2025 , DOI:
10.2991/978-2-38476-402-0_9.
[27] Park, K.; Ku, J.; Lee, J.; Ku, N. Real-time ship stability
evaluation program through deterministic method based
on second-generation intact stability. International
Journal of Naval Architecture and Ocean Engineering
2023, DOI: 10.1016/j.ijnaoe.2023.100526.
[28] Petacco, N.; Gualeni, P. Evaluation by a Quantitative
Index about Intact Stability Performance in Waves of a Set
of Megayacht Units. Journal of Marine Science and
Engineering 2023 ,DOI: 10.3390/jmse11040814.
[29] Safitri, A.D.; Lesmono, A.D.; Maryani; Wardoyo, A.A.
Development of learning media using VBA excel in
physical learning in senior high school. Journal of
Physics: Conference Series 2020, DOI: 10.1088/1742-
6596/1563/1/012035.
[30] Sapra, R.L. Using R2 with caution. Current Medicine
Research and Practice 2014, pp.130–134 ,DOI:
10.1016/j.cmrp.2014.06.002.
[31] Shigunov, V. Intact stability operational measures:
Criteria, standards and examples. Ocean Engineering
2023, DOI: 10.1016/j.oceaneng.2023.114446.
[32] Stanca, C.; Acomi, N.; Ancuta, C.; Georgescu, S.
Comparative analysis of different loading conditions on
large container ships from the perspective of the stability
requirement. IOP Conference Series: Materials Science
and Engineering 2015, DOI: 10.1088/1757-
899X/95/1/012072.
[33] Szozda, Z. Stateczność statku morskiego; Akademia
Morska w Szczecinie: Szczecin, 2006;
[34] Szozda, Z.; Krata, P. Towards evaluation of the second
generation intact stability criteria - Examination of a
fishing vessel vulnerability to surf-riding, based on
historical capsizing. Ocean Engineering 2022 ,DOI:
10.1016/j.oceaneng.2022.110796.
[35] Vidić, M.; Bačkalov, I. An analysis of stability
requirements for large inland passenger ships. Ocean
Engineering 2022, DOI: 10.1016/j.oceaneng.2022.112148.
[36] Więckiewicz, W. Podstawy Pływalności i Stateczności
statków Handlowych; Wydawnictwo Akademii Morskiej
w Gdyni, 2006; ISBN 83-7421-036-2.
[37] Woo, D.; Choe, H.; Im, N.-K. Analysis of the Relationship
between GM and IMO Intact Stability Parameters to
Propose Simple Evaluation Methodology. Journal of
Marine Science and Engineering 2021, DOI:
10.3390/jmse9070735.
[38] Woo, D.; Im, N.-K. A Methodology for Simply
Evaluating the Safety of a Passenger Ship Stability Using
the Index for the Intact Stability Appraisal Module.
Sensors 2022, DOI: 10.3390/s22051938.
[39] Zyczkowski, M.; Krata, P.; Szozda, Z. Implementation of
the operational guidance as a part of the second
generation intact stability criteria to the deterministic ship
weather routing. Ocean Engineering 2025, DOI:
10.1016/j.oceaneng.2025.121455.
[40] Zhaohao, S.; Intelligent Big Data Analytics: A
Managerial Perspective. Managerial Perspectives on
Intelligent Big Data Analytics, 2019, DOI: 10.4018/978-1-
5225-7277-0.
