Stability of the Ship Using Intact Stability Criteria and Empirical
Formulas
ALEXANDRU-STEFAN BACIOIU
IONELA GOIA
Transport Faculty
University Politehnica of Bucharest
ROMANIA
Abstract: Regarding ship stability and stability elements various problems should be addressed, however this
paper talks about some of the important, however often given less importance. It is a must onboard a ship to
recognize the stability problems which are not always present but they can be an issue which should be
addressed. Regarding ship stability issues there are various software which analyse and give an assessment
which is checked by the end user. A study on ship hull, stability and stability elements is presented in the paper.
Key-Words:autoship, stability, ship, shipping, intact stability criteria, imo
Received: August 15, 2021. Revised: April 11, 2022. Accepted: May 13, 2022. Published: June 24, 2022.
1 Introduction
Stability of the ship is in a direct link with the
logistical matters and the pressure on the
construction and stability elements due to increasing
demand of the goods carried. The cost of
transporting goods to centres of demand from
warehouses and logistical area need to be minimized
because this forms a part which is essential
regarding profitability for logistics companies. [2]
The transportation problem is a type of linear
programming problem made to minimize the cost of
distribution for products from shippers to receivers.
The most common practical application is of
moving a product from point A to point B or from
several points to several points depending on the
complexity of the factors involved. There are also
some constraints which must be satisfied like: the
number of transported goods must be equal or match
the demand for the locations, the number of goods
transported must be less of equal to the total supply,
the number of units to be transported must be
greater or equal to zero, therefore no negative values
are accepted. There is also the case of balanced
transportation problem, where the supply is equal to
the demand. This can be seen as a tool for allocating
resources in an optimal way, basically to optimize
the transfer of goods between ships and port.
2 Problem Formulation
It is important onboard a ship to recognize the
stability problems which are not always present but
they can be an issue which should be addressed.
Regarding ship stability issues there are various
software which analyse and give an assessment
which is checked by the end user. Programs like
Autoship, Autohydro or Autopower are used for
surface modelling, hydrostatics and stability
prediction, resistence and power prediction. Some of
the functions are intact stability calculation and
reporting, advanced reporting options for
hydrostatics, hull lines, damage stability, advanced
loading condition, floodable calculations,
probabilistic and deterministic calculations.
Therefore a good analysis of the ship stability
regarding cargo loading or unloading is to be
considered.[5]
3 Problem Solution
In the figures 1, 2 and 3 can be seen a ship structure
for stability using Autoship. This structure is for a
medium range ship, however can be scaled for a
bigger or smaller ship.
Fig. 1 Info about the project in Autoship
Engineering World
DOI:10.37394/232025.2022.4.1
Alexandru-Stefan Bacioiu, Ionela Goia
E-ISSN: 2692-5079
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Volume 4, 2022
Fig. 2 Ship view in Autoship
Fig. 3 Ship view in Autoship
Floating surface area calculation
The formula used to perform the calculation is:

󰇟   󰇠󰇟󰇠 (1)
- the half-widths measured at the
buttock i and the waterline j
 - distance between 2 buttocks:

Calculation of the abscissa of the geometric center
of the floating surface
The formula used to perform the calculation is:
 
 󰇣󰇛 󰇜 󰇛
󰇜󰇛 󰇜
󰇛 󰇜󰇤󰇟󰇠 (2)
Hull volume calculation
The formula used to perform the calculation is:
󰇟 󰇛 󰇜󰇛 󰇜
󰇛 󰇜󰇛
󰇜󰇠󰇟󰇠󰇛󰇜
t = draft / number of waterlines
Calculation of ship displacement
The formula used to perform the calculation is:
 , where ρ is the density of water and V is
the volume of the hull
Calculation of the height of the geometric center of
the hull.
The formula used to perform the calculation is:

󰇟 󰇛 󰇜
󰇛 󰇜󰇛
󰇜󰇠󰇟󰇠 (4)
There are systems of a larger complexity that appear
frequently appear in the present times in science,
technology and real life situations and many
different and constantly changing factors are usually
involved. As a result the data obtained from their
operation mechanisms cannot be easily determined
precisely and in practice estimates of them are used.
As this is the case with above formulas. [7]
There is also the need to talk about artificial
intelligence which can help in identify stability
problems. Artificial intelligence is technology
relatively new with high potential to modify the
world as we know it. It finds applications in many
fields of human activity, including services,
industry, education, social networks, transportation,
among others. The objective is to change the way
the artificial intelligence is trained and to add
specific conditions which are mostly rare, therefore
to develop a better ability to forecast any dangerous
situation.
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DOI:10.37394/232025.2022.4.1
Alexandru-Stefan Bacioiu, Ionela Goia
E-ISSN: 2692-5079
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Volume 4, 2022
There are specific IMO criteria for the stability of
the ships where is mentioned the minimum GM to
be maintained in order to maintain an intact stability
of the ship and can be found in the Intact Stability
Code which have the purpose of recommend
stability criteria and other measures for ensuring the
safe operation of all ships to minimize the risk to
such ships, to the personnel on board and the
environment. Initial GM or metacentric height
should not be less than 0.15 m. In simple terms, to
increase the stability of a ship the containers which
are heavier should be placed at a lower position in
order to increase the GM.[3]
Height of center of gravity
The formula used to perform the calculation is:




 󰇛󰇜
Table 1 Calculation of center of gravity
Notation
Value
S.I.
Uni
t

Empty ship
hull center
elevation
(value)
m
zi
m

Displacement
of empty ship
(value)
t
mi
t
Using table 1 and formula (5) the center of gravity
can be calculated depending on the cargoes onboard,
their elevation and weight.
In engineering, the foundation is a special element
of a building. In each construction a special group of
elements is designed and constructed, which is used
for the safe transfer of superstructure loads. [6]
Analyzing the data of vessels that behaved well, and
especially the data of vessels that did not survive
adverse conditions, various researchers and
regulatory authorities defined criteria for deciding if
the stability of a vessel is satisfactory. Therefore, it
is important to understand that the existing stability
regulations are codes of practice that provide
reasonable safety margins without giving 100%
guaranty that the vessel which meets the
requirements can survive all challenges.[4]
According to the International Code on Intact
stability, 2008, the following criteria are mandatory
for passenger and cargo ships constructed on or after
1st January 2010:[3]
1. The area under the righting lever curve (GZ
curve) should not be less than 0.055 metre-radians
up to 30° angle of heel.
2. The area under the righting lever curve (GZ
curve) should not be less than 0.09 metreradians up
to 40° angle of heel or the angle of downflooding if
this is less than 40°.
3. The area under the righting curve between the
angles of heel of 30° and 40° or between 30° and the
angle of downflooding if this angle is less than 40°,
should not be less than 0.03 metre-radians.
4. The righting lever GZ should be minimum 0.20 m
at an angle of heel equal to or greater than 30°.
5. The maximum righting arm should occur at an
angle of heel preferably exceeding 30° but not less
than 25°.
6. The initial metacentric height GMo should not be
less than 0.15 m.
7. Severe wind and rolling criterion (weather
criterion)
In addition to the criteria described above, ships
covered by the 2008 IS Code should meet a weather
criterion that considers the effect of strong beam
wind and waves applied when the vessel is in dead
ship condition.
4 Conclusion
International maritime transport has grown both in
terms of supply and demand. Future research can be
expanded to the subject and to develop further
methods of increasing ship stability or to correct it
when is necessary. Stability of the ship is in direct
link to the stowage plan, cargoes carried onboard,
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Alexandru-Stefan Bacioiu, Ionela Goia
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Volume 4, 2022
ballast water and other weights onboard. A more
detailed paper can be developed starting from this
point regarding this matter. More to be done exists,
although this matter is also a practical one and
additional constraints are to be taken into account.
There is the need to discuss about ships used for
deep sea shipping and ships used for short sea
shipping, however this can be a problem of a higher
complexity and can be developed in future papers.
There is also the need to discuss the future of
shipping regarding stability nowadays. The pressure
on the shipping industry is constantly increasing,
therefore also this matter is at utmost importance.
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[2] Bichou, K. (2009). Port Operations,
Planning And Logistics. New York:
Informa Law from Routledge.
[3] IMO. International Convention for the
Safety of Life at Sea (SOLAS) 1974.
[4] Kang, J.-G., & Kim, Y.-D. (2002). Stowage
Planning in Maritime Container
Transportation. Journal of the Operational
Research Society 53 (4), 415–426.
[5] Meiswinkel, S. (2018). On Combinatorial
Optimization and Mechanism Design
Problems Arising at Container Ports.
Wiesbaden: Springer Gabler.
[6] Philotheos Lokkas, Emmanouil
Papadimitriou, Nikolaos Alamanis,
Grigorios Papageorgiou, Dimitrios
Christodoulou, Theodoros Chrisanidis,
"Significant Foundation Techniques for
Education: A Critical Analysis" WSEAS
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[7] Voskoglou Michael Gr., Data Evaluation in
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