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1 INTRODUCTION

Railway transport represents one of the most effective

and reliable kind of transport of passengers and goods

[1, 2]. Regarding land transport, railway transport has

known advantages, such as low resistance to

movement, high axle load, possibilities of transport of

large volumes of goods, ecology and high standard of

transport safety [3-5]. In comparison with road

transport, long trainsets provide lower air drag [6]

which together with low rolling resistance of a couple

of a railway wheel and a rail [7-9] contribute to high

efficiency and lower energy losses of railway transport

[10-12]. Modern designs of freight wagons allow to

transport many types of goods [13]. The significant

advantages of rail transport are even more pronounced

when it comes to long-distance transport between

countries. Here, the combination with shipping is also

advantageous [14-16], where it is possible to transport

many wagons by a railway ferry across the water

without the laborious unloading and reloading of

wagons on the other side of the coast [17].

The integration of Ukraine into the system of

international transport corridors necessitates the

creation of combined transport systems. In this regard,

railway ferry transportation has developed. Ukraine is

one of the countries of the Black Sea basin that uses this

type of transportation [18, 19].

The development of railway ferry connections in

Ukraine began in 1954. Later, railway ferry routes

connected Ukraine with Bulgaria, Georgia and Turkey.

Given the relevance of this type of transportation, an

increase of the number of railway ferry routes is

predicted not only in the Black Sea area, but also in

other world water areas.

Bulk and bulk cargoes are of the most frequently

transported cargoes in wagons by the sea. These

cargoes cause pressure on the walls of an open wagon.

In a case of sea transportation, this pressure exceeds the

magnitude of that which occurs during operation on

main tracks. This can cause not only damage of wagon

bodies, but also threaten the safety of their

transportation by sea.

Features of Determining the Expansion Forces of Bulk

Cargo Acting on the Wagon Body Walls When

Transported by a Railway Ferry

J. Dižo, J. Gerlici, A. Lovska, M. Blatnický & M. Bučko

University of Žilina, Žilina, Slovak Republic

ABSTRACT: The results of the study are aimed at improving the safety of wagons transportation by the sea and

the efficiency of rail ferry transportation. The article highlights the features of calculating the expansion forces of

bulk cargo acting on the wagon body during its transportation by the sea. When determining the expansion forces

of bulk cargo, it is proposed to consider the dynamic load, which also affects its value in conditions of side sway.

As an example, an application of this method to an open wagon loaded by coal during its transportation through

the Black Sea is given.

An algorithm for considering the forces of bulk cargo pushing against the walls of an open wagon body during

sea transportation is proposed.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 4

December 2025

DOI: 10.12716/1001.19.04.32

1328

Therefore, it is important to study the loading of

wagon bodies during railway ferry transportation.

This will contribute not only to the adaptation of their

structures to the given operating conditions, but also to

the increase of railway ferry transportation.

In the work by I. M. Zemlezyn [20], the case of

wagon loading wagon with the efforts of bulk cargo

expansion during transportation by railway ferry is

considered. It is shown that the pressure of bulk cargo

on the wagon body walls is a function of the roll angles

during side swaying and the accelerations that arise in

this case. It is assumed that the total acceleration value

is the same for all cargo particles, when the inertial

effects of the bulk cargo on the wagon walls are taken

into account. It was established from these studies that

the difference between the horizontal accelerations of

the cargo during fluctuations of the load centre at the

level of the wagon centre of gravity and at the floor

level does not exceed 2 to 2.5%, and vertical

accelerations do not depend on the height of the centre

of gravity above the level of a rail head. The

disadvantages of the above method of determining the

inertial load on the side wall of the wagon body are the

inability to consider the course angle of the wave in

relation to the body of the railway ferry, as well as the

wind load acting on the surface projection of the

railway ferry with wagon bodies placed on its upper

deck.

In work [21], the features of determining the impact

of bulk cargo on the wagon body walls are highlighted.

At the same time, the body load was studied using the

mathematical and computer modelling methods.

However, the author did not determine the pressure of

bulk cargo on the wagon body walls during

transportation by railway ferry.

The determination of the strength of an open wagon

body of a lightweight design is highlighted in

publication [22]. The authors performed a topological

optimization to lighten the wagon container. The

calculation results proved the feasibility of the

proposed solutions. At the same time, the authors did

not consider the loads acting on it during

transportation by railway ferry when calculating the

wagon body. A similar drawback can be said about the

work [23], where a new design of a wagon made of

steel with improved properties is also proposed.

Solutions of improvement the technical and

economic indicators of a freight wagon are highlighted

in publications [24, 25]. The authors proposed the use

of materials with improved physical and mechanical

properties to create a body shell. However, when

calculating the strength of the wagon, the authors did

not consider the loads acting on it during

transportation by railway ferry.

The use of laminated composite panels was

proposed to improve the strength of the side wall shell

in the work [26]. The feasibility of such an

improvement was proven using the example of a

freight wagon. However, the strength of the wagon

body with such a shell during transportation by

railway ferry was not studied.

Hence, in can be concluded by analysing the works

[20-26], that the issue of determining the forces of

expansion of bulk cargo on an open wagon body

during its transportation by railway ferry requires the

research.

Therefore, the purpose of the study is to highlight

the features of determining the forces of expansion

from bulk cargo on an open wagon body walls during

transportation by railway ferry.

2 METHODOLOGY FOR DETERMINING THE

EXPANSION FORCES OF BULK CARGO ON

WAGON THE WALLS WHEN TRANSPORTED

BY A RAILWAY FERRY

It is proposed to use the Coulomb method to determine

the forces of the strut on the open wagon walls during

transportation by a railway ferry, according to which it

is equal to the equation [20]:

, Pa

sin( )





−

+−



  

(1)

where

G – pressure of the prism of the load displacement [Pa];

ϑ – angle of a plane slope of the horizontal line

declination [°];



−−=

;

ρ – angle of internal friction (it is equal to the angle of

natural slope for a perfectly free-flowing medium [°]

[20]);

δ – angle of friction between the load and the wall [°].

It is important to note that the maximum pressure

will correspond to the direction of the sliding plane. To

determine the value of the maximum pressure, the

method proposed by V. V. Sinelnikov [20] can be

applied, according to which it is necessary to replace

the variable ϑ in the condition of maximum pressure









, i. e. the angle of inclination of the sliding

plane. In a general case, it cannot be determined

analytically, for some variable x (in our case the angle

α = θ). The point A was chosen as the origin of the

coordinate system (Fig. 1). The x axis is directed at an

angle ρ to the horizontal plane, and the y axis is aligned

with the line AB, i.e. along the side wall of the wagon

body. The segment AD = x determines the position of

the slope plane.

Figure 1. A scheme of action of the bulk cargo forces on the

open wagon side walls

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It is proposed to use the formula (2) to determine

the pressure of bulk cargo on the open wagon side

walls [20]:

cos ( )

sin sin( )

1 cos

cos

, Pa

ρα

p γh

ρ ρ α







−





(2)

where

γ – volumetric mass of cargo [kg/m

];

h – a height of the open wagon body [m].

The formula for determining the pressure for the

opposite wall of the open wagon body has the

following form:

, Pa

cos ( )

sin sin( )

1 cos

cos

ρα

p γh

ρ ρ α











(3)

When transporting an open wagon by the sea, it is

also necessary to consider the magnitude of the

accelerations acting on it. The diagram of the action of

forces on the open wagon body during the rolling

movement of the railway ferry is shown in Fig. 2.

Figure 2. A scheme of the forces acting on the open wagon

body during roll movement of a railway ferry:



(y)



(z)

–

components of the acceleration of the wagon body; gx

(y)

, gx

(z)

–

components of the acceleration of a free fall; p – inertial force

acting on the wagon body; px

(y)

, px

(z)

– components of the

inertial force.

3 CONSIDERING THE DYNAMIC LOAD WHEN

DETERMINING THE EXPANSION FORCES

OF BULK CARGO ON THE OPEN WAGON

BODY WALLS

The features of determining the dynamic loading on

the wagon body during roll movement are given in

[18]. In this case, a mathematical model is used as

follows:

( )

( ) ,

I q q p F t



   



 +   = + 

   

   

(4)

where

I is the moment of inertia of the railway ferry [kg∙m

B is the width of the hull [m],

Λθ is the coefficient characterizing the resistance to

oscillations of the railway ferry [N·s/m],

F(t) is the law of action of the disturbing force [N],

p´is the wind force of the surface projection [N]

q is a generalized coordinate that characterizes the

movement of a railway ferry with wagons when tilted

[m].

When assigning a disturbing action, the heading

angles of the sea wave to the hull of the railway ferry

were considered [18]:

,mcosL



  





=

(5)

where

κλ is a coefficient that varies in the range from 0.5 to 0.8

depending on the shape of the vessel's hull contours;

L is the wave length [m];

χ is the wave heading angle [°] (0° to 180°).

The solution of this model using the example of the

Black Sea and the railway ferry “Geroi Shipki”

established that the acceleration acting on the wagon

body, which is located on the far side of the track from

the bulwark, is about 0.2g.

Since the load is distributed relative to the wagon

body wall, then the additional expansion force will be:

 

, Pa



(6)

where

FF – the inertia force acting on bulk cargo [N];

LK – the length of the side wall of the wagon body [m];

hK – the height of the side wall of the wagon body [m].

Then, the following formula can be used to

determine the force of the bulk cargo spreading on the

open wagon body walls when the railway ferry rolls:

 

, Pa

cos ( )

sin sin( )

1 cos

cos

ρα

p γh F

ρ ρ α







=

(7)

When determining the forces of bulk cargo

expansion on the side walls of the open wagon body

during railway ferry rolling, it is proposed to use the

law of a triangle with a maximum at the base (Fig. 3),

in accordance with [20].

Figure 3. A distribution of the force of the bulk cargo spread

on the open wagon body side walls

The approach of determining the pressure of bulk

cargo on the open wagon body walls when transported

by a railway ferry in the rough sea conditions differs

from [20] in the method of determining the inertial

1330

component, as well as the law of distribution of the

expansion force on the open wagon body wall.

The expansion force on the end walls when the

railway ferry is trim can be determined by the method

described above. This approach can also be used to

determine the expansion pressure of bulk cargo on the

walls of a container. However, in the case of its

placement on an open wagon [27-31] transported by a

railway ferry, this method must be modified

considering the additional dynamic loads caused by

the gaps between the fittings and fitting stops.

Coal (as one of the most common export cargoes)

with a bulk mass of kN/m

was chosen as the bulk

cargo to determine the numerical value of the bulk

cargo expansion force on the walls of the open wagon

body when transported by railway ferry across the

Black Sea. Based on the calculations performed for a

roll angle of the railway ferry of 12.2°, the value of the

bulk cargo pressure on the side wall of the open wagon

body was obtained and it was equal to the value about

15 kPa. This value exceeds the bulk cargo pressure

during the operation of wagons on main tracks by

more than 50%.

4 CONCLUSIONS FROM THE STUDY

AND PROSPECTS, FURTHER DEVELOPMENT

IN THIS DIRECTION

The results of the research allowed to obtain a refined

value of the pressure of bulk cargo on the open wagon

body side walls during transportation by a railway

ferry. This can be considered when designing and

calculating new generation wagon bodies with

improved technical and economic indicators at

wagons’ building plants. In turn, this will help to

ensure the strength of the load-bearing structures of

wagon bodies during transportation on railway ferries

in international traffic.

The future direction of this research will be an

experimental study of the loading of an open wagon

loaded by coal during sea transportation.

It is important to note that the authors have already

conducted similar tests. Some of their points are

reflected in the publication [18]. However, the task was

then to study the stresses in the areas of fastening of

wagon on the deck using chain ties. Therefore,

considering the existing basis, the authors plan to use

it in their subsequent studies in this direction.

Moreover, a further development of this research is

the influence of uneven loading of the body with bulk

cargo on the expansion force transmitted to the walls

of the open wagon body during its transportation by

the sea.

ACKNOWLEDGEMENT

This publication was prepared thanks to support of the

project VEGA 1/0308/24 “Research of dynamic properties of

rail vehicles mechanical systems with flexible components

when running on a track” and the project KEGA 031ŽU-

4/2023 “Development of key competencies of the graduate of

the study program Vehicles and Engines.”

„Funded by the EU NextGenerationEU through the Recovery

and Resilience Plan for Slovakia under the project No. 09I03-

03-V01-00131.”

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