Navigational Characteristics of Lower Sava – Determining Draught and Carring Capacity of Ships

This paper presents the procedure for calculation of possible values of draught of ships or barges in pushed convoy while navigating through certain sections of Lower Sava which have characteristic shapes and dimensions. The goals of the paper is to, based on known calculation procedures, determine the value of possible draughts of ships or pushed convoys through this section with restrictions in navigating conditions, or to determine periods of the year when ships or pushed convoys can achieve best results during exploitation.


INTRODUCTION
The Danube, besides that it connects Serbia and Croatia, at the same time connects the whole region not only to other countries on the Danube, but to the countries of the Middle East as well. This waterway carries significant part of international trade of the countries in the region. With the navigational connection Rhine-Mine-Danube ships have open access to waterways of Western Europe (France, Belgium, and The Nederland) as well as access to waterways of northern Germany and central Europe. At the same time Lower Sava presents a connection Croatia and Bosnia and Herzegovina with the Danube until the building of channel Šamac-Vukovar is finished (The idea of building this mentioned channel exists well over 40 years and so far it has remained only as an idea).
River Sava is the second longest tributary of the Danube and it is 945 km long and it is created when Sava Dolinka and Sava Bohinjka merge near Radovljice. To Ljubljana it is a mountain river and from Ljubljana to Zagreb the slope of the river is redu-ces significantly as it enters Pannonian Plain.
Between the mouth of river Kupa all the way to its mouth Sava river's slope has gradient of 42 mm/km, which makes it become a low land river which menders a lot. Due to such low gradient of the slope Sava river is not capable of transporting alluvium brought by its tributaries which then settles near mouths of those tributaries and creates large number of shallows and sand bars. These shallows and sand bars are mostly present downstream from mouths of rivers Bosna and Drina and between Kupa and Una, which during low navigation levels makes navigation difficult or completely impossible.  [1] River Sava is navigable for ships from the mouth of River Kupa on the river kilometre (rkm) 583 to its mouth into the Danube. Regarding the navigation and referring to specific characteristics of waterway river Sava can be divided into three characteristic parts: TEHNIKA -SAOBRAĆAJ (2018)  Research of exploitation characteristics of ships on Lower Sava sector is based on the results of previous analysis that the authors have done for certain sectors of the Danube [3], [4], [5], [6], and [7].
In order to complete the picture on navigational characteristics of river Sava the authors have used, apart from their own data, research and data from [8] and [9].

BASIC NAVIGATIONAL CHARACTERISTICS OF LOWER SAVA
Lower Sava from Sremska Mitrovica to Belgrade has all the characteristics of lowland riverlow speed of river flow, large number of river bends, large widths of river bed, large number of river islands and backwaters, as well as higher depths. Authoritative hydrological stations, according to which navigation on Lower Sava is managed, are in Sremska Mitrovica, Šabac and Belgrade. Hydrological station in Sremska Mitrovica, besides its significance for navigation on Lower Sava, is of special interest for navigation on Sector of Rača (from rkm 176 to rkm 168). Water level on hydrological station Šabac is very important for navigation on Šabac sector (from rkm 110 to rkm 78). Water level on Šabac hydrological station is especially important for the part of river from the village Kamičak (rkm 83) to the village Mrđenovci (rkm 95) which has a 180 cm deep and 24 m wide channel dug through when the level on Šabac hydrological station shows 0 cm.
Ships and pushed convoys need to pass this section with special attention while obeying all the norms of navigation. Each deviation from experience and valid rules can cause leaving the waterway, grounding of ships or parts of convoys, closing of the waterway, and even more severe accidents since the river bed on the sector of Kamičak is rocky.
On  Since ships and pushed convoys are designed to navigate both the Danube and Sava it is necessary for them to have technical and exploitation characteristics dictated by those two navigation areas. Starting from this fact this paper will analyze navigational characteristics of river Sava on the sector from the mouth of river Drina into Sava (rkm 175), in the so-called Šabac sector. Research includes changes in water level on hydrological station Šabac, which is used for planning the navigation on this sector of Sava, both from view point of low navigation levels and and high navigation levels. This is because low water levels on Sava are TEHNIKA -SAOBRAĆAJ (2018) 5 679 limiting factor for draught of ships and barges in pushed convoys, while high water levels limit the height of highest point of the ship-pushboat. This is the reason why it is necessary to determine navigation characteristics of river Sava on Šabac sector, especially from the view point of determination of actually possible draughts of ships and barges.
The research of water levels on Lower Sava sector for hydrological station Šabac has been done for the period between the 1st of January 1962 to the 31st of December 2013. To obtain the most precise state in the waterway on this part of the river Sava, from the view point of navigation of ships with large draughts, during the starting point of research was the assumption that the possible depth of waterway in Šabac sector is H=180 cm [1] when water hydrological station Šabac shows 0 cm, or in other words depth Н<180 when hydrological station shows negative values.
where the following are: H -possible depth of waterway on Šabac sector, cm; hVmeasured (current) water level at hydrological station Šabac, cm.
Besides that it is known that minimal depth of waterway for safe navigation (Hmin) is calculated according to the following expression: where the following are: Тmaxmaximal draught of ships or barges in pushed convoy, cm; hspare depth, which is the distance from the river bed and ship's hull, m; for ships and pushed convoys travelling at relatively low speeds spare depth is 30 cm. From the expression (2) it follows that maximal draught of ships and barges is:  For example, for hydrological station Šabac, for the value of the vessels draught of T≤250 cm probability for the use of the given draughts is PT≤250≥0,6981 while expected number of days for navigation is 254,79 days, for the value of the vessels draught T≤280 cm PT≤280≥0,6536 and expected number of days for navigation is 238,58 days, while for the value of the vessels draught T≤300 cm PT≤300≥0,62 and expected number of days for navigation is 226,31 days.

UTILIZATION OF SHIPS CARRYING CAPACITY
In the system of water transport ships have main productive role. This is the reason why it is necessary to direct the organization of ship's work towards more efficient use of ships and perfecting of methods for management of transport processes. Besides that, exploitation of ships in transport processes must be organized in such a manner which for given conditions provides the highest possible productivity of ships. One of the ways to determine the utilization of ships from a transport fleet and analyze their work is calculation of real values of exploitation parameters of each individual ships or for group of ships. For the purposes of this paper the utilization of ship's carrying capacity (ε) is determined based on calculated depths on the Šabac sector.
Calculation of the utilization of ship's carrying capacity (exploitation parameter of load, load coefficient and static coefficient of utilization are some of other names for this parameter) is done according to the expression (5) [11], [12]: where the following are: Qereally loaded amount of cargo in a vessel, t; ΣQereally loaded amount of cargo in all the vessels that create pushed convoy, t; Qrregistered carrying capacity of one ship for transport of cargo, t; ΣQrregistered carrying capacity of all the ships for transport of cargo that crate pushed convoy, t; It is obvious that with the change in water levels (as presented in the figure 4) conditions for navigation of ships change on daily bases, which is the reason why it is necessary to constantly adjust draughts of ships navigating through Šabac sector. Since the carrying capacity of ships or barges depend on their draught Qe=f(Te), this circumstance, at the same time, changes of the really loaded amount of cargo in one vessel or all the barges that create pushed convoy ΣQe. At (real possible, daily) draught Те carrying capacity of ship is determined by applying the rule of linear interpolation, according to the expression (6) [13]: where the following are: Тrregistered (maximal) draught of cargo ships, m; Те -(real possible) draught of cargo ships, m (expression 4); qspecific carrying capacity of cargo ship per 1 m of draught, t/m, calculated according to the expression (7) [13]: where Т0is the minimal draught of ship (draught of empty ship), m.
Based on expressions (5) and (6), for known ship types, utilization of ship's carrying capacity (ε) can be determined. This paper examines the change of this parameter according to the given method for several characteristic barge types which are being used and whose draughts are 220, 230 250 and 260 cm respectively. Figure 8 shows periods of limited values of carrying capacity-parameter of the utilization of ship's carrying capacity (ε) for stated barge types (draughts from 220 cm to 260 cm) within a year based on analysis of water levels on the hydrological station Šabac for the observed period between the 1 st of January 1962 to the 31 st of December 2013. Periods of limited carrying capacity of ships and barges based on utilization of ship's carrying capacity (ε) are presented in the table 1. Described method of linear interpolation, for known values of Qr, Tr and T0, specific carrying capacity (q) is calculated for several barge types with draughts as in the table 1. Table 2 presents basic characteristics of the barges that have been used for analysis. Based on given parameters the expressions for determination of the possible amount of cargo that can be loaded into ships have been determined for barges of certain type (Qe), by mathematical model of straight line through two points where the first point is (Т0; 0) and the second one (Тr; Qr). Expressions for calculation of exploitation carrying capacity (Qe) of several barges types present on river Sava are also shown in the table 2. By applying these expressions, and based on the change of possible draughts of vessels within a year, maximal theoretical amount of transported cargo (ΣQe) can be calculated, under the assumption that through Šabac sector one barge (ship) of observed type is passed through per day, by summing all the values of carrying capacities (as a function of change of draught) for one year. These values are also presented in the table 2. utilization of ships carrying capacity achieves values ε<1,0. This paper also presented graphs and expressions for calculation of probability of change in possible draughts of vessels and expected number of days for navigation with set draughts. Based on these expressions it can be established that barge (ship) whose maximal draught is T≤250 cm has expected number of days for navigation 254,79 while probability of appearance is PT≤250≥0,6981, for vessels draught T≤280 cm PT≤280≥0,6536 and expected number of days for navigation is 238,58 days, while for vessels draught T≤300 cm PT≤300≥0,62 and expected number of days for navigation is 226,31 days. Also by using expressions shown in the table 2 it is possible to determine maximal theoretical amount of transported cargo (ΣQe) that can be transported in one year, under the assumption that through Šabac sector one barge (ship) of observed type is passed through observed sector per day. Based on established values in such a manner it can be concluded that it is better to use barges with higher carrying capacities which are loaded with less cargo during periods of limited draughts compared to barges with lower carrying capacities during the whole year should the analysis of incomes and costs justify such exploitation principle for ships and barges.