ICE LOADS AND RESISTANCES ON A SMALL COMMUTER VESSEL: A comparative study of rule based design and analytical ice loads and resistances

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I

CE LOADS AND RESISTANCES ON A SMALL

COMMUTER VESSEL

A comparative study of rule based design and analytical ice loads and resistances

AXEL BERGGREN

EBBA LINDH

Centre for Naval Architecture

Master of Science Thesis Stockholm, Sweden 2014

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ABSTRACT

The aim of the thesis is to investigate what the results are when applying DNV ice class design rules on a vessel that falls outside the validity range and how it does compare to direct calculations. The vessel to be investigated is a smaller ice going commuter ferry intended for freshwater Lake Mälaren in Stockholm.

Due to increased need of public transport in the area, political decisions have been made to incorporate ferry lines in the public transport system. The number of commuters’ peak during January and February and it is thus necessary to design a ferry that works all year around, in all possible weather conditions, including the ice conditions that occur winter time (Rindeskär, 2014). In order to make a comparative study of the DNV ice class and direct calculations with regards to resistances and structural loads on the hull, a general arrangement of the ferry is developed. Icebreaking resistance models based on DNV ice class (Det Norske Veritas, 2014), Riska (Riska, Willhelmson, Englund, & Leiviskä, 1997) and Lindqvist (Lindqvist, 1989) can be compared based on the ferry’s main data. The bow section of the hull is designed to handle the DNV design pressure according to DNV ice class 1C. The structural response is investigated using a finite element model, applying different load cases given from DNV as well as from the studied semi empirical ice load models mentioned above.

The bow design is of great importance for the icebreaking performance and the speed. The greater the stem angles the higher the resistance. A large variation in the results was also noted as only Lindqvist’s model took the freshwater ice properties into account. Further measurements have to be made in freshwater for smaller vessels to validate the results.

In the FE-analysis it was seen that the hull structure coped well with the DNV design pressure of 1 MPa. However, the empirical design pressure of 1.5 MPa resulted in too high stresses in the structure. The result indicates that the design rules work well for the intended design pressure, but the minimum empirical design pressure is still higher than the DNV design pressure for the commuter vessel. It can be that the DNV design rules can be used in the case of the ferry, but further investigations has to be made with regards to minimum design pressure.

In general, the results can be used as a basis for further investigations in the field of vessels operating in freshwater ice conditions.

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PREFACE & ACKNOWLEDGEMENTS

First of all, we would like to express our deepest gratitude’s to all employees at SSPA Stockholm division, for letting us occupy desks and perform our study at their office. Their constant standby support and friendly attitude has been vital for the progress of the thesis work. Special thanks go to our supervisors, Torvald Hvistendahl, Jesper Lodenius and David Eckerdal, for their constructive ideas, dedication and guidance during our master thesis. Many thanks to Victor Westerberg at SSPA Gothenburg office for answering questions and giving advice on ice and resistance models. We would also like to thank our contacts at WÅAB, Morgan Rindeskär, Pelle Teiner, Sonny Österman and Per Hård, for helping us with relevant information and arranging visits onboard some of the vessels in their fleet. Lastly we would like to thank Ivan Stenius, our examiner at KTH who has listened to our thoughts, helped us sustain the academic level and aim of the project.

During our thesis we have ventured into the field of ice-vessel interaction, something we knew next to nothing about beforehand. We have learnt a lot in this field and at the same time implemented our newly gained knowledge in programs we have not worked with before. It has been a highly interesting and challenging task where we have stepped out our comfort zone and the help we have had from people around us have been valuable. Yet again, many thanks to those who have listened to our thoughts, discussed technical aspects, read our text, had us visiting onboard and given us feedback.

Stockholm, June 2014 Ebba Lindh

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NOMENCLATURE

Full name Abbreviation

Finish Swedish Ice Class Rules FSICR

Det Norske Veritas DNV

High pressure zone HPZ

American Bureau of Shipping ABS

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1. INTRODUCTION

The Stockholm region’s population grows and new districts are established. Offices and apartment buildings are built close to the water’s edge and old industrial areas in these locations are transformed to new urban districts. The increasing number of people in the Stockholm region results in a raising capacity demand on the commuting system. The main way of commuting in the city region is by land carried transport.

In order to achieve successful ferry-based commuter traffic, the ferries have to be easy access for every one and also well incorporated in the commuting system. A robust solution that will provide commuters a reliable year round service is of outmost importance. The number of commuters’ peak during January and February and it is thus necessary to design a ferry that works all year around, in all possible weather conditions (Rindeskär, 2014). The winter climate in Stockholm causes ice to form and thus ferries that will traffic all year around require ice-going capabilities and possibly ice breaking capacities.

Current ferries with ice breaking capacities operating in the Stockholm region are designed according to DNV ice classification. This results in icebreaking ferries running all year round although the ice breaking capacities are needed only a few months of the year. Traditionally an icebreaking vessel is sturdier than a non-icebreaking vessel and is heavy and inefficient in open water conditions.

Recent political decisions have been made regarding commuter traffic in Stockholm. Three commuter ferry lines are to traffic Lake Mälaren and provide commuters with an all-year round reliable service. The ferry line in question in this report runs from Ulvsunda to Södersjukhuset and has a total of nine stops along the route (including the end stations). At least 20 % of the commuters are expected to bring their bicycles on the ferry (Rindeskär, 2014).

The authority in charge of the commuter traffic, the Swedish Transportation Agency, has a subsidiary company, Waxholms Ångfartygs AB (WÅAB) as a managing company for their vessels. WÅAB is in charge of ordering new vessels and within the year they aim to classify all new builds to DNV standard (Malmsten, 2014) (Rindeskär, 2014).

1.1. PROBLEM STATEMENT

The problem statement of this thesis is as follows; what are the results when applying DNV ice class design rules on a vessel that falls outside the validity range? How does it compare to results from direct calculations?

1.2. METHOD & PROCESS

The aim was to investigate the structural design of a vessel that falls outside the boundaries of the ice class rules. The aim was also to investigate the design methods of ice-going and ice-breaking vessels and compare direct calculations of ice loads and resistances with the design loads from class rules for ice-going and icebreaking vessels. A section of the bow was modeled and designed to follow DNV ice class 1C standard. An iterative design process was used to find a light design. Resistances for breaking ice and running in channels were calculated for evaluation of the shape of the hull in order to find an appropriate bow shape. Ice loads and load areas from icebreaking were calculated and applied on the designed bow section in an FEA model to evaluate the design.

Icebreaking models and brash ice resistance based on work of Gustav Lindqvist (Lindqvist, 1989) and Kaj Riska (Riska, Willhelmson, Englund, & Leiviskä, 1997). The rule based resistances and design calculations are based on DNV ice rules for ships smaller than 100 m. The calculations are done in Matlab. The hull shape was produced and analyzed with regards to hydrostatic stability and open water resistance with Formsys programs Maxsurf, Hydromax and Hullspeed. The hull shape was

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checked against the capacity demand, rules and resistances in Matlab, making the hull design an iterative process. Rhinoceros was used to model the hull shape. Draftsight was used to obtain drawings of the commuter ferry. The load analysis was performed by modeling a section of the bow in Creo Parametric Academic Edition and simulating static load cases based on experimental pressures and DNV design pressures in Creo Simulate.

1.3REPORT STRUCTURE

The project consists of a number of different fields that are presented in different main chapters. The first chapters discuss the route and present the general arrangement of the commuter vessel. After the first chapters follows an investigation of the hull, including dimensioning of scantlings with regards to DNV ice class design rules.

The second part of the report is focused on designing the vessel for ice going and icebreaking capacities by using semi-empirical formula and ice mechanics. First general ice properties are presented followed by a chapter on resistance calculations. Then estimation of load case and a FE-analysis is presented.

Most chapters have a discussion and conclusions related to the specific topic handled by the chapter. The discussion, conclusion and future work chapters that incorporate the entire scope of the project are presented in 10 Main discussion, 11 Main conclusion and 12 Main future work.

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2. ROUTE AND ROUTE LIMITATIONS

In order to define the ice condition that the commuter ferry will face, a specific route is chosen with regards to feasibility and technical challenge. The route provide the information needed to predict ice loads and resistances found in chapters 5, 7 and 8, based on the prevailing ice conditions along the route.

2.1. DEFINITION OF ROUTE

The route of interest is located in the west part of Stockholm, in Mälaren, the freshwater parts in direct connection to the city. The route starts in Bällsta River and ends at Södersjukhuset. The length of the route, without any stops, is approximately 15.3 kilometres or 8.3 nautical miles. The main function of this route is to link densely populated areas close to Bällstaviken, Ulvsundasjön, Årstaviken and the waters in between. The main benefit of this route is passengers travelling in both directions as there are both office and residential areas along the route (Palmbeck, 2013), (Karlsson, 2013). The ferry route decreases the distance for some commuters that otherwise would have to cross the water by a bridge, as seen in Figure 1. The estimated amount of passengers and bicycles per day are seen in Table 1.

Figure 1: The route from Bällsta river to Södersjukhuset, including all stops (Google).

Table 1: Time table and estimated amount of passengers (Palmbeck, 2013).

Travelling time 52 minutes

Frequency of departure (06.00 – 22.00) 20-60 minutes

Number of departures per day 40

Est. number of travellers per day 940 passengers

Est. number of bicycles 690 units

Planned stops

Ulvsunda Solna Strand

Huvudsta Minneberg Hornsberg Alvik Lilla Essingen

Hornstull Årstadal Södersjukhuset Huvudsta Södersjukhuset Hornstull Lilla Essingen Minneberg Solna Strand Ulvsunda Hornsbergs Strand Alvik Årstadal

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2.2. DIMENSIONING FACTORS

External factors, who are rout dependant, will have a direct effect on the ship capacity. The factors having the largest impact to the list of criterions working as a foundation for the hull structure design are mentioned below.

2.2.1. Passenger demands

The ferry will be dimensioned to carry 150 passengers and 30% of them are estimated to bring their bicycles on board (Palmbeck, 2013). The number of passengers that the ferry can carry is slightly over dimensioned but as there is an unpredictable “popularity factor” for commuting with ferry, the number of passenger can be expected to increase (Karlsson, 2013), (Malmsten, 2014). The current plans involve side-to docking for the ferries to quicker load and unload passengers (Malmsten, 2014), (Rindeskär, 2014). The ferry developed in the further investigations will be based on these passenger requirements.

2.2.2. Speed

The time schedule (see Table 1) is based on a cruising speed of 12 knots. The limit is set by “experience” and is based on the speed limit in brash ice, which occurs in an ice channel winter time (Rindeskär, 2014), (Malmsten, 2014). A large part of the waters in central Stockholm also have a speed restriction of 12 knots. When breaking ice the speed of an ice breaking vessel is usually limited to approximately 5 knots. The maximum speed of the ferries is estimated to be around 14 knots. These values are the traditional speed limits based on empirical data and experience. The hull concept of the ferry can then be analysed more thoroughly.

2.2.3. Operational profile

The average operational profile for the vessel is 20 % running in brash ice channels, 2 % icebreaking and 78 % open water. This profile is based on weather data (SMHI, 2014) for the Stockholm region and ice growth models presented in 6.2

2.3. LIMITATIONS OF INVESTIGATION

Information that affects the details of the route but does not have an effect on the structural design of the ship hull, such as accessibility and bunkering, is not taken into account in this investigation.

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3. MAIN PARTICULARS AND HULL PERFORMANCE

This chapter contains information about the ferry in question. The level of detail presented here has to be put in perspective to the main aim of the thesis work. Numerical values are approximate and relevant simplifying assumptions concerning the general arrangement are defined and motivated. Principal layout and arrangement of main particulars are illustrated in the attached figures. The vessels main particulars are necessary to investigate hull resistances according to DNV rules, chapters 4.4 and 5, and the analytical/semi-empirical models in chapter 7.

3.1. MAIN PARTICULARS

The capacity demand and operational profile which is given in chapter 2.2 works as input when defining the main particulars of the vessel. Hull geometry, consistent with given data, is then produced and used to investigate the hydrostatic stability and open water resistance. Figure 2 below shows the starboard side of the ship and the main particulars for the given vessel are displayed in Table 2.

Figure 2: Side view of vessel.

Table 2: Main particulars for given vessel.

LOA 30 m Lwl 27 m DMLD 3.7 m TDES 1.5 m BWL 7.2 m BMLD 7.8 m DispMLD 115 ton

Main engine 2xVolvo Penta D13 450 (Volvo Penta, 2013)

Power 2x330 kW

Propulsion 2xAzimuth thrusters 1.1m diameter (Rolls Royce, 2014)

Bow thruster 50 kW electric bow thruster (Jastram manuevring competence, 2014) Auxiliary generator 77 kW (Volvo Penta, 2013)

Nominal capacity 150 passengers Maximum capacity 278 passengers

Seated 106 passengers

Standing 44 passengers

Bicycles/strollers 30 units 3.2. PASSENGER DECK

The ferry has a rated capacity for 150 passengers. The capacity also allows for 20% of the passengers to bring bicycles or strollers onboard. Boarding is done on either side in the aft or front through sliding doors, enabling direct access to the passenger compartment. The small foredeck in the bow is not to be used by commuters. Areas for bicycle storage are located in the most aft part of the

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passenger compartment, and in the front part of the ship behind the half circle shaped high bench. Seats are mounted in pairs of two or three and mounted to passenger deck by bolting or similar. Rearrangement of seat configuration is enabled through a modular seat solution. Passenger deck is equipped with one lavatory located in front of the aft port embarking door. It is supposed to be designed according to SJÖFS 2004:25, guaranteeing accessibility for people in wheelchairs and people with children in strollers (Sjöfartsverket, 2010). Illustrations are provided in Figure 2 and Figure 3.

Figure 3: Illustrative top view of passenger deck for given vessel.

Passenger deck layout is focused on maximizing capacity and comfort for travellers, independent of season. A wide isle centered along the length of the deck enables passengers to pass each other, carrying baggage or leading strollers or bicycles. Wide open areas in direct connection to the doors simplify embarking and disembarking. The half circle shaped high bench in front of the forward bicycle area can hold ten commuters, providing them with an enjoyable view.

3.3. LOWER DECK ARRANGEMENTS

The lower deck of the ship is divided into six compartments which are visible in Figure 2. From the bow to the aft, these are named and provided with the following functions as seen below.

3.3.1. Collision void

The void is left empty. 3.3.2. Bow thruster room

Holding the machinery and associated systems and tooling for the bow thruster. The fore part of this void also holds two ballast tanks which are placed on either side of the vessel, each with a capacity of approximately 2.5 m3.

3.3.3. Main engine room

Holding the two main engines and associated systems. Main fuel tanks are also located in this compartment.

3.3.4. Auxiliary engine room

Holds the auxiliary engines, bilge pumps, service pumps and associated systems. 3.3.5. Storage room

Holding tools and equipment used for maintenance, as well as the two aft ballast tanks on either side, each with a volume of 3.6 m3. This room can also be used as dressing room for the staff.

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3.3.6. Propulsion room

This room holds the steering equipment and systems for the electric azimuth propulsion. 3.4. WATERTIGHT COMPARTMENTS

Watertight compartments on lower deck are consistent with the compartment division. Longitudinal positioning and detailed measurements for further investigation of these compartments can be found in Table 3.

Table 3: Watertight compartments Compartment name Aft position

[m from transom]

Forward position

[m from transom] Collision void

Bow thruster room Main engine room Auxiliary engine room Storage room Propulsion room 26.8 21.5 16.1 10.0 6.9 0 29.6 26.8 21.5 16.1 10.0 6.9

3.5. PASSENGER AND CARGO CAPACITY

Width of passenger compartment is set to 6.4 meters, equal to the width of six sitting passengers, four standing passengers and the estimated width of one bicycle. This is assumed to be a sufficient width for the passenger compartment, resulting in an isle width of 3 meters. Estimated width of embarking ramps and passenger doors is set to 1.6 meters. Detailed measurements used for estimation of area demand concerning passenger deck are defined in Table 4.

Table 4: Detailed measurements for estimation of passenger deck area.

Unit Width [m] Length [m] Weight [kg]

Standing passenger 0.6 0.6 75

Sitting passenger 0.6 0.8 75

Bicycle 0.4 1.7 12

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4. HULL FORM AND FEATURES

The two main features governing the design of this hull form is functionality and reliability. Another main area of interest is to define certain hull features that might contribute to a decreased operational resistance, which in turn results in decreased overall operational costs. An ice breaking hull is often characterized by a rounded stem, sloping sides and a short mid ship body defined by a constant transverse sectional shape, all to improve maneuverability in icy conditions. The ice slides in under the vessel and breaks, often without creating a noticeable change in the icebreakers trim. These hull features does however result in poor hydrodynamic efficiency and makes the vessel susceptible to slamming loads. Operation in open waters on the other hand, is favored by a bow shape characterized by a sharper stem with a greater stem angle, a longer parallel mid ship section and straight sides.

It is hereby understood that the ships operational profile and regional location is of uttermost importance when choosing design features for the hull with the aim to minimize resistance. The operational profile of the ship is explained in 2.2.

Main effort in the evaluation concerning resistance minimizing hull features is hereby focused on the bow, from the stem reaching back to the point where the hull sectional area becomes constant. This is mainly because the bow shape has the largest impact on the operational resistance, but also because it is thoroughly processed in the rules as well as in the direct calculations.

DNV rules are coping with ice handling abilities in a way that secures the hull structure from being insufficiently strengthened. The detailed shape of the hull does however not affect the ice pressures for ice class ICE-1C, which the hull is designed for. There is no connection between certain hull features and ice loads given for this particular ice class. Thus no benefits would come from changing the hull shape with the aim to lower ice loads on the given hull structure. Brash ice resistance does however change with varying bow shape according to the rules (Det Norske Veritas, DNV service documents). The rule based expressions for ice loads and brash ice resistance is explained further in 5.3 and 5.5.

Direct calculations for certain hull shapes on the other hand, points toward that certain hull features contribute to dramatically decreased ice loads, thus leading to a more accurate estimation of the loads which the hull is exposed to. The connection between brash ice resistance and ice loads which the hull is exposed to is explained further in 5.3 and 5.5.

4.1. HULL SHAPE

The hull form, which has been developed to work as a foundation for this investigation, is illustrated in Figure 4 and 5 below. Underlying knowledge concerning earlier mentioned subjects have limited the design to what the authors believe is a “sufficient design”.

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The underwater body is shaped in consideration to hydrostatic stability, resistance minimization and ice handling abilities. The aft of the underwater body is shaped to be wide and flat, mainly to give space for the two azimuth thrusters, but also to give sufficient hydrostatic stability. The hull shape is produced based on results from calculations affecting the hull form, together with reasonable assumptions based on the operational profile of the vessel. The resulting bow shape is far from optimal when handling ice, but the operational profile leads to a tradeoff between what’s optimal in different conditions, and supports the chosen flare- and rake angle in the bow. The hull is equipped with a sharp stem with a rake angle of 27 degrees. The rake angle at B/4 from centerline at DWL is equal to 20 degrees and the angle of the waterline at B/4 is equal to 29 degrees. The bow shape is developed to fit the operational profile described in 2.2. The body plan for the hull in question is illustrated in Figure 5. The effect on hull resistance generated by thrusters and skegs are not considered in this analysis. Main particulars for the hull are illustrated in Table 5.

Figure 5: Body plan.

Table 5: Main hull particulars.

Annotation Description Value Unit

Δ Displacement 115 [Tons]

T Immersed depth 1.5 [m]

Lwl Waterline length 27 [m]

Bwl Beam waterline 7.2 [m]

WSA Wet surface area 169 [m2]

WPA Water plane area 155 [m2]

Cp Prismatic hull coefficient 0.55 -

Cb Block coefficient 0.38 -

Cwp Water plane area coefficient 0.79 -

4.2. HULL REGIONS STRENGTHENED FOR ICE HANDLING

Line 1 in Figure 6 marks the upper boundary for ice strengthened scantling. The lower boundary for this area exceeds the depth of the hull and is thereby not taken into consideration. Line 2 and 3 defines the area where hull plating must be strengthened for ice handling. These lines are defined for DNV ice class 1C. More about the ice strengthened part of the hull structure can be found in 5.4, 5.5 and 5.6.

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Figure 6: Ice strengthened regions. 4.3. STABILITY ANALYSIS

A full hydrostatic stability analysis falls outside the aim of this report and is thus not investigated here. Main focus for this analysis is to investigate whether the transversal hydrostatic stability is sufficient enough for different loading conditions. It provides vital information about the vessels capability of handling the capacity demands. An estimation of the weights of vital parts contributing to the complete displacement and stability works as a foundation for the load cases which are being investigated further in this chapter.

4.3.1. Estimation of weight and center of gravity for design load scenario

Table 6 below shows the estimation of center of gravity according to the design load scenario; nominal capacity load and full ballast tanks. The weights of different parts in Table 6 are approximated using different methods. Weights of structural components are estimated with the help of earlier knowledge in combination with reasonable assumptions. Weights of defined components, for example bow thruster, main engines, auxiliary engines and propulsion systems are all based on detailed product descriptions often used for ferries of this size.

Table 6: Estimation of weight and center of gravity. Weight estimation [tons] TCG [x-direction] LCG [y-direction] VCG [z-direction] Bridge 5 0 21.1 6.5 Passenger compartment 17.7 0 11.6 4.7 Passenger cargo 12 0 9.8 4 Main deck 15 0 15.5 3

Bow thruster system 0.6 0 25.4 1.5

Main engines 2x1.8 0 19.7 1.5

Auxiliary engine 1 0 13.7 1.5

Propulsion system 2x1.5 0 3.6 0.5

Hull structure 40 0 17.1 1

Other machinery equipment

and systems 0.9 0 15.5 1

Fluids 3.4 0 15.5 0.5

Forward ballast tanks 2x2.5 0 25.1 0.5

Aft ballast tanks 2x3.6 0 8.9 0.5

Total 115 tons 0 ~15 m ~2.3 m

The hydrostatic stability is investigated for two different load cases which are defined in Table 7 below. The varying number of passengers and their location are estimated to a point load in each

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load case, fixed in the ships reference system, one meter above passenger deck. This implies that the effect from the free surface moment induced by the moving mass of the passengers in large heeling angles is excluded from the analysis. The shape of the underwater body varies with changing heel, leading to a shift in LCB, which in turn induces a change in trim. The weight contribution from bicycles is not considered in any of the following load cases.

The two load cases are investigated for stability criteria´s according to SJÖFS 2006:1 (Sjöfartsverket, 2006) and displayed as seen in Table 8. Sufficient hydrostatic stability in both bad cases point toward the hull shape in question fulfilling basic stability demands. This implies that it is applicable as a sample ship, acting as a foundation for further investigations.

Table 7: Hydrostatic stability load case variation. Case number Number of passengers Total passenger weight

[tons]

Transversal center of gravity [m]

Ballast

Design case 150 12 0 Full

Load case 1 150 12 1.5 Empty

4.3.1.1. Large angle stability investigation for design case

This condition is considered to be the normal condition in which the ship will operate during icy periods. Ballast tanks are full to lower the position of thrusters in the water, thus increasing maneuverability. This also induces a lowered CG.

Figure 7: GZ curve for evenly distributed design load and full ballast tanks.

Transversal center of gravity is zero since the passengers are considered to be evenly distributed over the deck. Vertical center of gravity is equal to approximately 2.3 meters above baseline. Longitudinal center of gravity is equal to 15.6 meters from the transom.

4.3.1.2. Large angle stability investigation for load case 1

This load case is considered the most extreme load scenario with nominal capacity utilization. 150 passengers shifted to port side. Transversal center of passenger load is estimated to 1.5 meters from the centerline. TCG increases to 0.178 meters from centerline. Ballast tanks are empty, thus resulting in a VCG equal to approximately 2.5 meters measured from baseline. LCG is still 15.6 meters.

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Figure 8: Maximum heel induced by shifted nominal capacity and empty ballast tanks.

Figure 9: GZ-curve for unevenly distributed design load and empty ballast tanks.

Table 8: Criteria fulfilment for design load.

Criteria Design case Load case 1

1 OK OK 2 3 4 5 6 OK OK OK OK OK OK OK OK OK OK

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4.4. OPEN WATER RESISTANCE ESTIMATION

Different resistance prediction methods use a wide range of algorithms to estimate the resistance of a hull in open water. Every method is suitable for specific hull categories and thus some being more applicable than others in this particular case. Below follows a short description together with results from the applied prediction method. The propulsion efficiency is set to 100%, generating results which are correlated with the traction power needed to pull the vessel.

4.4.1. Slender Body Method

This is an analytical method that predicts the wave resistance of a port/starboard symmetrical monohull. Assumptions are made that the vessel has a slender shape, meaning high length-beam ratio and slenderness ratio (length-displacement ratio). Accurate results are gained for slenderness ratio between approximately 5.0 and 6.0. The minimum slenderness ratio for which the method is applicable is reduced if the length Froude number is reduced. Very high slenderness ratio has been found to generate reasonable results for Froude numbers up to 1.0. The method works equally well for round bilge hulls as for chine hull forms and deals automatically with transom sterns by adding a virtual attachment in the aft aligned with the bottom surface (Formsys, 2014) as illustrated in Figure 10.

Figure 10: Hull discretization with and without virtual appendage (Couser, Wellicome, & Molland, 1998)

The vessel in question has a slenderness ratio of approximately 6.2. This is however not a problem, since the length Froude number is below 0.4 at a speed of 12 knots.

The slender body method is hereby assumed to give reasonable estimated values for needed tractive power in the complete speed interval. Tractive power estimation as function of speed or Froude length number is illustrated in Figure 11.

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It can be seen that the tractive power estimation increases fast with increasing speed. Resistance seems to increase exponentially up to approximately 12.5 knots. The power estimation for speeds above 12.5 knots falls outside the operational profile and are thus considered irrelevant. About 550 kW is needed for 12 knots according to this method. This power is however not equal to the installed engine power, since the propulsion efficiency used in the performed calculations is set to 100%.

4.5. BRASH ICE RESISTANCE

The nature of rule based brash ice resistance estimation is presented in detail in 5.3.1. This estimation is as explained in 5.3.1 however only valid for a speed equal to 5 knots. Brash ice thickness in the channel is, according to the DNV rules, set to 0.6 meters for the chosen ice class 1C. It is clear from this method that a ship of this size and shape, by applying the defined angles and main particulars of the given hull, reaches a design brash ice resistance around 30 kN (5.3.1). This results in an approximated minimum engine output requirement of 220 kW, which is well within the limits of what is accounted for concerning propulsive power. It is however also clear that this engine output falls outside the validity range of the rule based brash ice resistance calculations defined in 5.3.4, which clearly is a problem when trying to construct the vessel according to the DNV rules. Required service speed is also preventing the calculations from generating sensible results, since the DNV based calculations are tuned for a speed of 5 knots. Brash ice resistance estimation based on DNV rules might therefore be far from reality, since the vessel is expected to operate in 12 knots in these conditions. This implies that the resistance estimation for this operational condition might be heavily underestimated, making it a subject for further investigation.

4.6. ICE BREAKING RESISTANCE

The DNV rules for dimensioning ice breaking resistance is usually applied for ice class 1A*. Other ice classes are allowed to exclude the resistance contribution due to a consolidated layer of brash ice in an ice channel. Total resistance at a speed of 5 knots in a brash ice channel with a consolidated layer of ice on top is, according to chapter 5.3.2 estimated to approximately 48 kN for this particular vessel. Minimum engine output requirement is given by chapter 5.3.3 and is equal to approximately 392 kW, which again is within the technical limits for the chosen engine arrangement, but outside the validity range of minimum engine power output given in 5.3.4.

4.7. DISCUSSION

The operational profile defined in 2.2 points toward the importance of the ship being able to follow the timetable all year around. Breaking ice is considered an exceptional operational condition, meaning that the demand for speed according the operational profile is left aside. An assumption that the vessel should be able to make a speed of 5 knots in these conditions is however made. This is based on the nature of DNV resistance estimation rules which are limited to a design speed of 5 knots.

Values for required engine power output calculated above can be used as a foundation in combination with the operational profile to revise the engine arrangement and choose machinery optimal for this vessel. This revision is however left aside since it is considered too far from the main goal of the thesis.

The hull shape has been developed through an iterative process involving open water resistance and hydrostatic stability calculations, while in the same time controlling main deck measurements, displacement and bow shape angles. This work has been performed using the hull shape development tool Maxsurf (Formsys, 2014).

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The first design loop in the iterative development process is complete. Main parameters stated here are recurrent in the overall work and used as a foundation for the rest of the analytical conclusions in this report.

Hydrostatic stability for this particular vessel is a subject for revision, which ultimately might lead to a change in the main parameters of the vessel. Effective methods for achieving a sufficient hydrostatic stability are for example to investigate the possibility of lowering center of gravity by altering the superstructure, or changing the shape of the underwater body. Reconfiguration of watertight bulkheads to increase ballast tank capacity might also be a relevant subject for further investigation. The hydrostatic stability analysis has to be refined to achieve sensible results for the different load cases. Free surface moments induced by partially filled tanks are one obvious point for refinement which can be crucial for the overall stability. This is however left for future design loops in the development process.

The ice thickness which is applied when designing vessels for a particular ice class does not govern the operability of the ship alone. This particular vessel is for example according to its ice class, supposed to be able to make a speed of 5 knots in 0.6 meters of brash ice. Continuously operating the vessel in these conditions will increase the risk of mayor damage to propulsion systems and appendages. Further studies are therefore needed to ensure sufficient overall strength in these systems as well.

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5. ICE CLASS RULES

This chapter treats rules obtained by the DNV classification society concerning design regulations for vessels less than 100 meters trafficking icy waters. Main focus is aimed toward describing the design procedure of the hull structure. Specific decisions are made in the process to limit the investigation to the forward part of the hull and main particulars defined in chapter 3 are used as input values for the calculations. Results generated in this part of the report are partly recurring in other parts of the report.

DNV rules are commonly accepted as equivalent to the Finnish Swedish ice class rules. Parts of the DNV rules for classification of ships processed in this chapter are listed below.

 Part 1 chapter 2: “Class notations”

 Part 3 chapter 2: “Hull Structural Design, Ships with Length Less than 100 meters”  Part 5 chapter 1: “Ships for Navigation in Ice”

5.1. GUIDELINES FROM THE SWEDISH TRANSPORT AGENCY

A ship shall be designed and constructed so that the strength of the hull, closures, rigging and equipment provides adequate safety for all conditions in which the ship is intended to operate and for all damage conditions which the ship is designed to survive. Special attention should be given to the static stresses appearing in the structure induced by the most severe load condition, usually a combination between the maximum load and the most severe load distribution. Special attention should also be taken to the dynamic stresses that might occur as result of the usage according to the operational profile.

Ships shall be constructed in accordance to a legislated framework issued by a recognized organisation such as DNV GL, Lloyd’s Register or the American Bureau of Sipping. The Swedish

Transport Agency can allow direct calculations as foundation for new types of ships or new design

concepts, for which there are no applicable set of rules. These calculations together with all assumptions made, shall be reported to the Swedish Transport Agency for analytic review and approval. The documentation which is reported shall support the ships structural standard which is relevant for its operational profile (Swedish Transport Agency, 2013).

5.2. USE OF CLASSIFICATION RULES IN ENCLOSED WATERS

A service area notation is always given ships with specific modifications to general arrangement, structural scantling or equipment. This notation is marked R, followed by a number or a letter according to Table 9 below

Table 9: Service area restrictions (Det Norske Veritas, 2014).

Service area notation Seasonal zones

Winter Summer Tropical

R0 250 No restrictions No restrictions R1 100 200 300 R2 50 100 200 R3 20 50 100 R4 5 10 20 RE Enclosed waters

Relevant service area notation for investigated vessel is RE. This restriction limits operation to enclosed waters such as rivers or lakes, which is considered suitable given the operational profile presented in chapter 2.2. The service area restriction notation is used in the rule based design process to obtain relevant results for the given vessel (Det Norske Veritas, 2014). Following requirements in relevant sections of the rules are modified in relation to the choice of service area;

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 Design hull girder loads

 Design pressures on shell, weather decks, superstructures and deckhouses  Anchoring and mooring equipment

 Arrangement  Stability

5.3. RULE BASED RESISTANCE CALCULATION

Resistance of the ship in a channel with brash ice and a consolidated layer of ice is given in the rules according to

(5.1)

Factors C1 and C2 are usually only taken into account when designing for ice class ICE-1A*, which is

equated to operation in consolidated ice. The operational profile defined in chapter 2.2 does however not exclude the vessel from operation in conditions resulting in breaking consolidated ice in a brash ice channel; hence these constants need to be included in the resistance estimation for this particular operational condition.

5.3.1. Brash ice resistance

As explained earlier, C1 and C2 are excluded for this operational condition. C3 , C4 and C5 are all

empirical coefficients set to 845 kg/m2s2, 42 kg/m2s2 and 825 kg/s2. Coefficients C𝜇 and C𝜓 are dependent on the shape of the bow accordingly:

(5.2) (5.3) The minimum value of C𝜇 is set to 0.45. C𝜓 is equal to 0 if 𝜓 exceeds 45 . The rake of the bow (𝜑2) and

the water entrance angle (α), at the waterline at B/4 from the centerline, are both defined in degrees and illustrated in Figure 12 below.

Figure 12: Definition of bow angles according to DNV rules.





2





₂ 3 1 2 3 4 5 2 wf CH F M F PAR F

A

LT

R

C

C C

H

B C H

C L

H

C

B

L

 





 



_

_





2

0.15 cos sin sin

C 









0.047 2.115

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The flare angle 𝜓 is also given in degrees and is calculated for each location using local values for φ

and 𝛼 according to

, (5.4)

The flare angle in this specific case is calculated using φ = φ2. HF is the thickness of the brash ice layer

displaced by the bow (m) and is calculated according to

, (5.5)

HM is the brash ice layer thickness in the middle of the channel (m) and is set to 0.6 for ice class

ICE-1C. B, L and T is the maximum breadth of the ship (m), length of the ship between perpendiculars (m) and the actual ice class draught of the ship (m). LPAR and LBOW is the length of the parallel mid ship

body (m). Awf is the area of the waterline in the bow and is estimated according to

, (5.6)

See Figure 12 for further clarification. All imbedded parameters in expression (5.1) are hereby defined and the brash ice resistance can be investigated as a function of rake angle (φ2) and water entrance angle ( ). This relationship is illustrated in Figure 13 below.

Figure 13: Brash ice resistance according to DNV rules.

It is clear that small rake angles at the bow will result in minimized brash ice resistance. The calculated resistance rises when this angle increases above approximately 20 degrees. Somewhat similar, it can be seen that small waterline angles at the bow, according to these calculations, will result in a minimized brash ice resistance, although dependent on given rake angle. Integrated safety factors create redundancy in the system which can be spotted as discontinuities in the surface in Figure 13. This is a clear indication that the bow design dramatically affects the rule based resistance

 

1

tan

sin

















_



_









0.5 0.26 F M H   H B 0.6 wf BOW A L  B



15 20 25 30 35 40 45 50 55 0 20 40 60 80 100 20 30 40 50 60 70 80  [degrees] X: 29 Y: 20 Z: 24.57

Rulebased brash ice resistance at 5 knots & stem angle at 27 degrees

₂ [degrees] R e si st a n ce [ kN ] 25 30 35 40 45 50 55 60 65 70

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for operation in brash ice. Worth mentioning is also that these calculations are based on a simplified version of reality and that they are restricted to a speed of 5 knots.

5.3.2. Ice breaking resistance

The last part of Equation (5.1) share some resemblance with Riska’s analytical expression for ice breaking resistance, presented in 7.3. Ice breaking resistance in a brash ice channel with a brash ice thickness in the middle of the channel equal to 0.6 meters is defined according to the DNV rules for ice class 1C by including the resistance contribution from C1 and C2 in expression (5.1) presented in

5.3.1 above. C1 is calculated according to







1 1 1 0.021 1 2 3 4 2 1 PAR BOW BOW BL C f f B f L f BL T B



      (5.7)

The parameter f1 is set to 23 N/m2, f2 to 45.8 N/m, f3 to 14.7 N/m and f4 to 29 N/m2 (Det Norske

Veritas, 2014). LBOW and LPAR is as explained earlier, equal to the length of the bow and midship

section as illustrated in Figure 12. C2 is calculated using the following expression







2 2

1 0.063

1 1 2 3

1 1.2

T

B

C

g

g B

g

B

L







 



_



_





(5.8)

The value of g1 is set to 1530 N, g2 to 170 N/m and g3 to 400 N/m1.5 (Det Norske Veritas, 2014). These

parameters are tuned by DNV and differ from the values obtained in Riska (Fel! Hittar inte

referenskälla.).

Figure 14 illustrates icebreaking resistance in relation to bow angles α and φ2 can now be visualized in the same way as with the brash ice resistance in Figure 13. Comparing these two figures clarifies that the different resistance estimations behave in the same way and that the rule based ice breaking resistance for the commuter ferry is about 17 kN higher than the brash ice resistance, only given the choice of stem angle.

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Figure 14: Brash ice resistance with a consolidated layer of ice on top. 5.3.3. Rule based minimum power requirement

The rule based ice breaking resistance from Figure 14 gives the minimum value for delivered power in kW from engines to thrusters according to DNV.

, (5.9)

Ke is a factor that is depending on the number of propellers, if they have controllable pitch or if they

are fixed. This factor is generally set to a value given by the rules. Approval may be given by DNV for defining this factor based on model tests, resulting in a more exact value. The rule based value for this factor is equal to 1.6, given the ship is equipped with two propellers with fixed pitch. DP is the

diameter of the propeller and is set to 1.1 meters, which is a diameter used for vessels of this size (Maritime Journal, 2005). RCH is as explained in 5.3.1 and 5.3.2 calculated using (5.1). The relationship

between minimum value for delivered power and bow angles, for operation in both ice breaking and brash ice conditions, can now be illustrated according to Figure 15. The top layer illustrates the minimum power requirement for ice breaking, while the brash ice minimum power requirement is the lower layer.

15 20 25 30 35 40 45 50 55 0 20 40 60 80 100 40 45 50 55 60 65 70 75 80 85 90  [degrees] X: 29 Y: 20 Z: 41.72

Rulebased ice breaking resistance at 5 knots & stem angle at 27 degrees

₂ [degrees] R e si st a n ce [ kN ] 45 50 55 60 65 70 75 80 85 3 2 min 1000 CH e P R P K D       

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Figure 15: Minimum power requirement for according to DNV for operation in ice breaking and brash ice conditions as functions of bow angles.

The equations for estimating resistance and power requirement, (5.1) and (5.9), is not used in the rules as foundation for calculating the design ice pressure presented in (5.12), as in the case with the direct calculations for brash ice and ice breaking resistances. There is no connection between the ice load estimation and the minimum power requirement estimation in the set of equations given by DNV. It can however still be used as a decision support for defining bow angles as well as engine arrangement, which are presented further in chapter 3. The chosen bow angles results in a minimum engine power output illustrated in the top layer in Figure 15.

5.3.4. Validity range

DNV design rules only give a viable result within certain intervals. The model is, for example, only valid when minimum required engine output (Pmin) exceeds 1000 kW. Bow angles for the vessel

under investigation fulfill the validity criteria’s. All validity perimeters governing whether the model is applicable or not is presented further in Table 10.

Table 10: Parameter validity range.

Parameter Symbol Minimum Maximum Value Validity

Water entrance angle α 15 55 29 Valid

Stem angle φ1 25 90 27 Valid

Angle at B/4 φ2 10 90 20 Valid

Length over all L 65.0 250.0 27 Invalid

Beam B 11.0 40.0 7.8 Invalid

Draught T 4.0 15.0 1.5 Invalid

Length of bow/L LBOW/L 0.15 0.40 0.48 Invalid

Length of parallel midbody/L LPAR/L 0.25 0.75 0.10 Invalid

DP/T 0.45 0.75 0.73 Valid

Awf/(L∙B) 0.09 0.27 0.29 Invalid

Minimum power enginge output Pmin 1000 kW - 400 kW Invalid

15 20 25 30 35 40 45 50 55 0 20 40 60 80 100 0 200 400 600 800 1000 1200 1400  [degrees] X: 29 Y: 20 Z: 177.2 X: 29 Y: 20 Z: 392

Rulebased resistance in icy conditions at 5 knots & stem angle at 27 degrees

₂ [degrees] R e si st a n ce [ kW ] 200 300 400 500 600 700 800 900 1000 1100 1200

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5.4. DEFINITION OF ICE BELT REGION

The DNV ice class regulations divide the hull into three major regions, bow, mid body and stern region, which are to be strengthened for ice loads (Figure 16). The bow region consists of three sub regions; upper bow ice belt, ice belt bow region and fore foot region.

Figure 16: Ice belt regions according to DNV.

Main focus for this work is the ice belt bow region, reaching from the stem to a line parallel to and 4 % of L aft of the forward borderline seen in Figure 16. This borderline is the forward borderline marking the forward end of the mid body where the waterlines run parallel to the centre line. The ice belt region does however not need to exceed 5 meters aft of the borderline for the chosen ice class (ICE-1C).

Vertically, this region covers the sides from the Upper Ice Water Line (UIWL) down to the Lower Ice Water Line (LIWL). These waterlines can be broken lines and should be the envelopes of the highest and lowest waterline at which the ship is intended to operate in ice (Det Norske Veritas, 2014). The vertical extension of ice-strengthened areas on ship hulls is dependent on the choice of ice class. Type of structural member is also affecting the extent of this region. Rule based values for the vertical extension of this region for ice class ICE-1C is defined in Table 11.

Table 11: Vertical extension of ice belt plating and framing for ice class ICE-1C (Det Norske Veritas, 2014).

Structural member Region Above UIWL [m] Below LIWL [m]

Plating Bow 0.4 0.70 Mid ship 0.60 Stern Framing Bow 1.0 1.6 Mid ship 1.3 Stern 1.0

5.4.1. Definition of hull region under investigation

Chosen area of the hull which is under investigation concerning sufficient hull scantling in terms of strength and minimum structural thicknesses is limited by the total span in which the immersed

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depth can vary in combination with the values in Table 11, together with the chosen longitudinal boundaries. The stem of the ship is defining the forward boundary of the investigated area. Aft boundary is coinciding with the third watertight bulkhead from the bow which is forming the aft wall of the bow thruster room. The third bulkhead is located at approximately 70 % of the total ship length measured from the aft. The choice of region for further investigation is motivated by the fact that it is assumed to be exposed to the greatest ice pressure according to the rules. Other motivational factors acting as foundation for the choice of hull region under investigation is the validity of the corresponding analytical load model presented further on in chapter 8. Maximum vertical span of the ice belt region in the bow is 1.36 meters for plating and 2.86 meters for framing. Ship hull region under investigation is marked in red in Figure 17.

Figure 17: Investigated area subjected to ice loads.

5.5. CALCULATION OF PRESSURE LOADS

The investigation is focused on DNV’s local ice loads and local sea pressure loads acting on the side structure. Sea pressure loads on bottom structure given by the DNV rules are acting on a part of the hull located below the ice belt region, which in this case is located below the physical boundaries of the ferry hull. This is the single main reason to why no further investigation is performed for these pressures.

5.5.1. Side structure

Loads given in Table 12 are in general applicable on the side structure of ship hulls according to the DNV rules. This particular investigation is limited to p1 and p2 in Table 12, which are the sea pressure

estimations in direct connection to the summer load waterline, acting on the investigated ice belt region (Det Norske Veritas, 2014).

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Table 12: Design loads applicable on side structures (Det Norske Veritas, 2014).

Equation for p1 given in Table 12 is dependent on h0 found in Table 14 and the pdp is defined

accordingly

(5.10) Where

(5.11) Factor y in equation (5.10) is the horizontal distance from center line to the load point (a minimum of

B/4 meters), B is the greatest molded depth in meters measured at the summer load waterline, T is

the mean molded summer draught in meters and z is the vertical distance from the baseline to the load point. The parameter ks in equation (5.11) is varying over the ship length according to Table 13. ks is varied linearly between specified areas defined in column three in Table 13. The change of ks

along ship length is illustrated in Figure 18.

Table 13:Variation of ks over ship length.

ks

At aft perpendicular and aft

Between 0.2L and 0.7L from aft perpendicular At forward perpendicular and forward





135 1.2 75 dp l y p p T z B     





0.8 0.15

l s W f

V

p

k C

k

L









_



_





2.5

3

_B B

C





2

4.0

3

_B B

C





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Figure 18 Variation of the parameter ks over the length of the ship

The illustration of how ks varies over the ship length indicates that the greatest design load appears

in the bow. Parameter kf is the smallest of T and the vertical distance from the waterline to the top of

the ship side at considered transverse section. Factor CW is set to 0.0792 times the ship length. An

attempt to deepen the understanding of how the sea pressure above and below the waterline in theory changes over the ship hull side according to DNV can be seen in Figure 19 below.

Figure 19: Design sea pressure on side structure.

It is hereby evident that the greatest sea pressure is given by p1, located at the bow in level with the

baseline. Worth mentioning is the discontinuity in the surface seen in the Figure 19. It illustrates that the design pressure used above summer load waterline is limited to a minimum value based on the ship length. When comparing this pressure to the design pressure applied below the same line, one

0 5 10 15 20 25 30 0 2 4 6 8 10 12 Variation of k

s over ship length

ks

[

m

]

Ship length measured from the aft [m]

0 5 10 15 20 25 30 0 0.5 1 1.5 2 2.5 3 -10 0 10 20 30 40 50 60

Longitudinal location on hull side from aft [m]

[Sea pressure onto hull side]

Vertical location on hull side from keel [m]

P re s s u re [ k N /m ^2 ] 0 10 20 30 40 50

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can see that this pressure also should be restricted in the same manner. This empirical sea pressure formula has been tuned over time to handle nonlinear effects and was initially based on strip theory calculations (Det Norske Veritas, 2014).

5.5.2. Loads from operation in ice

The hull is, according to DNV rules and depending on relevant ice class, dimensioned for operation in sea conditions corresponding to an ice thickness not exceeding h0 (Table 14). The actual ice pressure

acting somewhere on the ice belt region at an arbitrary point of time is considered to be acting on a surface with a height h equal to a fraction of the ice thickness. This is why the design height h is smaller than the level ice thickness h0. Values for these two parameters are dependent on ice class

and are defined in Table 14 below (Det Norske Veritas, 2014).

Table 14: Values for h and h0 (Det Norske Veritas, 2014).

Ice Class h0 [m] h [m] ICE-1A* ICE-1A ICE-1B ICE-1C 1.0 0.8 0.6 0.4 0.35 0.30 0.25 0.22

Dimensioning ice thickness is according to Table 14 limited to 0.4 meters for ice class ICE-1C. The selected ice class 1C corresponds well to current estimations of ice thickness in the region under investigation defined in 6.2.1. The design height h is partly used for defining thickness of the shell plating in the ice belt region.

Ice loads acting on the ice belt region of the hull differ over time and accurate measurements of these loads show that they are completely random, best simulated by a stochastic pattern of pressure peaks, which is described further in 8.2. General simplification of ice loads are being used in the DNV rules.Observations have shown that the load distribution on a frame might be higher than on the shell plating in the middle between the frames, illustrated as p in Figure 20. Assumptions have been made and the distribution of design ice pressure on the hull structure is defined as

p

according to Figure 20.

Figure 20: Assumed ice pressure distribution on hull structure. The design ice pressure is calculated accordingly

p

=

p

0

×

c

d

×

c

1

×

c

a (5.12)

Where p0 is the nominal ice pressure set to 5600 kN/m2, cd is a factor influenced by engine output

and size, c1 is a factor that takes into account the probability that the design ice pressure will occur

on a certain part of the hull for a specific ice class and ca is a factor which takes into account that the

full length of the considered area will be under pressure at the same time (Det Norske Veritas, 2014).

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



1000 d

a k b

C    (5.13)

The value of k is determined using the following expression

k

=

D

f

×

P

S

1000

(5.14)

Δf is the displacement in tons at maximum ice class draught and PS is the actual continuous engine

output in kW. Factors a and b in equation (5.13) are defined in the rules according to Table 15. Table 15: Values for a and b for different regions and k-values.

Region

Forward Midship & Aft

a b k<=12 k>12 k<=12 k>12 30 230 6 518 8 214 2 286

The factors c1 and ca are both probability factors which take into account that the design ice pressure

occurs in a certain region of the considered hull, and the probability that the full length of the area under consideration will be exposed to the design ice pressure. The value of c1 and ca are both

defined according to Table 16 and equation (5.15) below. Table 16: Values of c1.

Ice Class Region

ICE 1A* ICE 1A ICE 1B ICE 1C

Forward Midbody Stern

1.0 1.0 1.0 1.0 1.0 0.85 0.70 0.50 0.75 0.65 0.45 0.25

c

_a

=

l

0

l

_a

; 0.35

£

c

a

£

1.0, l

0

=

0.6 m

(5.15)

la is the distance between supporting elements in meters. This value changes depending on type of

framing according to Table 17 (Det Norske Veritas, 2014). It is hereby clear that large la values gives

small probability factors, hence inducing smaller design loads. Table 17: Values of la.

Structure Type of framing la Approximated value [m]

Shell Transverse Frame spacing 0.4

Longitudinal 1.7 X frame spacing 0.7

Frames Transverse Frame spacing 0.4

Longitudinal Span of frame 1.5

Ice stringer Span of stringer 3.8

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5.5.3. Load comparison

A load comparison can hereby be performed to investigate the differences in design loads given by the rules. Estimated maximum design ice pressure onto the hull plating, located in the bow, reaches according to Figure 21 below a value of 1330 kPa for plates and frames. Maximum value for the ice stringer is approximately 530 kPa. The significantly lower design pressure for the ice stringer is due to the fact that the probability for the design ice pressure to act on the whole length of the stringer is smaller compared to the probability that it would act on a surface equal to the size of a plate.

Figure 21: Design ice pressure along the waterline.

The great discontinuity of the design ice pressure along the ship hull seen in Figure 21 is due to the nature of the DNV rule based ice pressure calculations, where safety factors are integrated into the equations. The great increase of design pressure in the front illustrates the effect from these safety factors in DNV:s systematic approach. The design load which will generate the ruling minimum plate thickness criteria is the DNV ice pressure design load.

5.6. CALCULATION OF PLATE THICKNESSES

Plate thicknesses in the hull structure are differing dependent on the size of the hull plate, where it is located and how the hull is constructed. Since the side structure is in focus, other parts are left out in this chapter. The investigation has been further limited to simply focus on the ship bow, reaching from the stem to approximately 70% of the overall length measured from the aft. The hull plates are assumed to be of rectangular shape with the side dimensions defined accordingly

0 5 10 15 20 25 30 0 200 400 600 800 1000 1200 1400

Design Ice pressure

Longitudinal location measured from aft [m]

P re s s u re [ k P a ]

Shell design pressure Ice stringer design pressure