Department of Aeronautical and Vehicle Engineering
Bow design for operation in brash ice
Kjell Teepen
Using a vessel for public transport can possibly save large amounts of time in a city as Stockholm. The transport is easy during the period of the year where there is no ice cover on the waters, however during the time when there is ice, the vessels used face more extreme conditions. Swedish Steel Yachts (SSY) now wants to have a design for their “Shuttle Ferry Concept” intended for operation all year round.
SSY has developed a special way of designing a ship’s hull structure, using this design together with the super duplex stainless steel alloy, SAF2507, SSY hopes to re-volutionize the ship building industry. The aim of this thesis is to deliver a bow design that is able to combine operation in brash ice with good performance in open water using the special SSY design together with the super duplex stainless steel.
This thesis presents to you basic knowledge regarding operation in ice, ice theory, the SSY design concept more in detail and finally a design development of a suitable structure.
Genom att använda en båt som kommunalt färdmedel kan man troligen spara stora mängder tid i en stad som Stockholm. Transporten sker enkelt på tiden av året då det ej finns ett istäcke på vattnet, dock, under tiden det finns is, upplever båtar mycket ex-trema förhållanden. Swedish Steel Yachts (SSY) vill nu ha en design för deras "Shuttle Ferry Concept" ämnad för bruk året runt.
SSY har utvecklat ett speciellt sätt att designa deras skrovkonstruktion, genom att använda denna design, tillsammans med ett super duplext rostfritt stål (SAF2507) hoppas SSY revolutionera sjöfartsbranschen. Målet med detta examensarbete är att leverera en design på ett förskepp som kan kombinera drift i isförhållanden med bra egenskaper för öppet vatten, detta skall uppnås genom användning av SSY’s speciella design tillsammans med det super duplexa rostfria stålet.
Detta examensarbete presenterar grundläggande kunskaper om drift i isförhål-landen, isteori, SSY’s designkoncept mer i detalj och till sist ett designförlopp av fören.
1 Glossary and abbreviation 1 2 Introduction 2 2.1 Background . . . 2 2.1.1 SSY . . . 2 2.2 Problem . . . 2 2.2.1 Purpose . . . 3
2.3 Design of the vessel . . . 3
2.3.1 The SSY design . . . 4
2.4 Operating in ice . . . 5 2.4.1 Brash ice . . . 5 2.4.2 Grease ice . . . 6 2.5 Area of operation . . . 6 2.5.1 Ice thickness . . . 7 2.6 Requirements . . . 9
3 Goals and structure of this thesis 11 3.1 Goals . . . 11
3.1.1 Results . . . 12
3.2 Structure of this thesis - the logical way . . . 12
4 Limitations 13 5 Operation in ice 14 5.1 Design . . . 14 5.1.1 Speed . . . 14 5.1.2 Hull shape . . . 14 5.2 Ice class . . . 17 5.2.1 FSICR Notations . . . 17 5.2.2 DNV GL Notations . . . 18
5.2.3 Sets of ice class rules . . . 18
5.2.4 How to classify a SSY design? . . . 19
5.2.5 Strengthening . . . 19
5.2.6 Performance . . . 20
6 Ice Theory 22
6.1 Loads . . . 22
6.1.1 Strategy . . . 22
6.1.2 Loads due to brash ice . . . 22
6.1.3 Loads due to ice breaking . . . 25
6.1.4 Design Loads from DNV-GL . . . 32
6.1.5 Jordaan . . . 38 6.1.6 Masterson . . . 40 6.1.7 Suyuthi . . . 41 6.1.8 Su B., Riska K., Moan T . . . 41 6.1.9 Discussion . . . 43 6.2 Resistance . . . 43
6.2.1 Brash ice resistance from DNV-GL . . . 44
6.2.2 Myland & Ehlers (Lindqvists) formulas . . . 45
6.2.3 Riska a.o.; Level ice resistance . . . 50
6.2.4 Open water resistance . . . 54
6.3 Discussion . . . 57
7 SSY design 58 7.1 Hull . . . 58
7.1.1 Conventional hull structure . . . 58
7.1.2 SSY . . . 59
7.1.3 Plate thickness . . . 59
7.1.4 Stringer . . . 60
7.2 Steel . . . 61
7.3 Evaluation of current design . . . 62
8 Design 65 8.1 Concept design . . . 65
8.1.1 Geometry . . . 65
8.1.2 Shuttle Ferry concept . . . 66
8.1.3 Modern ice breaker . . . 67
8.1.4 Combination . . . 68
8.1.5 Combination with bulbous . . . 69
8.1.6 Concept design with other angle . . . 70
8.1.7 Evaluation matrix . . . 71
8.2 Basic design . . . 72
8.2.1 Stringer design . . . 73
8.2.2 Web frame design . . . 73
8.2.3 Shuttle Ferry Concept . . . 74
8.3.6 Comparison . . . 112
8.4 Final design . . . 114
9 Results and discussion 117 9.1 Geometry . . . 117
9.2 Design . . . 117
9.2.1 Design parameters . . . 118
9.2.2 Flexibility of the entire structure . . . 119
Glossary and abbreviation
Abbreviation Long form
∆ Displacement (m3)
CFD Computational Fluid Dynamics (Flow simulation software) DNV GL De Norske Veritas Germanischer Lloyd
SAF Sandvik Austenitic-Ferritic (Material name) SSY Swedish Steel Yachts
Stem The stem is the most forward part of a boat or ship’s bow and is an extension of the keel itself.
Flare Flare is the angle at which a ship’s hull plate or planking departs from the vertical in an outward direction with increasing height. Buttock A buttock line is a curve indicating the shape of an air foil or
naut-ical equivalent in a vertnaut-ical plane parallel to the longitudinal axis of the craft or vessel.
Stern The stern is the back or aft-most part of a ship.
Ice horn The ice horn is a triangular ship constructional part at the stern of a ship. It serves the helm of the ship to protect against unbroken and broken ice, especially when driving astern.
Ridge A ridge develops in an ice cover as a result of a stress regime estab-lished within the plane of the ice. A ridge is an extra strong part of the ice cover, creating higher loads and increasing the possibility a ship gets stuck.
FSICR Finnish-Swedish Ice Class Rules
Introduction
This thesis is an investigation regarding the special SSY way of designing a vessel, us-ing the SAF2507 super duplex stainless steel together with a different way of designus-ing the load transfer, this technique will now be investigated for the usage in an harsher environment. In the Stockholm area a shuttle ferry concept is supposed to operate all year round. This challenges the vessel a lot, it will encounter ice loads during the winter and at the same time it should be able to perform well during the ice-free period of the year. A few different geometries are examined and listed with pros and cons. From that, the most suitable one is selected and a structural arrangement is given. It is then investigated for the different load cases a vessel will encounter in this environ-ment. This leads to a final design which is compared to the traditional way of design-ing a hull, with the traditional technique and steel. From this pros and cons for the different designs are discussed.
2.1
Background
This thesis is done as a request from Swedish Steel Yachts, (SSY) in Gävle, Sweden. The author has been working with guidance from KTH, SSY and Cervino Consulting.
2.1.1
SSY
SSY has since the start in 2011 developed a different way of designing ships. This new thinking together with a special kind of steel has up to this moment resulted in one full scale prototype and a number of ship designs (11.5 – 17.1 m, with concepts up to 50 m). The existing prototype has been tested successfully for operation in ice (20 knots in 4-5 cm), although it does not have a design specifically for ice conditions. SSY now wants to develop a design of a bow that is capable of operating in brash ice, for given preconditions.
2.2
Problem
The assignment is to create a design of a bow for a ship intended for transporting pas-sengers. Namely the SSY concept of a Shuttle Ferry (1601_1-Sea Shuttle 25) a 25 m
long vessel with the purpose of acting as a shuttle ferry in Stockholm city and the inner archipelago. The bow should be designed to be able to operate in brash ice. The bow should therefore be able to withstand the loads exposed to it when operating in the given area and thereby fulfil the criteria stated in Table 2.4. Ice classification for the vessel is hard to perform due to the special design and because the DNV ice regulations are primarily meant for ice breakers which are much bigger vessels, it will however still be presented.
The bow is designed to be able to be integrated into the existing method of hull designs by SSY. This structure should be built from a special kind of stainless steel, SAF 2507. The steel used for the SSY technique of designing a hull is both in weight and price comparable to a traditional aluminium hull (the steel weighs more and is more expensive, but a lesser amount of material, and thereby money is needed to achieve the same weight as the aluminium hull). And again compared to an aluminium hull, the SAF2507 one has much better properties in corrosion, fatigue, strength and hard-ness according to Sandvik [16] and SSY.
The study is done by comparing different geometries and picking the most suit-able for the purpose, later this geometry is given a structure and then the entire struc-ture is evaluated against the same geometry using a traditional strucstruc-ture and the same amount of material.
2.2.1
Purpose
The purpose of this thesis is to examine how the SSY technique performs in brash ice in terms of ice loads, from that a suitable design is suggested.
2.3
Design of the vessel
Figure 2.1: Shuttle Ferry Concept
The ship characteristics are shown in Table 2.1.
Table 2.1: Ship characteristics
Parameter Symbol Value Unit
Length between perpendiculars Lpp 24.8 m
Waterline length LW L 24 m
Beam B 6.75 m
Draught (high) D 1.23 m
Loaded displacement (LWT + DWT) M 64 000 kg
Block coefficient Cb 0.31
The vessel is equipped with 2 x 590 kW machinery.
2.3.1
The SSY design
Special kind of steel
corrosion (which can be caused by salt-water, which in turn causes fracture of a mater-ial). All metal under the waterline is mirror polished.
The steel hull retains its mechanical properties despite tough conditions over a long period of time. This is a major advantage compared with aluminium boats, which may deteriorate over a number of years losing mechanical properties and are thereby prone to fatigue [16], [21]. Plastic and carbon fiber vessels don’t have this problem, however they are non-recyclable and are prone to cracking and delaminating upon im-pact.
Table 2.2: SAF 2507 properties [16]
Parameter Symbol Value Unit
Density ρ 7800 kg/m3
Proof strength Rp0.2 ≥550 MPa Rp1.0 ≥ 640 MPa
Tensile strength Rm 800 - 1000 MPa
2.4
Operating in ice
Not all ships are built to an ice class. Building a ship to an ice class means that the hull must be thicker, and more scantlings must be in place. Most of the higher classes require several forms of rudder and propeller protection. Two rudder pintles are usually required, and strengthened propeller tips are often required in the higher ice classes. More watertight bulkheads, in addition to those required by a ship’s normal class, are usually required. In addition, heating arrangements for fuel tanks, ballast tanks, and other tanks vital to the ship’s operation may also be required depending on the class [13].
2.4.1
Brash ice
The definition of Brash ice is, "Accumulations of floating ice made up of fragments not more than 2 meters across, the wreckage of other forms of ice." [3]
Figure 2.2: Brash ice
2.4.2
Grease ice
The definition of Grease ice is, "Ice at that stage of freezing when the crystals have co-agulated to form a soupy layer on the surface. Grease ice is at a later stage of freezing than frazil ice (a collection of loose, randomly oriented needle-shaped ice crystals in wa-ter) and reflects little light, giving the sea a matte appearance." [3]
Figure 2.3: Grease ice with some pancake ice
Grease ice is assumed to be the closest definition of the ice that will freeze over night which the vessel has to be able to break in the morning.
2.5
Area of operation
Figure 2.4: Area of operation
2.5.1
Ice thickness
Properties of ice
In the table below a number of properties for ice is shown, those can vary a lot depend-ing on for example salinity and temperature, the ones from below are taken from an experiment in the Baltic sea and will be used throughout the report.
Table 2.3: Ice properties from the Baltic sea [19]
Parameter Symbol Value Unit
Density ρ 880 kg/m3
Young’s modulus E 5400 MPa
Poisson ratio γ 0.33
-Crushing strength σc 2.30 MPa
Flexural Strength σf 0.55 MPa
Frictional coefficient µi 0.15
-Brash ice
From the graphs in Figure 2.5 on the ice thickness in the Stockholm area an estima-tion of the ice floe sizes the vessel will interact with can be made. From the following report, [11] the largest possible ice floe in the Stockholm area has been modelled as a cylinder with the diameter 1.79 m and a height of 0.21 m. This gives a volume of 0.52
Figure 2.5: Ice thickness in the Stockholm area [11]
Grease ice
Figure 2.6: Overnight ice thickness [8]
Time span during the year with ice coverage
Based on available weather and ice data [18] the worst possible winter conditions for a ferry in Stockholm could include 3-4 months of ice with a maximum thickness of 0.4 m. An ice thickness of 0.4 is rare and requires a really severe winter. A severe winter requires the ferries to run in brash ice channels which eventually get clogged with brash ice requiring new channels to be broken. This means that the ferries have to be able to break relatively thick ice occasionally. However, some winters there is hardly any ice [18] and it is questionable if a ferry should be dimensioned to the most extreme con-ditions that rarely occur. In this thesis the Ferry is assumed to only operate in brash ice channels and a thin ice layer frozen over night.
2.6
Requirements
Table 2.4: Requirements
Parameter Symbol Value Unit
Design speed v 20 knots
Brash ice speed vbi 10 knots
Grease ice speed vgi 10 knots
Maximum brash ice floe size Vbi 0.33 m3
mbi 300 kg
Maximum grease ice thickness hgi 0.05 m
The design speed of 20 knots is taken from the concept description given by SSY. The brash ice and grease ice speed is set somewhat lower then the design speed at 10 knots. For higher velocities the resistance increases a lot which makes it more environ-mental friendly to operate at lower velocities. The loads will also increase a lot if the speed is to high.
Goals and structure of this thesis
3.1
Goals
The goal for this thesis is to give SSY a foundation to a design philosophy on what to think of when designing a vessel with the purpose of operating in the given area of op-eration. At the same time this basic philosophy is used to propose a bow design to SSY suitable for operation in the given area. Also the pros and cons for using the SSY tech-nique together with the super duplex stainless steel (SAF2507) are delivered compar-ing this with the effects of uscompar-ing a traditional hull structure with a traditional material (structural steel).
To make the results credible the following questions will have to be answered, • What is a typical bow shape for a vessel operating in ice?
• Which design rules apply when operating in ice and how can they be used on the SSY design concept?
• Which load cases are to be expected in the area of operation, and how does the hull absorb those loads?
• Is it possible to tell how much the resistance is increasing due to the passage in ice?
• How does the SSY distinguish itself from a traditional design? • What are the pros and cons for the SSY design concept? • What are the pros and cons for a traditional design?
• How is the SSY design concept affected by the use of the special steel the com-pany is using?
• How is a traditional design affected if it would be built using the same kind of steel as SSY is using?
• Does the SSY design have any advantages compared to a traditional design when operating in ice?
• Does the special steel have any advantages compared to a traditional steel when operating in ice?
3.1.1
Results
The results of the thesis are presented in form of numbers in showing maximum stresses encountered and maximum deformation of the structure. The final recommended design is also presented, along with FEM pictures on the stresses and deformations.
3.2
Structure of this thesis - the logical way
The structure of this thesis after this chapter is as follows, the chapters are put in a logical way which makes it easy for the reader to follow, the list of questions from the previous section will be answered in a chronological order as the chapters go on.
• Chapter 4: Limitations of this thesis, what will be excluded from the investiga-tion
• Chapter 5: Operation in ice, some basic knowledge regarding the special design of a ship intended for operation in ice and classification rules is presented. This gives the reader a theoretical background which is later used in the design Chapter. • Chapter 6: Ice theory, Loads and resistances, what loads and resistances are
ex-pected? Theory from few different sources is presented and discussed upon. This gives the reader a theoretical background which is later used in the design Chapter. • Chapter 7: SSY design, what is special with the SSY design? How does the design
differ from a conventional design? What is the theory behind the design? An evaluation of the current design is performed and discussed upon.
• Chapter 8: Design, here will the design process be presented, starting with a Con-ceptual design then a Basic design followed by a Detailed design and finally a Fi-nal design. The theory discussed in Chapter 5,6 and 7 is used as foundation. • Chapter 9: Results and discussion, here the results are presented, including the
Final design of the bow. A discussion on the results will also be performed. • Chapter 10: Conclusions, the final chapter will show what conclusion the author
Limitations
In this project the purpose is to develop a bow design and perform calculations on it. It is thereafter highly recommended to perform an evaluation on the entire vessel using the bow design as input to gather results on the overall performance of the vessel.
The focus of the project is to deliver a technical report of a design applicable for the certain case stated above. Due to the limited amount of time of the project these areas will need further investigation,
• Design
Is it enough to only have the bow modified or does the ice change the load cases for the rest of the ship as well?
• Fatigue due to ice
Due to the fact that the ice will cover all of the operational area fatigue is a big part of this. The vessel will constantly encounter different loads from both the grease ice and the brash ice were the loads can differ quite a lot.
Due to the high quality of the steel fatigue is however not considered an issue. Critical for fatigue might be for example the weld joints.
• Stability
The stability of the vessel should also be taken in to consideration, from the spe-cifications of the vessel it can be seen that the current draught is only 1.23 m. If the vessel is lifted up from the brash ice it might get a even lower draught and the roll stability might become an issue.
Operation in ice
At first a pre-study is performed to get to know the subject. This chapter gives inform-ation on how a vessel is designed for operinform-ation in ice, what classificinform-ation rules exist and how the rules suggest vessels should be strengthened for operation in ice.
In this chapter the first two bullets from the list of goals are answered.
The performance of a merchant vessel in ice is determined by its ability to pro-ceed forward in ice, an ability which usually is measured with travel times through ice-covered areas and the energy consumed in making the transits. Good performance in ice is characterized by low ice resistance, high propulsion efficiency and power, result-ing in high thrust and also experience of the crew in manoeuvrresult-ing the ship through ice. Good ice performance means also that the ship should not get stuck in ice.
The requirement of good ice performance leads to hull shapes that are not op-timal in open water. Especially the seakeeping characteristics may suffer. Further the increased machinery power and thus price and weight of the machinery together with higher fuel consumption makes the ice-going ship somewhat less economical in open water. [14]
5.1
Design
For a ship to be considered an icebreaker, it requires the three attributes most ships lack: a strengthened hull, an ice-clearing shape and the power to push through sea ice.
5.1.1
Speed
The thicker the ice, the lower the speed of the vessel. Ice breakers are designed for one purpose, breaking the ice. Speed does not matter that much, when the velocities are greater the ice sheet is much thinner.
5.1.2
Hull shape
The bow shape is not as streamlined as a regular vessel, this is because the purpose is to break ice as efficient as possible. The bow shapes for icebreakers may be described
by the stem, flare, buttock, and water-line angles. These angles contribute to the icebreak-ing, submergence, and clearing efficiency. Recent trends in the design of icebreakers are to increase flare angles, to reduce water-line angles, and to reduce stem and buttock angles [14].
The selection of a midbody shape must consider its effect on resistance, manoeuv-rability, construction cost, and the required deadweight. The midbody may be charac-terized by a flare angle (over the full depth or locally), a parallel midbody, and a lon-gitudinal taper.
The stern design on icebreaking ships is controlled mainly by the number of pro-pellers, which is a function of the required power and operational requirements. The stern must, to the greatest extent possible, provide protection to the rudder(s) and pro-peller(s). To provide this protection, a number of design options can be selected. The conventional stern, typical of Canadian Coast Guard icebreakers, is rounded to provide good icebreaking astern performance, and is usually fitted with an ice horn to protect the rudder. A transom, or ramped, stern is installed on several icebreakers. The ob-jective of this stern is to allow the broken ice pieces to move upward to the surface well ahead of the propeller(s).
The hull shape design of ice breaking ships aims at,
• Minimizing the ice resistance by selecting optimal beam and bow shape; • Ensuring good manoeuvring characteristics;
• Enabling the ship to go astern as much and as well as the operational description requires
• Ensuring a proper undisturbed operation of the propeller(s) by minimizing the amount of ice impacting on the propeller(s).
The most important parameters for ice resistance are the beam B and the stem angle
φ1, which is the angle between the stem and the waterline as displayed in Figure 5.1.
Figure 5.1: Definition of stem angle
Figure 5.2: Modern icebreaker design
From the hull shape perspective, the stern shoulder area is crucial for good man-oeuvring characteristics. If the stern shoulders break ice in bending, the ship turns bet-ter as the resisting force for turning this way is minimized. The performance asbet-tern is important if the ship has to navigate independently. When encountering ridges, the ships often gets stuck and in order to be able to proceed, the ship must be able to re-verse and ram again. Good reversing performance is reached by avoiding blunt lines at the stern. Many merchant ships that are only ice strengthened need not to go astern in ice but can count on icebreaker escort in heavier ice conditions. In this case the design of the stern shape is less important.
plough [13].
Bulbous bow
Present experience shows that most merchant ships need not to break ice as they either sail in broken channels or follow an icebreaker. Thus ice strengthened ships often have bulbous bow which is not a handicap in broken ice. The reason for this is that broken ice is displaced around the hull in a way that resembles the hydrodynamic flow. Only in ice going ships and icebreakers which must break the ice themselves the bulbous bow is not appropriate. By shaping the bulbous bow for ice, much of the additional ice res-istance can be avoided [17].
5.2
Ice class
The ice class determines the ice conditions of which the vessel is approved to operate in according to rules. A vessel with an ice class has a sufficiently strong hull, depending on ice class, suitable hull shape, strong enough engine and technical solutions that fit the purpose of the vessel. When operating in ice the hull experiences higher loads then usual which are concentrated to a certain area. The hull therefore needs reinforcements where the ice hits the vessel.
There are different ice class denotations depending on which classification societies or maritime authority assigns them.
5.2.1
FSICR Notations
The following are the ones from Sweden/Finland, FSICR (Finnish-Swedish Ice Class Rules) [2],
Table 5.1: Ice classes in the Baltic
FSICR Ice thickness
IA Super > 100 cm IA > 50 cm IB 30 - 50 cm IC 15 - 30 cm II (not strengthened) 10 - 15 cm IA Super
Ships with such structure, engine output and other properties that are normally cap-able of navigating in difficult ice conditions without the assistance of icebreakers.
IA
IB
The same as above for ice class IA.
IC
The same as above for ice class IA.
II
Ships that have a steel hull and that are structurally fit for navigation in the open sea, and that, despite not being strengthened for navigation in ice, are capable of navigating in very light ice conditions with their own propulsion machinery.
III
Ships that do not belong to the ice classes referred to in the sections above.
5.2.2
DNV GL Notations
DNV GL has formed number of different notations for vessels operating in ice [1], some of them are listed below and for some of them the equivalent FSICR notation is given for comparison. For a full explanation, the DNV GL guidelines regarding ships for navigation in ice should be read but basically they provide a full handbook on how to design a structure for a vessel for each notation.
• ICE-1A*F
• ICE-1A* (FSICR, 1A Super) • ICE-1A (FSICR, 1A)
• ICE-1B (FSICR, 1B) • ICE-1C (FSICR, 1C) • ICE-C
• ICE-E (FSICR, Intended for light localised drift ice in mouths of rivers and) coastal areas.
As discussed before the DNV GL guidelines are written for building a conven-tional vessel, see section 7.1.1 this makes it hard to apply those rules to the SSY design, however, for example a design load could probably be obtained.
5.2.3
Sets of ice class rules
5.2.4
How to classify a SSY design?
Classification of the SSY vessels is quite hard because the structural arrangement is quite different. In this case a classification is not of interest, however some input from the current set of ice class rules can be used.
5.2.5
Strengthening
Traditional ice strengthening of ships is done by adding plating and ordinary stiffeners and primary supporting members. Depending on ice class designed for the extension of the ice strengthened area is defined as "x m above LWL (Load Water Line)" and "x m below BWL (Ballast Water Line)". The fore foot is the area below the ice strengthened area extending from the stem to a position five ordinary stiffeners spaces aft of the point where the bow profile departs from the keel line. The upper fore is the area ex-tending from the upper limit of the ice strengthened area to 2 m above and from the stem to a position at least 0,2 L aft of the forward perpendicular. [15]
Figure 5.3: Strengthening
The hull is usually divided into three parts,
• The Bow Area: From the stem to a line parallel with and 0.04 · L and behind the front border line for the part of the hull where the water line is parallel with the centre line.
• The Midship Area: From the rear of the bow to a line parallel with and 0.04 · L rear of the stern border line for the part of the hull where the water line is paral-lel with the centre line.
The strengthening for this vessel is as follows (Note that the UIWL and LIWL are put in approximately due to the lack of information on this, the designed draught is how-ever 1.23 m which is almost in the middle of the total height of the vessel),
Figure 5.4: Ice strengthening for the concept vessel
The geometries created in the design part are 8 m long which gives an area of investigation as seen in Figure 5.4. The vertical extension of the ice belt for the low-est ice class is shown in Table 5.2. Having a normal draught of 1.23 m, the vertical extension covers a major part of the bow. From a manufacturing point of view it is most convenient to have the strengthening over the entire bow, which is chosen for the design created.
Table 5.2: Vertical extension of ice belt
Ice class Region Above UIWL (m) Below LIWL (m)
Bow 0.70
ICE 1C Midbody 0.40 0.60 Stern
Discussion
Even though the vessel is not supposed to be ice classed it would be recommended to use some kind of strengthening of the bow to start with. If FEM-investigations later show that this is not necessary the plate thickness can always be reduced. Because the entire bow would need to be strengthened for a vessel of this size it does not matter if the FEM-analysis starts with a slightly thicker bow plating than perhaps is necessary.
The framing of the vessel is also supposed to be strengthened according to the DNV-GL guidelines, however, because of the special conditions the SSY-design (see Chapter 8) provides us this is not necessary.
5.2.6
Performance
certain speed.
Turning performance
Turning performance in ice is measured by the diameter of the turning circle (divided by the ship length).
5.3
Loads and resistances
Ice Theory
6.1
Loads
6.1.1
Strategy
In this chapter the third and the fourth bullet from the list of goals are answered. From the theory part it is expected to examine theory regarding how the loads for the Shuttle Ferry Concept will be calculated, that will be encountered when travelling through a brash ice channel in the area of operation. These loads are then applied to the design created in Chapter 8 to see that the requirements are fulfilled.
Three load cases are assumed to be relevant to investigate considering the purpose of the vessels operational criteria,
• Breaking of thin ice: When the ferry starts its working day in the morning it will have to break some ice that has frozen during the night.
• Brash ice: Due to the fact that the vessel will operate as a shuttle it will travel between two locations during the day. The route will be through an broken ice channel with brash ice in it.
• DNV GL ice load: A design load given by DNV GL from the guidelines for ice operation. [1]
6.1.2
Loads due to brash ice
One definition of brash ice is, "Accumulations of floating ice made up of fragments not more than 2 meters across, the wreckage of other forms of ice" [3]. This means that the vessel will travel through a channel of broken ice where smaller pieces of ice are gathered. The vessel will hit the pieces of ice at a certain speed encountering different load magnitudes. For a certain area of operation these differences could be represented by a distribution on the different sizes of pieces of ice and thereby the corresponding loads.
Weibull distribution (3P)
When operating in brash ice the loads experienced can vary a lot in size. One way to represent the different loads that the bow is exposed to is to use a probabilistic dis-tribution of the magnitude of the loads. This can be represented by for example a 3 parameter Weibull distribution as shown in Figure 6.1. From the graph the distribu-tion between the different sizes of the ice floes is illustrated. The majority of the floes are really small with some exceptions, the maximum floe size stated in Table 2.4 would be expected to be found far to the right on the x-axis at a very low frequency of occur-rence.
Figure 6.1: Weibull distribution of loads
From a number of test results performed in [12], Equation 6.1 is developed, by using a best-fit line and fitting it to the top 20 % peak pressures of each distribution.
Fx(x) = 1 − exp(−(x − x0)/α) (6.1)
where x0 and α are constants for a given area, and x is a random quantity
denot-ing pressure. The parameter α is the inverse slope of the best-fit line, and x0 is the
Figure 6.2: How to obtain x0 and α
Another interesting parameter is the pressure per area, the parameter α is a func-tion of area, represented by the curve α = CaD , where a is the local area of interest, and C and D are constants that depend on the physical characteristics of ice.
In [6] the following parameters for the equation are presented,
α = 1.25a−0.7 (6.2)
Figure 6.3: Pressure over area curve
From the tests performed in the paper [6], the equation seems reasonable for the ice properties in that area. Ice is however dependent on a lot of different parameters, so if this would be interesting for the Stockholm area a actual test will have to be per-formed to be able to confirm the equation parameters.
6.1.3
Loads due to ice breaking
One of the scenarios considered is when the vessel operates in ice that has frozen dur-ing the night to a thin layer of solid ice. When the vessel starts its round in the morn-ing with the first passengers it will need to break the thin ice layer.
The ice load is a statistical quantity and thus the design load value must in prin-ciple be determined assuming a probability level or return period of the load. The load level in FSICR is, however, determined based on the experience from the hull damages caused by ice. A more ambitious approach would be to define a certain risk or safety level. The design load value can be given by selecting a return period of occurrence for the load, like once per lifetime, once per ice season, or once per voyage. The selected return period of the load must be in balance with the consequences of exceeding the al-lowable structural responses. This procedure of defining the design points requires thus,
• Definition of the loads in probabilistic terms
• Definition of the limit states in order to ensure a consequent risk implied by the failure of different structural components (e.g. shell plating and frames).
Figure 6.4 shows how a ship usually operates through ice, here can be seen that smaller contact zones appear due to the breaking pattern of the ice. These contact zones can be defined as so called High Pressure Zones [5].
Figure 6.4: Ship breaking ice
From what can be seen in Figure 6.5 a certain area of the ice (an ice wedge) is broken given a set of input variables [19]. The ice braking radius can be given by the following formula,
R = Cll(1.0 + Cvvnrel) (6.3)
where vrel
n is the relative normal velocity between the ice and the hull node, Cl
and Cv are two empirical parameters obtained from field measurements, and l is the
characteristic length of the ice:
l = Eh3 i 12(1 − v2)ρ wg 1/4 (6.4)
By using Equation 6.3 above and assuming the empirical parameters to be 1, the plot in Figure 6.6 is obtained.
Figure 6.6: Radius of ice wedge for different velocities
The ice is broken by the procedure shown in Figure 6.7 and Figure 6.8 below. The ship forces the ice down at a certain angle defined by the stem of the ship. The ship thereby applies a force on the ice sheet which then gets crushed by the ship (the crush-ing force obtained by the area of contact times the crushcrush-ing strength of the ice) [19]. The force can be divided into a vertical and horizontal component as seen in Figure 6.8.
Figure 6.8: Loads from ice on ship
As seen in Figure 6.9, depending on the angle (β) of the ship side the ice will either fail in shear and bending or only due to shear.
Figure 6.9: Loads from ice on ship [4]
Shear vs. Bending failure
When the angle of the ship side is 0◦ the ice will only fail in shear. The Crushing strength (Compressive strength) of the ice used in this report is around 2.30 MPa.
If the angle of the ship side is larger then 0◦ the ice will fail due to shear and bend-ing. The Flexural strength of the ice used in this report is around 0.55 MPa.
The values are obtained from Table 2.3
From this we can see that the Crushing strength is about 4.2 larger then the flex-ural strength. This means that it is much easier to break the ice when the incline of the ship side is greater then 0◦.
Global loads vs. Local loads
Local loads are experienced by stiffened panels, girders, beams, & stringers.
Loads at the stem The stem is the most forward part of a vessel. The stem will encounter the first hit of the ice and thereby encounter the largest stresses.
Loads at bow The bow is the structural part right behind the stem and will en-counter loads almost in the same way as the stem, from an ice sheet High Pressure Zones will occur as a strip along the length of the bow from the stem going aft.
Ice bending failure
The following equation is proposed in [19], where Pf is the bending failure force in N. Pf = Cf
θ π
2
σfh2i (6.5)
where θ is the opening angle (see Figure 6.5) of the idealized ice wedge, σf is the
flex-ural strength of the ice, hi is the thickness of the ice, and Cf is an empirical parameter
which is obtained from measurements. In Figure 6.10 the characteristics of the bend-ing failure of ice is shown for different ice thickness’s and openbend-ing angles. It can be seen that when the opening angle and the ice thickness increase the bending failure in-creases even more.
Figure 6.10: Bending failure of ice for different thickness’s
Forces
Ice Crushing Force
The Force seen in Figure 6.7
Fcr = σcAc (6.6)
Frictional forces
The frictional forces are divided into a vertical and horizontal component.
fH = µiFcrvtrel/ q (vrel t )2+ (vreln,1)2 (6.7) fV = µiFcrvn,1rel/ q (vrel t )2+ (vreln,1)2 (6.8)
Vertical and Horizontal components
From the ice crushing force and the frictional forces a vertical and horizontal compon-ent can be obtained which is visualized in Figure 6.8 and the equations below,
FH = Fcrsin(φ) + fVcos(φ) (6.9)
FV = Fcrcos(φ) − fVsin(φ) (6.10)
Using the reasoning above, comparing the bending failure and the vertical com-ponent of the force and varying the area of contact it can be seen what area of contact is required for a few different parameters (ice thickness and stem angle) tested below. The velocity components are estimated and kept constant (vrel
n,1 = 3 m/s and vtrel = 5
m/s) during the investigation.
In Figure 6.11 the ice thickness and the opening angle are kept constant at 5 cm and 45 ◦ while the plot shows the bending failure for three different stem angles, 15◦, 45◦ and 70◦. Because the thickness of the ice is constant Pf only has one line while FV
Figure 6.11: Vertical force needed for different stem angles at 5 cm ice thickness
In Figure 6.12 the stem angle and the opening angle are kept constant at 30◦ and 45◦ while the plot shows the bending failure for three different ice thickness’s, 3, 5 and 10 cm. This implies that FV only is area dependent, while PF has three different lines
Figure 6.12: Vertical force needed for different ice thickness’s at 30 ◦ stem angle
Conclusions
From Figure 6.11 it can be seen that when the stem angle increases, the crushing fail-ure takes place at a smaller area of contact, creating a larger load and thereby easier breaking the ice. In Figure 6.12 the ice thickness is varied showing what area of contact is needed to break the ice.
6.1.4
Design Loads from DNV-GL
Figure 6.13: Idealization of loads
Ice pressure is not measured directly, it is always ice force F that is measured on a certain gauge area Ag and then the pressure is deduced as F/Ag.
In the DNV-GL rules given for "Ships for Navigation in ice" [1] a set of design loads is given (Sec. 3, B. Design Loads).
B 100 Height of the ice load area
An ice strengthened ship is assumed to operate in open sea conditions corresponding to a level ice thickness not exceeding h0. The design the ice height (h) of the area actually
under ice pressure at any particular point of time is, however, assumed to be only a fraction of the ice thickness. The values for h0 and h are given in the following table,
Table 6.1: Values of h and h0
Ice class h (m) h0(m) ICE-1A* 1.0 0.35 ICE-1A 0.8 0.30 ICE-1B 0.6 0.25 ICE-1C 0.4 0.22 B 200 Ice pressure
In the subsection, B 200 Ice pressure, the design ice pressure can be calculated by a presented formula based on a nominal ice pressure of 5600 kN/m2,
p = 5600cdc1ca(kN/m2) (6.11)
where cd is a factor which takes account of the influence of the size and engine
output of the ship. This factor is taken as maximum cd = 1. It is calculated by the
cd= ak + b 1000 (6.12) where, k = q (∆fPs) 1000 (6.13)
Table 6.2: Values of a and b Region
Bow Midbody and Stern k ≤ 12 k > 12 k ≤ 12 k > 12
a 30 6 8 2
b 230 518 214 286
∆f = displacement (t)
Ps = machinery output (kW)
c1 = a factor which takes account of the probability that the design ice pressure occurs
in a certain region of the hull for the ice class in question.
Table 6.3: Values of c1
Ice class Region
Bow Midbody Stern ICE-1A* 1.0 1.0 0.75
ICE-1A 1.0 0.85 0.65 ICE-1B 1.0 0.7 0.45 ICE-1C 1.0 0.5 0.25
ca = a factor which takes account of the probability that the full length of the area
un-der consiun-deration will be unun-der pressure at the same time. It is calculated by the for-mula, ca= s l0 la , (6.14)
with a maximum of 1.0 and a minimum of 0.35, l0 = 0.6 m.
Table 6.4: Values of la
Structure Type of framing la
Shell transverse frame spacing longitudinal 1.7 x frame spacing Frames transverse frame spacing
longitudinal span of frame
Ice stringer span of stringer
Web frame 2 x web frame spacing
This will give a few different pressure values for the different ice class requirements and areas of the ship investigated.
Result
Using the DNV-GL guidelines from above the design ice pressure is calculated as,
pice= 965 kN/m2 (6.15)
The design pressure can now be used to calculate the shell plating thickness ac-cording to Pt.5 Ch.1 Sec.3 C. Shell Plating
Shell plating
C 100 Vertical extension of ice strengthening for plating For the bow in the lowest ice class (1B and 1C) the extension shall be placed 0.40 m above UIWL and 0.70 m below LIWL, see Figure 5.2.
C 200 Plate thickness in ice belt For the longitudinal framing the thickness of the shell plating shall be determined by the formula,
t = 21.1s
s
p f2σF
+ tc(mm) (6.16)
s = stiffener spacing i m measured along the plating between ordinary and/or interme-diate stiffeners.
p as given in equation 6.16
f2 = 0.6 +
0.4
(h/s), when h/s ≤ 1, 0.33 in our case h = as given in Table 6.1
σf = yield stress of the material (N/mm2)
tc = increment for abrasion and corrosion (mm); normally 2 mm. If a special surface
Result
The resulting plate thickness in the ice belt is calculated as,
t = 12.94 mm (6.17)
This is a really thick plate which is not desired in this case, in the Figure below the stiffener spacing is plotted against the required plate thickness to show the different thickness’s and the corresponding spacing of the stiffeners.
Figure 6.14: Stiffener spacing vs. Plate thickness
Discussion
Figure 6.15: Traditional structure
As can be seen in Figure 6.16 the spacing between the load transfers (red lines) is not constant which will create problems interpreting the DNV-GL rules, it can either be X1 or Y1 as stiffener spacing.
Figure 6.16: SSY structure
In the calculations above, the stiffener spacing is however chosen as the maximum between them, Y1 = 0.675 m. This gives a really large plate thickness compared to
nor-mal plate thickness for the SSY vessels, to reduce the thickness naturally the stiffener spacing has to be reduced as seen in Figure 6.14.
H 100 Stem, baltic ice strengthening
Figure 6.17: Stem designs
Scantlings
The DNV-GL rules also state scantlings for the structural parts which the hull struc-ture consist of, this is however not relevant because of the special design SSY uses to build there vessels.
Loads from other sources
Other sources than DNV-GL have also been examined, this is to see if the design loads from DNV-GL differ a lot to the other load formulas obtained by other sources. These sources might also give a better design load for the case of brash ice.
6.1.5
Jordaan
(a) Contact between ice sheet and vessel seen from the side
(b) Contact between ice sheet and vessel seen from above
Figure 6.18: High Pressure Zones
the SSY vessel. The forces however do very rarely reach above 20 MN, this could give some indication on what forces our vessel will need to be designed for. It will travel at a much higher speed, but the ice conditions wont even be close to the ones the ice breakers in question operate in.
6.1.6
Masterson
In [9] the authors have performed empirical tests on offshore structures and ship hulls exposed to ice loads. This work resulted in a few different equations where the first tests were performed on multi-year ice in the Beaufort sea, however in the end an-other test was performed which according to the authors was closer to the conditions one could expect in the Baltic (even though the results of there equation might still be higher than the once encountered in the Baltic). The result from this is as follows,
p = 4.0A−0.5 (6.18)
This then gives a relationship as shown in Figure 6.19 below.
Figure 6.19: Area vs. Pressure
The linear regression is according to the authors only tested for areas above 1 m2
for areas below 1 m2 this is what it looks like. The reason why this might be
interest-ing is due to the fact that the vessel investigated is quite small and the load areas are expected to be quite small as well.
Discussion
The Masterson expression is expected to show a slightly exaggerated result, this is be-cause of the different ice conditions in the Beaufort sea vs. Stockholm city/inner ar-chipelago. It also has been measured for areas that are slightly larger than the design created will have which also makes it a bit questionable.
6.1.7
Suyuthi
In [20] the author shows how a a typical time history of ice induced loads on a vessel can look like. This is shown in Figure 6.20,
Figure 6.20: Typical ice loads over time
When the hull gets in contact with the ice edge, a crushing failure mechanism takes place first and consequently the spike is getting higher and higher. Looking care-fully at the spike-like load, there is evidence of a typical saw-tooth shape which indic-ates infrequent crushing when the hull is advancing into the ice. When the accumu-lated force is high enough to initiate bending failure of the ice at a certain distance in front of the contact surface, a sudden drop of the load is observed. Afterwards, there is no event in the time series record until the next contact of the hull with the next ice edge at which the same spike-like load is repeated.
6.1.8
Su B., Riska K., Moan T
Figure 6.21: Typical ice loads over time
From the figure a typical load pattern can be seen, when breaking ice, even though the tests are performed in much thicker ice then the vessel in this thesis is intended for it gives an idea of what to expect in terms of load pattern but not load size.
In Figure 6.22 it is shown how the peak values of the loads are distributed. The measurements are taken on the same vessel as above at an ice thickness of 0.125 m at the same frame as before.
6.1.9
Discussion
All formulas obtained from the sources above are semi-empirical which makes them dif-ficult to use while they sometimes depend on constants obtained from empirical tests.
6.2
Resistance
Ice resistance refers to the time average of all longitudinal forces due to ice acting on the ship. These ice forces are divided into categories of different origin,
• Breaking forces • Submergence forces • Sliding forces
In different ice conditions the relative importance of these components varies, in level ice the breaking component is usually the largest but in brash ice or when hitting smaller ice floes the other two components become more important. The breaking force is related to the breaking of the ice i.e. to crushing, bending and turning the ice. Sub-mergence is related to pushing ice down along the ship hull whereas the sliding forces include frictional forces. Usually the velocity dependency of the ice resistance is attrib-uted to the last component.
The ice resistance is usually expressed as follows,
RiT OT = Ri+ Row (6.19)
that is, the total resistance is the ice resistance plus the open water resistance [13]. The ice resistance is then divided into different components as mentioned above,
Ri = RB+ RS+ RF (6.20)
where the first component is from breaking the ice, the second from submerging the ice and the last from friction against the hull due to sliding. Most methods used to calculate the ice resistance are based on regression on full scale and model scale data. The regression assumes the ice resistance to be linear with ship speed and to consist of these three components. Thus the calculation methods for ice resistance are at best semi-empirical, and these methods should be used cautiously, especially outside the range of validity. The calculation methods to determine the ice resistance should be used only in the conceptual design phase as these methods cannot account for the de-tails of the hull shape. When the design proceeds, ice model tests should be carried out to finalize the hull shape.
6.2.1
Brash ice resistance from DNV-GL
From the DNV guidelines [1] the following equations are obtained regarding brash ice resistance in a channel with brash ice and a consolidated layer. The formulas have some limits regarding ship parameters (Length, Breadth, Draught, etc.) to be valid, the ship in this assignment falls outside these parameters, however due to lack of more suit-able theory the formulas still might give a hint on how to design a bow for minimum resistance. Figure 6.23: Definitions RCH = C1+ C2+ C3Cµ(HF + HM)2(B + CψHF) + C4LP ARHF2 + C5( LT B2) Awf L (6.21) Where, Cµ = 0.15cos(φ2) + sin(ψ)sin(α) ≥ 0.45, Cψ = 0.047ψ − 2.115 and 0 if ψ ≤ 45◦ HF = 0.26 + (HMB)0.5
HM = 0.6 (for ICE-1C, closest to what is desired) C1 and C2 are set to zero
be-cause they take a consolidated upper layer of brash ice into account. ψ = arctan(tan(φ2)
Figure 6.24: Brash ice resistance
From the figure above the minimum resistance is obtained at α = 15◦ and φ2 =
90◦. Having a vertical bow at B/4 of the vessel is however not that good from an open water water resistance perspective. Another promising point according to the figure is at the lower extremes of each angle, at α = 15◦ and φ2 = 10◦, this gives a total
resistance of 7.88 kN.
6.2.2
Myland & Ehlers (Lindqvists) formulas
Figure 6.25: Hull parameters
Ice breaking resistance The breaking component is further divided into a bending component, RBi = ( 27 64)σfB (h1.5ice) s E 12(1 − ν2)ρ wg (tan(ψi) + µ cos(φi) cos(ψi)sin(αi) )(1 + 1 cos(ψi) ) (6.22)
and a crushing component,
RC = 0.5σfh2ice(tan(φ) + µ cos(φ) cos(ψ)) , (1 − µsin(φ) cos(ψ))) (6.23)
where RB is the bending resistance, σf the flexural strength, B the ship breadth, hice the ice thickness, ν the Poisson’s ratio, ρw the density of water, g the gravitational
acceleration, ψ the normal angle, µ the friction coefficient between ship hull and ice,
φ the stem angle, α the waterline entrance angle and RC the crushing resistance. The
normal angle is calculated from the waterline entrance angle and the stem angle ac-cording to,
ψ = atan(tan(phi)/sin(α)) (6.24)
Both components are derived from semi-empirical approximation of the physical process of ice breaking. The formulas consider only roughly the mechanical and geo-metrical parameters.
RS = ρgghiceB( T (B + T ) B + 2T + µ(0.7L − T tan(φ) − B 4tan(α) +T cos(φ)cos(ψ) s 1 sin(φ)2 + 1 tan(α)2)) (6.25)
where RS is the submersion resistance, ρg the density difference, T the ship draught
and L the ship length between perpendiculars.
The influence of a plough is not considered in the formula, whereas the ships draft and the density difference between ice and water are taken into account. The total es-timated bottom coverage of the vessel is 70%, since the stern of the vessel is in general not completely covered by ice.
Total resistance The main resistance components are extended by speed dependent components based on empirical constants. Thus, the resulting ice resistance is reported by Lindqvist as, Rice = (RC + RB)( 1 + 1.4 ∗ v √ ghice ) + RS( 1 + 9.4 ∗ v √ gL ) (6.26)
where Rice is the ice resistance and v the ship velocity.
Figure 6.26: Re-defined geometry for better results
Results
Figure 6.28: Crushing resistance
Figure 6.30: Total resistance
Discussion
In the Figures above it can be seen that the formulas provide some very extreme res-ults for some angles, whereas other angles give really small values. To try to visualize the plots better the logarithmic values of the results have been plotted instead.
This tells us that either the values are actually very low at those angles where very little is shown or that the formulas are somehow limited to a certain range of angles.
6.2.3
Riska a.o.; Level ice resistance
Riska explains that there exist a wide variation in ice resistance predictions obtained by different formulations. This variation has been the subject of several studies, e.g. Bachér (1983) and Kämäräinen (1993). Instead of adopting any of the former level ice resistance formulations, a simplified version based mainly on three formulations is de-rived here. The three formulations used are those of Ionov (1988), Lindqvist (1989) and Kämäräinen (1993).
The parameter ice resistance depends on may be divided into three groups [2]. The first group consists of external variables: ice thickness, hi and ship speed, v. The
two other groups contain the shape of the ship (φ, B/T, L/B, Lbow/L, Lpar/L) and the
size of the ship (Lpp, B, T ). This way the ice resistance is, Ri = f (hi, v, φ, B T, L B, Lbow L , Lpar L , Lpp, B, T ) = C1+ C2v (6.27)
The constants C1 and C2 dependent of ship particulars must now be determined.
angle at the bow, α0, or along the waterline, α, are not included in the formulation
be-cause their influence on resistance is contradictory in the three references mentioned earlier. This angle is also difficult to define for all but wedge-like waterlines. The flare angle, ψ(= tanφ/sinα) has been suggested to influence the resistance significantly (En-qvist & Mustamäki 1986) but as the angle α is neglected then only the influence from the stem angle φ remains.
The equations for the functions C1 and C2 are,
C1 = f1
1 2T
B + 1
BLparhi+ (1 + 0.021φ)(f2Bh2i + f3Lbowh2i + f4BLbowhi) (6.28) C2 = (1 + 0.063φ)(g1h1.5i + g2Bhi) + g3hi(1 + 1.2 T B) B2 √ L (6.29)
where the values for the constants are shown in Table 6.5, these values have been developed based on performances measured on large ice classed ships between 96 and 193.7 m long.
Table 6.5: Values of fi and gj
f1 = 0.23 kN/m3 g1 = 18.9 kN/(m/s x m1.5)
f2 = 4.58 kN/m3 g2 = 0.67 kN/(m/s x m2)
f3 = 1.47 kN/m3 g3 = 1.55 kN/(m/s x m2.5)
f4 = 0.29 kN/m3
The influence of the stem angle φ on the ice resistance is usually proportional to the tangent of this angle. The dependence of ice resistance on the stem angle is made somewhat less dominating in the above equation because many merchant vessels have quite vertical bows without the icebreaking performance suffering that much. The stem angle is to be measured without accounting for the bulb.
Figure 6.31: Speed vs. Resistance at 5 cm ice sheet and stem angle 30◦
Figure 6.32: Stem angle vs. Resistance at 5 cm ice sheet and speed 20 m/s
In Figure 6.33 the speed and the stem angle are varied giving a 3D-plot showing the resistance for different combination of these variables. From this the same conclu-sion can be drawn as before, when increasing the speed the resistance increases a lot, while when the stem angle changes the resistance only changes very little.
Figure 6.33: Stem angle vs. Resistance at 5 cm ice sheet and speed 20 m/s
Discussion
The results seem quite reasonable here, because the thickness of the ice is really small the stem angle should not matter that much. As can be seen in Figure 6.9 the ice breaks easier when bending then when buckling, but in this case the buckling force is really low which means that the ice breaks quite well regardless of the stem angle. There is of course a small increase in resistance when the stem angle increases which implies that the ice breaking force goes from bending to buckling. The formulas of course neglect the water resistance which would increase a lot when changing the stem angle.
The large increase in resistance when changing the speed might be quite intuitive, whenever the speed of a vehicle is increased also the resistance is increased. This can be easily explained using the expression for drag force,
FD =
1 2ρv
2
CdA (6.30)
From this it is seen that the drag force increases by a power of two when the speed increases (the rest of the variables are kept constant).
6.2.4
Open water resistance
The open water resistance is of great importance when choosing the best geometry for the bow that is going to be developed later in this paper. Due to limitations a CFD analysis wont be performed, to still get some knowledge about the open water resist-ance the Holtrop & Mennen formulas could be of use.
Holtrop & Mennen
The Holtrop & Mennen formulas [7] are probably the most used when this resistance has to be calculated analytically. The problem however is that they have a hard time accounting for smaller changes in the bow geometry. This makes them complicated to use when the geometries are similar in size but have different geometrical properties.
Holtrop & Mennen developed the following formula to estimate the resistance of a ship,
RT = RF(1 + k1) + RAP P + RW + RB+ RT R+ RA (6.31)
Here, RF is the frictional resistance according to the ITTC 1957 friction formula
= 0.5ρV2SC
F. ρ is the fluid density, V is the ship speed, S the wetted area of the hull
and CF the frictional coefficient. The frictional resistance is the net fore-and-aft forces
upon the ship due to tangential fluid forces. Frictional resistance accounts for nearly 80 percent of total resistance in slow-speed ships like oil tankers and as much as 50 per-cent in high-speed ships like container vessels. Frictional resistance is due to the viscos-ity of the fluid.
The frictional coefficient as calculated according to the ITTC (1957), CF = 0.075/(log10Re−
2)2, Re is the Reynolds number. The frictional coefficient can be calculated in a lot of
different ways, however the Holtrop & Mennen formulas seem to be based on the ITTC way of calculating it.
The Reynolds number, Re = ρV L/µ, ρ again representing the fluid density, V, the ships speed, L the length of the ship, and µ the viscosity of the fluid.
1 + k1, Form factor describing the viscous resistance of the hull form in relation to
RF. k1 can be determined using the Watanabe formula, k1 = −0.095 + 25.5
CB (L B) 2 s B T
The equation is visualized in Figure 6.34, the form factor is calculated as CB =
∆
Figure 6.34: Form factor
Appendage resistance, RAP P = 0.5ρV2SAP P(1 + k2)CF, where SAP P is the wetted
area of the appendages and 1 + k2 the appendage resistance factor. Appendages include
for example rudders, shafts, fins and keels.
Table 6.6: Values of k2
Rudder behind skeg 1.5 - 2.0 Rudder behind stern 1.3 - 1.5 Twin-screw balance rudders 2.8
Shaft brackets 3.0 Skeg 1.5 - 2.0 Strut bossings 3.0 Hull bossings 2.0 Shafts 2.0 - 4.0 Stabilizer fins 2.8 Dome 2.7 Bilge keels 1.4
The equivalent 1 + k2 value for a combination of appendages is determined from,
(1 + k2)eq =
P
(1 + k2)SAP P
P
SAP P
Wave-making and wave-breaking resistance, RW. In the KTH Naval architecture
Figure 6.35: Form factor coefficient, CR
Using a prismatic coefficient, CP = ∆/(AMLP P) of 0.5 which is the closest to the
measured one of 0.41 and a Froude number of 1.28, this gives a CR of around 5.6 ∗ 10−3.
The actual value of ∆/L1/3 is 6.2, using interpolation C
R is corrected to 5.56 ∗ 10−3.
For reasons explained in the literature CR is calculated as the difference between CT M
and Cf M, which means that the the CR coefficient is scale dependent and is obtained
of the model is 4 m, using ITTC-78
RB, Additional pressure resistance due to bulbous bow near the water surface RT R, Additional pressure resistance of immersed transom stern
RA, Model-ship correlation resistance
6.3
Discussion
For both the loads and resistances the formulas found are most often semi-empirical, basing constants on results from model or full-scale tests, this shows how hard it ac-tually is to deal with ice. The forms and physical properties of an ice sheet constantly change, there can be brash ice, pancake ice, level ice, grease ice, ice from salt water, ice from fresh water and so on. These differences make it really hard to formulate exact formulas for all conditions or for that sake a general condition applicable for all types of ice. The formulas presented can however show how things change when a certain parameter is modified, it can show what kind of magnitudes to expect on resistances or loads for example. A lot can be learnt from studying them.
For more exact results for a certain ship or some earlier unexplored geometry a model test could be of great value. Unfortunately there are not that many facilities around that can perform these tests in an basin with the possibility of growing an ice sheet and it is also rather expensive.
SSY design
This chapter will present the SSY design theory, showing the hull structural design and other features that differ from a conventional design. This chapter presents the answer to the fifth bullet from the list of goals.
The SSY design technique has been developed from looking at ships used during the Viking period, the Vikings’ long and relatively narrow wooden longships were ex-tremely lightweight and fast. One of their secrets that allowed them to sail over vast oceans was that the Viking longship hull was flexible in construction, which allowed it to absorb the force from powerful waves. In modern times, several Viking ships have been built, including the Ormen Långe in Stensund near Trosa in the 1950s. More re-cently, a Viking ship was built on the historic island of Björkö in Lake Mälaren. There are extensive archeological remains from a large Viking settlement from around the year 1000 AD. The island is now known as Birka and has a famous museum. The Birka ship has sailed up to 18 knots.
Håkan Rosén, the founder of the SSY technique has now incorporated the Viking’s flexible hull structure into the modern SSY steel boats. This has been done by design-ing flexible longitudinal strdesign-ingers (which are patented), which together with Sandviks stainless steel makes it possible to build extremely lightweight boats entirely from stain-less steel.
7.1
Hull
7.1.1
Conventional hull structure
Traditionally a hull structure is built up as a typical framework. The loads from the sea are absorbed through a number of structural parts, starting with the outer plates, the plates distribute the loads to stiffeners, the stiffeners to girders/stringers and then through the web frames to the ship as a whole.
