MARL041 — Apply advanced principles of trim, stability and stress

1 Apply Simpson’s First and Second Rules to calculate areas, volumes and displacement of ship shapes using tonnes per centimetre (TPC) values

• 1.1Simpson’s (Mid-Ordinate) First Rule and Second Rule, with typical applications, using half and full ordinates is explained and applied to find typical and non-conforming shipboard areas
• 1.2Areas of water planes, transverse sectional areas to determine underwater volumes, bulkheads and elemental areas are calculated
• 1.3Problems of immersed hull volume, appendage volumes and non-standard tank volumes are solved
• 1.4Archimedes principles of buoyancy are explained
• 1.5TPC with application of Simpson’s Rules to find displacement is explained
• 1.6Change in draught with mass addition and removal using TPC to give parallel sinkage or rise is explained
• 1.7Problems of vessel displacement given water plane areas or TPC values are solved
• 1.8TPC curves and displacement curves for given values are constructed

2 Apply ship form coefficients and changes in draught associated with fluid density

• 2.1Ship form coefficients and their uses are defined
• 2.2Coefficients are calculated given underwater form particulars
• 2.3Problems of ship form coefficients following change in length and draught are solved

3 Calculate changes in draft due to fluid density

• 3.1Load line freeboard measurement and markings required for change in fluid density are explained
• 3.2Formula for change in mean draft due to change in density is derived
• 3.3Change in draft between fluids of two densities are calculated
• 3.4Formula to derive freshwater allowance is applied
• 3.5Changes in mean draft due to changes in density and loading are calculated
• 3.6Density correction formula is defined

4 Solve stability problems

• 4.1Calculations are performed to solve problems associated with adding, removing and transferring masses on ships
• 4.2Centre of gravity of a suspended mass is explained
• 4.3Calculations are performed to solve problems associated with suspended masses
• 4.4How centre of gravity (CG) and linear congruential generator (LCG) can be obtained from stability information is explained
• 4.5Creation of overturning moments by mass addition, removal or transfer transversely, including cargo shift or loss, is explained
• 4.6Calculations are performed to solve problems of small angle transverse stability
• 4.7Purpose of inclining experiments, weighing tests and roll period tests to determine stability characteristics are explained
• 4.8Calculations are performed to solve problems associated with inclining experiments and roll period tests

5 Calculate loss of transverse stability due to fluid free surface

• 5.1Principles of free surface loss of metacentric height (GM) are explained
• 5.2Principles of metacentric data height are explained
• 5.3Application of the second moment of area using parallel axis theorem to obtain free surface moment of inertia and use of density correction between vessel and free surface fluids is explained
• 5.4Calculations are performed to solve problems of liquid free surface for simple compartments, including correction for free surface on GM and fluid mass on CG
• 5.5CG solid is differentiated from CG fluid
• 5.6Second moment of area is applied to obtain free surface moment of inertia and is related to stability criteria for standard conditions
• 5.7Problems of liquid free surface for simple and complex geometry compartments, including variation in filling rates, are solved
• 5.8Wall-sided formula and factors that lead to negative GM creating an angle of loll are explained
• 5.9Problems involving correction of loll angle are solved

6 Calculate large angle transverse static and dynamical stability

• 6.1How GZ and KN righting levers are obtained from cross curves of stability is explained
• 6.2KN values are converted to GZ
• 6.3Dynamical stability is explained
• 6.4IMO requirements for intact and damaged stability cases as well as different vessel types, using typical values from stability files are applied
• 6.5Problems of large angle transverse stability, including changes due to redistribution of mass onboard, are solved and results against IMO requirements are evaluated
• 6.6Graphical solutions to large angle transverse stability problems identifying key points are prepared

7 Solve problems of hydrostatics

• 7.1Importance of area and volume centroids is explained
• 7.2Methods of determining centre of buoyancy (CB), longitudinal centre of buoyancy (LCB), longitudinal centre of flotation (LCF) and bulkhead area centroids are explained
• 7.3Calculations are performed to determine centroids of shipboard areas and volumes
• 7.4Impact of hydrostatic pressure and load on vertical and horizontal surfaces is explained
• 7.5Methods of calculating pressure, load, shear force and bending moment diagrams for typical tank structures are applied
• 7.6Problems are solved in hydrostatics relating to pressure and loads on ship structures, including graphical solution of shear force diagrams of rectangular bulkheads and their elemental stiffeners
• 7.7Effective weld area of bulkhead attachment is calculated

8 Perform trim and draft calculations

• 8.1Meaning of trim and how trim occurs is explained
• 8.2Standard trimming moments resulting from mass addition, removal, transfer, flooding or combinations of these factors are explained
• 8.3Change of trim is calculated using moment to change trim 1 cm (MCT1cm), longitudinal metacentre height (GML) and longitudinal metacentre radius (BML)
• 8.4Problems of applied trimming moments to determine final vessel draughts are solved
• 8.5True mean draft is differentiated from apparent mean draft by applying correction for layer
• 8.6Calculations are performed to solve problems associated with true mean draft
• 8.7Problems of combined trim and transverse stability from typical fluid transfer in both a longitudinal and transverse direction are solved

9 Calculate voyage and daily fuel consumption

• 9.1Problems of fuel consumption are solved using the admiralty coefficient for various speed indexes
• 9.2Optimum vessel speed for combined propulsive and auxiliary fuel consumptions is determined
• 9.3Calculations are performed to show relationships between fuel consumption and displacement
• 9.4Calculations are performed to show relationships between daily fuel consumption and speed
• 9.5Calculations are performed to show relationships between voyage consumption, speed and distance travelled

10 Apply principles of loading to ship structures to determine strength characteristics

• 10.1Distribution of concentrated and point masses, buoyancy, load, shear force and bending moments are explained using simple loaded beam principles
• 10.2Calculations and diagrams are used to solve problems involving loaded conditions of simple box-shaped vessels, identifying location and value of maximum shear force and bending moments
• 10.3Empirical formula is applied to solve problems involving bending and direct stress in beams

11 Apply empirical formula to solve vibration problems

• 11.1Causes and adverse effects of ship vibration are explained
• 11.2Natural hull vibration is explained
• 11.3Schlick formula is applied to determine natural frequency of ship hull vibrations
• 11.4Ways of preventing or reducing local vibration are identified

12 Solve buoyancy problems and problems related to symmetrical flooding

• 12.1Calculations are performed to solve problems of lost buoyancy and sinkage into homogeneous mud due to tide fall with insufficient under keel clearance
• 12.2Calculations are performed to solve problems of simple box-shaped and standard hull forms involving change in trim due to flooding end compartments
• 12.3Volume lost-volume gained relationship for flooded compartments is explained
• 12.4Modified volume lost by compartment subdivision is explained using horizontal flat
• 12.5Modified volume lost by compartment permeability is explained, including consideration of cargo stowage factor and relative density details
• 12.6Problems of symmetrical flooding of simple box-shaped and standard hull forms involving flooding above and below horizontal subdivisions and different permeabilities are solved

13 Perform rudder structural calculations

• 13.1Types of rudders in use on ships are outlined
• 13.2Reasons for using balanced rudders are identified
• 13.3Application of force acting normal to a rudder surface (Fn), its components and the influence of propeller race effect is explained
• 13.4Rudder centre of effort for ahead and astern conditions is obtained to determine torque on rudder stock for conventional rudders or equivalent twisting moment (ETM) for spade rudders
• 13.5Calculations are performed involving simple and complex rudder shapes to calculate speed limitations ahead and astern for stated safety factor and material properties
• 13.6Calculations are performed involving simple and complex rudder shapes to determine rudder stock and coupling bolt diameters

14 Perform rudder resistance and power calculations

• 14.1Frictional resistance to motion of a vessel given the empirical formulae for frictional coefficient ‘f’ of the form is determined
• 14.2Froudes laws of comparison are explained
• 14.3Meaning of the term ‘corresponding speed’ is explained
• 14.4Law of comparison is applied to determine residuary resistance of a ship if residuary resistance of a scale model of vessel is known or can be determined
• 14.5Differentiation is made between effective power (naked), effective power and ship correlation factor
• 14.6Effective power requirements of a full-sized ship given total resistance to motion measured on a scale model of vessel towed at corresponding speed are calculated
• 14.7Problems of resistance and powering for full size vessels and models are solved

15 Solve propeller and powering problems

• 15.1Factors that influence the speed of advance are explained
• 15.2Calculations are performed to solve problems of single screw vessels
• 15.3Relationships between propulsive coefficient, quasi-propulsive coefficient and related powers together with typical values of losses for transmission, hull and propeller are explained
• 15.4Components of hull resistance are explained
• 15.5Calculations are performed to show impact of resistance augmentation and thrust deduction factors on powering of full-size vessels
• 15.6Causes, effects and methods of reducing cavitation are explained

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