Stability Revision

a) Centre of Gravity.The centre of gravity of a body is the point at which all the mass of the body may be assumed to be concentrated and is the point through which the force of gravity is assumed to act vertically downwards.The point at which the body would balance.

GG1 = wxdFinal displacement = (Meters)

w = mass removed or loaded.d = distance between CG of the mass and the CG of the body.

When a weight is suspended its CG is considered to be at the point of suspension.

Conclusions:-The CG of the ship will move directly towards the CG of any weight loaded.

The CG of the ship will move directly away from the CG of any weight discharged.

The CG of the ship will move directly parallel to the CG of any weight shifted.

The position of the CG of the ship can only be altered by loading/discharging and shifting weights.

a) List.List: A ship is said to list when she is inclined by forces within the ship.Heel: A ship is said to heel when inclined by external forces. E.g. waves, wind.

CG is considered to act vertically downwards with a force equal to the weight of the ship. (KG is the vertical CG of the ship. VCG)

The centre of buoyancy B is considered to act vertically upwards with a force equal to the weight of water displaced (KB is the vertical centre of buoyancy of the ship. VCB)

To float at rest in still water a vessel must displace her own weight, andThe centre of gravity must be in the same vertical line as the centre of buoyancy.

KM= KB+BM also KM= KG+GM.

Metacentre = The vertical through the centres of buoyancy at two consecutive angles of heel at a point called the metacentre.

The KM depends upon the ships underwater Form.Stable equilibrium = If a ship is inclined she tends to return to the initial position. The Centre of gravity must be below the metacentre. (E.g Positive initial metacentre.)If moments are taken about G there is a moment to return the ship to upright.(GZ) this is called the Moment of Statical Stability)The moment is equal to the product of the force W and the Length of the righting lever GZ.

Moment of Statical stability = W X GZ(tonnes-meter)

GZ = perpendicular distance between the CG and the vertical through the centre of buoyancy.

At angles less than 15 degrees GZ=GM X sin angle X Moment of Statical stability = W X GM X sin angle.

Unstable equilibriumWhen a ship which is inclined to a small angle tends to heel over still further, she is said be in unstable equilibrium. For this to occur the ship must have a negative GM. G above M.The moment of Statical stability is a capsizing moment.

A ship having a small negative GM need not necessarily capsize.Develop a angle of Loll.

Neutral equilibrium.When G and M are together zero GM. If inclined to a small angle she will tend to remain at that angle of heel until another external force is applied. No moment to bring the ship upright or heel her over further.

Correcting unstable or Neutral The CG of the ship is to be lowered.1. Weights already onboard the ship lowered.2. Weights may be loaded below the CG.3. Weights may be discharged from positions above the CG.4. Free surfaces within the ship removed.

The time period of a ship is the time taken by the ship to roll from one side to the other and back again to the initial position.

Stiff ShipWhen a ship has a large GM 2,3 meters the righting moments at small angles of heel will be comparatively large. It will then require larger

righting moments to incline the ship. When inclined she will return more quickly to the initial position. The result is the ship will have a comparatively short time period and will roll quickly and perhaps violently from side to side.(8 seconds)

The CG should be raised within the ship.

Tender Ship.When the GM is comparatively small, for example 0.16m to 0.20m the Righting moments at small angles of heel will be small. The ship will thus be much easier to incline and will not tend to return so quickly to the initial position. The time period will be long 30s to 35s.

The CG should be lowered within the ship.

A time period of 20s to 25s would be the most acceptable for those onboard.

a) Voyage changes in stability.

1. Consumption of fuel and storesLoss of weight from double bottom tanks causes a rise in G thereby reducing the metacentric height and therefore the GZ curve.

2. Free surface effectThe consumption from full tanks will create free surface effectThis will reduce the metacentric height and GZ curve.(Keep slack tanks to a minimum)Filling partially full tanks or completely empting the tank will have the opposite effect.

3. Deck Cargoes.These may gain weight due to water absorption and ice accretionThus raising G and reducing the metacentric height. The GZ curve willTherefore be adversely effected.Timber deck cargo can absorb up to 15% of its own weight.Pipes can trap considerable amount of water. (Supply boats)

4.Reduction in displacement. This will usually be relatively small.

5. Seas on deckThis will raise G due to added weight and free surface effect.

6.Icing The added weight will cause G to rise.

All the effects are adverse.

The stability is examined for the departure condition and also the arrival condition before initial departure.

Loadline Rules 1998.

The design and construction of the ship shall be such as to ensure that her stability in all probable loading conditions will be sufficient for the freeboard to be assigned to her.

1. The area under the curve of righting levers (GZ Curve) Shall not less than:1. 0.055 metre-radians up to 30 degrees2. 0.09 metre-radians up to 40 degrees or any less angle at which the angle of deck edge immersion would be immersed.3. 0.03 metre-radians between 30 and 40 degrees. Or lesser angle as in 2.

2. The maximum righting lever GZ shall not occur at an angle less than 30 degrees and the shall be at least 0.20m

3. The initial metacentric height shall not be less than 0.15mIn the case of a ship carrying timber deck cargo which (A) by taking into account the volume of timber deck cargo ,the initial transverse metacentric height shall not be less than 0.05m

Special Procedures.

In order that the required minimum bow height is always maintained the forward draught not exceed……….

Sequence of ballasting to ensure adequate stability the voyage.

Warning about effects of strong winds upon ships carrying containers or deck cargoes, especially if trading in the Great Lakes.

Dangers of icing in artic waters.

Any special features regarding the stowage or behaviour of cargos to be carried.

Tug Stability.

Girding.This is the sideways pull on a tug by the towline when the ship is pulling away from the tug, which is lying abeam to the direction of pull.The result of this heeling moment may be large enough to capsize the vessel.The effect is minimised by use of a gob rope over the towline to bring the stern of the tug in line with the direction of pull.

Towline Another stability problem encountered by tugs is when the towline hasa large vertical component which may effect the vessels metacentric height (GM).

Supply Vessel Considerations.

The loading and discharging at sea will affect the vertical and transverse CG of the vessel. This will be of particular relevance since the vessel will be rolling and pitching in a seaway. 1. Some vessel use their own crane which will raise the vessels CG2. Free surface affect as liquids are discharged.3. The working deck can retain water in pipes and equipment. Up to 30%of the volume can be retained.( stability allowance of 10% to 30% is usually made to the calculations)4. Icing resulting in added weight.

Operation of Stability tanks.

Counter productive in some sea conditions for example when working with cargo or handling wires.Consider the free surface effect. The stability flume tanks are often abovethe vessels CG they may need to be dumped in critical stability conditions.

Stern trim

Considerable stern trim can develop due to loaded weights longitudinally and when towing and anchor handling. This can cause the working deck to become awash, and therefore reduce the waterplane area and reduce stability (Free Trim)

Precautions.

Deck cargo:1. Deck cargo should not be stowed to block hatches, doors, watertight closures and freeing ports, drainage.2. When pipe carrying adequate arrangements made to allow for drainage. Use pipe plugs if possible.3. Ensure all cargo secured against movement before departure.

(In all loaded condition the minimum freeboard at the stern not less than0.005L)

Load/Discharge at Sea

1. Discharge from the top of the stow first.2. Consider ballast before taking onboard any cargo at sea.3. Minimise free surface effect and check the stability before discharging the liquid and bulk cargos at sea.4. When ballasting at sea to counteract the act of removal of cargo. Ensure allowance is made for the adverse initial effect of free surface.5. Load and Discharge in an order to maintain adequate stern freeboard.Ballast if necessary.

General Precautions

1. Beware of the large free surface effect of the stabiliser tanks. Check the Emergency dump valves regularly.2. Close cross-connected tanks before going to sea.3. When towing it is recommended that deck cargo is not carried.4. Doors and hatches onto the cargo deck kept closed at sea.

Free Trim.

When a supply vessel heels the vessel may trim rapidly by the stern Because most of the reserve buoyancy is forward.This may cause the after deck to become flooded therefore reducing the waterplane area and therefore the BM. (BM= I/V) will be smaller.Hence the KM will be smaller and the GM thus reducing the GZ after the angle of Deck edge immersion.

Initial stability calculations assume no change of trim when the vessel is heeling. This assumption will overestimate the stability of a supply vessel so the stability calculations must be based on free trim during heeling.(GZ curves will state corrected for free trim.)

Angle of Loll:

As the angle of heel increases, the centre of buoyancy will move out further to the low side. If the centre of buoyancy moves out to a position vertically below G, the capsizing moment will have disappeared.The angle of heel at which this occurs is called the angle of loll At an angle of loll the GZ is zero. G remains at the centre line of the ship.If the ship is heeled beyond the angle of loll the centre is buoyancy willStill move out towards the low side this will create a moment to return her to the angle of loll.The ship will flop around the angle of loll, instead of the vertical

If the centre of buoyancy does not move out far enough to get vertically under G, to create an angle of loll the ship will capsize.There is always the danger that G will rise above M and create a unstable equilibrium.. This will cause capsizing of the ship.

Correcting an angle of loll

1. Check that the list is due to a negative GM rather than a off centre weight.2. Angle of loll is caused by G being too high , effort is to made towards lowering it.3. If filling a double bottom tank ensure it is divided to minimise free surface tank. ( or narrow tank)3. Fill only one tank at a time.4.Always fill tank on low side first.5.Where there are three tanks fill the centre tank first then the low side tanks.6. Where there are four tanks fill low side centre then low side then centre high side then high side.

When filling a tank a tank there will be an initial rise in G due to free surface effect before the added weight causes a reduction in G.

Free Surface Effect.

Define virtual loss in GM. Liquid in a partially filled tank moves to the low side as the vessels heels, It will have a adverse effect on the vessels stability.The transverse movement of the liquid causes G to move transversely and so reduces the GZ to the same value as if G had moved vertically upwards to GGv, which is the virtual loss of GM due to free surface. Free surface effect can be seen as a reduction in the vessel GM

Free surface effect is not affected by the depth of liquid in the tank.Formula FSE=

In practice the free surface is calculated by Free Surface Moments. Which is not affected by change in displacement.

Ships stability tables show FSM for each tank at an assumed RD usually 1.000 FW. This must be corrected for actual density.

Corrected FSM= Tabulated x Actual RDAssumed RD

Effect of a subdivision.

Subdividing a substantially reduces the effect.

New FSM = Original FSM x 1/Nsquared

N number of tanks created by subdivision.

Factors effecting Free surface.

Loss in GM1. Increases with tank length2. Increases with tank breadth3. Reduces with displacement4. Reduces with subdivided tanks5. Increases with increase density6. Unaffected by tank position or depth of liquid in tank.

Wide tank particularly bad for stability e.g. stabilizer tank.

Inclining Experiment.

To find Lightship KG.

Carried out in the lightship condition (or as near as possible)

Known weights are shifted transversely across the deck and the inclination of the vessel measured using plumbline and battens.

Diagram:-

Tan = Opposite /Adjacent.

Tan heel = GG1/GM so BC/AB

But GG1 = wxd/WSo Tan list = wxd/ WxGM

By taking moments about the keel, allowance is made for weights on board the ship to bring to the light ship condition.

Precautions: 1. Little wind any wind on the bow/stern2. Ship floating freely e.g. no barges and mooring rope slackened down (consider water depth for effect of squat.)3. All lose weights secured4. No free surface effect. (Water boilers at working levels.)5. The ship upright during the commencement of the experiment.6. All surplus persons removed.7. Ensure slack water

Note remember boiler water always part of the light ship KG to working levels.

Hydrostatic information supplied to ships:

1. Maximum Deadweight diagram or table.2. Maximum GM diagram3. Maximum KG diagramWith all methods the vessel present draft or displacement is used to obtain max/min values permissible.

KN Curves/(cross curves of stability)

These give data on the righting levers at various angles of heel for a range of displacements.The KG of the vessel is assumed zero , therefore the actual KG must be subtracted.

GZ= KN-correction. GZ= KN-KG sin angle.

These figures allow a GZ curve to be draw for the vessel present condition.Then the following information found1. Range of stability (approx)2. Angle of vanishing stability3. Max GZ and angle in occurs 4. Approx GM5. Angle of deck edge immersion.

GZ Curves/ Statical Stability Curve.

Obtained by plotting righting levers over a range of angles of heel.

Typical GZ curve.

GZ

Information on Curve.1. Range of stability: the range of angles which the vessel has positive stability.2. Angle of vanishing stability: angle of heel the lever is Zero.3. Maximum GZ and angle it occurs.4. Angle of deck edge immersion/point of contra flexure. Change from curve up to curve down.5. Initial GM (approx) vertical line drawn from one radian 57.3 upwards.

6. Dynamical stability: work down to incline the vessel to a particular angle. Area under the curve x Displacement.

GZ curve – large/small GM (effect of raising/ lowering)

GZ Curve – Zero GM

GZ Curve- Negative GM (Unstable)

GZ Curve- List condition (G offcentre)

Effect of increasing Freeboard.

1. No effect on GZ curve up to angle of deck edge immersion.2. Max GZ Increased3. Angle of max GZ Increased4. Angle of deck edge immersion Increased 5. Range of stability Increased6. Initial GM Unchanged7. Dynamical stability Increased after angle of deck edge immersion.

Deck edge immersion delayed due to increased free board.

Effect of increasing beam.

1. Max GZ Increased2.Angle max GZ little change3.Angle of deck edge immersion Reduced4.Angle of vanishing stability Increased slightly5. Range of stability Increased slightly6. Initial GM Increased7.Dynamical stability Increased

Effect of timber cargo

Increase in freeboard in solid stow.Decrease in GM due to G being raised

Effect: Less stability at smaller angles, more at larger angles range of stabilityOften increased.

Effect of water tight structures

Watertight structure has a similar effect to increase in freeboard providedThe superstructure is distributed equally about the longitudinal centre of buoyancy.(focle to stern)

If the superstructure is not uniform like a supply vessel there will be an increase of buoyancy at the superstructure end of the vessel as she heels. This will cause the a shift of the centre of buoyancy towards that end, causing the vessel to trim

in the other end.(Free trim) In affects the vessel waterplane area. Reduces stability. Free trim causes a reduction of the vessels righting levers.

Effect of change in displacement

The displacement may be changed by without affecting the position of G by increasing the length of the vessel.Here there will be no effect on the angle of deck edge immersion and little effectOn the GZ curve

However the displacement will affect the righting moment (WxGZ) and also the dynamical stability (W X Area under curve)

In practice change of displacement will affect the GZ curve because of such factors as change in freeboard and change in waterplane area (KM) – these effects are directly visible on the cross curves/KN tables.

Limitations of GZ curves

GZ curves are the best way of assessing vessels stability.Limitations:-1. No account for large angles of heel, flooding through ventilators, cargo shift.2. Based on assumed trim conditions, which may not be the actual trim.3. Free trim where the vessel changes its trim as it heels.

Wallsided Formula

The moment of Statical stability at large angles of heel (over 15 degrees)

GZ=sin Ø (GM + ½ BM tan2 Ø)At angles of heel over 15 degrees the force of buoyancy cannot be considered to act vertically upwards through M. The centre of buoyancy has moved out further to the low side.

GZ is no longer equal GM sin Ø. Up to the angle at which deck edge immersed may be found by Wallsided formula.

See Diagram:-

The angle of loll formula is derived for the Wallsided formula.At the angle of loll GZ = zero

Angle of loll caused by a negative GM

Ø = the angle of lollGM = a negative initial GMBM = the BM when upright.

Question: The difference between angle of list and angle of loll?

Angle of list.1. G the centroid of a loaded weight has moved off centre.2. GM positive, GM will increase at an angle of list compared to the upright.3. Stable equilibrium.4. In still water the ship will remain at a fixed angle of heel. (List to one side only)5. To bring upright place a weight at the other side of the ship.

Angle of Loll1. GM= zero2. G remains on the centre line3. The ship is in neutral equilibrium4. More dangerous situation because if G rises above M she will capsize.5.The angle of may be say 3 port depending on the external forces acting on the vessel, she may suddenly flop from one side to the other and back again.6. To improve the condition G must be brought below MMove weights lower down towards the keelAdd water ballast into db tanksRemove weights from above the ship G

Diagram angle of loll.

Existence of a effective GM at an angle of loll.

After the position in which the vessel has an angle of loll GM = Zero. If the vessel is inclined to a greater angle than that of angle of loll a positive righting lever will be produced to return the ship to the angle of loll,1. GZ at loll is zero2. GZ at angle less than angle of loll is negative3. GZ at angles greater than loll is positive up to angle of vanishing stability.Range of stability is then measured from loll to vanishing stability

Diagram

GM = 2xInitial GM at angle of loll.Cos loll

Grain Regs

The term grain includes: - Wheat, Barley, Rice, and Seeds etc Cargoes with a low angle of repose.These if not effectively secured will shift in a seaway as the vessel rolls. Due to the friction grain does not behave like liquid. So a reduction in GM is not good enough.If the vessel rolls to a large angle some of the grain will shift and when it rolls back not all the grain will shift back again. Therefore grain is potentially more hazardous than liquid.

IMO Grain Regs are based upon the recognition that voids in compartments arebound to occur. Because:1. Difficultly in trimming to fill behind girders, hatch ends2. The cargo settling during the voyage.

An assumed pattern of grain shift is therefore calculated in the void spaces above the grain. Also a calculation is made of the assumed grain shift of unsecured grain surfaces in partially filled compartments.

The resulting Total grain Heeling moments is then used to determine the reduction in the righting lever at various angles of heel.The loss of righting arm is called Heeling arm and is plotted as a secondary curve on the GZ curve diagram.

The basis of the rules is to ensure the vessel has adequate residual stability after taking into account the assumed pattern of grain shift, then she will be allowed to load grain.

Intact Stability Requirements (apply throughout the voyage)1. Angle of heel due to grain shift not to exceed 12 degrees or angle of deck edge immersion (which ever least).2. In the Statical stability diagram, the net or residual area between the heeling arm curve and the righting arm curve up to the heel of maximum difference between the two curves or 40 degrees or angle of flooding which ever is least.In all conditions of loading not be less than 0.075 meter – radians3. The initial metacentric height (GM) after correction for free surface effects in tanks shall not be less than 0.30m

Statical Stability Diagram

The heeling arm takes in to account the transverse shift of the grain.(Shift of G) port/stbd.

The vertical shift of G Upwards/downwards is allowed for either by 1. Assume that the CG of the cargo is at the volumetric centre of the space.2. Multiply the grain heeling moment by a factor of

1.06 for full compartments1.12 for partially full compartments.

When calculating grain heeling moments it is assumed that the grain shifts through an angle of 15 degrees in a full compartmentsAnd 25 degrees in a partially full compartment.

All full compartments should be trimmed so that as far as possible all spaces under the deck and hatch covers are filled. If they are not filled a grain shift of 30 degrees.

Boundary surfaces inclined at 30 degrees or more to the horizontal are assumed to be self-trimming.

Improving the condition:1. Improve the vessels stabilitya) Reduce free surface effect (increase fluid GM)b) Increase solid GM by lowering weights or adding weights low down.

2.Reduce Grain Shift.(Full Compartments)a) Fitting shifting boards (Longitudinal subdivisions)b) Bagged cargo in a saucerc) Dundling in bulk

Partially filled compartments.

a) Over stow with other cargob) Over stow with bagged grainc) Strapping and lashing using steal straps and bottle screws

Document of Authorisation. The National Administration for ships intending to carry bulk grain issues this document. Evidence that the ship is capable of complying with the regulations.

Carried onboard with the Grain loading stability booklet.

Grain loading Stability Booklet.

Sufficient information to allow the master to determine in all reasonable loading conditions the heeling moment due to grain shift.Contents:-1. Criteria for Loadline rules and IMO grain rules2. General arrangement plan, Stability data including hydrostatic data KN tables Capacities and centroids of compartments Free surface moments of liquids

3. Curves or tables of grain heeling moms for every compartment Filled or partly Effects of shifting boards etc.

4. Tables of maximum permissible heeling moms/ allow compliance with the rules.5. Details of Shifting boards etc scantlings specs

6. Typical loaded and arrival conditions, intermediate worst conditions. Worked examples for grain stowage at diff SF. Eg 1.25,1.53,1.81

7. Special instructions necessary to maintain adequate stability, such a ballasting tanks during passage.

8. Other information such as Ships particulars, lightship displacement, KG.

Maximum Permissible Grain Heeling Moments.

Simplified method of establishing whether the vessel complies with the stability requirements of the grain rules.

1. Enter table with Displacement and KG (Extract the maximum permissible grain heel moms)2. Determine the Total volumetric heeling moment of all cargo spaces(Full or Partly)3.Convert to weight heeling moms by dividing by Stowage factor.

Weight H.M = volumetric H.MS.F

4. Compare total weight heeling moment with max heeling mom from the table to determine if within limit.

The approx angle of heel due to grain shift =

Approx angle of heel= total heeling mom x 12 degrees. Max heeling mom

Wind heeling moments.

Large angles of heel may be produced by strong beam winds up on large lateral areas of the ship due to their large freeboard and tiers of containers on deck.

The wind heeling moment is the moment of force tending to incline the vessel.

Diagram

Total wind heeling moment. = force x windage area x distance (centroid area ½ draft) 1000

The vessel will continue to heel over until an equal and opposite force is produced.The righting moment of equal value.

GZ at angle of heel= heeling momW

When the height of the lateral windage area from the load waterline to the top of the cargo containers is greater than 30% of the beam of the ship.

Statical stability curve must be produced in the form of righting moments for the worst condition.To include 1. Total windage area

2. Position of centroid and the lever to half draught.

For the worst condition the following information is to be included on the curve of Statical stability.

a) Angle of heel under steady wind load 48.5kg/m (Force 10) applied to the total windage area on lever to mid draft.( )

b) The angle of dynamical heel assuming a 15 degree roll to windward in association with a gusting wind 150% of steady wind condition.

c) The minimum valve of angle of deck edge immersion.

d) The minimum angle at which progressive flooding can occur.

Diagram.

Recommended Requirements.(Loadline rules)

a)

b)

If the vessel is to trade in areas where ice maybe expected then the calculation must take into account the added weight through ice deposited.