Home Page Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll
Guide 2 – Stability Calculations This guide will cover the following… • Loadline, Fresh Water Allowance • Dock Water Allowance • Draft, Mean Draft, Trim • Displacement and Block Coefficient • Hydrostatic Tables, TPC • Movement of G in the transverse plane • Movement of G in the longitudinal plane • Free Surface and Loll
Guide 3 (the third and final guide in this series) The next guide will cover stability calculations using MV Twosuch , an excerpt from a ship’s stability booklet that will be used for examination purposes. by Stevehdc
1 Basic Stability – Guide 2… Calculations Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll
Loadlines
Loadlines from a Ship Stability perspective often involve calculations to determine how much to sink the summer loadline in dock water so that the vessel will be on her Top of F summer marks when entering salt water.
Fresh Water Allowance (FWA) Top of S Assume a vessel loaded in Fresh Water of RD 1.0 so that the water level is at the TOP of the F load line.
If the vessel was then placed into Salt Water of RD 1.025 the vessel would float with the water level at the TOP of the S loadline due to the density of the water changing.
FWA
Fresh Water Allowance can be found in the ship’s stability manual.
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Dock Water Allowance ( DWA ) Calculation The number of millimetres by which the Summer Load Line can be submerged in Dock Water so that the vessel will be at its Summer Load Line when the vessel To determine the DWA enters Salt Water (density 1025 kg/m³)
(ퟏퟎퟐퟓ − 풅풐풄풌 풘풂풕풆풓 풅풆풏풔풊풕풚) Dock Water Allowance ( DWA ) - Calculation 푫푾푨 = 푭푾푨 × A calculation is required to determine how much you can (ퟏퟎퟐퟓ − ퟏퟎퟎퟎ) sink your Summer load line below the water at a river berth, so you can be on your Summer Load Line when entering the (ퟏퟎퟐퟓ − 풅풐풄풌 풘풂풕풆풓 풅풆풏풔풊풕풚) 푫푾푨 = 푭푾푨 × ocean (ퟐퟓ)
FWA units millimetres DWA units millimetres Orals Question A common Orals question is Calculation of DWA The following examples will assist you in becoming competent with this important calculation
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Dock Water Allowance - Calculation A vessel is loading cargo in Dock Water density 1012kg/m³, if the vessel has a FWA of 160 mm, how much can the Summer Load Dock Water Allowance - Calculation Line be submerged in Dock Water, so that the vessel will float at her Summer Marks on entering Salt Water? (density 1025 kg/m³)
(ퟏퟎퟐퟓ − 풅풐풄풌 풘풂풕풆풓 풅풆풏풔풊풕풚) 푫푾푨 = 푭푾푨 × Try the following examples to check your ability to carry out (ퟏퟎퟐퟓ − ퟏퟎퟎퟎ) this important calculation. (ퟏퟎퟐퟓ − ퟏퟎퟏퟐ) 푫푾푨 = ퟏퟔퟎ × Question FWA Density (ퟐퟓ) mm kg/m³ 푫푾푨 = ퟖퟑ. ퟐ 풎풎 1 150 1016 2 120 1006 3 110 1018 4 110 1012
Answers shown on next page …
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Dock Water Allowance - Calculation Dock Water Allowance - Calculation (ퟏퟎퟐퟓ − ퟏퟎퟏퟔ) 푫푾푨 = ퟏퟓퟎ × (ퟐퟓ) 1 Question FWA Density 푫푾푨 = ퟓퟒ 풎풎 mm kg/m³ (ퟏퟎퟐퟓ − ퟏퟎퟎퟔ) 푫푾푨 = ퟏퟐퟎ × 1 150 1016 (ퟐퟓ) 2 2 120 1006 푫푾푨 = ퟗퟏ. ퟐ 풎풎
3 110 1018 (ퟏퟎퟐퟓ − ퟏퟎퟏퟖ) 푫푾푨 = ퟏퟏퟎ × 4 110 1012 3 (ퟐퟓ) 푫푾푨 = ퟑퟎ. ퟖ 풎풎 (ퟏퟎퟐퟓ − ퟏퟎퟏퟐ) 푫푾푨 = ퟏퟏퟎ × 4 (ퟐퟓ) 푫푾푨 = ퟓퟕ. ퟐ풎풎
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Displacement The total weight of the vessel and everything on board that Draft Marks … how to read vessel. (Often abbreviated to 'W‘.) (assume the blue lines represent Q. How can we determine the displacement of a vessel? the water level) A. By observing the draft. 1.30 metres Draft Sometimes written as "Draught" The measurement of "how deep 1.20 metres the vessel sits in the water" This is measured at specific points of the vessel...eg. the forward draft or after draft.
Mean Draft 10cm The mean draft is the arithmetical mean of the fore and aft drafts. 2 That is the fore and aft drafts added together and divided by 2. 1.10 metres 10cm
Trim The difference in draft readings between the forward draft 1M 10cm marks and the after draft marks. 1 metre
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Trim (by head or stern) Mean Draft and Trim If the forward reading is larger, the vessel is considered to be trimmed by the head. Consider a vessel with the following drafts: If the after reading is larger, the vessel is considered to Fwd draft = 3.60m be trimmed by the stern. Aft draft = 3.80m Find mean draft and the trim of the vessel Calculations for mean draft and trim are commonplace on board ship 푓푤푑 푑푟푎푓푡 + 푎푓푡 푑푟푎푓푡 푚푒푎푛 푑푟푎푓푡 = 2 Hydrostatic Table 3.60 + 3.80 This table is found in the Stability manual on 푚푒푎푛 푑푟푎푓푡 = 2 board the vessel. The table lists variables used in the calculation 풎풆풂풏 풅풓풂풇풕 = ퟑ. ퟕퟎ풎 of stability. On smaller vessels, the mean draft is calculated 푇푟푖푚 = 푎푓푡 푑푟푎푓푡 ~푓푤푑 푑푟푎푓푡 and used to enter the hydrostatic table. 푇푟푖푚 = 3.80~3.60 Displacement and other variables can then be 푻풓풊풎 = ퟎ. ퟐퟎ풎 풃풚 풕풉풆 풔풕풆풓풏 determined by inspection. On larger vessels a further calculation to convert mean draft to draft at the LCF is required.
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Hydrostatic Table (extract from stability booklet M.V. Twosuch)
Hydrostatic Displacement TPC MCT 1 cm LCF KM Draft (m) (tonnes) (t-m) (m aft 0) (m) 2.60 156.5 1.168 1.438 -1.072 3.94 2.65 162.5 1.172 1.465 -1.065 3.91 2.70 168.0 1.180 1.480 -1.060 3.89 2.75 174.0 1.185 1.500 -1.050 3.87
If the table is entered with a mean draft of 2.60m the values associated with this draft can be viewed … our Displacement would be 156.5 tonnes and all the other values in the table in this row would be valid for this draft.
If the vessel had a draft of 2.75m the Displacement would be 174.0 tonnes.
If the vessel had a displacement of 168 tonnes, the mean draft would be 2.70 metres.
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TPC Tonnes per centimetre immersion, the amount of weight in Calculation using TPC tonnes required to change the draft of the vessel by 1 cm Vessel can submerge the Summer If a vessel is box shaped, it would have the same TPC value Load Line by 83.2 mm or 8.3cm. irrespective of its draft. How much cargo can be loaded if the vessel has a TPC value of 8? Ships vary in shape as their draft changes and consequently the TPC will vary as the draft changes. Look at how the Hydrostatic table shows change of TPC value with change in draft. 퐴푚표푢푛푡 푡표 푙표푎푑 = 푠푖푛푘푎푔푒 × 푇푃퐶
퐴푚표푢푛푡 푡표 푙표푎푑 = 8.3 × 8 Up to now we have determined the change in draft measured in mm or cm. By using TPC we can convert a change in draft to an amount 푨풎풐풖풏풕 풕풐 풍풐풂풅 = ퟔퟔ. ퟒ 풕풐풏풏풆풔 of weight in tonnes.
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KG Height of the centre of gravity of the ship above the baseline, weight referred to as KG. (from the keel ‘K’ to the centre of gravity ‘G’) Vessel with Movement of G – Load and discharge weight on The height of G will change as weights are loaded or deck discharged. It is important for the person in charge of G monitoring the stability of the vessel, to know how G will move in all cases.
The basic principles of movement of G are as follows:
G moves towards the loaded weight Weight is discharged G moves away from the discharged weight
G G moves away from the discharged weight
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Movement of G - a weight already on board Assume the weight is already on board and is shifted on deck weight
Vessel with weight on deck The height of G will not change as the weight height will not change G
Movement of G in this case: weight G moves parallel to the shifted weight Weight is shifted G G moves parallel to the shifted weight
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Movement of G - Lifting a Weight When a weight is lifted by a crane or derrick, the The weight is weight is considered to act at the head of the crane or considered to derrick. Subsequent lifting or lowering of the hoist act at the head wire will not change the position of the vertical centre of gravity of the weight. of the crane
weight This is an important consideration as the centre of gravity of the vessel, “G “ will now rise a considerable amount as the weight is initially lifted and remain at that height until the crane or G moves G2 derrick head is lowered. towards the head of the crane when G1 the weight is lifted clear of the deck
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G moves towards the loaded weight Calculation – Vertical Shift of G
In order to calculate the shift of G from its original A weight of 10 tonnes is loaded on the position to its new position the following formula is used: centre line. It is loaded at a KG of 8.5 m. The KG of the vessel prior to loading was 6.0m.The vessel has a displacement of 풘×풅 1,000 tonnes. Find the vertical shift of G GG1 = for a loaded weight. 푾+풘
Where GG1 = the vertical shift of G in metres 풘×풅 ퟏퟎ×(ퟖ.ퟓ−ퟔ.ퟎ) GG1= GG1= d = distance weight is located from the KG of the vessel in 푾+풘 ퟏ,ퟎퟎퟎ+ퟏퟎ metres w = the weight in tonnes W the displacement of the vessel in tonnes GG1 = ퟎ. ퟎퟐퟓ풎
Vertically upwards towards the loaded weight
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G moves away from the discharged weight Calculation – Vertical Shift of G
A weight of 10 tonnes is discharged from the centre line. It is discharged When a weight is discharged note the change in sign to (-) from a KG of 7.5m The KG of the vessel 풘×풅 prior to loading was 6.0m.The vessel GG1 = 푾−풘 has a displacement of 1,000 tonnes. Find the vertical shift of G
Where GG1 = the vertical shift of G in metres 풘×풅 ퟏퟎ×ퟏ.ퟓ d = distance weight is located from the KG of the vessel GG1= GG1= 푾−풘 ퟏퟎퟎퟎ−ퟏퟎ in metres w = the weight in tonnes GG1= ퟎ. ퟎퟏퟓ풎 W the displacement of the vessel in tonnes Vertically downwards away from the discharged weight
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G moves parallel to the shifted weight Calculation – Horizontal Shift of G
In order to calculate the shift of G from its original position A weight of 10 tonnes is shifted 8 metres to its new position the following formula is used: to starboard. The vessel has a displacement of 1,000 tonnes. Find the horizontal shift of G 풘×풅 GG1 = for a shifted weight. 푾
Where GG1 = the horizontal shift of G in metres 풘×풅 ퟏퟎ×ퟖ GG1= GG1= d = distance weight moved in metres 푾 ퟏ,ퟎퟎퟎ w = the weight in tonnes W the displacement of the vessel in tonnes GG1 = ퟎ. ퟎퟖ풎
Horizontally to starboard parallel to the shifted weight
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It is important for the mariner to know how G moves on board the vessel during the process of loading or discharging a Step 1 weight .
In this case we will discharge one lift of G₁ product from the vessel via grab using a shipboard crane to the wharf and follow G₀ Wharf the movement of G during this operation.
Step 1 The crane takes a grab of cargo and lifts it clear of the cargo within the hold. G of the cargo moves immediately to Step 2 the top of the crane block. KG of the vessel moves vertically upwards G₀ to G₁ G₁ G₂ Step 2 the crane swings to starboard and G₀ G of the vessel moves parallel to the Wharf movement of the grab from port to starboard. G₁ to G₂
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Step 3 The crane jib is lowered, lowering Step 3 the KG of the vessel, the grab moves outboard to plumb the wharf and the KG of the vessel moves from G₂ to G₃ G₁ G₂
Step 4 The grab is lowered to the wharf G₀ G₃ Wharf and opened, discharging the cargo onto the wharf. The parcel of cargo is no longer on board the vessel and the effect is to move the vessel’s KG from G₃ to G₄ Step 4
₁ ₂ Wharf ₀ ₃ G₄
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Some Longitudinal Stability Terms ... Bow Waterline at the Stern Summer Draft
Forward Perpendicular FP
After Perpendicular AP
Amidships - halfway between FP and AP
Check the Glossary for more detail
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Longitudinal centre of buoyancy (LCB) ... the longitudinal centre of the underwater volume, the point through which buoyancy acts, vertically upwards.
LCB
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Longitudinal centre of gravity (LCG) ... the longitudinal centre gravity. The point through which the weight of the vessel acts, vertically downwards
LCG
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When there is a difference in the location of LCG and LCB, the vessel will want to trim in the direction of the location of LCG.
LCG LCB
Vessel will trim by the stern
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Due to the difference in waterplane area forward and aft, the Longitudinal Centre of Flotation (the centre of the waterplane area) will vary depending upon the draft of the vessel. The vessel will trim about the LCF
LCF Vessel seen From above
LCF
Often the LCF is shown as a triangle to denote the fulcrum, point around which the vessel trims
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Free Surface Effect Free Surface Effect is the effect that liquid (or a product that behaves like a liquid eg. grain), free to move from side to side in a tank, will have on the transverse stability of the vessel.
Partially filled tank Free Surface Effect will reduce the transverse stability of the vessel by effectively reducing the Vessel heels size of the GZ (righting lever). and liquid moves ... see This will cause a virtual reduction in GM and in extreme cases, the vessel may capsize. next page for details This effect can be reduced by : (i) Filling the tank completely so water cannot move freely across the surface of the tank. (ii) Empty the tank so there is no water within the tank. (iii) Have a continious longitudinal watertight bulkhead(s) separating the tank into two or more compartments
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As the vessel heels to starboard, the centre of gravity of the vessel moves towards the movement of liquid piling up on the starboard side of the vessel. G moves to G₁. GZ The consequence of this movement of G is M a reduction of righting lever (GZ) shown as G₁Z Virtual Rise in G ͮ Z G¹Z This has the same effect as though G had moved up to G ͮ. This effect is termed a “virtual rise in G” G
G¹ Z The danger in this situation is the possibility B of the GZ becoming too small to be able to return the vessel to the upright. B¹
Had G remained on the centre line, assuming a full tank or if the tank was empty, the vessel would have had a much larger righting lever with increased stability.
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Loll Loll usually occurs due to a combination of events Capsizing that allows the centre of gravity of the vessel to rise Unstable Vessel lever to a point where G is located above M.
This can be due to loss of bottom weight caused by G fuel and water consumption, combined with a Z . . virtual rise in G due to free surface effect.
If operating in high latitudes, ice accretion on the M. superstructure will add weight high up on the vessel. If working on a timber carrier, water absorption into the timber deck cargo will add weight high up on the vessel. In both cases this will cause cause G to rise. B. . B¹ If G rises above M, the situation is known as an unstable condition and the GZ in this case is acting as Capsizing lever rather than a Righting lever and will cause the vessel to heel further
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Loll The vessel will continue to roll in this unstable condition until B moves vertically under G. At this point there will Vessel at angle of loll be no capsizing or righting lever, the vessel will now U (upthrust) rest at an Angle of Loll. G If the vessel is inclined further by the effects of wind or . waves, the vessel will roll around its angle of loll as a righting lever will be generated once B moves outboard B and G in same of G. vertical line ᶿ° There is a danger due to external forces. Angle of loll ᶿ°
Assume the vessel is lying at an angle of loll to starboard. Wind or waves would cause the vessel to B. move back to the upright. At this point the capsizing B¹ lever generated would cause the vessel to flop to port. When the vessel rolls to port, the momentum built up by the roll may cause the vessel to capsize. W (displacement)
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Steps to recover from Loll To remedy loll G must be lowered. It is important to know the difference between List and Considering the adverse effect wind or Loll. Why? waves could have on the vessel, it is recommended that the weather is placed Assume a vessel is listed to starboard due to G moving sufficiently on the high side to prevent the off the centre line (unequal use of tanks, cargo shifting vessel rolling to the opposite side. etc.) then G would be corrected by adding or moving weight to the high side. (port side) Fill up any slack tanks on the LOW side. Fill one tank at a time. If the angle of heel is due to loll and a weight is shifted Use tanks with a small free surface effect. or added to the high side of the vessel, the vessel would When an empty tank is filled, be aware of initially move towards the upright then as the vessel the free surface effect and a consequent became upright, the vessel would flop over to port due reduction in righting lever. to its capsizing lever but at a much faster rate as now there would be extra weight on the port side. Once you have calculated that G is below M, take steps to bring the vessel from a In this case the vessel would develop additional state of list to the upright. momentum and may capsize. If tanks alone cannot reduce G you may be forced to jettison cargo (from the high side)
27 Basic Stability – Guide 2… Calculations Conclusion Guide 2 Loadline Displacement G-Transverse G- Longitudinal Free Surface & Loll
At Master 4 level, longitudinal stability calculations are based upon simplified stability data provided for vessels.
The next Guide in the series will provide full working for problems associated with determining the draft, trim and stability for any stage of loading or discharge.
The Booklet used at examination is "Simplified Stability Information for MV Twosuch" and excerpts from this will be used to provide several loading scenarios for students to gain experience in the determination of draft, trim and transverse stability.
From calculations undertaken, students will determine if the vessel meets limiting requirements for KG and Trim.
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