Basic Stability Guide 2… Calculations - Wikispacesparticipationandskills.wikispaces.com/file/view/Guide_2_Basic... · Basic Stability – Guide 2… Calculations Loadline Displacement

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.

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Fresh Water Allowance (FWA) 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.

Top of S

Top of F

FWA

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. Fresh Water Allowance can be found in the ship’s stability manual.

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 summer marks when entering salt water.

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Dock Water Allowance ( DWA ) 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 enters Salt Water (density 1025 kg/m³)

Dock Water Allowance ( DWA ) - Calculation A calculation is required to determine how much you can sink your Summer load line below the water at a river berth, so you can be on your Summer Load Line when entering the ocean

To determine the DWA

FWA units millimetres DWA units millimetres

Calculation

𝑫𝑾𝑨 = 𝑭𝑾𝑨 ×(𝟏𝟎𝟐𝟓 − 𝒅𝒐𝒄𝒌 𝒘𝒂𝒕𝒆𝒓 𝒅𝒆𝒏𝒔𝒊𝒕𝒚)

(𝟏𝟎𝟐𝟓 − 𝟏𝟎𝟎𝟎)


(𝟐𝟓)

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


(𝟏𝟎𝟐𝟓 − 𝟏𝟎𝟎𝟎)

𝑫𝑾𝑨 = 𝟏𝟔𝟎 ×(𝟏𝟎𝟐𝟓 − 𝟏𝟎𝟏𝟐)

(𝟐𝟓)

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 Line be submerged in Dock Water, so that the vessel will float at her Summer Marks on entering Salt Water? (density 1025 kg/m³)

𝑫𝑾𝑨 = 𝟖𝟑. 𝟐 𝒎𝒎

Try the following examples to check your ability to carry out this important calculation.

Answers shown on next page …

Question FWA mm

Density kg/m³

1 150 1016

2 120 1006

3 110 1018

4 110 1012

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Question FWA mm

Density kg/m³

1 150 1016

2 120 1006

3 110 1018

4 110 1012 𝑫𝑾𝑨 = 𝟏𝟏𝟎 ×

(𝟏𝟎𝟐𝟓 − 𝟏𝟎𝟏𝟖)

(𝟐𝟓)

𝑫𝑾𝑨 = 𝟓𝟒 𝒎𝒎

𝑫𝑾𝑨 = 𝟏𝟐𝟎 ×(𝟏𝟎𝟐𝟓 − 𝟏𝟎𝟎𝟔)

(𝟐𝟓)

𝑫𝑾𝑨 = 𝟏𝟓𝟎 ×(𝟏𝟎𝟐𝟓 − 𝟏𝟎𝟏𝟔)

(𝟐𝟓)

𝑫𝑾𝑨 = 𝟏𝟏𝟎 ×(𝟏𝟎𝟐𝟓 − 𝟏𝟎𝟏𝟐)

(𝟐𝟓)

𝑫𝑾𝑨 = 𝟗𝟏. 𝟐 𝒎𝒎

𝑫𝑾𝑨 = 𝟑𝟎. 𝟖 𝒎𝒎

𝑫𝑾𝑨 = 𝟓𝟕. 𝟐𝒎𝒎

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Displacement The total weight of the vessel and everything on board that vessel. (Often abbreviated to 'W‘.) Q. How can we determine the displacement of a vessel? A. By observing the draft. Draft Sometimes written as "Draught" The measurement of "how deep the vessel sits in the water" This is measured at specific points of the vessel...eg. the forward draft or after draft. Mean Draft The mean draft is the arithmetical mean of the fore and aft drafts. That is the fore and aft drafts added together and divided by 2.

Draft Marks … how to read (assume the blue lines represent the water level)

1M

2 10cm

10cm

10cm

1 metre

1.10 metres

1.30 metres

1.20 metres

Trim The difference in draft readings between the forward draft marks and the after draft marks.

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Trim (by head or stern) If the forward reading is larger, the vessel is considered to be trimmed by the head. If the after reading is larger, the vessel is considered to be trimmed by the stern. Calculations for mean draft and trim are commonplace on board ship

Mean Draft and Trim

Consider a vessel with the following drafts: Fwd draft = 3.60m Aft draft = 3.80m Find mean draft and the trim of the vessel

𝑚𝑒𝑎𝑛 𝑑𝑟𝑎𝑓𝑡 =𝑓𝑤𝑑 𝑑𝑟𝑎𝑓𝑡 + 𝑎𝑓𝑡 𝑑𝑟𝑎𝑓𝑡

2

𝑚𝑒𝑎𝑛 𝑑𝑟𝑎𝑓𝑡 =3.60 + 3.80

2

𝒎𝒆𝒂𝒏 𝒅𝒓𝒂𝒇𝒕 = 𝟑. 𝟕𝟎𝒎

𝑇𝑟𝑖𝑚 = 𝑎𝑓𝑡 𝑑𝑟𝑎𝑓𝑡 ~𝑓𝑤𝑑 𝑑𝑟𝑎𝑓𝑡

𝑇𝑟𝑖𝑚 = 3.80~3.60

𝑻𝒓𝒊𝒎 = 𝟎. 𝟐𝟎𝒎 𝒃𝒚 𝒕𝒉𝒆 𝒔𝒕𝒆𝒓𝒏

Hydrostatic Table This table is found in the Stability manual on board the vessel. The table lists variables used in the calculation of stability. On smaller vessels, the mean draft is calculated and used to enter the hydrostatic table. Displacement and other variables can then be 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 Draft (m)

Displacement (tonnes)

TPC MCT 1 cm (t-m)

LCF (m aft 0)

KM (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 tonnes required to change the draft of the vessel by 1 cm

If a vessel is box shaped, it would have the same TPC value irrespective of its draft.

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. 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 of weight in tonnes.

Vessel can submerge the Summer Load Line by 83.2 mm or 8.3cm. How much cargo can be loaded if the vessel has a TPC value of 8?

Calculation using TPC

𝐴𝑚𝑜𝑢𝑛𝑡 𝑡𝑜 𝑙𝑜𝑎𝑑 = 𝑠𝑖𝑛𝑘𝑎𝑔𝑒 × 𝑇𝑃𝐶

𝐴𝑚𝑜𝑢𝑛𝑡 𝑡𝑜 𝑙𝑜𝑎𝑑 = 8.3 × 8

𝑨𝒎𝒐𝒖𝒏𝒕 𝒕𝒐 𝒍𝒐𝒂𝒅 = 𝟔𝟔. 𝟒 𝒕𝒐𝒏𝒏𝒆𝒔

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KG Height of the centre of gravity of the ship above the baseline, referred to as KG. (from the keel ‘K’ to the centre of gravity ‘G’) Movement of G – Load and discharge The height of G will change as weights are loaded or discharged. It is important for the person in charge of 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 G moves away from the discharged weight

G

G

G moves away from the discharged weight

weight

Weight is discharged

Vessel with weight on deck

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Movement of G - a weight already on board Assume the weight is already on board and is shifted on deck

The height of G will not change as the weight height will not change

Movement of G in this case: G moves parallel to the shifted weight

G

G

G moves parallel to the shifted weight

weight

Weight is shifted

Vessel with weight on deck

weight

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weight

Movement of G - Lifting a Weight When a weight is lifted by a crane or derrick, the weight is considered to act at the head of the crane or derrick. Subsequent lifting or lowering of the hoist wire will not change the position of the vertical centre of gravity of the weight.

The weight is considered to act at the head of the crane

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 derrick head is lowered.

G2 G moves towards the head of the crane when the weight is lifted clear of the deck

G1

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G moves towards the loaded weight In order to calculate the shift of G from its original position to its new position the following formula is used:

GG1 = 𝒘×𝒅

𝑾+𝒘 for a loaded weight.

Where GG1 = the vertical shift of G in metres d = distance weight is located from the KG of the vessel in metres w = the weight in tonnes W the displacement of the vessel in tonnes

A weight of 10 tonnes is loaded on the 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 1,000 tonnes. Find the vertical shift of G

GG1= 𝒘×𝒅

𝑾+𝒘 GG1=

𝟏𝟎×(𝟖.𝟓−𝟔.𝟎)

𝟏,𝟎𝟎𝟎+𝟏𝟎

GG1 = 𝟎. 𝟎𝟐𝟓𝒎

Vertically upwards towards the loaded weight

Calculation – Vertical Shift of G

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Calculation – Vertical Shift of G

A weight of 10 tonnes is discharged from the centre line. It is discharged from a KG of 7.5m The KG of the vessel prior to loading was 6.0m.The vessel has a displacement of 1,000 tonnes. Find the vertical shift of G

GG1= 𝒘×𝒅

𝑾−𝒘 GG1=

𝟏𝟎×𝟏.𝟓

𝟏𝟎𝟎𝟎−𝟏𝟎

GG1= 𝟎. 𝟎𝟏𝟓𝒎

Vertically downwards away from the discharged weight

G moves away from the discharged weight

When a weight is discharged note the change in sign to (-)

GG1 = 𝒘×𝒅

𝑾−𝒘

Where GG1 = the vertical shift of G in metres d = distance weight is located from the KG of the vessel in metres w = the weight in tonnes W the displacement of the vessel in tonnes

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G moves parallel to the shifted weight In order to calculate the shift of G from its original position to its new position the following formula is used:

GG1 = 𝒘×𝒅

𝑾 for a shifted weight.

Where GG1 = the horizontal shift of G in metres d = distance weight moved in metres w = the weight in tonnes W the displacement of the vessel in tonnes

A weight of 10 tonnes is shifted 8 metres to starboard. The vessel has a displacement of 1,000 tonnes. Find the horizontal shift of G

GG1= 𝒘×𝒅

𝑾 GG1=

𝟏𝟎×𝟖

𝟏,𝟎𝟎𝟎

GG1 = 𝟎. 𝟎𝟖𝒎

Horizontally to starboard parallel to the shifted weight

Calculation – Horizontal Shift of G

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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 weight . In this case we will discharge one lift of product from the vessel via grab using a shipboard crane to the wharf and follow 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 the top of the crane block. KG of the vessel moves vertically upwards G₀ to G₁ Step 2 the crane swings to starboard and G of the vessel moves parallel to the movement of the grab from port to starboard. G₁ to G₂

Wharf

Wharf

G₀

G₁

G₀

G₁

G₂

Step 1

Step 2

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Wharf

Wharf

G₀

G₁ G₂

G₃

G₄

₁ ₂

₃ ₀

Step 3 The crane jib is lowered, lowering the KG of the vessel, the grab moves outboard to plumb the wharf and the KG of the vessel moves from G₂ to G₃ Step 4 The grab is lowered to the 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 3

Step 4

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Waterline at the Summer Draft

Amidships - halfway between FP and AP

Forward Perpendicular FP

Some Longitudinal Stability Terms ...

Check the Glossary for more detail

After Perpendicular AP

Stern

Bow

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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.

LCB LCG

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

Often the LCF is shown as a triangle to denote the fulcrum, point around which the vessel trims

LCF

Vessel seen From above

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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. Free Surface Effect will reduce the transverse stability of the vessel by effectively reducing the size of the GZ (righting lever). This will cause a virtual reduction in GM and in extreme cases, the vessel may capsize. 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

Partially filled tank

Vessel heels and liquid moves ... see next page for details

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G G¹

B B¹

G¹Z

Z

GZ

Virtual Rise in G ͮ Z

M

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. The consequence of this movement of G is a reduction of righting lever (GZ) shown as G₁Z This has the same effect as though G had moved up to G ͮ. This effect is termed a “virtual rise in G” The danger in this situation is the possibility of the GZ becoming too small to be able to return the vessel to the upright. 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 that allows the centre of gravity of the vessel to rise to a point where G is located above M. This can be due to loss of bottom weight caused by fuel and water consumption, combined with a virtual rise in G due to free surface effect. If operating in high latitudes, ice accretion on the 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. 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

G

B B¹

Capsizing lever

Z

M

Unstable Vessel

.

.

.

.

.

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The vessel will continue to roll in this unstable condition until B moves vertically under G. At this point there will be no capsizing or righting lever, the vessel will now rest at an Angle of Loll. 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 of G. There is a danger due to external forces. Assume the vessel is lying at an angle of loll to starboard. Wind or waves would cause the vessel to move back to the upright. At this point the capsizing 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.

G

B B¹

B and G in same vertical line

Vessel at angle of loll

.

.

W

U (upthrust)

(displacement)

Loll

ᶿ° Angle of loll ᶿ°

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It is important to know the difference between List and Loll. Why? Assume a vessel is listed to starboard due to G moving off the centre line (unequal use of tanks, cargo shifting etc.) then G would be corrected by adding or moving weight to the high side. (port side) If the angle of heel is due to loll and a weight is shifted or added to the high side of the vessel, the vessel would initially move towards the upright then as the vessel became upright, the vessel would flop over to port due to its capsizing lever but at a much faster rate as now there would be extra weight on the port side. In this case the vessel would develop additional momentum and may capsize.

Steps to recover from Loll To remedy loll G must be lowered. Considering the adverse effect wind or waves could have on the vessel, it is recommended that the weather is placed sufficiently on the high side to prevent the vessel rolling to the opposite side. Fill up any slack tanks on the LOW side. Fill one tank at a time. Use tanks with a small free surface effect. When an empty tank is filled, be aware of the free surface effect and a consequent reduction in righting lever. Once you have calculated that G is below M, take steps to bring the vessel from a state of list to the upright. If tanks alone cannot reduce G you may be forced to jettison cargo (from the high side)

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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.

Conclusion Guide 2

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Basic Stability Guide 2… Calculations - Wikispacesparticipationandskills.wikispaces.com/file/view/Guide_2_Basic... · Basic Stability – Guide 2… Calculations Loadline Displacement