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INTRODUCTION TO SHIP STABILITY TUTORIAL QUESTIONS Chris Patterson Version 1 November 2009 Contents Tutorial Sheet - Buoyancy and Floatation of Box shaped Vessels........................2 Tutorial Sheet – Hydrostatic Curves: Draught and Displacement........................3 Tutorial Sheet – Hydrostatic Tables: Draught and Displacement.........................4 Tutorial Sheet – Small Angle Stability - Metacentric Height..............................5 Tutorial Sheet - Centres Of Gravity...........................................................6 Tutorial Sheet - List .............................................................................7 Tutorial Sheet - Free Surface Effects........................................................8 Tutorial Sheet – Exam Practice Questions...................................................9


Introduction to Ship Stability and Construction Tutorial Sheet - Buoyancy and Floatation of Box shaped Vessels Question 1: A ship has an underwater volume of 4000m 3 in salt water, density 1.025 tonnes/m 3. Calculate the displacement of the ship. (4100 tonnes) Question 2: A box shaped vessel is 50 metres long, with a beam of 15 metres. The barge floats at a draft of 2 metres in salt water. Calculate the displacement of the barge. (1537.5 tonnes) Question 3: A box shaped vessel is 40 metres long, with a beam of 10 metres. The barge floats at a draft of 2.1 metres in fresh water. Calculate the displacement of the barge. (840 tonnes) Question 4: A box shaped vessel is 60 metres long, with a beam of 12 metres. The barge floats at a draft of 3 metres in dock water, relative density 1.015. Calculate the displacement of the barge. (2192.4 tonnes) Question 5: A box shaped vessel is 50 metres long, 13 metres wide and has a displacement of 832.81 tonnes. Calculate the draft of the vessel in salt water if it is on an even keel with no list. (1.250 metres) Question 6: A box shaped vessel is 70 metres long, 15 metres wide and has a displacement of 4221 tonnes. Calculate the draft of the vessel in dock water, relative density 1.005, if it is on an even keel with no list. (4.000 metres) Question 7: A box shaped vessel is 55 metres long with a beam of 11 metres. In dock water, relative density 1.007, the barge floats on an even keel draft of 2 metres. Calculate the draft if the vessel is towed into salt water. (1.965 metres) Question 8: A box shaped vessel has a displacement of 656 tonnes at a draft of 1 metre in salt water. Determine the draft if the displacement is increased to 1000 tonnes. (1.524 metres) Question 9: A box shaped vessel has a length of 50 metres and a beam of 8 metres. The vessel has a draft of 2 metres in salt water. The vessel must move into a fresh water harbour with a maximum depth of 1.5 metres. An under keel clearance of 0.5 metres is required. Determine how much cargo must be offloaded to bring the vessel to the required draft. (420 tonnes) Question 10: A box shaped raft has a length of 40 metres and a beam of 10 metres. The lightship draft is 2 metres. The raft is used to transport an anchor for a mooring, made from a cube of steel 1m by 1m by 1m. The relative density of steel is 7.8. Determine the draft of the vessel with the anchor aboard, and the draft with the anchor suspended just below the vessel but clear of the seabed. (2.019 metres with the anchor on deck, 2.017 metres with the anchor suspended).


Introduction to Ship Stability and Construction Tutorial Sheet – Hydrostatic Curves: Draught and Displacement Question 1: MV Warsash 2 has a draught of 4.63m in seawater. What is its displacement? (4370t) Question 2: MV Warsash 2 has a displacement of 5650t in seawater. What is its draught? (5.71m) Question 3: MV Warsash 2 has a draught of 5.10m in seawater before loading 1300t of cargo. What is its displacement after loading? (6210t) Question 4: MV Warsash 2 has a draft of 3.40m in seawater before loading 3200t of cargo. What is its draught after loading? (6.17m) Question 5: MV Warsash 2 has a draft of 6.75m in seawater before discharging 84t of cargo. What is its draught after loading? (6.688m) Question 6: MV Warsash 2 has a draught of 6.20m in freshwater. What is its displacement? (6107.3t) Question 7: MV Warsash 2 has a displacement of 3800t in freshwater. What is its draught? (4.207m) Question 8: MV Warsash 2 has a draught of 4.35m in dockwater of density 1.008t/m 3. What is its displacement? (3992.7t) Question 9: MV Warsash 2 has a displacement of 6230t in dockwater of density 1.016t/m 3. What is its draught? (6.224m) Question 10: MV Warsash 2 is in the lightship condition moored at the dockside in water of density 1009 kg/m3. The following items are now loaded: Fuel oil 930t, Stores 38t Freshwater 60t. Determine the amount of cargo that can now be loaded and the resulting draught of the vessel so that when the vessel reaches its destination, in 14 days time, it can safely enter port. The following information is also required: Destination port is a fresh water port with a maximum permissible draught of 6.25metres. MV Warsash 2 has a daily fuel consumption of 56 tonnes per day. MV Warsash 2 has a daily freshwater consumption of 3.5 tonnes per day. (3363t, 6.847m)


Introduction to Ship Stability and Construction Tutorial Sheet – Hydrostatic Tables: Draught and Displacement Question 1: MV Warsash 2 has a draught of 4.63m in seawater. What is its displacement? (4370t) Question 2: MV Warsash 2 has a displacement of 5650t in seawater. What is its draught? (5.713m) Question 3: MV Warsash 2 has a draught of 5.13m in seawater before loading 1300t of cargo. What is its displacement after loading? (6248t) Question 4: MV Warsash 2 has a draft of 3.44m in seawater before loading 3200t of cargo. What is its draught after loading? (6.207m) Question 5: MV Warsash 2 has a draft of 6.75m in seawater before discharging 84t of cargo. What is its draught after loading? (6.688m) Question 6: MV Warsash 2 has a draught of 6.21m in freshwater. What is its displacement? (6123t) Question 7: MV Warsash 2 has a displacement of 3800t in freshwater. What is its draught? (4.204m) Question 8: MV Warsash 2 has a draught of 4.35m in dockwater of density 1.008t/m 3. What is its displacement? (3990t) Question 9: MV Warsash 2 has a displacement of 6230t in dockwater of density 1.016t/m 3. What is its draught? (6.218m) Question 10: MV Warsash 2 is in the lightship condition moored at the dockside in water of density 1009 kg/m3. The following items are now loaded: Fuel oil 930t, Stores 38t Freshwater 60t. Determine the amount of cargo that can now be loaded and the resulting draught of the vessel so that when the vessel reaches its destination, in 14 days time, it can safely enter port. The following information is also required: Destination port is a fresh water port with a maximum permissible draught of 6.25metres. MV Warsash 2 has a daily fuel consumption of 56 tonnes per day. MV Warsash 2 has a daily freshwater consumption of 3.5 tonnes per day. (3363t, 6.846m)


Introduction to Ship Stability and Construction Tutorial Sheet – Small Angle Stability - Metacentric Height Question 1: A box barge has a draught of 3.684 metres. Calculate the vertical height of the centre of buoyancy (KB). (1.842 metres) Question 2: MV Warsash 2 has a draught of 5.2 metres. Determine the vertical height of the centre of buoyancy (KB). (2.825 metres) Question 3: A box barge, length 50m and beam 14m, has a draught of 5m. Calculate the vertical distance between the centre of buoyancy and the metacentre (BM). (3.267 metres) Question 4: A box barge, length 60m and beam 12m, has a draught of 4m. Calculate the vertical distance between the keel and the metacentre (KM). (5.000 metres) Question 5: MV Warsash 2 has a draught of 6.1 metres. Determine the vertical distance between the keel and the metacentre (KM). (7.025 metres) Question 6: A ship has a displacement of 4100 tonnes in salt water, density 1.025 tonnes/m 3. The transverse inertia, measured through the centreline of the ship, is 5600 m 4. Calculate the vertical distance between the centre of buoyancy and the metacentre (BM). (1.400 metres) Question 7: A ship has a displacement of 4300 tonnes in dock water, density 1.015 tonnes/m 3. The transverse inertia, measured through the centreline of the ship, is 5900 m 4. The centre of buoyancy of the ship is 4.594 metres above the keel. Calculate the vertical height of the metacentre above the keel (KM). (5.987 metres) Question 8: A box shaped vessel, 30 metres long with a beam of 8 metres, has a vertical centre of gravity 3 metres above the keel. The barge floats on an even keel draft of 2.2 metres in salt water. Calculate GM, and hence determine if the vessel is stable, neutral or unstable. (0.524m, therefore stable) Question 9: MV Warsash 2 has a displacement of 5150 tonnes in salt water. The vertical centre of gravity of the ship (KG) is 7 metres above the keel. Calculate the vertical height of the metacentre above the centre of gravity (GM) and hence determine if the vessel is stable, neutral or unstable. (-0.073 metres, therefore unstable) Question 10: A ship has a displacement of 4900 tonnes in salt water. The transverse inertia, measured through the centreline of the ship, is 7200 m 4. The centre of buoyancy of the ship is 3.111 metres above the keel. The vertical centre of gravity of the ship (KG) is 4.500 metres above the keel. Calculate the vertical height of the metacentre above the centre of gravity (GM). (0.117 metres)


Introduction to Ship Stability and Construction Tutorial Sheet - Centres Of Gravity Question 1: A vessel has a displacement of 5000 tonnes and a lightship KG of 2 metres. A load of 500 tonnes is added at a KG of 4 metres. Find the final KG for the vessel. (2.182 metres) Question 2: A vessel has a displacement of 8000 tonnes and a loaded KG of 5 metres. A load of 700 tonnes is removed at a KG of 2.5 metres. Find the final KG for the vessel. (5.240 metres) Question 3: A vessel has a displacement of 10000 tonnes and a loaded KG of 8 metres. A load of 500 tonnes is removed from a KG of 8 metres. A load of 600 tonnes is added at a KG of 4 metres. Find the final KG for the vessel. (7.762 metres) Question 4: A vessel has a displacement of 4000 tonnes and a loaded KG of 5.5 metres. A load of 150 tonnes is moved 4 metres vertically upwards. Find the final KG of the vessel. (5.65 metres) Question 5: A vessel has a displacement of 4000 tonnes and a loaded KG of 5.5 metres. A load of 150 tonnes is moved 4 metres vertically downwards. Find the final KG of the vessel. (5.35 metres) Question 6: A vessel has a displacement of 5500 tonnes and a loaded KG of 5.2 metres. A load of 75 tonnes is lifted by a crane, with the derrick head 12 metres above the original stowed position of the load. Find the final KG for the vessel. (5.364 metres) Question 7: A vessel has a displacement of 8250 tonnes and a loaded KG of 7.2 metres. A load of 90 tonnes is lifted by a crane, from a stowed KG of 3 metres, with the derrick head 16 metres above the keel. Find the final KG for the vessel. (7.342 metres) Question 8: A vessel has a displacement of 1000 tonnes and a loaded KG of 6.0 metres. How far must 100 tonnes of cargo, already aboard, be raised by the get the final KG equal to 6.4 metres? (4.0 metres) Question 9: A box shaped vessel has a length of 70 metres, a beam of 15 metres and a lightship KG of 4 metres. In dock water, relative density 1.019, the barge floats in the lightship condition on an even keel with no list, at a draft of 2 metres. The ship is then loaded as shown below. Calculate GM for the vessel in the loaded condition in salt water, and hence determine if the vessel is stable, neutral or unstable. Item Stores Cargo 1 Cargo 2 Cargo 3

Mass (Tonnes) 5 1000 3000 3000

KG (m) 1.00 5.50 8.00 6.00 (0.324m, therefore stable)

Question 10: A box shaped vessel has a length of 60 metres, a beam of 9 metres and a lightship GM of 0.503 metres. The vessel floats at a draft of 2.30 metres in salt water. 25 tonnes of stores is to be loaded aboard, so that GM remains constant. Determine the vertical position to load the stores. (1.820 metres)


Introduction to Ship Stability and Construction Tutorial Sheet - List Question 1: A box shaped vessel, 50 metres long with a beam of 7 metres, floats on an even keel with no list at a draft of 2 metres in salt water. In this condition, the centre of gravity is 3 metres above the keel. A ten tonne mass, already aboard, is moved 0.5 metres transversely to port. Calculate the final list angle. (9.49 degrees to port) Question 2: A ship, displacement 5000 tonnes, BM = 2.1 metres, KB = 3.2 metres, KG=3 metres, has a 200 tonnes mass, initially on the centreline, moved 3 metres to starboard. A 600 tonne mass, initially on the centreline, is moved 2 metres to port. Calculate the final list angle. (2.99 degrees to port) Question 3: A ship, displacement 4000 tonnes, KM = 4 metres, has a centre of gravity 3 metres above the keel. 100 tonnes of cargo is added to the ship 3 metres to starboard of the centreline, at a height of 4 metres above the keel. 400 tonnes of cargo is added to the ship 2 metres to port of the centreline, at a height of 3 metres above the keel. If KM is constant, calculate the final list. (6.48 degrees to port) Question 4: A ship, displacement 5000 tonnes, is alongside a quay in a lightship condition. The KM value of the ship is 3 metres, and can be assumed to remain constant through the loading process. Two 50 tonne masses, on the quay a distance of 15 metres from the ship centreline, are to be loaded aboard using the ships own heavy lift derrick, with the head of the derrick a height of 18 metres above the keel. The masses are to be loaded 2 metres to port and starboard of the centreline, at a height of 3 metres above the keel. If the lightship KG of the ship is 1.1 metres, calculate the maximum list angle during the loading operation. You may assume the mass stowed nearest to the quay is loaded first. (5.55 degrees towards the quay when the first mass is stowed aboard and the second mass is just lifted.) Question 5: A ship, displacement 6000 tonnes, is alongside a quay. The KM value of the ship is 6 metres, and can be assumed to remain constant through the loading process. Two 90 tonne masses, on the quay a distance of 14 metres from the ship centreline, are to be loaded aboard using the ships own heavy lift derrick, with the head of the derrick a height of 22 metres above the keel. The masses are to be loaded 4 metres to port and starboard of the centreline, at a height of 5 metres above the keel. You may assume the mass stowed nearest to the quay is loaded first. If the list angle during the loading operation must not exceed 5 degrees, calculate the maximum initial KG value before loading commences. (Initial KG = 2.689 metres.) Question 6: A ship with a displacement of 4000 tonnes is to lift a 60 tonne mass from a point on a quay 12 metres to port of the vessel centreline. The KM of the vessel is 4 metres and can be assumed to remain constant. The derrick head is 15 metres above the keel of the vessel. It is required to limit the list to 5 degrees during the lift. Determine the maximum allowable initial KG before lifting to meet this requirement. (1.778 metres) Question 7: A vessel has a displacement of 5000 tonnes, and a list of 2 degrees to port. KG in this condition is 4 metres. KM is 5.4 metres. 500 tonnes of cargo remains to be loaded aboard. Space is available to load in locations 3 metres to port and 2 metres to starboard. Determine the distribution of the remaining cargo so that the vessel finished loading upright. (151.111 tonnes to port, 348.889 tonnes to starboard)


Introduction to Ship Stability and Construction Tutorial Sheet - Free Surface Effects Question 1: A ship has a displacement of 4000 tonnes. The vessel has a partially filled tank containing oil, density 0.9 tonnes/m3. The inertia of the free surface is 200m 4. The tank has one compartment. Calculate the loss in GM due to the free surface effect. (0.045 metres) Question 2: A ship has a displacement of 2500 tonnes. The vessel has a partially filled tank containing oil, density 0.867 tonnes/m3. The inertia of the free surface is 400m4. The tank has two equal size compartments. Calculate the loss in GM due to the free surface effect. (0.035 metres) Question 3: A ship has a partially filled oil tank which is rectangular, 20 metres long and 5 metres wide, containing oil fuel, density 950kg/m 3. The vessel also has a partially filled ballast tank, which is rectangular, 25 metres long and 8 metres wide, containing salt water. In this condition, the solid GM is 0.5 metres and the displacement is 5500 tonnes. Calculate the fluid GM. (0.265 metres) Question 4: A box shaped vessel has a length of 80 metres, a beam of 6 metres and a lightship draft of 2 metres, with a lightship KG of 1.2 metres. The vessel has a main deck 3 metres above the keel. On the main deck is a pool, 20 metres long, extending the full beam of the vessel. The pool is filled with salt water to a depth of 1.2 metres. Calculate GM after filling the pool. (0.62m) Question 5: A ship has a solid KG of 5 metres. In this condition, there is a rectangular tank 9 metres long, 4 metres wide, with a centreline fluid tight bulkhead. The tank is partially filled with fresh water. In this condition there is also a rectangular oil tank, 8 metres long, with a beam of 6 metres. This is partially full, with oil, density 0.95t/m3. In this condition, the displacement of the vessel is 800 tonnes. Find the fluid KG. (5.186 metres) Question 6: A box shaped vessel has a length of 50 metres, a beam of 8 metres and a draft of 4 metres. In this condition GM is 0.333m. The vessel has a double bottom tank, running transversely from the centreline of the vessel to the side of the vessel, 5 metres long, and 3 metres deep. The tank is then filled with sea water to a depth of 2 metres. Determine the angle of list. (7.26 degrees) Question 7: MV Warsash 2 is alongside a berth, having taken on fuel, cargo and ballast. There are no free surfaces present, and the vessel has a KG of 7 metres with a displacement of 7467 tonnes. She has a list of 1 degree to starboard. The vessel is to take on additional sea water ballast in both of the Number 2 Double Bottom Tanks, so that the sounding of ballast in both tanks is 0.8m. She is also to load 362.8 tonnes of additional deck cargo, at a KG of 10 metres and TCG of 1 metres to port. a) Determine the effective metacentric height of the vessel after ballasting the Number 2 Double Bottoms and loading the additional deck cargo. (0.285m) b) Determine the angle of heel after loading. (8.2 degrees)


Introduction to Ship Stability and Construction Tutorial Sheet – Exam Practice Questions Question 1: MV Warsash 2 is in the lightship condition moored at the dockside in water of density 1009 kg/m3. The following items are now loaded: Fuel oil 930t, Stores 38t Freshwater 60t. Determine the amount of cargo that can now be loaded and the resulting draught of the vessel so that when the vessel goes to sea she is floating at her summer draught. (3686t, 7.085m) Question 2: A box shaped vessel has a length of 50 metres, a beam of 6 metres, a draft of 1 metres and a Kg of 1.5 metres. The vessel is then loaded with cargo as shown below in table Q1. Determine the final list of the vessel, and comment on the potential accuracy of the solution. (29.7 degrees, therefore too large for reasonable limits of small angle theory)

Table Q1

Item Cargo Cargo Cargo Stores

Mass (t) 500 600 450 35

KG (m) 2 5 4 3

TCG (m) -0.5 0.3 0.7 -0.8

Question 3: A box shaped vessel has a length of 66 metres, a beam of 11 metres, a draft of 1.2 metres and a Kg of 5 metres. A rectangular fuel tank, with a length of 12 metres and a width of 8 metres, is partially filled to a depth of 1.5 metres, with oil fuel, density 960kg/m3. The vessel is then loaded with cargo as shown below in table Q3. Determine the final list of the vessel. (3.88 degrees) Item Cargo Cargo

Mass (t) 350 375 Table

KG (m) 4 6 Q3

TCG (m) -0.1 0.25

Introduction to Ship Stability Tutorial Book  

A set of ship stability tutorial sheets with answers.

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