Metacentric diagrams
It has been mentioned in Chapter 6 that the officer responsible for loading a ship should aim to complete the loading with a GM which is neither too large nor too small. See table of typical GM values on p. 49 for merchant ships when fully loaded. A metacentric diagram is a figure in graph form from which the KB, BM, and thus the KM can be found for any draft by inspection. If the KG is known and the KM is found from the diagram, the difference will give the GM. Also, if a final GM be decided...
The coefficient of fineness of the waterplane area Cw
The coefficient of fineness of the water-plane area is the ratio of the area of the water-plane to the area of a rectangle having the same length and maximum breadth. In Figure 9.1 the area of the ship's water-plane is shown shaded and ABCD is a rectangle having the same length and maximum breadth. Coefficient of fineness Cw ---- - A Area of the water-plane L X B X Cw
Bilging amidships compartments
When a vessel floats in still water it displaces its own weight of water. Figure 21.1 a shows a box-shaped vessel floating at the waterline WL. The weight of the vessel W is considered to act downwards through G, the centre of gravity. The force of buoyancy is also equal to W and acts upwards through B, the centre of buoyancy. b W. Now let an empty compartment amidships be holed below the waterline to such an extent that the water may flow freely into and out of the compartment. A vessel holed...
Exercise 10
1 A ship's load water-plane is 60 m long. The lengths of the half-ordinates commencing from forward are as follows 0.1, 3.5, 4.6, 5.1, 5.2, 5.1, 4.9, 4.3 and 0.1m respectively. Calculate the area of the water-plane, the TPC in salt water, and the position of the centre of flotation, from amidships. 2 The half-ordinates of a ship's water-plane, which is 60 m long, commencing from forward, are as follows 0, 3.8, 4.3, 4.6, 4.7, 4.7, 4.5, 4.3, and 1m respectively. Find the area of the water-plane,...
Effect of hog and sag on draft amidships
When a ship is neither hogged nor sagged the draft amidships is equal to the mean of the drafts forward and aft. In Figure 25.1 d the vessel is shown in hard outline floating without being hogged or sagged. The draft forward is F, the draft aft is A, and the draft amidships KX is equal to the average of the drafts forward and aft. Now let the vessel be sagged as shown in Figure 25.1 d by the broken outline. The draft amidships is now K1X, which is equal to the mean of the drafts forward and aft...
Heel due to turning
When a body moves in a circular path there is an acceleration towards the centre equal to v2 r where v represents the velocity of the body and r represents the radius of the circular path. The force required to produce this acceleration, called a 'Centripetal' force, is equal to -, where M is the In the case of a ship turning in a circle, the centripetal force is produced by the water acting on the side of the ship away from the centre of the turn. The force is considered to act at the centre...
Angle of loll
When a ship with negative initial metacentric height is inclined to a small angle, the righting lever is negative, resulting in a capsizing moment. This effect is shown in Figure 24.1 a and it can be seen that the ship will tend to heel still further. At a large angle of heel the centre of buoyancy will have moved further out the low side and the force of buoyancy can no longer be considered to act vertically upwards though M, the initial metacentre. If, by heeling still further, the centre of...
True mean draft
In previous chapters it has been shown that a ship trims about the centre of flotation. It will now be shown that, for this reason, a ship's true mean draft is measured at the centre of flotation and may not be equal to the average of the drafts forward and aft. It only does when LCF is at average Consider the ship shown in Figure 25.1 a which is floating on an even keel and whose centre of flotation is FY aft of amidships. The true mean draft is KY, which is also equal to ZF, the draft at the...
List with zero metacentric height
When a weight is shifted transversely in a ship with zero initial metacentric height, the resulting list can be found using the 'Wall sided' formula. The ship shown in Figure 38.1 has zero initial metacentric height. When a weight of mass 'w' is shifted transversely through a distance 'd', the ship's centre of gravity shifts from G to G1 where the direction GG1 is parallel to the shift of the centre of gravity of the weight shifted. The ship will then incline to bring the centres of gravity and...
Bonjean Curves
Bonjean Curves are drawn to give the immersed area of transverse sections to any draft and may be used to determine the longitudinal distribution of buoyancy. For example, Figure 41.11 a shows a transverse section of a ship and Figure 41.11 b shows the Bonjean Curve for the same section. The immersed area to the waterline WL is represented on the Bonjean Curve by ordinate AB, and the immersed area to waterline W1L1 is represented by ordinate CD. In Figure 41.12 the Bonjean Curves are shown for...
Using the hydrostatic curves
After the end drafts have been taken it is necessary to interpolate to find the 'mean draft'. This is the draft immediately below the LCF which may be aft, forward or even at amidships. This draft can be labelled dH. If dH is taken as being simply the average of the two end drafts then in large full-form vessels supertankers and fine-form vessels container ships an appreciable error in the displacement can occur. See Fig. 16.8. Displacement in metric tonnes 15000 20000 25000 30000 35000 40000...
Effect of trim on tank soundings
A tank sounding pipe is usually situated at the after end of the tank and will therefore only indicate the depth of the liquid at that end of the tank. If a ship is trimmed by the stern, the sounding obtained will indicate a greater depth of liquid than is actually contained in the tank. For this reason it is desirable to find the head of liquid required in the sounding pipe which will indicate that the tank is full. In Figure 27.1, 't' represents the trim of the ship, 'L' the length of the...
Exercise 13
1 A ship of 5000 tonnes displacement has KG 4.2 m, KM 4.5 m, and is listed 5 degrees to port. Assuming that the KM remains constant, find the final list if 80 tonnes of bunkers are loaded in No. 2 starboard tank whose centre of gravity is 1 metre above the keel and 4 metres out from the centre line. 2 A ship of 4515 tonnes displacement is upright and has KG 5.4 m, and KM 5.8 m. It is required to list the ship 2 degrees to starboard and a weight of 15 tonnes is to be shifted transversely for...
The virtual loss of GM after taking the blocks overall
When a ship takes the blocks overall, the water level will then fall uniformly about the ship, and for each centimetre fallen by the water level P will be increased by a number of tonnes equal to the TPC. Also, the force P at any time during the operation will be equal to the difference between the weight of the ship and the weight of water she is displacing at that time. A ship of 5000 tonnes displacement enters a drydock on an even keel. KM 6 m. KG 5.5 m, and TPC 50 tonnes. Find the virtual...
List due to bilging side compartments
When a compartment in a ship is bilged the buoyancy provided by that compartment is lost. This causes the centre of buoyancy of the ship to move directly away from the centre of the lost buoyancy and, unless the centre of gravity of the compartment is on the ship's centre line, a listing moment will be created, b w. Let the ship in Figure 34.1 float upright at the waterline WL. G represents the position of the ship's centre of gravity and B the centre of buoyancy. Now let a compartment which is...
Exercise 18
1 A sealed box is made of metal and is capable of withstanding a pressure of 15.54 kN per sq m. Find to what depth the box may be submerged in salt water before it collapses. 2 Find the water pressure, in kilo-newtons per sqm, on the keel of a ship which is floating upright on an even keel in salt water at a draft of 6 metres. 3 A ship is floating on an even keel in salt water at a draft of 7 metres. She has a flat plate keel which is 100 m long and 2 m wide. Find the water pressure and the...
Maximum Permissible Deadweight Moment Diagram
This is one form of simplified stability data diagram in which a curve of Maximum Permissible Deadweight Moments is plotted against Displacement in tonnes on the vertical axis and Deadweight Moment in Tonnes metres on the horizontal axis, the Deadweight Moment being the moment of the Deadweight about the keel. The total Deadweight Moment at any Displacement must not, under any circumstances, exceed the Maximum Permissible Deadweight Moment at that Displacement. Diagram 3 Figure 44.1 illustrates...
Example Paa
Mw Mb SWBM b-B-L2-5 x 10 3 WBM Fig. 42.5. Line diagram for solution using Murray's method. To find the Still Water Bending Moment SWBM To find the Still Water Bending Moment SWBM Mean Buoyancy Moment MB 'LCB 2 '25 Still Water Bending Moment SWBM MW - MB 229 225 - 211875 SWBM 17 330 t m Hogging because MW gt MB Wave Bending Moment WBM b-B-L25 X 10-3tm WBM Hogging 9.-95 X 30 X 2002'5 X 10-3 tm 166 228 tm WBM Sagging 11.02 X 30 X 2002'5 X 10-3 tm 18-01-tm TBM Hogging WBM hogging SWBM hogging 166...
2 Statical Stability curves
The curve of statical stability for a ship in any particular condition of loading is obtained by plotting the righting levers against angle of heel as shown in Figures 16.4 and 16.5. Curve for a ship with positive initial metacentric height. Curve for a ship with positive initial metacentric height. From this type of graph a considerable amount of stability information may be found by inspection The range of stability. This is the range over which the ship has positive righting levers. In...
The Moment to Change Trim one centimetre MCT 1 cm or MCTC
The MCT 1 cm, or MCTC, is the moment required to change trim by 1 cm, and may be calculated by using the formula W the vessel's displacement in tonnes GML the longitudinal metacentric height in metres, and L the vessel's length in metres. The derivation of this formula is as follows Consider a ship floating on an even keel as shown in Figure 15.3 a . The ship is in equilibrium. Now shift the weight 'w' forward through a distance of 'd' metres. The ship's centre of gravity will shift from G to...
The moment of statical stability at a large angle of heel
At a large angle of heel the force of buoyancy can no longer be considered to act vertically upwards through the initial metacentre M . This is shown in Figure 14.3, where the ship is heeled to an angle of more than 15 degrees. The centre of buoyancy has moved further out to the low side, and the vertical through B1 no longer passes through M , the initial metacentre. The righting lever GZ is once again the perpendicular distance between the vertical through G and the vertical through B1, and...
Exercise 24
1 Will a homogeneous log of square cross-section and relative density 0.7 be stable when floating in fresh water with two opposite sides parallel to the waterline If not, what will be the angle of loll 2 A box-shaped vessel 30 m X 6mX 4m floats in salt water on an even keel at 2 m, draft F and A. KG 3 m. Calculate the angle of loll. 3 A ship is upright and is loaded with a full cargo of timber with timber on deck. During the voyage the ship develops a list, even though stores, fresh water and...
General Ship Knowledge BTECSQAHND Part 1
a General ideas on ship construction and on plans available onboard ship. General definitions of main dimensions. The names of the principal parts of a ship. The candidate will be expected to show his practical acquaintance with Longitudinal and transverse framing Beams and beam knees Watertight bulkheads Hatchways and closing appliances Rudders Steering gear Shell and deck plating Double bottoms and peak tanks Bilges Propellers and propeller shafts Stern tubes Sounding pipes Air pipes The...
The midships coefficient Cm
The midships coefficient to any draft is the ratio of the transverse area of the midships Section Am to a rectangle having the same breadth and depths. In Figure 9.3 the shaded portion represents the area of the midships section to the waterline WL, enclosed in a rectangle having the same breadth and depth. The prismatic coefficient of a ship at any draft is the ratio of the volume of displacement at that draft to the volume of a prism having the same length as the ship and the same...
Murrays Method
Murray's Method is used to find the total longitudinal bending moment amidships on a ship in waves and is based on the division of the total bending moment into two parts a the Still Water Bending Moment, and The Still Water Bending Moment is the longitudinal bending moment amidships when the ship is floating in still water. When using Murray's Method the wave bending moment amidships is that produced by the waves when the ship is supported on what is called a 'Standard Wave'. A Standard Wave...
Ship to ship Interaction
Consider Figure 36.5 where a tug is overtaking a large ship in a narrow river. Three cases have been considered G centre of gravity B centre of bouyancy m metacentre Fig. 36.4. Transverse squat caused by ships crossing in a confined channel. Suction effect takes place here Ships are drawn to each other, both heel slightly Vessel squats and grounds. Bilge keel may be bent or broken off Fig. 36.4. Transverse squat caused by ships crossing in a confined channel. Both ships go to port Tug heads for...
Exercise 5
1 A ship displaces 7500 cu. m of water of density 1000 kg per cu. m. Find the displacement in tonnes when the ship is floating at the same draft in water of density 1015 kg per cu. m. 2 When floating in fresh water at a draft of 6.5 m a ship displaces 4288 tonnes. Find the displacement when the ship is floating at the same draft in water of density 1015 kg per cu. m. 3 A box-shaped vessel 24 m X 6mX 3m displaces 150 tonnes of water. Find the draft when the vessel is floating in salt water. 4 A...
The variable immersion hydrometer
The variable immersion hydrometer is an instrument, based on the Law of Archimedes, which is used to determine the density of liquids. The type of hydrometer used to find the density of the water in which a ship floats is usually made of a non-corrosive material and consists of a weighted bulb with a narrow rectangular stem which carries a scale for measuring densities between 1000 and 1025 kilograms per cubic metre, i.e. 1.000 and 1.025 t m3. The position of the marks on the stem are found as...