angle of heel when turning

8/10/2019 Angle of Heel When Turning

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Increase in draught due to list / heel


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Learning Objectives Explains angle of heel due to turning and the effect on

stability

Calculates angle of heel due to turning Explains increase in draught due to list / heel

Calculates increase in draught due to list / heel


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Jul 2006


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Definitions Transfer

This is the distancetravelled by the ship'scentre of gravity in adirection perpendicularto the ship's initialcourse.

It is usually quoted fora 90 change ofheading..


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Definitions Tactical diameter

This is the distancetravelled by the ship'scentre of gravity in adirection perpendicularto the ship's initialcourse when the ship

has altered its course by180 and is on areciprocal heading.


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Definitions Steady turning circle

radius This is the steady radius

of the turning circlewhen a steady rate ofturn is achieved.

This state is usuallyachieved by the timethe ship has alteredcourse between 90 and180 however this will

vary from ship to ship..


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DefinitionsYaw

This is the anglebetween the ship's foreand aft line and thedirection of travel ofthe ship's centre ofgravity at any instant

during the turn.


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FORCES THAT CAUSE THE SHIP TO

HEEL DURING TURNING Consider a ship turning to starboard. When the rudder

is put over the thrust on the starboard face of therudder has an athwartships component F which acts atthe centre of pressure P of the rudder

An equal and opposite force, F1 arises, resisting theathwartships motion set up by the force on the rudder.


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HEEL DURING TURNING This reaction acts on the port side at the centre of

lateral resistance (CLR) and is located at the geometriccentre of the underwater longitudinal area and isinvariably higher than P.

The two forces, F at P, and F1 at the CLR set up aninward heeling couple for which the moment is givenby: F x PQ


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HEEL DURING TURNING Once the ship has achieved a steady rate of turn, the

inward heel is overcome by the effect of the centrifugalforce acting outwards through the ship's centre of

gravity (G). This causes the characteristic outward heel to develop

in the turn.

The centrifugal force is given by:

'W' is the ship's displacement in tonnes; 'V' is the speed of the ship in metres persecond;

g' is the acceleration due to gravity (9.81 rn/s"),and;

'R' is the radius of the turning circle in metres.


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HEEL DURING TURNING The centrifugal force is opposed by the equal and

opposite centripetal force acting through the CLR,where the CLR (for purpose of formula derivation) isassumed to be at the same height above the keel as thecentre of buoyancy, B.


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HEEL DURING TURNING The initial inward heeling moment is overcome by the

outward heeling moment created by both thecentrifugal and centripetal forces.

If the initial inward heeling moment is ignored, theship will heel outwards to an angle of steady heel ()when the outward heeling moment balances thenormal righting moment for the angle of heeldeveloped.


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HEEL DURING TURNING


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Example Calculate the angle of heel developed when a ship

doing 20 knots achieves a steady rate of turn tostarboard and the radius of the turning circle is 300 mgiven that: KM = 8.00 m, KG = 6.00 m & KB = 2.5 m


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Example 20 Knot = 20 * 1852 metres per hour /(60*60) =10.289

meter / second

GM=KM-KG = 8.00- 6.00 = 2.00 m BG = KG - KBBG = 6.00 - 2.50 = 3.50 m

Tan = (10.2892x 3.50) / 9.81 x300 x2.00 = 0.06295

angle of heel = 3.6 to Port


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Example 2 Calculate the maximum speed on a turning circle of

diameter 620 m in order that the heel developed doesnot exceed 6 given that: KM = 15.88 m KG = 14.26 mKB = 8.05 m

maximum speed = 17.75 knots


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INCREASE IN DRAUGHT DUE TO

List / HEEL


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ExampleA ship heels 50 as it makes a turn. If the draught when

upright is 7.60 m calculate the draught when heeled giventhat the breadth is 18 m.


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Example

Draught when heeled = (0.5 x 18 x Sin 5) + (7.60 x Cos 5)

Draught when heeled = 8.355 m


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Jul 2006

angle of heel when turning

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