Angle of Heel When Turning
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Transcript of 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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FORCES THAT CAUSE THE SHIP TO
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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FORCES THAT CAUSE THE SHIP TO
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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FORCES THAT CAUSE THE SHIP TO
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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FORCES THAT CAUSE THE SHIP TO
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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FORCES THAT CAUSE THE SHIP TO
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