Ship Stability: Centre of Gravity and Metacentre
TRANSVERSE STATICAL STABILITY
CENTRE OF GRAVITY
:-
IS THE POINT ABOUT WHICH FORCE
OF GRAVITY ACT VERTICALLY DOWNWARDS EQUAL TO THE
WEIGHT OF THE BODY. DENOTED BY LETTER “G”.
CENTRE OF BUOYANCY
:-
IS THE POINT THROUGH WHICH
THE FORCE OF BUOYANCY IS CONSIDERED TO ACT
VERTICALLY UPWARDS WITH THE FORCE EQUAL TO THE
WEIGHT OF WATER DISPLACED. IT IS THE CENTRE OF
GRAVITY OF THE UNDERWATER VOLUME. DEOTED BY LETTER
“B”.
TO FLOAT AT REST IN STILL WATER, A VESSEL MUST DISPLACE
HER OWN WEIGHT OF WATER, AND THE CENTRE OF
GRAVITY MUST BE IN THE SAME VERTICAL LINE AS THE
CENTRE OF BOUYANCY
.
METACENTRE
METACENTRE
CONSIDER A SHIP FLOATING UPRIGHT IN STILL WATER AS SHOWN IN PREVIOUS SLIDE.
CENTRE OF GRAVITY IS AT G AND B.
WHEN SHIP IS INCLINED BY AN EXTERNAL FORCE TO A SMALL ANGLE THERE IS NO CHANGE IN
THE DISTRIBUTION OF WEIGHT AND HENCE CENTRE OF GRAVITY WILL REMAIN AT “G” AND
WEIGHT OF THE SHIP “W” WILL ACT DOWNWARD THROUGH THAT POINT.
WHEN HEELED , THE WEDGE OF BOUYANCY WOW1 IS BROUGHT OUT OF WATER AND AN
EQUAL WEDGE LOL1 BECOMES IMMERSED. IN THIS WAY A WEDGE OF BOUYANCY HAVING ITS
CENTRE OF GRAVITY AT g IS TRANSFERRED TO A POSITION WITH CENTRE OF GRAVITY AT g1.
THE CENTRE OF BOUYANCY , BEING THE CENTRE OF GRAVITY OF UNDERWATER VOLUME SHIFT
FROM B TO B1.SUCH THAT BB1 IS PARALLEL TO gg1 AND
BB1=v*gg1/V
WHERE v=VOLUME OF TRANSFERRED WEDGE
V=SHIPS VOLUME OF DISPLACEMENT
THE VERTICAL THROUGH THE CENTRE OF BOUYANCY AT TWO CONSEQUETIVE ANGLES OF HEEL
INTERSECT AT A POINT CALLED THE METACENTRE. WHILE THE VERTICAL DISTANCE BETWEEN G AND
M IS CALLED METACENTRIC HEIGHT.
STABLE EQUILIBRIUM
A SHIP IS IN STABLE EQUILIBRIUM IF G IS BELOW M I.E SHIP HAVE
POSITIVE INITIAL METACENTRIC HEIGHT IN THIS CASE SHIP WHEN
INCLINED WILL COMES BACK TO ITS INITIAL POSITION. IN THE PREVIOUS
SLIDE WE SEE THAT WHEN THE SHIP IS INCLINED IN A CLOCKWISE
DIRECTION THERE IS A MOMENT PRODUCED BY THE COUPLE OF WEIGHT
OF THE SHIP AND BOUYANT FORCE IN ANTI CLOCKWISE DIRECTION
AND HENCE PRODUCING A COUNTER EFFECT TO BRING BACK THE SHIP
TO INTIAL POSITION. THIS IS CALLED MOMENT OF STATICAL STABILITY.
MOMENT OF STATICAL STABILITY=W* GZ TONNES
METRES
WHERE W= FORCE
GZ= LENGTH OF RIGHTING LEVER
UNSTABLE EQUILIBRIUM
WHEN SHIP IS INCLINED TO A SMALL ANGLE AND IT
STILL HEELS FURTHUR THEN THE SHIP IS SAID TO BE
IN UNSTABLE EQUILIBRIUM. THIS CONDITION ARISES
WHEN M IS BELOW G I.E INITIAL GM IS NEGETIVE.
IN THE FIGURE WE CAN SEE THAT WHEN SHIP
INCLINES TO CLOCKWISE DIRECTION THERE IS A
MOMENT DUE TO THE COUPLE OF W AND B
WHICH FURTHUR SUPPORT THE INCLINATION AND
SHIP INCLINE FURTHER TO CLOCKWISE DIRECTION
ONLY WHICH CAN LEAD TO CAPSIZE OF THE SHIP
NEUTRAL EQUILIBRIUM
WHEN G AND M COINCIDES THEN THAT
CONDITION IS NEUTRAL EQUILIBRIUM. HENCE
MOMENT OF STATICAL STABILITY=0. HENCE IF
SHIP IS INCLINED THEN IT WILL REMAIN INCLINED
TO THAT POSITION ONLY AS THERE IS NO
RIGHTING MOMENT.
Exploring the concepts of transverse statical stability, centre of gravity, centre of buoyancy, metacentre, stable equilibrium, unstable equilibrium, and neutral equilibrium in ship stability. The relationship between these key points determines a ship's stability and ability to maintain a steady position in water.
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Presentation Transcript
TRANSVERSE STATICAL STABILITY CENTRE OF GRAVITY :- IS THE POINT ABOUT WHICH FORCE OF GRAVITY ACT VERTICALLY DOWNWARDS EQUAL TO THE WEIGHT OF THE BODY. DENOTED BY LETTER G . CENTRE OF BUOYANCY:- IS THE POINT THROUGH WHICH THE FORCE OF BUOYANCY IS CONSIDERED TO ACT VERTICALLY UPWARDS WITH THE FORCE EQUAL TO THE WEIGHT OF WATER DISPLACED. IT IS THE CENTRE OF GRAVITY OF THE UNDERWATER VOLUME. DEOTED BY LETTER B . TO FLOAT AT REST IN STILL WATER, A VESSEL MUST DISPLACE HER OWN WEIGHT OF WATER, AND THE CENTRE OF GRAVITY MUST BE IN THE SAME VERTICAL LINE AS THE CENTRE OF BOUYANCY.
METACENTRE CONSIDER A SHIP FLOATING UPRIGHT IN STILL WATER AS SHOWN IN PREVIOUS SLIDE. CENTRE OF GRAVITY IS AT G AND B. WHEN SHIP IS INCLINED BY AN EXTERNAL FORCE TO A SMALL ANGLE THERE IS NO CHANGE IN THE DISTRIBUTION OF WEIGHT AND HENCE CENTRE OF GRAVITY WILL REMAIN AT G AND WEIGHT OF THE SHIP W WILL ACT DOWNWARD THROUGH THAT POINT. WHEN HEELED , THE WEDGE OF BOUYANCY WOW1 IS BROUGHT OUT OF WATER AND AN EQUAL WEDGE LOL1 BECOMES IMMERSED. IN THIS WAY A WEDGE OF BOUYANCY HAVING ITS CENTRE OF GRAVITY AT g IS TRANSFERRED TO A POSITION WITH CENTRE OF GRAVITY AT g1. THE CENTRE OF BOUYANCY , BEING THE CENTRE OF GRAVITY OF UNDERWATER VOLUME SHIFT FROM B TO B1.SUCH THAT BB1 IS PARALLEL TO gg1 AND BB1=v*gg1/V WHERE v=VOLUME OF TRANSFERRED WEDGE V=SHIPS VOLUME OF DISPLACEMENT THE VERTICAL THROUGH THE CENTRE OF BOUYANCY AT TWO CONSEQUETIVE ANGLES OF HEEL INTERSECT AT A POINT CALLED THE METACENTRE. WHILE THE VERTICAL DISTANCE BETWEEN G AND M IS CALLED METACENTRIC HEIGHT.
STABLE EQUILIBRIUM A SHIP IS IN STABLE EQUILIBRIUM IF G IS BELOW M I.E SHIP HAVE POSITIVE INITIAL METACENTRIC HEIGHT IN THIS CASE SHIP WHEN INCLINED WILL COMES BACK TO ITS INITIAL POSITION. IN THE PREVIOUS SLIDE WE SEE THAT WHEN THE SHIP IS INCLINED IN A CLOCKWISE DIRECTION THERE IS A MOMENT PRODUCED BY THE COUPLE OF WEIGHT OF THE SHIP AND BOUYANT FORCE IN ANTI CLOCKWISE DIRECTION AND HENCE PRODUCING A COUNTER EFFECT TO BRING BACK THE SHIP TO INTIAL POSITION. THIS IS CALLED MOMENT OF STATICAL STABILITY. MOMENT OF STATICAL STABILITY=W* GZ TONNES METRES WHERE W= FORCE GZ= LENGTH OF RIGHTING LEVER
UNSTABLE EQUILIBRIUM WHEN SHIP IS INCLINED TO A SMALL ANGLE AND IT STILL HEELS FURTHUR THEN THE SHIP IS SAID TO BE IN UNSTABLE EQUILIBRIUM. THIS CONDITION ARISES WHEN M IS BELOW G I.E INITIAL GM IS NEGETIVE. IN THE FIGURE WE CAN SEE THAT WHEN SHIP INCLINES TO CLOCKWISE DIRECTION THERE IS A MOMENT DUE TO THE COUPLE OF W AND B WHICH FURTHUR SUPPORT THE INCLINATION AND SHIP INCLINE FURTHER TO CLOCKWISE DIRECTION ONLY WHICH CAN LEAD TO CAPSIZE OF THE SHIP
NEUTRAL EQUILIBRIUM WHEN G AND M COINCIDES THEN THAT CONDITION IS NEUTRAL EQUILIBRIUM. HENCE MOMENT OF STATICAL STABILITY=0. HENCE IF SHIP IS INCLINED THEN IT WILL REMAIN INCLINED TO THAT POSITION ONLY AS THERE IS NO RIGHTING MOMENT.
