TRANSVERSE STATICAL STABILITY CENTRE OF GRAVITY IS THE

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

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 WOW 1 IS BROUGHT OUT OF WATER AND AN EQUAL WEDGE LOL 1 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 g 1. THE CENTRE OF BOUYANCY , BEING THE CENTRE OF GRAVITY OF UNDERWATER VOLUME SHIFT FROM B TO B 1. SUCH THAT BB 1 IS PARALLEL TO gg 1 AND BB 1=v*gg 1/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=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

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.