GZ CROSS CURVE OF STABILITY :-
THESE ARE A SET OF CURVES FROM WHICH THE RIGHTING LEVER ABOUT AN ASSUMED CENTRE OF GRAVITY FOR AN ANGLE OF HEEL AT ANY PARTICULAR DISPLACEMENT MAY BE FOUND BY INSPECTION. THE CURVE IS PLOTTED FOE AN ASSUMED KG AND IF ACTAUL KG DIFFERS FROM THIS , A CORRECTION MUST BE APPLIED TO THE RIGHTING LEVERS TAKEN FROM THE CURVE.
LET US UNDERSTAND IT BY THE HELP OF AN EXAMPLE:-
USING A STATICAL STABILITY CURVE FOR A SHIP , LET US FIND GZ’S AT15 DEGREE INTERVALS BETWEEN 0 TO 90 DEGREE HEEL WHEN DISPLACEMENT OF THE SHIP IS 35000 TONNES AND KG= 9 MTRS.
NOW FIRST MAKE A PERPENDICULAR FROM DISPLACEMENT 35000 TONNES. THE GZ VALVE WFOR DIFFERENT ANGLES WILL BE:
ANGLE OF HEELS 0 15 30 45 60 75 90
GZ IN METERS 0 0.86 2.07 2.45 1.85 0.76 -0.5
THIS GZ IS FOR KG=9 MTRS. BUT IF KG IS OTHER THAN 9 MTRS. THEN CORRECTION MUST BE APPLIED TO THE GZ WE GOT FROM THE CURVE. NOW IN THE FIGURE ABOVE WE HAVE BEEN GIVEN THE CORRECTION FOR EVERY 1 MTR DIFFERENCE IN HEIGHT OF CENTRE OF GRAVITY FROM SHIPS ACTUAL KG I.E 9 MTRS.
TO FIND CORRECTION TO GZ, MULTIPLY CORRECTION TAKEN FROM TABLE FOR THE ANGLE OF HEEL CONCERNED BY THE DIFFERENCE IN KG.
NOTE:-
1. WHEN SHIP’S ACTUAL KG IS GREATER THAN ASSUMED KG THEN THEN SHIP IS LESS STABLE AND CORRECTION MUST BE SUBTRACTED.
2. WHEN ACTUAL KG IS LESS THAN ASSUMED KG THEN SHIP IS MORE STABLE AND CORRECTION MUST BE ADDED.
NOW LET ACTUAL KG BE 8.5 THEN VALUE OF CORRECTED GZ’S WILL BE:
CORRECTION=(DIFFERENCE B/W ACTUAL AND ASSUMED KG)*SIN(ANGLE OF HEEL)
=(9-8.5)*SIN(ANGLE OF HEEL)= 0.5*SIN(ANGLE OF HEEL)
HEEL GZ AT 9 MTRS. CORRECTION CORRECTED GZ
0 0 O.5*0=0 0+0=0
15 0.81 0.5*0.259=0.129 O.81+0.13= 0.94
30 1.9 0.5*0.5=0.25 1.9+0.25=2.15
45 2.24 0.5*0.707=0.353 2.24+.353=2.59
60 1.7 0.5*0.866=0.433 1.7+0.433=2.13
75 0.68 0.5*0.966=0.483 0.68+0.483=1.16
90 -0.49 0.5*1.0=0.5 -0.49+0.5=.01