Page 262 - statbility for masters and mates

250 Ship Stability for Masters and Mates
Or
Example 1
Virtual loss of GM GG1 P KG W P
A ship of 6000 tonnes displacement enters a drydock trimmed 0.3 m by the stern.KM 7.5m,KG 6m.MCTC 90tonnesm.Thecentreof¯otationis 45mfromaft.Findtheeffectivemetacentricheightatthecriticalinstantbefore the ship takes the blocks overall.
Note. Assume that the trim at the critical instant is zero. P MCTC t
Method (a)
l
90 30 45
P 60 tonnes
Virtual loss of GM MM1 P KM
6000 0:075m
W
60 7:5
Original GM 7:5 6:0 1:500 m Ans.NewGM 1:425m
Method (b)
Virtual loss of GM P KG W P
GG1 60 6 5940
0:061 m Original GM 1:500 m
Ans. New GM 1:439 m
From these results it would appear that there are two possible answers to the same problem, but this is not the case. The ship's ability to return to the upright is indicated by the righting moment and not by the effective metacentric height alone.
To illustrate this point, calculate the righting moments given by each method when the ship is heeled to a small angle (y )
Method (a)
Righting moment W GM1 sin y
6000 1:425 sin y
8550 sin y tonnes m.