Page 100 - statbility for masters and mates

88 Ship Stability for Masters and Mates
12 Ordinate SM Area function Levers Moment function
Aft0120 41 0 122 32 7 2112 3 3 9 4 4 16 2 32
5 e 5 5 4 3
2 10 1 10 4 20 0 0
2 10
4 16 1 12 4.5
1 10 2 32 3 1 13:5
224.0 32 14 Forward 0 12 0 4 0
85:5 S1 11:5 S2 CI 75 9:375 m
8
S1 denotes ®rst total.
S2 denotes second algebriac total.
The point having a lever of zero is the fulcrum point. All other levers ve and ve are then relative to this point.
Distance of C. F. from admidships S2 CI S1
11:5 9:375 85:5
1:26 m Ans. C. F. is 1.26 metres forward of amidships
To ®nd the KB
The centre of buoyancy is the three-dimensional centre of gravity of the underwater volume and Simpson's Rules may be used to determine its height above the keel.
First, the areas of water-planes are calculated at equidistant intervals of draft between the keel and the waterline. Then the volume of displacement is calculated by using these areas as ordinates in the rules. The moments of these areas about the keel are then taken to ®nd the total moment of the underwater volume about the keel. The KB is then found by dividing the total moment about the keel by the volume of displacement.
The ve sign shows it is forward of e .