Page 99 - statbility for masters and mates

Simpson's Rules for areas and centroids 87
12 Ordinate SM Products for area Levers from A* Moment function
Aft01 0 0 0 54 20 1 20 92 18 2 36
e 9 4 36 3 108 92 18 4 72 74 28 5 140
Forward01 0 6 0 120 S1 376 S2
* The Levers are in terms of the number of CI from the aft ordinate through to the foremost ordinate.
S1, because it is the ®rst total.
S2, because it is the second total.
Fig. 10.16
This problem can also be solved by taking the moments about amidships as in the following example:
Example 2
A ship 75 m long has half-ordinates at the load water-plane commencing from aft as follows:
0, 1, 2, 4, 5, 5, 5, 4, 3, 2 and 0 metres respectively.
The spacing between the ®rst three semi-ordinates and the last three semi- ordinates is half of that between the other semi-ordinates. Find the position of the Centre of Flotation relative to amidships.
e
Fig. 10.17
Use ve the sign for levers and moments AFT of amidships (e ). Use ve sign for levers and moments FORWARD of amidships (e ).