Page 98 - statbility for masters and mates

86 Ship Stability for Masters and Mates
L
Example 1
Area of the WP 2E
yEdx
O
The value of the integral is found using the formula:
L h
yEdx 3 a 4b 2c 4d e O
Thus, the value of the integral is found by Simpson's Rules using values of the variable y as ordinates.
Moment of strip about OY xEyEdx L
Moment of 12 WP about OY Moment of WP about OY 2E
The value of this integral is found by Simpson's Rules using values of the product xEy as ordinates.
Let the distance of the centre of ¯otation be X from OY, then: X Moment
L
2E O yEdx
xEyEdx L
xEyEdx
O
O

2E L xEyEdx O
S2
S CI
1
Area
A ship 150 metres long has half-ordinate commencing from aft as follows: 0, 5, 9, 9, 9, 7 and 0 metres respectively.
Find the distance of the centre of ¯otation from forward (see Fig. 10.16). Note. To avoid using large numbers the levers used are in terms of CI the common interval. It is more ef®cient than using levers in metres (see table on facing page).
Area of the water-plane 23 CI S1
23 25 376 sq. m
Distance of C. F. from aft S2 CI S1
376 CI 120
78:33 m
Ans. C. F. is 78.33 m from aft