Page 89 - statbility for masters and mates
P. 89
Simpson's Rules for areas and centroids 77
Thus:Area1 h 5a 8b c or 1 CI S3 12 12
Also:Area2 h 5c 8b a or 1 CI S3 12 12
S3 is used because it is a total; using Simpson's Third Rule. Consider the next example.
Example
Three consecutive ordinates in a ship's water-plane, spaced 6 metres apart, are 14m, 15m, and 15.5m respectively. Find the area between the last two ordinates.
Fig. 10.6(d)
Shaded Area h 5a 8b c 12
6 77:5 120 14 12
Ans. Area 91:75sqm
Volumes of ship shapes and similar ®gures
Let the area of the elementary strip in Figures 10.7(a) and (b) be `Y' square metres. Then the volume of the strip in each case is equal to Y dx and the
volume of each ship is equal to 4h Y dx. O
The value of the integral in each case is found by Simpson's Rules using the areas at equidistant intervals as ordinates. i.e.
or
Volume h3 A 4B 2C 4D E CI S1
3
Thus the volume of displacement of a ship to any particular draft can be found ®rst by calculating the areas of water-planes or transverse areas at
