Page 96 - statbility for masters and mates

84
Ship Stability for Masters and Mates
The spacing between the ®rst three and the last three half-ordinates is half of the spacing between the other half-ordinates. Find the area of the water-plane.
Area 13 CI S1 2 CI 72=8 9 m
Area of WP 13 9 117:6 2
Ans. Area of WP 705:6 sq. m
Note. It will be seen from this table that the effect of halving the common interval is to halve the Simpson's Multipliers.
S1 is because it is using Simpson's First Rule.
Areas and volumes having an awkward number
of ordinates
Occasionally the number of ordinates used is such that the area or volume concerned cannot be found directly by use of either the First or the Second Rule. In such cases the area or volume should be divided into two parts, the area of each part being calculated separately, and the total area found by adding the areas of the two parts together.
Example 1
Show how the area of a water-plane may be found when using six semi- ordinates. Neither the First nor the Second Rule can be applied directly to the whole area but the water-plane can be divided into two parts as shown in Figure 10.13 Area No. 1 can be calculated using the First Rule and area No. 2 by the Second Rule. The areas of the two parts may then be added together to ®nd the total area.
Fig. 10.13
An alternative method would be to ®nd the area between the half-ordinates a and e by the First Rule and then ®nd the area between the half-ordinates e and f by the `®ve-eight' Rule.
Example 2
Show how the area may be found when using eight semi-ordinates.
Divide the area up as shown in Figure 10.14. Find area No. 1 using the
Second Rule and area No. 2 using the First Rule.
An alternative method is again to ®nd the area between the half-ordinates a