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Simpson's Rules for areas and centroids 73
Fig. 10.5(a)
If the common interval and the ordinates are measured in metres, the area found will be in square metres.
Let this rule now be applied to a water-plane area such as that shown in Figure 10.5(b).
Fig. 10.5(b)
141 141
141
combined 1 4 2 4 2 4 1 multiplier
The water-plane is divided into three separate areas and Simpson's First Rule is used to ®nd each separate area.
Area 1 h=3 a 4b c Area 2 h=3 c 4d e Area 3 h=3 e 4f g
Areaof 12 WP Area1 Area2 Area3
;Areaof 12 WP h=3 a 4b c h=3 c 4d e h=3 e 4f g
orAreaof 12 WP h=3 a 4b 2c 4d 2e 4f g
This is the form in which the formula should be used. Within the brackets the half-ordinates appear in their correct sequence from forward to aft. The
