Page 88 - statbility for masters and mates

76 Ship Stability for Masters and Mates
This is the form in which the formula should be used. As before, all of the ordinates appear in their correct order within the brackets. The multipliers are now 1332331. Had there been ten ordinates the multipliers would have been 1332332331. Note how the Simpson's multipliers begin and end with 1, as shown in Figure 10.6(b).
Example
Find the area of the water-plane described in the ®rst example using Simpson's Second Rule.
No. 12 ord. SM Area function
a010 b 3.7 3 11.1 c 5.9 3 17.7 d 7.6 2 15.2 e 7.5 3 22.5 f 4.6 3 13.8 g 0.1 1 0.1
80:4 S2
S2 is used because it is a total; using Simpson's Second Rule: Area WP 38 CI S2 2 for both sides
38 20 80:4 2
Ans. Area WP 1206 sq m (compared to 1207 sq. m previous answer)
The small difference in the two answers shows that the area found can only be a close approximation to the correct area.
The Five/Eight Rule (Simpson's Third Rule)
This rule may be used to ®nd the area between two consecutive ordinates when three consecutive ordinates are known.
The rule states that the area between two consecutive ordinates is equal to ®ve times the ®rst ordinate plus eight times the middle ordinate minus the external ordinate, all multiplied by 1 of the common interval.
Fig. 10.6(c)
12