Page 86 - statbility for masters and mates

74 Ship Stability for Masters and Mates
coef®cients of the half-ordinates are referred to as Simpson's Multipliers and they are in the form: 1424241. Had there been nine half-ordinates, the Multipliers would have been: 142424241. It is usually much easier to set out that part of the problem within the brackets in tabular form. Note how the Simpson's multipliers begin and end with 1, as shown in Figure 10.5(b).
Example
A ship 120 metres long at the waterline has equidistantly spaced half-ordinates commencing from forward as follows:
0, 3.7, 5.9, 7.6, 7.5, 4.6, 0.1 metres respectively.
Find the area of the water-plane and the TPC at this draft.
Note. There is an odd number of ordinates in the water-plane and therefore the First Rule can be used.
No. 12 ord. SM Area function
a010 b 3.7 4 14.8 c 5.9 2 11.8 d 7.6 4 30.4 e 7.5 2 15.0 f 4.6 4 18.4 g 0.1 1 0.1
90:5 S1 S1 is used because it is a total; using Simpson's First Rule:
h 120 the common interval CI 6
; CI 20 metres
Area of WP 13 CI S1 2 for both sides
13 20 90:5 2 Ans. Area of WP 1207 sq m
TPCSW WPA 1207 97:56 97:56
Ans. TPC 12:37 tonnes
Note. If the half-ordinates are used in these calculations, then the area of half the water-plane is found. If however the whole breadths are used, the total area of the water-plane will be found. If half-ordinates are given and the WPA is requested, simply multiply by 2 at the end of the formula as shown above.