Page 93 - statbility for masters and mates

Simpson's Rules for areas and centroids 81
Area 1 13 CI S1 Area 1 93 149:7 Area 1 449:1 sq. m
Appendage 50:0 sq. m Area 2 Area of WP 499:1 sq. m
Subdivided common intervals
The area or volume of an appendage may be found by the introduction of intermediate ordinates. Referring to the water-plane area shown in Figure 10.11, the length has been divided into seven equal parts and the half ordinates have been set up. Also, the side is a smooth curve from the stem to the ordinate `g'.
Fig. 10.11
If the area of the water-plane is found by putting the eight half-ordinates directly through the rules, the answer obtained will obviously be an erroneous one. To reduce the error the water-plane may be divided into two parts as shown in the ®gure.
Then,
Area No. 1 h=3 a 4b 2c 4d 2e 4f g
To ®nd Area No. 2, an intermediate semi-ordinate is set up midway between the semi-ordinates g and j. The common interval for this area is h/2.
Then, or,
Area No. 2 h=2 13 g 4h j
AreaNo.2 h=3 12 g 2h 12 j
If CI is halved, then multipliers are halved, i.e. from 1, 4, 1 etc. to 12, 2, 12.
Areaof12 WP Area1 Area2
h=3 a 4b 2c 4d 2e 4f g
h=3 12 g 2h 12 j h=3 a 4b 2c 4d 2e 4f g 12 g
2h 12 j