Page 91 - statbility for masters and mates

Simpson's Rules for areas and centroids 79
Underwatervolume 13 CI S1 13 1:0 7918 2639 13 Cu. m
SW displacement 2639 13 1:025 tonnes Ans. SW displacement 2705:3 tonnes
Load TPCSW WPA 97:56
660 97:56
6:77 tonnes
FWA Displacement 4 TPC
2705:3 4 6:77
Appendages and intermediate ordinates
Appendages
It has been mentioned previously that areas and volumes calculated by the use of Simpson's Rules depend for their accuracy on the curvature of the sides following a de®nite mathematical law. It is very seldom that the ship's sides do follow one such curve. Consider the ship's water-plane area shown in Figure 10.8. The sides from the stem to the quarter form one curve but from this point to the stern is part of an entirely different curve. To obtain an answer which is as accurate as possible, the area from the stem to the quarter may be calculated by the use of Simpson's Rules and then the remainder of the area may be found by a second calculation. The remaining area mentioned above is referred to as an appendage.
Similarly, in Figure 10.9 the side of the ship forms a reasonable curve from the waterline down to the turn of the bilge, but below this point the curve is one of a different form.
Fig. 10.8
Ans. FWA 99.9 mm or 9.99 cm