C L DUBEY – EXERCISE – 02 : Simpson’s Rule

Ordinate	SM	Product	Lever	Moment
14.4	1	14.4	12h	172.8h
12.0	3	36.0	15h	540h
9.3	3	27.9	18h	502.2h
6.0	1	6.0	21h	126h
		SOP=84.3		SOM = 1341h

Moment = (3 ⨯ 3/8) ⨯ 1341
= 1508.625

Area = 9/8 ⨯ 84.3
= 94.83

Total moment = 2685.825
Area = 299.43

Therefore,
Geometric Centre = ( Total moment / Area)

= 8.97m from top.

Q9. A ship’s water plane is 216m in length. The half ordinates of the waterplane commencing from forward are as follows;
0.4, 4.4, 8.8, 11.0, 11.6, 11.8, 11.8, 11.6, 9.6, 7.0, 0.4 respectively.
The spacing between the first three and last three ordinates is half of the spacing between the other half ordinates. Calculate her waterplane area and the position of the CF with respect to the midlength.

Solution –

Ordinate	SM	Product	Hours	Moment
0.4	0.5	0.2	0h	0h
4.4	2	8.8	0.5h	4.4h
8.8	1.5	13.2	h	13.2h
11.0	4	44.0	3h	8.8h
11.6	2	23.2	3h	69.6h
11.8	24	47.2	4h	181.8h
11.8	1.5	23.6	5h	118h
11.6	4	46.4	6h	278h
9.6	1.5	14.4	7h	100.8h
7.0	2	14.0	7.5h	105h
0.4	0.5	0.2	8h	1.6h
		SOP=235.2		SOM=967.8h

Area = 2 ⨯ 27/3 ⨯235.2
= 4233.6m²

COG from one end = 111.099