Solution Naval Numerical 21

Numerical 21. With the aid of sketches: a. Explain various lines plan. b. The half -breadths of water plane of a ship of 120m length ad 15m breadth are given below:b. The half -breadths of water plane of a ship of 120m length ad 15m breadth are given below:Station 0 1 2 3 4 5 6 7 8. Half breadths 1.6 2.8 5.5 6.4 7.3 6.2 4.2 2.0 0 Calculate i) Water plane area ii) TPC in salt water iii) Cw iv) LCF from Mid-ship.

Solution: (a)(b)

Half breadth	SM	PRODUCT For area	LEVER from Aft station	PRODUCT For moment
1.6	1	1.6	0	0
2.8	4	11.2	1	11.2
5.5	2	11	2	22
6.4	4	25.6	3	76.8
7.3	2	14.6	4	58.4
6.2	4	24.8	5	99.2
4.2	2	8.4	6	50.4
2.0	4	8	7	56
0	1	0	8	0
		∑a = 105.2		∑i = 374

Common interval (h) = 120/8 = 15
(i) Area of water plane  (Aw) = 2 x (h/3) x ∑a
= 2 x (15/3) x 105.2
= 1052 m-sq.
(ii) TPC = Aw x ρ /100 = 1052 x 1.025 /100 = 10.782 tonne.
(iii) Cw = Aw/LxB = 1052 /(120 x 15) =0.584
(iv) LCF from mid ship = (L/2) - LCF from Aft station
= (L/2) - h x (∑i/∑a)
= 60 - 15 x 374/105.2
= 60 - 53.327
= 6.673m aft of mid ship