A ship 140 m long and 18 m beam floats at a draught of 9 m. The immersed cross-sectional areas at equal intervals are 5, 60, 116, 145, 152, 153, 153, 151, 142, 85 and 0 m2 respectively. Calculate: (a) displacement (b) block coefficient (c) midship section area coefficient (d) prismatic coefficient.

 A ship 140 m long and 18 m beam floats at a draught of 9 m. The immersed cross-sectional areas at equal intervals are 5, 60, 116, 145, 152, 153, 153, 151, 142, 85 and 0 m2 respectively.

Calculate:

(a) displacement

(b) block coefficient

(c) midship section area coefficient

(d) prismatic coefficient.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 3.3

 

Solution:

a)

Cross-section	SM	f(vol)
5	1	5
60	4	240
116	2	232
145	4	580
152	2	304
153	4	612
153	2	306
151	4	604
142	2	284
85	4	340
0	1	0
		∑ f(vol) = 3507

 

Common interval, h = 140/10 = 14

Displacement  = h/3 * ∑ f(vol) * 1.025

                        = 14/3 * 3507 * 1.025

                        = 16775.15 tons

b)

Block Coefficient, C_b = volume displacement/L*B*d

                                    = 16775.15/140*18*9*1.025

                                    = 0.722

c)

Midship Section Area Coefficient, C_m = midship area/B*d

                                                              = 153/18*9

                                                              = 0.944

d)

Prismatic Coefficient, C_p = C_b/C_m

                                         = 0.722/0.944

                                             = 0.764