The length of a ship is 7.6 times the breadth, while the breadth is 2.85 times the draught. The block coefficient is 0.69, prismatic coefficient 0.735, waterplane area coefficient 0.81 and the wetted surface area 7000 m2. The wetted surface area S is given by Denny's formula S = 1.7 Ld + (∇/d) Calculate:
(a) displacement in tonne
(b) area of immersed midship section
(c) waterplane area
Given
L = 7.6b
b = 2.85d ; d = b/2.85
Cb = 0.69
Cp = 0.735
Cw = 0.81
S = 7000 m2
To find
1.Displacement
2. Am
3.Aw
Solution
We know that Cb = ∇ / (L x b x d)
∇ = Cb x L x b x d
= 0.69 x 7.6b x b x b/2.85
∇ = 1.84b3
S = 1.7 Ld + (∇/d)
7000 = 1.7 x 7.6b x b/2.85 + (1.84b3 / (b/2.85))
= 4.53b2 + 5.24b2
= 9.77b2
b = 26.76 m
L = 7.6 x 26.76 = 203.38 m
d = 26.76/2.85 = 9.389 m
∇ = 1.84 x b3
= 35259.5
1. Displacement = ∇ x density
= 35259.5 x 1.025
= 36140 t
2. Midship coefficient Cm = Cb/Cp
= 0.69/0.735
= 0.938
We know that Cm = Am / b x d
Am = Cm x b x d
= 0.938 x 26.76 x 9.389
= 235.9 m2
3. Cw = Aw / L x b
Aw = Cw x L x b
= 0.81 x 203.38 x 26.76
= 4408m2
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