The relation between a wetted surface area and displacement of two similar ship

Two bodies or shapes are said to be similar if their liner dimensions are proportional.
If the areas of two similar figures are A₁ and Az and their lengths are L₁ and L₂, then A₁/A2 = (L1/L2)².
If the volumes of these two similar figures are V₁ and V₂, then:

V₁/V2 = (L1/L2)³

If L = length, B = beam, d = draught, S = Wetted surface area and A =displacement, two ships are said to be similar, if L₁/L₂ B₁/B₂ = d₁/d2 = A1/A2 and have the same coefficients of form CB, Cm, Cw, etc.

If two ships are similar, then A1/A₂ = (L₁/L2)³ = (B₁/B₂)³ = (d₁/d₂)³

or L₁/L2 = (A1/A2)¹/3

S₁/S₂ = (L₁/L2)² = (A1/A₂)²/3

and (A1/A₂) = (S1/S₂)³/2


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