Curve of areas

The curve of areas, or sectional area curve, plots the immersed cross-sectional area of each station against longitudinal position, from the after perpendicular to the forward perpendicular. The area under the curve equals the displaced volume, and its centroid longitudinally is the LCB, so it encodes both displacement and trim balance directly. Its nondimensional shape, area over the maximum midship area against length, has a length-mean ordinate equal to the prismatic coefficient Cp, which is why naval architects design and fair the curve of areas first: it sets the longitudinal buoyancy distribution that governs wave-making resistance. The slopes at the ends fix the fineness of the entrance and run, and a hollow-free curve is a precondition for low resistance.