The surface area of the part of the hull below the waterline is called the wetted surface area.

To obtain the wetted surface area, the areas of the surfaces in contact with water must be summed while taking the inclination of the hull surface into account.

This article first finds the underwater length of a transverse section, and then considers how to calculate the wetted surface area of the entire hull.

1.4.1 Finding the Underwater Length of a Transverse Section

Let $x[\mathrm{m}]$ be the distance measured forward from the aft perpendicular (A.P.), $z[\mathrm{m}]$ the height measured vertically upward from the baseline (B.L.), and $d[\mathrm{m}]$ the draft.

Let $b(x,z)[\mathrm{m}]$ be the half-breadth, measured from the hull centerline to the side of the hull on one side.

Here, we consider a hull that is symmetric to port and starboard, and express the surface on one side as the curved surface $y=b(x,z)$.

For the transverse section at position $x$, let $s(x,d)[\mathrm{m}]$ be the length of the underwater part of the hull contour. It is obtained from the following equation.

Here, $\partial$ is the symbol for partial differentiation.

$\frac{\partial b(x,z)}{\partial z}$ represents how much the half-breadth changes with height $z$ when the longitudinal position $x$ is held fixed. In other words, it indicates the slope of the transverse section contour.

By integrating the length along the contour while taking this slope into account, and doubling the result for one side, the combined length for both port and starboard sides is obtained.

Note that what is calculated here is the length of the hull contour in contact with water; it does not include the straight segment across the waterline.

1.4.2 Finding the Wetted Surface Area Considering the Inclination of the Hull Surface

The hull surface is inclined not only in the vertical direction but also in the longitudinal direction.

$\frac{\partial b(x,z)}{\partial x}$ represents how much the half-breadth changes with the fore-aft position $x$ when the height $z$ is held fixed.

Taking the inclination in both directions into account, the wetted surface area $S(d)[\mathrm{m^2}]$ of the hull surface under consideration is expressed by the following equation.

Here, $L_{PP}[\mathrm{m}]$ is the length between perpendiculars, the horizontal distance from the aft perpendicular (A.P.) to the forward perpendicular (F.P.).

The inner integral sums over the vertical range and the outer integral sums over the longitudinal range, giving the surface area of both sides.

1.4.3 Approximate Calculation Using the Length of Transverse Sections

In Eq. (1.4-2), if the effect of the term due to longitudinal inclination, $\left(\frac{\partial b(x,z)}{\partial x}\right)^2$, is sufficiently small compared with the remaining terms, this term can be omitted as an approximation.

In this case, the wetted surface area is expressed as follows.

Multiplying the section length $s(x,d)$ obtained from Eq. (1.4-1) by a small longitudinal width $dx[\mathrm{m}]$ approximates the surface area of that portion.

Summing these along the length of the ship gives the wetted surface area of the entire hull.

However, the method of integrating the section lengths is an approximation that omits the effect of longitudinal inclination.

1.4.4 Relationship Between Wetted Surface Area and Hull Resistance

The wetted surface area is also used when evaluating the resistance acting on the hull.

Let $\rho[\mathrm{kg/m^3}]$ be the density of water, $U[\mathrm{m/s}]$ the ship speed, $C_T$ the total resistance coefficient, and $R_T[\mathrm{N}]$ the total resistance. The following relationship holds.

The total resistance coefficient $C_T$ is dimensionless and includes components corresponding to frictional resistance and residual resistance.

From Eq. (1.4-4), if the water density, ship speed, and total resistance coefficient are the same, a larger wetted surface area results in a larger total resistance.

However, actual resistance is not determined by the wetted surface area alone.

In a study on hull roughness, the change in resistance for the same hull form was estimated using test results for different coated surfaces and rough surfaces simulating biofouling. The results show that resistance also changes depending on the condition of the hull surface.

Therefore, when considering resistance, factors such as ship speed and the condition of the hull surface must be taken into account in addition to the wetted surface area.

About This Article

References

• An Introduction to Naval Architecture in One Volume, edited by the Maritime College Career Education Research Association
• “Predicting the Effect of Hull Roughness on Ship Resistance Using a Fully Turbulent Flow Channel,” R. Ravenna et al.

(Last accessed: October 12, 2026)


*This article was compiled based on the author’s understanding and practical knowledge, with reference to the above literature.