To calculate a ship’s displacement volume and displacement, it is necessary to understand the shape of the submerged portion of the hull.

One of the fundamental calculations involved is determining the cross-sectional area of the hull at each longitudinal position.
First, consider the submerged cross-sectional area at the midship section.

As shown in Figure 1.1-1, the vertical distance from the baseline (B.L.) to the waterline is defined as the draft d.

At a height z above the baseline, the horizontal distance from the centerline (C.L.) to the hull surface is defined as the half-breadth b_M(z).

Figure 1.1-1 Concept of the Submerged Cross-Sectional Area at the Midship Section

Because the midship section is symmetrical about the hull centerline, the submerged cross-sectional area on one side can be calculated by integrating the half-breadth b_M(z) from the baseline to the waterline.

Therefore, the cross-sectional area on one side is expressed as follows.

b_M(z): Half-breadth of the midship section at height z [m]
z: Height above the baseline [m]
d: Draft [m]

For the entire midship section, this area exists on both sides of the hull centerline. Therefore, multiplying it by two gives the submerged cross-sectional area A_M(d).

A_M(d): Submerged cross-sectional area of the midship section at draft d [m²]

In other words, this equation calculates the area on one side by summing the half-breadths that vary with the height of the hull and then doubles that area to obtain the total submerged cross-sectional area of the midship section.

The cross-sectional area at any longitudinal position x can be determined in the same manner.

If the half-breadth at height z at that position is denoted by b(x,z), the submerged cross-sectional area A(x,d) at draft d is expressed by the following equation.

A(x,d): Submerged cross-sectional area at longitudinal position x and draft d [m²]
b(x,z): Half-breadth of the hull at longitudinal position x and height z [m]

A_M(d) represents the cross-sectional area at the midship section, whereas A(x,d) represents the cross-sectional area at any longitudinal position x.

By calculating the cross-sectional area A(x,d) at each longitudinal position and then integrating these areas along the length of the ship, the displacement volume of the submerged portion of the hull can be determined.

About This Article

Reference
・Kore Issatsu de Senpaku Kōgaku Nyūmon [Introduction to Naval Architecture in One Volume], edited by the Maritime College Career Education Research Association


※This article was prepared with reference to the source listed above and organized based on the author’s understanding.