Ship Hull Calculation Functions

Gaël Porée
Engineering school student at SeaTech - Intern at NTNU
Supervised by Henrique Murilo Gaspar - April to June 2024

Introduction

I'm a French student in the second year of my engineering school. I completed a 3-month internship at NTNU, and during this internship, I programmed various JavaScript functions to calculate and visualize different ship characteristics. The purpose of this page is to show you these functions and how they work.
All of these functions use a JSON file. This file contains all the information about the ship being studied. To generate the examples that will follow, you can download any JSON file using the link and then import the file below. By default, the calculations will be performed using the JSON file of the Gunnerus ship.

Ship specs examples

The JSON file contains a Half-Breadths table that allows for reconstructing the shape of the ship's hull. The values in this table will be normalized between 0 and 1. To standardize these values into an unit, they must be multiplied by the calculation parameters'values. In this table, we find the waterlines which represent the Z-axis values (cf. Figure No. 1), as well as the stations which represent the X-axis values. At the intersection of these values are the buttocklines values. These values represent the Y-axis and, due to the symmetry of the boats, start at 0 in the middle of the ship.

I] Submerged volume value

The JSON file includes the Half-Breadths table, which provides information about the shape of the ship's hull. Using this table and the Draft value - also included in the JSON -, the submerged volume can be calculated. To calculate it, the area of each waterline - represented in Figure No. 2 - is computed using the Half-Breadths table. Then, the distance between two areas - represented by the "d" in Figure No. 2 - is multiplied by their average to obtain the volume.

$$\mathrm{V\; =}\sum _{i=0}^n{\mathrm{((Aw}}_{\mathrm{i}}+{\mathrm{Aw}}_{\mathrm{i+1}}\mathrm{2)}{\mathrm{*\; d}}_{\mathrm{i,i+1}}$$

By clicking the button below, you can calculate the submerged volume of the boat. The values have already been multiplied by the calculation parameters'values.

Calculate the submerged volume

V =

II] Coefficient values

Several coefficients exist to characterize the hull of a ship. Each of them defines the ship's water-penetrating power. The smaller the coefficient, the less power the ship will need to penetrate the water.

The waterplane coefficient Cw is obtained as follows:

The Block coefficient Cb is obtained as follows:

The Prismatic coefficient Cp is obtained as follows:

The Midship Section coefficient Cm is obtained as follows:

All of these coefficients are calculated from the JSON file, you can click the following button to display them. The calculated values are in the expected orders of magnitude but could not be verified.

Calculate the coefficients

III] Stability values

To determine the stability of a ship, calculations of various points are necessary. The center of Gravity of the boat is one of them. The closer it is to the center of Buoyancy - which represents the center of gravity of the submerged volume - the more stable the ship is.
By clicking the button below, you can calculate the submerged volume of the boat. The values have already been multiplied by the calculation parameters' values.

$$B_{\mathrm{x}}\sum _{i=0}^n[V_{\mathrm{i}}*d_{\mathrm{i}}/\sum _{i=0}^n{d}_{\mathrm{i}}$$ Calculate Centers

The Y value is zero for both points because we consider here that there is no trim. Since the boats are symmetrical, the Y value is zero.

Conclusion

The functions presented allow for the calculation of characteristic values of a boat's hull based on data present in a JSON file. The coefficient values could not be verified, and the quality of the results greatly depends on the accuracy of the Half-Breadths table. The more points provided, the more accurate the calculations will be.
However, if the Draft value lies between two waterlines, a new waterline is created by interpolation. This helps to make the values of the submerged volume, Cw, and the coordinates of the Buoyancy point more accurate.

Webography

[1] Interpreting the Lines Plan