Check the box-barge hydrostatics
Check by hand how a deeper draught changes the initial stability of a box barge, then compare the calculation with the hydrostatics tool.
This optional exercise accompanies Chapter 4, Example 4.1. You can read the book and use its calculators without opening the separate tool.
Read first
Begin with Chapter 1 for hull dimensions and axes, Chapter 2 for volume and waterplane moments, and Chapter 3 for flotation. Chapter 4 uses these quantities to find whether a small heel produces a restoring moment.
1. Load the box barge
The barge is 60 m long, 12 m wide and 6 m deep. Its centre of gravity is 4 m above the keel. The supplied file is an original closed box mesh, including its deck; its flat faces represent this geometry exactly.
The tool opens in a separate tab so you can keep these inputs and answers beside it.
In Inputs → Hull geometry, select Mesh file and open the downloaded file. Use metre and x fwd, y port, z up. Leave the three values of Then move the hull by at 0, and leave The file holds one side only unchecked: the file contains both sides.
The extent should be x = 0 to 60 m, y = −6 to 6 m and z = 0 to 6 m. A different extent means the file or its units need checking.
2. Set the waterplanes
| Field | Value |
|---|---|
| LPP | 60 m |
| B | 12 m |
| Water density | 1.025 t/m³ |
| Mean draughts T | 2, 3, 4 m |
| Trim | 0 m (even keel) |
| Compute the GZ curve | Unchecked |
This run computes the upright hull at three specified waterplanes. It does not solve a loading condition or assess stability criteria. We use KG = 4 m in the hand calculation below; there are no slack tanks or other free-surface corrections in this example.
Choose Analysis & results → Compute, then find the Upright hydrostatics table. These upright values are the starting point of Example 4.1; its heeled righting moment is a separate calculation.
3. Check the answer
For this rectangular box, displaced volume ∇ = 60 × 12 × T; displacement mass Δm = 1.025∇; KB = T/2; and the transverse metacentric radius BMT = 12²/(12T). Then KMT = KB + BMT and GMT = KMT − 4.
| T (m) | ∇ (m³) | Δm (t) | KB (m) | BMT (m) | KMT (m) | GMT (m) |
|---|---|---|---|---|---|---|
| 2 | 1440 | 1476 | 1.00 | 6.00 | 7.00 | 3.00 |
| 3 | 2160 | 2214 | 1.50 | 4.00 | 5.50 | 1.50 |
| 4 | 2880 | 2952 | 2.00 | 3.00 | 5.00 | 1.00 |
Compare the displayed volume and mass within 1 m³ and 1 t, and KB, BMT and KMT within 0.01 m. These allowances cover the displayed rounding for this exact box; they are not uncertainty estimates for a curved hull. If a value differs by more, check the units, axes, density, draughts and trim before continuing.
The 3 m row reproduces the upright values in Example 4.1. As T increases from 2 to 4 m, KB rises but BM falls faster, so KM falls. With KG held at 4 m, GM therefore falls too. A real loading change may also move G: the table isolates the effect of draught at a fixed KG.
4. Change one quantity
Keep the 3 m draught and imagine raising KG from 4 m to 5 m without changing the displacement. Predict what happens before reading the answer.
Show the answer
KB, BM and KM stay the same because the upright hull and waterplane have not changed. GM falls from 1.50 m to 0.50 m. The barge is still stable to a small heel, but has a smaller restoring moment at the same small angle. Positive GM by itself does not establish adequate stability at large angles.
Continue with Example 4.1 to calculate the small-angle righting moment. The book develops loading changes, free surfaces and large-angle stability in the chapters that follow.
Keep or report your result
Under Downloads and run record, save hydrostatics.csv and run.json, and keep the box mesh with them. To see the results again, choose Open saved results on the Analysis & results page and open the file that Download results JSON saves; to compute them again, load the same mesh and enter the inputs above. The run record documents the calculation; keep it with your results and input file.
Send feedback about this exercise. Include the tool version, inputs, expected value and result if they disagree.