Bulk Carrier Loading Plan

What is modelled

A ship floats where the weight of the ship and cargo equals the weight of the displaced water, and it trims until the centre of buoyancy lies under the centre of gravity. Along the hull the weight and the buoyancy are not equal, metre by metre, so the hull is loaded like a beam: the difference between them integrated once is the shear force and integrated twice is the bending moment. Filling only some holds raises that moment sharply.

Equations

• Mean draught T = W / (ρ B Cb L).
• Trim slope τ = 12 Σ w (x − L/2) / (ρ B Cb L3), so the draught at x is T + τ (x − L/2).
• Shear F(x) = ∫ (b − w) dx, bending moment M(x) = ∫ F dx, with b = ρ g B Cb (draught).

Checks run in the page

• Shear and moment close to zero at the bow end.
• A midship weight gives W g L / 8.
• Draught in fresh against salt water follows the density ratio.
• Trim from bisection against the closed form.

Honest simplifications

The hull is a box with a constant block coefficient, the lightship weight is spread by a simple rule, waves and the real hull shape are ignored and the moment limit is a round number chosen for teaching, not a class rule value. Real loading uses a loading computer approved by the classification society.

• Press Alternate holds and compare the peak moment with Even loading.
• Press Fresh river berth and read the draught change.
• Shift the cargo forward and watch the trim by the head.