About this calculator
Cargo on a barge or ship deck moves with the vessel: it rolls, pitches and heaves. These motions create inertia forces at the cargo's centre of gravity, which the sea-fastening — lashings, stoppers and welded seafastening — must resist so the cargo does not slide or tip.
This calculator uses the simple harmonic-motion approach common in marine warranty guidelines and standards such as DNV for first calculations. For a roll of amplitude φ and period T, the transverse acceleration = g·sin φ + φ·ω²·z, with ω = 2π/T and z the height of the cargo CoG above the motion centre (often taken at the waterline). The deck-normal acceleration = g·cos φ ± (heave + φ·ω²·transverse distance). The pitch case is worked out the same way in the longitudinal direction. Roll and pitch are checked separately, each combined with heave.
From these forces the calculator checks sliding: the lateral force less friction μ × the smallest vertical force; the remainder must be taken by lashings. Tipping compares the moment of lateral force × CoG height with the restoring moment of weight × half the base width. The number of lashings follows from the calculated strength = MSL ÷ safety factor times the cosine of the lashing angle. Motion presets are provided for large barges (roll 20°, pitch 12.5°, 10 s) and small barges (30°, 15°), default values often quoted for barge transports. Results are for education/estimation; project sea-fastening design uses a motion analysis and surveyor approval.
Worked example
Cargo 50 t on a large barge (roll 20°/10 s, pitch 12.5°/10 s, heave 0.2 g), CoG 6 m above the waterline, 4 m off the centreline, 20 m from midship, 1.5 m above the deck, base 3 × 5 m, μ 0.1, lashing MSL 100 kN at 30°, SF 1.5:
- Roll: 9.807 × sin 20° + 0.3491 × (2π/10)² × 6 = 4.18 m/s² → 209.0 kN transverse
- Minimum vertical 9.807 × cos 20° − (1.961 + 0.551) = 6.70 m/s² → friction 33.5 kN → 175.5 kN needed
- Capacity per lashing 100 ÷ 1.5 × cos 30° = 57.7 kN → 4 lashings per side; no tipping (313.6 < 502.7 kN·m)
- Pitch: 132.0 kN longitudinal, 102.5 kN needed → 2 lashings per end
How to use it
Choose motion criteria
Pick the large or small barge preset, or enter your own roll and pitch angles and periods plus heave.
Enter cargo and position
Enter weight, CoG height above the motion centre, distance from the centreline and from midship, CoG height above the deck and base size.
Enter friction and lashings
Choose the friction coefficient of the contact surfaces and enter lashing MSL, angle and safety factor.
Read the result
See transverse and longitudinal forces, securing needed after friction, the tipping check and lashings per side.