Ship Lift: Winch Load Sharing

What is modelled

A rigid cradle is held by many ropes that behave as linear springs. The load goes to the ropes in proportion to their stiffness and their stretch, which depends on the height and tilt of the cradle. An off-centre ship moves the tension towards its side, and a winch that is out of step pulls or pays out its rope by a few millimetres, which loads that rope through its stiffness.

Equations

• Rope tension Ti = ki (c + si − a xi − b yi) with stiffness k = EA/ℓ, sync error si and cradle height and tilts c, a, b.
• Equilibrium ΣT = W, ΣT x = W ex, ΣT y = W ey, solved as three linear equations with slack ropes removed.

Checks run in the page

• Force and moment residuals of the solution.
• A separate direct search for the minimum of the elastic energy minus gravity work.
• The ideal centred case, where every rope carries W divided by 20.
• A planar sync error that tilts the cradle without changing any tension.

Honest simplifications

The cradle is rigid, ropes are linear with constant stiffness, the winches are position-controlled at a fixed offset, the sync error pattern is a fixed sine, and rope sway, dynamics and brakes are ignored. The tilt is shown exaggerated. This is a visualisation of static load sharing, not an engineering certification of any lift.

• Press Ship loaded off-centre to see the tension shift to one side and the cradle tilt.
• Press Sync error only and watch the largest tension grow while the mean stays fixed.
• Press Overweight and off-centre to push a rope above half its breaking load and the weaker side towards slack.