Offshore Lift and Dynamic Load

What is modelled

When a wind-turbine part is lifted from or onto a vessel at sea, the crane tip heaves up and down with the ship while the payload hangs on a long wire rope. The rope is a spring, so the payload and the moving tip form a mass-spring-damper driven at the wave frequency. If the wave period is close to the natural period of the rope-payload system the tension swings far beyond the weight, and in rough seas the rope can go slack and then snap tight again.

Equations

• Ship heave amplitude z = a · ωn2 / √[(ωn2 − ω2)2 + (2 ζ ωn ω)2].
• Rope stiffness k = E A / L; payload m ⋯ = k e + c ė − m g with tension T = max(0, k e + c ė).
• Dynamic amplification Tmax / m g = 1 + (z ω2 / g) / √[(1 − r2)2 + (2 ζ r)2], with r = ω / ωrope.
• Snatch load Tmax = m g + √[(m g)2 + k m v2].

Checks run in the page

• The ship heave from a Runge-Kutta integration against the response formula.
• The rest tension of the rope equal to the weight.
• The peak tension in the time-domain simulation against the amplification formula, or slack detection.
• The snatch load of an undamped rope against the energy formula.

Honest simplifications

The wave is regular rather than a random sea, only heave is modelled and no roll, pitch or crane flexibility, the vessel has the one-degree-of-freedom response of a floating box, the rope is a linear spring with a fixed effective modulus and the payload has no wind load or pendulum motion. Real offshore lifts follow detailed lift plans with measured motion data.

• Press Calm sea and then Heave resonance and compare the amplification and the peak tension.
• Press Rough sea, slack rope risk and watch the rope turn dashed when the tension falls to zero.
• On the amplification curve, move the rope length to see how a stiffer short rope moves the resonance.