Deck Crane Lab

What is modelled

A boom of length L is hinged on a pin and held up by a hydraulic ram that pushes at a point a short way along the boom. The load moment grows with L cos of the angle; the ram has to supply it through a lever arm that is only the perpendicular distance from the pin to the line of the ram. A heaving ship adds accelerations that make the load heavier at the bottom of each swell.

Equations

• Load moment M = g cosφ (m L + μ L2/2) (1 + az/g), with μ the boom mass per metre.
• Ram force F = M / arm, with arm = |A × (A − B)| / |A − B| for the pin at the origin, the attachment A and the ram base B.
• Oil pressure p = F / (π D2/4), relief valve at pmax.
• Peak heave factor 1 + Ah (2π/T)2 / g.
• Virtual work F dl/dφ = M.

Checks run in the page

• The moment arm by cross product and by Heron's formula for the triangle.
• Force and moment equilibrium, with the moments taken about the boom tip.
• The virtual-work identity from a numerical derivative of the ram length.
• The sampled peak of the heave load factor and the safe load at the relief pressure.

Honest simplifications

The hoist wire hangs vertically, the load does not swing, the boom is a uniform beam, there is no friction in the ram or pin, the ship only heaves, and the telescoping section is added without changing the boom weight per metre. It is a classroom model and not a crane load chart.

• Press Long reach and see the safe load fall as the boom is extended and lowered.
• Press Rough sea and follow the oil pressure over a heave cycle.
• Press Relief valve opens, then raise the boom angle to bring the pressure back down.