The number the whole study leans on

Every downstream result in a dropped object study — damage frequency, release frequency, the case for a protection cover — leans on one physical quantity: the energy the object delivers when it arrives at the target. Get that wrong and the rest of the study is arithmetic performed on a fiction. Yet impact energy is routinely treated as a lookup, when it is really the output of three pieces of physics that deserve to be understood: terminal velocity, drag and added mass.

Terminal velocity: the water decides, not the drop height

In air, a dropped object keeps accelerating and the drop height dominates the arrival energy. In water the picture inverts. Within a modest distance of entry, drag balances submerged weight and the object settles to a terminal velocity that it holds for the rest of the descent. For most offshore water depths, the seabed impact velocity is the terminal velocity — the height of the crane boom above the waterline has almost nothing to do with it.

The balance is between the object's weight in water and the drag it generates:

v_T = √[ 2g(m − Vρ_w) / (ρ_w C_D A) ]

where m is the mass in air, V the displaced volume, ρ_w seawater density, C_D the drag coefficient and A the projected area normal to the motion. Two consequences follow immediately.

First, the numerator is the submerged weight. A dense, compact object — a drill collar, a lump of structural steel — barely notices the buoyancy correction and arrives fast. A large, light object loses much of its weight to buoyancy and arrives slowly. At the limit, an object whose displaced volume outweighs its mass never arrives at all: it floats, and its seabed impact energy is exactly zero. A method that cannot recognise a floating object will happily assign impact energy to something that is bobbing on the surface.

Second, the projected area A is not a single number. A tubular falling end-on presents a fraction of the area it presents broadside, and the terminal velocity differs accordingly. An honest calculation carries both bounds: minimum and maximum projected areas give maximum and minimum terminal velocities, and therefore a defensible energy range rather than a false point estimate.

Drag: shape is data, not decoration

The drag coefficient does the quiet work in the denominator. A blunt, bluff body sheds energy into the water efficiently and settles slowly; a slender, streamlined shape slips through and keeps its pace. Between a scaffold tube falling end-on and a flat plate falling face-on sit most of the objects on a lift manifest, and their drag coefficients can differ by a factor of several — which, since energy goes with the square of velocity, moves the arrival energy by more than most analysts expect.

This is why object definitions in a well-constructed study carry their own drag coefficient rather than inheriting a global default. The lift manifest is not homogeneous, and the energy picture should not pretend it is.

Added mass: the water that arrives with the object

The subtlest of the three effects is added mass. An object moving through water sets a volume of surrounding water moving with it, and when the object stops against a target, that entrained water does not politely stop first — its momentum is delivered into the impact too. The effective impact energy is therefore calculated on the combined mass:

E_E = ½ (m + m_a) v_T², with m_a = ρ_w C_a V

where C_a is the added mass coefficient. For a dense, compact object the correction is small. For a large-volume object — a container, an empty basket, large-bore pipe — the entrained water can be a substantial fraction of the object's own mass, and ignoring it under-states the impact energy at precisely the point where the target's damage response is being judged. The same object that buoyancy slowed on the way down hits harder than its velocity alone suggests, because it does not arrive alone.

From physics to frequency: two defensible routes

DNV-RP-F107 distributes hit frequency across six energy bands, from below 50 kJ to above 800 kJ. How the hits are spread across those bands is a method choice, and both options have their place.

The traditional route uses the standard's class-based probability distributions: each object class carries a fixed distribution across the energy bands, independent of the specific object's calculated energy. It is standardised, comparable across studies, and appropriate when object-specific data is thin.

The physics-based route uses the calculated effective energies directly: the minimum and maximum effective impact energies define a distribution, and the hit frequency is spread across the energy bands according to it. It is object-specific, it honours the terminal velocity, drag and added mass actually calculated for each object, and it screens floating objects out of the energy picture automatically. When the object data exists, it is the sharper instrument — and because both routes are implementations of the same standard's framework, a reviewer can reconcile one against the other rather than taking either on faith.

DORAS implements both methods side by side, selected at study level, precisely so that a consultancy can run the class-based distribution for comparability and the calculated method for sharpness, and show a client where and why they differ.

What this means for your next study

Three practical checks fall out of the physics. First, confirm the energy calculation uses submerged weight and recognises buoyant objects — a floating object with an assigned impact energy is a red flag for the whole energy table. Second, look for energy bounds from minimum and maximum projected areas rather than a single orientation assumed for every object. Third, ask whether added mass is in the effective energy; for high-volume objects its absence materially understates the loading on the target.

None of this is exotic. It is the difference between an energy table that came from a lookup and one that came from the object actually being lifted — and it is the foundation under every damage and release frequency the study reports. Read how DORAS implements DNV-RP-F107 end to end, or start a free 30-day evaluation and put your own lift manifest through it.