船舶运动 RAO：从波浪谱到吊臂端点运动

作者： Tord Martinsen，首席执行官 · 方法与资料来源已核查 2026年8月 · 阅读时间14分钟

For a 船舶-based 吊装, 波高 is only the environmental input. The useful engineering quantity is the 运动 of the actual 吊点 — and that requires the 船舶 响应, its 相位, the 起重机 geometry and the sea 频谱 to be treated together.

A tall sea can produce modest 吊臂端点 运动 when most of its 能量 sits outside the 船舶’s responsive 周期s. A lower sea can be worse when its 能量 overlaps a 升沉, 纵摇 or 横摇 peak. Loading condition, 浪向 and 起重机 position can change the answer again.

The link between the sea and the 船舶 is the 响应幅值算子，简称 RAO。船舶与吊装之间的联系是 吊臂端点 RAO. That distinction matters: the compensator does not see 波高 directly. Its primary kinematic excitation is 运动 at the 吊臂端点.

船舶运动 RAO 实际包含什么

An RAO describes a first-order linear 响应 to a 单位 规则波, as a function of 波浪 周期 or 频率 and 波浪 浪向. A 升沉 RAO of 0.80 m/m at T = 10 s means that a 规则波 with 1 m 单振幅 produces 0.80 m of 升沉 single 振幅 at that 频率, for the stated 浪向 and 船舶 condition.

A complete 响应 carries both 幅值, how large the 响应 is, and 相位 — when it occurs relative to the 波浪. The file normally contains both for all six rigid-body 运动s: surge, sway, 升沉, 横摇, 纵摇 and yaw. It must also identify the RAO 原点, 坐标轴, positive rotations, 装载工况, 浪向 convention, 船舶 speed and 频率 convention.

RAOs may come from a radiation–diffraction analysis combined with the 船舶 mass, inertia, restoring and 阻尼 model; from model testing; or from an approved 船舶运动 manual. They are specific to the modelled condition. A transit-draft set does not automatically describe the same 船舶 at working draft with different ballast, trim, deck cargo or 起重机 configuration.

Read the overlap, not the tallest curve

Three regions commonly appear in a 升沉 响应. At very long 波浪lengths relative to the 船舶, the zero-speed 升沉 RAO in m/m generally approaches its quasi-static limit near 1. At very short 周期s, rigid-body displacement 响应 generally tends towards zero. Between them, inertia, hydrostatic restoring and 阻尼 produce peaks or shoulders in one or more 运动s.

Roll and 纵摇 curves require more care because their usual 单位 are angle per metre of 波浪. A rotational RAO of 1 deg/m does not mean the 船舶 moves “more than the 波浪”. The useful question is what that angle does at the 吊点.

These are tendencies, not operating rules. Heading can be an effective operability lever, but it is constrained by stationkeeping, wind and 海流, thruster limits, 起重机 offlead and sidelead, 吊装 path, nearby assets and the approved procedure.

从船舶 RAO 到吊臂端点运动

The hydrodynamic reference point is rarely the 吊点. A 起重机 mounted forward, aft or off the centreline turns 转动 运动 into 垂向 travel.

For small rigid-body 运动s, the 复数 垂向 吊臂端点 RAO is:

其中 H_3, H_4 和 H_5 are the 升沉, 横摇 and 纵摇 RAOs; x_P 和 y_P are signed offsets from the RAO 原点; omega 为频率， beta 为浪向。转动 RAO 在乘以力臂前必须采用 rad/m。

Every term is 复数. Magnitude and 相位 are combined first; only then is the final magnitude taken. Adding the three plotted magnitudes throws away the timing.

从波浪谱到运动统计量

A real sea contains many 频率 components. For a long-crested sea at one 浪向, the first-order 吊臂端点 响应谱 is:

对于方向性海况，应沿方向对响应积分：

This matters when wind sea and swell arrive from different directions, or when spreading reaches both 纵摇-sensitive and 横摇-sensitive 浪向s. The 波浪 spectra, H_s 和 T_p article covers the environmental side of the calculation.

The 响应 statistics then come from spectral moments:

^* Narrow-band Gaussian approximation. A design maximum also needs a stated exposure duration, 响应 bandwidth, statistical model and probability criterion.

If the 船舶 has meaningful forward speed, the analysis must distinguish 波浪 频率 from encounter 频率. Station-kept construction 船舶s are often assessed near zero speed; transit, towing and some installation cases are not.

RAO 的边界与吊装模型的起点

A 吊臂端点 运动 频谱 is not yet a hook load, compensator 行程, DAF or allowable sea state. It becomes the excitation for the 起重机, winch, 钢丝绳, 索具, compensator and 负载.

Where 波浪s also act directly on the 负载, generate 波面高程, particle kinematics and 船舶 响应 from the same directional components, or the same time-domain realisation, so their relative 相位 is preserved.

This is the boundary between 船舶 响应 and the 动力放大系数 (DAF): RAOs describe imposed 运动; DAF reports a named peak load 响应 relative to a stated reference after the load path has responded. For marine-吊装 hydrodynamics and dynamic analysis, see the DNV-RP-N103 海上作业指南.

船舶运动筛选所需的输入资料

A usable 船舶-运动 package contains more than a PDF plot. Before calculating, check that the data answer each of the questions below.

An 海上吊装作业能力筛选 follows this chain across the H_s–T_p plane. It reports the workable region by 浪向 and identifies the gate that closes it, rather than returning one unqualified 运动 number.

Generic or class-prescribed 运动s may support concept screening only where the governing method permits and its validity range is satisfied. They are not inherently conservative across 周期, 浪向, 装载工况 or 起重机 location. Final weather limits and equipment sizing should use the project-accepted 船舶 basis, or document why a substitute is adequate.