Subsea module on a heavy crane wire crossing the splash zone at dusk, water streaming off the frame

Passive heave compensation

A gas spring and a damper between the hook and the load — no external power.

Passive Heave Compensation Basics

Q: What is passive heave compensation?

A way to reduce the vertical motion transferred from a crane hook to a suspended payload, without external power. A gas spring supports the payload weight while hydraulic damping dissipates the wave energy — the compensator acts as a buffer between hook and load.

Q: What are the main components of a passive heave compensator?

Three: a nitrogen gas spring that carries the payload weight, a hydraulic cylinder whose oil flows through controlled orifices, and damping valves that restrict the flow to dissipate wave energy.

Q: How efficient is passive heave compensation?

It depends on spring stiffness, damping tuning, stroke length and payload matching. The motion ratio between payload and hook can be estimated from the wave period, gas-to-oil ratio, stroke and payload properties — a well-sized PHC transmits only a fraction of the hook motion, and the design goal is to keep the system natural period well above the wave periods of the operation.

Q: When is a passive compensator the right choice over active?

When the job is absorbing wave-induced motion in splash-zone crossings, subsea landings, tensioning or retrieval: passive systems need no external power, have fewer failure modes, and their performance is predictable from the physics. Active systems are reserved for cases where residual motion must be actively driven toward zero.

Q: Which Norwegian Dynamics compensator fits which lift?

RIGEL is the basic passive unit (55–1,000 t) for straightforward splash-zone and compensation tasks; ANTARES adds automatic damping control and quick-lift ability (30–4,000 t) for demanding multi-phase lifts; CYGNUS covers heavy and deepwater lifts from 12.5 up to 10,000 t.

How a passive heave compensator uses a gas spring and hydraulic damping to cut the motion passed from crane hook to payload, with no external power. Covers what is inside the unit, how to read the motion ratio, damping choices, and where RIGEL, ANTARES and CYGNUS differ.

By Tord Martinsen, CEO · October 2025 · Reviewed August 2026 · 15 min read

Practical application: this physics is what our passive range is built on: meet RIGEL Basic PHC and ANTARES Adaptive PHC.

Passive heave compensation (PHC) is a technique used in offshore operations to reduce the vertical motion transferred from a crane hook to a suspended payload. It works without external power by using a gas-spring and hydraulic damper system that absorbs wave-induced motion.

When a vessel moves up and down with the waves, the crane hook follows. Without compensation, the payload experiences the same motion — creating dangerous dynamic loads during splash zone crossings, subsea landings, and other critical operations. A passive heave compensator acts as a buffer, absorbing much of this motion.

Comparing systems? Compare passive heave compensators (RIGEL, CYGNUS and ANTARES) capacity bands, damping control and how each is sized to DNV-RP-N202.

How Does a Passive Heave Compensator Work?

A PHC consists of three main components:

Gas spring — nitrogen gas under pressure provides a spring force that supports the payload weight
Hydraulic cylinder — contains oil that flows through controlled orifices
Damping valves — restrict oil flow to provide damping, dissipating the wave energy

Inside the unit: cylinder and gas accumulator

A search for a “heave compensation cylinder” finds half the machine. The working cylinder hangs in tension in the lift wire — but the spring is not inside the cylinder at all. It lives in a separate gas accumulator connected to it:

The unit hangs in the wire, rod down to the load. Above the working piston the cylinder is evacuated. Below the piston, the rod-side chamber is oil-filled and connected through a damping restriction to the accumulator, where nitrogen sits over the oil. When hook and load move apart, the unit extends: rod-side oil is displaced through the restriction into the accumulator, the nitrogen compresses, and wire tension rises — that pressure–volume curve is the gas spring. The restriction is the damping: wave energy leaves the system as heat in the oil squeezed through it.

Family differences sit on the accumulator’s gas side: ANTARES adds a charge valve and gas bottles so the spring can be re-tuned between lift phases; CYGNUS carries a bleed-off valve for datum setting. The geometry above is common to the whole passive family.

Key Applications

Splash zone crossings — reducing dynamic loads as the payload passes through the wave zone
Subsea landings — controlling the landing speed for precise placement
Resonance avoidance — preventing amplification of motion at certain wave periods
Tension management — reducing tension variation in a taut cable or riser within the configured stroke and operating range
Shock absorption — protecting the payload and crane from impact loads

PHC Performance Factors

The efficiency of a passive heave compensator depends on stiffness (spring rate), damping tuning, stroke length, and payload weight matching.

Short version

Reading this to choose a unit?

What follows is the derivation — worth the time if you are sizing a compensator yourself. If you are choosing hardware, this is what actually separates the three passive lines.

Simplest

Routine splash-zone crossings

The straightforward case: one compensation duty, damping set on deck and left alone for the lift.

SWL: 55 – 1 000 t
Stroke: 1.0 – 6.0 m
Damping: Manual, set on deck

Widest capacity band

Heavy and deepwater landings

Large subsea structures and deep landings — the broadest SWL range in the family, from small units up to the heaviest lifts.

SWL: 12.5 – 10 000 t
Stroke: 1.0 – 6.0 m
Damping: Manual, set on deck

Most adaptable

Lifts that change as they run

Multi-step subsea lifts where the load changes through the operation — automatic damping control and quick-lift ability, on battery, with no umbilical.

SWL: 30 – 4 000 t
Stroke: 2.5 – 8.0 m
Damping: Automatic

Side by side, including power and certification: RIGEL, ANTARES or CYGNUS — at a glance. To match a unit to a specific payload, stroke and sea state, use the product selector.

How does passive heave compensation work for reduction of landing speed?

Heave means vertical motion, in our context vertical motion of the crane hook, caused by waves. Passive heave compensation can be thought of as a spring-mass-damper system with the objective of reducing wave induced motion below the compensator. The below simplified sketch illustrates our scenario:

Simplified passive heave compensator model: crane hook imposing sinusoidal motion, PHC spring stiffness k with damping neglected, submerged payload with weight, buoyancy, drag and added mass in water — Figure 1 — The simplified model behind the derivation. The crane hook imposes ζ cos(ωt); the PHC contributes stiffness k (damping neglected, per the assumption list below); the submerged payload of mass m, density ρ and cross-section A⊥ carries weight mg, buoyancy F_B and added mass m_A in water of density ρ_w. Positive z is downward.

The crane hook motion follows the sinusoidal given by $\zeta \cos(\omega t)$ , the PHC has stiffness $k$ , the water has mass density $\rho_w$ , while the payload has basic properties $\rho, m, A_\perp$ , respectively for payload mass density, mass and area perpendicular to the heave motion.

Since we in this example are assuming that the payload is subsea it is important to take into account buoyancy, drag and added mass that affects the payload. These three effects change the response in different ways (buoyancy shifts the equilibrium load, added mass changes the effective inertia, drag dissipates energy) and each can help or hurt depending on the case and frequency.

Added mass

m_A = \rho_w C_A V_R

Where $C_A$ is the added mass coefficient (can be found in DNV RP-N103) and $V_R$ is the reference volume.

Drag

F_D = \tfrac{1}{2}\rho_w C_D A_\perp \dot z |\dot z|

Where $C_D$ is the drag coefficient and $\dot z$ is the payload vertical velocity.

Buoyancy

F_B = \rho_w V g

Where $V$ is the displaced volume of the payload and $g$ is the acceleration of gravity.

PHC gas spring

We can define a screening stiffness for the PHC gas spring — a secant value: the force difference from equilibrium stroke to full stroke, divided by the stroke change:

k = \frac{p_1 A_0 - p_0 A_0}{\Delta S}

Where $p_0$ is the equilibrium pressure and $A_0$ is the piston area of the PHC. A secant value is a screening simplification — the small-motion stiffness at equilibrium differs, so everything built on it below is an equivalent-linear estimate rather than an exact property.

Let us assume the following:

The full stroke length is $S$ , and we are at mid-stroke during equilibrium.
We use the ideal gas law with adiabatic compression to calculate the pressure change.
The equilibrium force should be equal to the force of gravity minus buoyancy.

From these assumptions, we then get:

k = \frac{(\rho - \rho_w) \, V \, g}{0.5 \, S}\left[\left( \frac{V_{\mathrm{eq}}}{V_{\mathrm{eq}} - 0.5 \, A_0 \, S} \right)^\gamma - 1\right]

$\gamma$ is the adiabatic exponent.

We could further assume that the equilibrium volume can be defined as:

V_{\mathrm{eq}} = (R - 0.5) \, A_0 \, S

Where $R$ is the gas-to-oil ratio, which is set by the case-specific accumulator and cylinder configuration. A larger value of $R$ corresponds to a softer spring.

We then get the following expression for the PHC stiffness $k$ :

k = \frac{2 (\rho - \rho_w) \, V \, g}{S}\left[\left( \frac{R - 0.5}{R - 1} \right)^\gamma - 1\right]

Which we can rewrite as:

k = \frac{2 \, m \, g}{S}\left( 1 - \frac{\rho_w}{\rho} \right)\left[\left( \frac{R - 0.5}{R - 1} \right)^\gamma - 1\right]

Hydraulic flow restriction of PHC

Fluid flow through a restriction is typically given as:

Q = A_f \, \alpha \, \sqrt{\frac{2 \, \Delta p}{\rho}}

Where:

$Q$ is the fluid volumetric flow,
$A_f$ is the smallest flow area,
$\alpha$ is the pressure loss coefficient, and
$\Delta p$ is the pressure loss.

Using this as a basis, we can find the force due to hydraulic restriction:

F_h = A_0 \, \Delta p= A_0 \, \frac{\rho}{2}\left( \frac{A_0 \, \dot{S}}{A_f \, \alpha} \right)^2

Also note that the sign of the hydraulic force will depend on extension or retraction of the rod.
Further, it may have a different magnitude if check valves are present.

The trick with this equation is to know $\alpha$ , which is not easy to calculate.
It should be found using CFD or measurements and may also have many variables.

—

Seal friction of PHC

Seal friction is a very complicated topic. It depends on many factors such as:

Pressure of fluid
Pretension of elastic element
Seal material
Speed of piston or piston rod
Surface roughness
Fluid type
Width of seal
Seal configuration

A full seal-friction model is beyond the scope of this introduction; the practical point is that friction varies with every factor above.

Differential equation

Now let us use the above with the following assumptions:

Seal friction is ignored (in reality it can be significant).
Hydraulic restriction is ignored here to keep the model illustrative — in the real unit that restriction is the designed damping, and it is exactly what caps the resonant peak and controls the landing response.
Drag is ignored (for a high performing PHC this assumption is OK).
Ignore stiffness and damping of rigging/wire rope.
Ignore hydrodynamics of PHC.
Ignore self weight of PHC.

A more accurate numerical solution with everything included (and a more precise equation of state for the gas pressure) is available from Norwegian Dynamics.

We can apply Newton’s second law to the payload mass to find out how it moves relative to the crane hook.
Let us assume that downwards is the positive direction:

(m + m_A) \, \ddot z = m g - F_B - k \, [ z + z_0 + \zeta \cos(\omega t) ]

This has a steady-state solution given as:

z(t) = \frac{k \, \zeta}{(m + m_A)\, \omega^2 - k} \, \cos(\omega t)

What we want to know is the ratio between the payload motion and the hook motion.

\frac{z(t)}{\zeta \, \cos(\omega t)} = \frac{k}{(m + m_A)\, \omega^2 - k}

We can then change $\omega$ to $\frac{2 \pi}{T_P}$ , where $T_P$ is the wave period, and replace $k$ with our expression above:

\frac{z(t)}{\zeta \cos\!\left(\frac{2\pi t}{T_p}\right)}=\frac{1}{\displaystyle\underbrace{\left(\frac{m+m_A}{m}\right)}_{\text{Added mass}}\underbrace{\frac{\rho}{\rho-\rho_w}}_{\text{Buoyancy}}\underbrace{\frac{2\pi^2}{g\,T_p^2}}_{\text{Wave period}}\underbrace{\frac{S}{\left[\left(\frac{R-0.5}{R-1}\right)^{\gamma}-1\right]}}_{\text{PHC}}-1}

Based on this ratio we can define the passive heave compensation efficiency. If the ratio is 0 the payload does not move at all; below 1 the compensator is isolating the payload; above 1 the motion is amplified. Resonance is the specific condition where the undamped model’s denominator goes to zero, amplification near that period is the warning sign. The calculator below evaluates that undamped, single-frequency screening expression with the secant stiffness above. It is prefilled with the worked example’s values — replace them with your case. It cannot size a unit: damping, drag, irregular seas, stroke and pressure limits, landing speed and structural loads sit outside this model, and come from a lift screen in CONSTELLATION.

Payload-to-hook motion-ratio magnitude versus wave period for the aligned worked-example inputs, with gas-to-oil ratios 4, 8 and 12 and natural periods marked — Figure 2 — Motion-ratio magnitude from the expression above, using the worked example's inputs (m = 100 t, m_A = 20 t, ρ = 7 850 kg/m³, ρ_w = 1 030 kg/m³, S = 6 m and γ = 1.4) for gas-to-oil ratios R = 4, 8 and 12. Below 1.0 the PHC isolates the payload; at T_n the undamped model resonates. Real damping caps the peak, and project results are case-specific.

Passive Heave Compensation Efficiency Calculator

Fixed screening constants: seawater density ρ_w = 1 030 kg/m³, adiabatic exponent γ = 1.4 and g = 9.81 m/s².

Payload mass m (tonnes):

Added mass mₐ (tonnes):

Payload density ρ (kg/m³):

Wave period Tₚ (s):

Stroke length S (m):

Gas-to-oil ratio R:

Enter values and select Calculate.

We can also define the natural period of the PHC as:

T_n = \pi \sqrt{\frac{m + m_A}{m} \,\frac{\rho}{\rho - \rho_w} \,\frac{2S}{\,g\!\left(\left(\dfrac{R - 0.5}{R - 1}\right)^{\!\gamma} - 1\right)}}

Worked example: reading the motion ratio

Take the calculator’s kind of case: a 100 t steel payload (ρ = 7 850 kg/m³) with 20 t added mass, on a PHC with 6 m stroke and gas-to-oil ratio R = 12, in waves of period T_p = 8 s (γ = 1.4):

Spring softness. The gas-spring bracket ((R − 0.5)/(R − 1))^γ − 1 ≈ 0.064 — a high R and long stroke make a soft spring.
Natural period. T_n ≈ 16 s, comfortably above the 8 s waves — the system operates in its isolation range.
Motion ratio. The expression above gives ≈ 0.33: the payload sees about a third of the hook motion — roughly two-thirds of the wave-induced motion is removed.

The closed-form model is undamped and conservative near resonance — real damping caps the peak and adds some transmission in the isolation range. For sizing, the full numerical solution (gas state, damping, drag, rigging) is what a CONSTELLATION study runs.

Damping: what kind, and how much

The gas spring stores the energy — the damper decides where it goes. Undamped, the compensator is a spring-mass system that would ring at its natural period after every disturbance. As the piston strokes, oil is forced through orifices or control valves and the flow resistance converts kinetic energy to heat: a force that grows with velocity, capping resonance, settling transients and giving descent-speed control for landing.

Damping types in passive heave compensators — characteristic force law and where each is met.
Damping type	Characteristic	Where you meet it
Linear	Force ∝ velocity	Simple to model — rare in real hardware
Quadratic	Force ∝ velocity²	The natural behaviour of orifice flow — strong at speed, gentle when slow
Variable	Adjustable orifices / proportional valves	Damping changed per operational phase — the adaptive route

TOO LITTLEResonates dangerously — transients ring on and on

IN THE BAND≈ 5 – 15% of critical in ND’s screening models for normal lowering — set case by case; raised temporarily for splash zone and landing

TOO MUCHThe system goes stiff — vessel motion transmits, efficiency drops

Variable damping in practice: ANTARES adjusts its level automatically between lift phases; RIGEL and CYGNUS are set manually on deck.

Other subsea uses

Passive heave compensation units can also give other benefits for subsea installations:

Ability to maintain wire tension throughout the landing phase, which prevents sudden vessel heeling.
Mitigation of peak loads in the event of re-lifting of the payload.
Provide tensioning during subsea retrieval to prevent overloading when fixed to seabed.

Choosing the Right PHC

Norwegian Dynamics offers three passive heave compensator product lines:

ANTARES Adaptive PHC — advanced adaptive passive heave compensator with automatic damping control, multiple operating modes, and depth ratings to 3000m. Best for operations requiring high performance and flexibility.
RIGEL Basic PHC — simple, reliable, low-cost passive heave compensator. Best for straightforward splash zone crossings and basic compensation tasks.
CYGNUS PHC — passive heave compensator for heavy and deepwater lifts, with capacities from 12.5 to 10,000 tonnes. Best for large subsea structures and deepwater landings.

→ Need help selecting? See our Heave Compensator Selection Guide or contact our engineers.

RIGEL, ANTARES or CYGNUS — at a glance

RIGEL, ANTARES and CYGNUS passive heave compensators compared — type, damping, SWL range, stroke, power, strengths, certification and typical use.

Type	Passive	Adaptive passive	Passive
Damping	Manual, set on deck	Automatic damping control	Manual, set on deck
SWL range	55 – 1 000 t	30 – 4 000 t	12.5 – 10 000 t
Stroke	1.0 – 6.0 m	2.5 – 8.0 m	1.0 – 6.0 m
Power	No external power	Battery — no umbilical	Battery — no umbilical
Stands out	Simplest, lightest unit	Quick-lift ability	Heavy / deepwater capacity band
Certification	Designed & classed · DNV-ST-0378 (Type Approval in progress)	Designed & classed · DNV-ST-0378	Designed & classed · DNV-ST-0378
Best for	Straightforward splash-zone crossings and basic compensation	Demanding multi-phase lifts needing automatic damping	Heavy and deepwater subsea lifts

First-pass guidance — the passive vs active heave compensation guide walks the choice question by question.

Passive heave compensation — frequently asked

What is passive heave compensation?

A way to reduce the vertical motion transferred from the crane hook to the payload, without external power: a nitrogen gas spring carries the weight while hydraulic damping dissipates the wave energy.

What are the main components of a passive heave compensator?

A gas spring (nitrogen under pressure), a hydraulic cylinder with oil flowing through controlled orifices, and damping valves that restrict the flow to dissipate energy.

How efficient is passive heave compensation?

A well-sized PHC transmits only a fraction of the hook motion — in the worked example above, about a third at T_p = 8 s. The design goal is to keep the system natural period well above the operation’s wave periods; the calculator on this page gives a first indication.

When is a passive compensator the right choice over active?

Passive wins on simplicity, reliability and zero external power for splash-zone, landing, tensioning and retrieval work; active is reserved for cases where residual motion must be driven toward zero. The active-vs-passive comparison covers the trade-offs.

Which Norwegian Dynamics compensator fits which lift?

RIGEL for straightforward passive compensation; ANTARES when automatic damping control or quick lift matters; CYGNUS for heavy and deepwater lifts up to 10 000 t. The table above compares them line by line.

Selecting a passive compensator for your next lift?

We size PHCs against the operating range — Hs, Tp, payload, water depth. Send the case and we'll come back with a recommended product.

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