RIGEL passive heave compensator hanging vertically in-line on the crane wire as the payload crosses the splash zone at dusk
Passive heave compensation

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

Passive Heave Compensation Basics

By Tord Martinsen, CEO · October 2025

Practical application: For practical application of this topic, see 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:

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

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
  • Tensioning — maintaining constant tension in cables or risers
  • 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.

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 FB and added mass mA in water of density ρw. 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. All these three effects can improve the performance of the PHC.

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 an average stiffness of the PHC gas spring as the difference in force from equilibrium stroke to full stroke divided by the change in stroke:

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.

Let us assume the following:

  1. The full stroke length is S, and we are at mid-stroke during equilibrium.
  2. We use the ideal gas law with adiabatic compression to calculate the pressure change.
  3. 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 typically is in the range 2–12 for a PHC. 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:

  1. Q is the fluid volumetric flow,
  2. A_f is the smallest flow area,
  3. \alpha is the pressure loss coefficient, and
  4. \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:

  1. Pressure of fluid
  2. Pretension of elastic element
  3. Seal material
  4. Speed of piston or piston rod
  5. Surface roughness
  6. Fluid type
  7. Width of seal
  8. Seal configuration

It is too complicated to discuss details in this brief introduction.

Differential equation

Now let us use the above with the following assumptions:

  1. Seal friction is ignored (in reality it can be significant).
  2. Hydraulic restriction is ignored (usually this can be low if the PHC design is good).
  3. Drag is ignored (for a high performing PHC this assumption is OK).
  4. Ignore stiffness and damping of rigging/wire rope.
  5. Ignore hydrodynamics of PHC.
  6. 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 then the efficiency is 100%, if the absolute value is bigger than 1 then it means we will have resonance. The calculator below can be used as a rough indicator of passive heave compensation performance.

Payload-to-hook motion ratio versus wave period for gas-to-oil ratios 4, 8 and 12: isolation below ratio 1, resonance peaks at the natural period, softer springs push the natural period to longer wave periods
Figure 2 — The motion ratio plotted from the expression above, using the calculator's default payload (m = 100 t, mA = 20 t, ρ = 7 850 kg/m³, S = 4.5 m) for three gas-to-oil ratios R. Below 1.0 the PHC isolates the payload; at Tn it resonates. The model is undamped — real PHC damping caps the resonant peak. The design goal is visible: a softer spring (higher R, longer stroke) pushes Tn well above the wave periods you operate in.

Passive Heave Compensation Efficiency Calculator













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 Tp = 8 s (γ = 1.4):

  1. 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.
  2. Natural period. Tn ≈ 16 s, comfortably above the 8 s waves — the system operates in its isolation range.
  3. 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 typeCharacteristicWhere you meet it
LinearForce ∝ velocitySimple to model — rare in real hardware
QuadraticForce ∝ velocity²The natural behaviour of orifice flow — strong at speed, gentle when slow
VariableAdjustable orifices / proportional valvesDamping changed per operational phase — the adaptive route
TOO LITTLEResonates dangerously — transients ring on and on
IN THE BAND≈ 5 – 15% of critical for normal lowering — best efficiency with resonance safety; 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:

  1. Ability to maintain wire tension throughout the landing phase, which prevents sudden vessel heeling.
  2. Mitigation of peak loads in the event of re-lifting of the payload.
  3. 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

RIGELANTARESCYGNUS
TypePassiveAdaptive passivePassive
DampingManual, set on deckAutomatic damping controlManual, set on deck
SWL range55 – 1 000 t30 – 4 000 t12.5 – 10 000 t
Stroke1.0 – 6.0 m2.5 – 8.0 m1.0 – 6.0 m
PowerNo external powerBattery — no umbilicalBattery — no umbilical
Stands outSimplest, lightest unitQuick-lift abilityHeavy / deepwater capacity band
CertificationDesigned & classed · DNV-ST-0378 (Type Approval in progress)Designed & classed · DNV-ST-0378Designed & classed · DNV-ST-0378
Best forStraightforward splash-zone crossings and basic compensationDemanding multi-phase lifts needing automatic dampingHeavy and deepwater subsea lifts

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

Related Reading

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?
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 it?
A well-sized PHC transmits only a fraction of the hook motion — in the worked example above, about a third at Tp = 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.
Passive or active — how do I choose?
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 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.

Working on a lift that needs this?

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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Related Articles

ND SolutionRIGELRIGEL →Passive heave compensator — proven reliability for standard operations.ND SolutionANTARESANTARES →Adaptive passive system for demanding conditions.
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