Vessel RAO Calculator v1

Price: £50.18 (£50.18 Inc. VAT)

Calculator for the response amplitude operators of a vessel in waves


RAO stands for response amplitude operator which refers to the movement of a floating vessel in six degrees of freedom; Surge, Sway, Heave, Roll, Pitch and Yaw due to a passing hydrodynamic wave.

These RAOs are used as input data for calculations that define the displacements, accelerations and velocities at any given location on a ship (see CalQlata’s Vessel Motions calculator), which are in turn used to identify forces imposed on structures and/or equipment.

Surge, Sway and Heave are linear movements in the x,y,z directions respectively, and Roll, Pitch and Yaw are rotary movements about the x,y,z axes respectively.

Heave, Roll and Pitch are subject to gravitational restoring forces (stiffness or spring coefficients), which means that they can be oscillated at a natural frequency; something to be avoided in practice at all costs.

Surge, Sway and Yaw are not subject to restoring forces, which means that they cannot be oscillated at a natural frequency.


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RAO calculates response amplitudes in all six degrees of freedom, i.e. those with restoring forces and those without.

RAO includes the effect of damping and added mass, which means that the relationship between the response amplitude and the associated wave height is not always linear. Therefore, RAO does not calculate operators, it calculates actual (theoretical) response amplitudes (RAs) at a given angle through a wave
i.e. you do not multiply RAO’s calculated values by a wave height, amplitude or slope.

RAO includes a pictorial demonstration of the vessel's movement in beam, deck and aft views relative to the profile of the passing wave.

When entered (or imported) into Vessacc, the response amplitudes calculated in the RAO calculator will be converted into 'x,y,z' displacements, velocities and accelerations at a specified location on the vessel.

For help using this calculator see Technical Help

Vessel Motions Calculator - Options

Response Amplitudes

Calculates the response amplitudes of a floating vessel at a given angle through a specified wave including the effects of added mass and damping.

You enter and the vessel RAO calculator will provide:
  • Angle through wave
  • Wave height
  • Wave period
  • Water depth
  • Vessel heading angle
  • Vessel speed
  • Vessel mass
  • Vessel length
  • Vessel beam
  • Vessel draft
  • Height to CofG
  • Distance to CofG
  • Height factor of CofB
  • Density of water
  • Gravitational acceleration
  • Wave period (encounter)
  • Wave angular velocity (encounter)
  • Wave number
  • Wave celerity
  • Wave profile (height)
  • Wave profile (slope)
  • Surge
  • Roll
  • Sway
  • Pitch
  • Heave
  • Yaw
  • Phase lag (heave)
  • Phase lag (roll)
  • Phase lag (pitch)
  • Natural period (heave)
  • Natural period (roll)
  • Natural period (pitch)
  • Damping ratio (heave)
  • Damping ratio (roll)
  • Damping ratio (pitch)
  • Non-dimensional frequency ratio (heave)
  • Non-dimensional frequency ratio (roll)
  • Non-dimensional frequency ratio (pitch)
  • Transverse metacentric height
  • Transverse righting arm
  • Longitudinal metacentric height
  • Longitudinal righting arm

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