Motion Analysis

Computation

Ship Dynamics has the capacity to determine vessel motion levels in waves through computational seakeeping analysis.  The procedures adopted are based on theoretical hydrodynamic methods where the routines have been implemented by a leading research institution.

Prior to any form of model testing, and during the early stages of design, a hull motion analysis can alert the designer and owner to any issues with the vessel's seakeeping performance. This will avoid costly and unexpected outcomes.

System Comparison

Mono- or multi-hulled vessels can be modelled both with and without motion control devices.  Comparing these two configurations is a useful indication of the potential effectiveness of a stabilisation system fitted to a new, existing or a proposed vessel design.  In the case of a new design proposal, it allows for early intervention to advise whether further improvements of the hull motions in waves might be achieved through changes in hull form or weight distribution before the hull form has been finalised.  It is important to note that it is not always widely understood that hull motions in waves can often be improved through early hull design changes prior to any consideration of a stabiliser or motion control system.

Motion Types

In a typical analysis the hull motions in waves are usually assessed for a range of hull locations depending on the type of functions the vessel is to undertake.  For example, in the case of a passenger ferry it is reasonable for all locations in the passenger compartment to be taken into account as it is equally likely that all seats within this area may be utilised.  Alternatively, the operational areas on a military vessel such as the bridge or helicopter deck will be utilised for some proportion of time and must therefore be considered.  The type of motions that can be assessed in this way include

1. motion sickness incidence (MSI);
2. motion induced interruptions (MII);
3. probability of hull slamming;
4. probability of green water on deck;
5. air exposure of under water components such as propellers, fins and keel;
6. linear motions in 6 DOF (surge, sway, heave, roll, pitch and yaw) in displacement, velocity and acceleration.
7. forces in the body fixed coordinate system that include
   • lateral force estimator (LFE);
   • vertical force estimator (VFE), and
   • longitudinal force estimator (LON).

 Reported results can be displayed in a range of alternative units that include standard deviation, single significant amplitudes (SSA) and probable maximum for a nominal duration. All wave headings are usually considered.

Procedure

Generally, the procedure for conducting an analysis involves a number of steps.

Defining the hull requires a digital representation of the hull in the form of a NURBS surface, which is then converted to transverse sections and points in a format compatable with the computational input.

Transfer functions and the corresponding phase function provide the normalised response of a vessel to regular waves.  Each transfer function and phase function is unique to each combination of

• vessel loading condition;
• degree of freedom (6 for a rigid hull form);
• vessel speed;
• wave direction, and
• stabiliser configuration.

They are based on the assumption that the vessel’s response is linear with wave height and that the irregular wave motion response of the vessel can be derived from the regular wave motion response.  However, the effect of a stabiliser device on the hull’s motion attenuation is not linear with wave height and therefore must be applied with due care and in an appropriate manner by a skilled analyst should motion control devices be included in a computation.

Calculation of this information can be done through model tests at a towing tank facility but they can also be economically determined with often quite reasonable results through computational techniques.  For a general hull calculation with one loading condition, one stabiliser configuration, six degrees of freedom, one speed and twenty five wave directions amounts to 150 transfer functions and 150 phase functions.  This of course multiplies with each additional combination.

Combining the transfer function with a wave spectrum produces the hull response spectrum.  Wave spectra vary for different oceans and conditions, therefore standardized spectra are often used for an analysis such as the Jonswap, Pierson Moskowitz or Bretschneider wave spectrums.

For a particular wave spectrum and transfer function, the response spectrum represents the vessel’s response in an irregular wave environment.  Presenting all these is not often done as it represents too much information to be useful.  However, a skilled analyst combined with other presentation techniques is able to select those of interest for the purpose of design and feedback.

Other formats that provide a compact way of viewing this type of data include the contour polar charts shown below.  Here a typical output showing the MSI levels calculated in the bridge of a nominal vessel where the radial coordinates represent the mean zero-crossing wave period and the polar coordinates the wave heading relative to the vessel.

Similarly, the chart below illustrates a result for the output of Lateral Force Estimator (LFE) obtained for a vessel.