The results may be viewed graphically or in tabular format. Also the results may be copied from the tables and pasted into a spreadsheet for further analysis.

The results displayed in the table and plotted in the graphs correspond to the condition selected in the Results toolbar:

To view the results table, select Results from the Window menu.

You may view different sets of results by selecting the different tables of the Results window. The tables are described more fully in the following sections.

This table displays m₀, RMS and significant amplitude of the different motion, velocity and acceleration spectra of the vessel for the specified conditions. The mean square, m₀, of the spectrum is the area under the spectrum and gives a measure of the total response of the vessel. The RMS is the square root of the mean square, and for seakeeping calculations, the significant amplitude is twice the RMS value. (The significant height, measured peak to trough, is twice the significant amplitude.)

The mean square of the spectrum is given by:

where S(w) is the density of the spectrum of interest.

The first 12 rows describe the conditions specified for the analysis: wave spectrum modal period; wave spectrum characteristic wave height; spectrum type; wave heading; vessel speed; vessel displacement, vessel trim, analysis method and gyradii.

The next two rows provide a check of the calculations by displaying the integrated wave spectrum values. The first row, labelled Wave spectrum, has been obtained by integrating the wave spectrum as viewed by a stationary observer; the second (Encountered wave spectrum) from integrating the waves as experienced by the moving vessel. Both should give the same answer. Also the significant amplitude should be approximately half the specified characteristic wave height of the spectrum.

If these values do not match, then the rest of the results are in question. You should increase the frequency range and redo the calculations.

The following row gives the added resistance of the vessel in the specified sea conditions. The added resistance is given by:

where is the added resistance coefficient in regular waves, and  is the encountered wave energy spectrum.

The next 9 rows give the vessels integrated heave, roll and pitch motions, velocities and accelerations.

The vertical absolute and relative motions, velocities and accelerations are then given for all the specified remote locations.

The last row for each remote location gives the MII per hour for sliding, fore-and-aft tipping and side-to-side tipping. The table below correlates MII rate to risk. Note that the lateral acceleration used to calculate the MII is that due to roll only.

MII Risk level

Source: Standard material requirements for RAN ships and submarines, vol 3, part 6.

The SM and MSI for 2 hours exposure and the specified exposure time are presented in the Summary results table. The last row for each remote location gives the SM in the second column, then MSI for 2 hours exposure using the O’Hanlon and McCauley 1974 method in the fourth column and in the MSI for the specified exposure period is given in the sixth column.

Subjective magnitude is on a scale of zero to 30:

  0 –   5     Moderate

  5 – 10     Serious

10 – 15     Severe: necessary to “hang on”

15 – 20     Hazardous

20 – 30     Intolerable

See: Calculation of Subjective Magnitude and Motion Sickness Incidence on page 69 for details of the calculations performed.

The majority of the results calculated in the Summary table may be plotted in the Polar Plot window provide that the response for at least two speeds and a range of headings has been calculated.

Although not strictly MSI accelerations integrated over 1/3 octave bins are plotted against acceleration limits defined by these two standards. The likely discomfort can be gauged by how close these acceleration curves approach the defined acceleration limits.

The second table gives the acceleration curves at the specified remote locations. The data for the standard ISO and BSI curves are also given. The MSI acceleration is calculated from the equation below:

where the frequency interval w_e1 to w_e2 is the 1/3 octave range centred about w_{e centre} and S_{vert accel} is the absolute vertical acceleration at the point of interest on the vessel.

Existing comparison of accelerations compared with ISO and BS standards

The next table gives the computed vessel RAOs for the principal degrees of freedom, at the vessel's centre of gravity. These have been non-dimensionalised with wave height for heave and with wave slope for roll and pitch motions. The phase lag of the motions is also given.

Finally the added resistance coefficient in regular waves, , is given. This value is dimensional, and has units of Force / Length². There are several accepted ways of non-dimensionalising added resistance. Gerritsma and Beukelman use the following:

Added resistance coefficient = ; where B is the vessel beam and L the vessel length.

This table gives the specified wave spectrum, in wave and encounter frequency domains. The response spectra for the principal degrees of freedom, at the vessel's centre of gravity are also calculated in the encounter frequency domain. For the spectra the horizontal axis is always in rad/s.

The various spectra are calculated as follows:

The added resistance spectrum is also provided. It is calculated as follows:

This table repeats the encountered wave spectrum and gives the response spectra at the specified remote location. Absolute and relative vertical displacement, velocity and acceleration spectra are calculated. The vessel is assumed to be a rigid body and the effects of heave, roll and pitch are combined; the relative motions are the absolute motions relative to the local wave surface.

The remote location for which the spectra are displayed may be selected from the pull-down menu in the Results window toolbar:

These are the integrated coefficients, cross-coupling terms and excitation forces in the equations of motion of the vessel. These are the total values for the complete vessel.

The added mass, damping, stiffness and wave excitation for each of the sections of the hull at each of the frequencies of interest. For each frequency, these values are integrated along the vessel's length to give the global coefficients in the equations of motion.

The remote location for which the spectra are displayed may be selected from the pull-down menu in the Results window toolbar:

Choosing a section from the pull down menu, will display the variation of terms with frequency for the selected section; similarly, selecting a frequency will display the variation of terms along the length of the vessel for the selected frequency.