Seakeeper calculates a number of crew/passenger comfort indices, these are Subjective Magnitude parameter (SM) and Motion Sickness Incidence (MSI).
The calculation of the Subjective Magnitude follows the method described in Lloyd 1998 pages 306 to 309 and is summarised below.
, where A depends on the encounter frequency, 
, in rad/s and is given by:
;
, and the vertical acceleration 
can be evaluated from
the vertical motion spectrum:
, where 
is the 4th
spectral moment of the vertical motion spectrum at the location of interest in
m/s2;
g is acceleration due to gravity;
and the average frequency of the motions can be
estimated by: 
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
Motion sickness incidence (MSI) is the percentage of subjects who vomit in the specified time that subjects are exposed to the motions. The data were derived from test on healthy, young, males students who were subjected to vertical motions for a period of up to two hours. Thus extrapolation to other demographics or longer durations of exposure can be difficult. There are three different ways in which motion sickness incidence is calculated in Seakeeper.
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 MSI acceleration depends on the magnitude of the vertical acceleration at the point of interest on the vessel. This is computed by integrating the power spectrum density (PSD – given the symbol Svert accel below) over a one third octave range centred about the frequency of interest:
where the frequency interval we1 to we2 is the 1/3 octave range centred about we centre and Svert accel is the absolute vertical acceleration at the point of interest on the vessel.
By varying the centre frequency, a graph of vertical MSI acceleration is built up and this is compared with the standard curves.
The motion sickness incidence derived from the formulation original 1974 paper of O’Hanlon and McCauley is calculated for a fixed exposure time of 2 hours. Seakeeper evaluates the MSI using the method described in Lloyd 1998, pages 304 to 306.
The MSI is given by Lloyd as:
, where 
is the cumulative
normal distribution function up to x for a normal distribution with zero
mean and unity standard deviation. (see Excel function NORMDIST(x, 0, 1,
TRUE).
Lloyd gives the factor 
with 
in radians/s this is almost the same as the original equation
of O’Hanlon and McCauley:
, with 
in Hz, noting that 
. Seakeeper uses the latter. The same frequency as that used
in the SM calculations is used, namely: and the acceleration, 
, is given by 
.
McCauley et al. 1976 reanalysed the original O’Hanlon and McCauley 1974 data and presented a formulation whereby the exposure time could be accounted for. This method is also computed by Seakeeper and is the only place where the MSI exposure time for the remote location is used.
The exposure time can be specified for each remote location (you can define multiple remote locations at the same point on the vessel and give them different exposure times if you wish).
The procedure described by Colwel 1994 is used with the frequency and acceleration values given by Lloyd for the 2 hour MSI, above.
, where 
;
and 
;
, with the acceleration, in g, given by 
.
The effect of exposure time on MSI can be seen in the figure above. When the exposure is longer than about two hours, there is relatively little increase in MSI, this is especially true at higher accelerations, i.e. all those victims that are going to vomit have already done so within two hours. As the acceleration decreases, the exposure time required to achieve near-maximum MSI decreases slightly. The frequency of the acceleration in this case was 0.1 Hz which is near the worst case.
The effect of acceleration on MSI is shown for an exposure period of two hours in the figure above. It can be seen that both formulations give very similar results. The frequency of the acceleration in this case was 0.107 Hz.