Pre-processing
The possible vertical motions a ship can encounter in the analysis period are used in a monte carlo simulation to construct the time/location diagram which shows the safe segments. During that simulation we wish to get a possible vertical motion (most probable extreme) and motion period for a range of given circumstances. These circumstances are randomly drawn from the prediction distributions between 25.000.000 and 100.000.000 times. Because of this high frequency we cannot calculate the vertical motions "on demand", so PROTIDE calculates a range of possible motions in advance and stores them in a 5 dimensional matrix. This matrix can be used in the simulation to quickly get a possible vertical motion for a given course, depth/draft ratio, speed, swell height and wave height.Depth / draft ratio
The depth / draft ratio is the way the water level is modeled in the vertical motion calculation. The three categories 1.1, 1.2 and 1.4 are used which correspond to 10%, 20% and 40% UKC.Course
The angles of the channel segments that are not damped for waves (see the article Calculation settings) are used as possible ship headings. By default the angles are given for the inbound direction, therefore for the outbound trajectory they are corrected with 180 degrees.Speeds
Speed regimes are given as speed over the ground, but for ship movements we need the speed through the water. Because we do not know the water direction and speed in this phase a list is constructed with possible speeds. This list consists of all speeds over the ground plus extra values varying between maximum upstream and maximum downstream. The list is dynamically built depending on the extremes of the water speed prediction. A minimum of four speeds through the water that have a maximum difference of one knot, are used to model a speed over the ground.Swell and wave height categories
To model the wave conditions swell and wave height categories are made. For each category a random selection (Number of wave spectra to select setting in the Calculation settings) of historical wave spectra is done from the PROTIDE database. The categories in the figure below are the combinations available in the historical wave spectra database. Only the combinations possible in the analysis period are calculated. These valid possibilities are based on the extremes of the wave height and swell height predictions.Calculate vertical motions
For the given ship for each depth / draft ratio (3 values) an Amarcon-OCTOPUS session is started to calculate the response amplitude operator (RAO) and the probable sinkages (squat) per speed. Next, for each wave category (about 20 to 30 with a maximum of 53 values) all the responses are calculated for all given wave spectra in that category (Number of wave spectra to select is now set to 35). For all different headings (2 or 3) we now do Number wave direction iterations (setting in the Calculation settings is now set to 35) from the given wave direction distribution (also given in the Calculation settings) to collect the ship responses with that wave impact direction for each possible speed (about 8 tot 10 values). From each response we select the position of the ship that shows the highest response and store that response (most probable extreme and motion period) as a possible option for the corresponding depth/draft, heading, speed, wave height and swell height.
The result is a matrix of 5 dimensions (depth/draft, heading, speed, wave height and swell height) with between 1500 and 5000 "buckets" of possible vertical motions. Each bucket corresponds to a specific set of circumstances and contains all the possible vertical motions that can happen to the ship under those circumstances (a maximum of 1225 responses). This gives a total of up to 5.000.000 different responses that can be selected during the monte carlo simulation to construct the time/location diagram.