P(bottom-touch)

The determination of the probability of a ship hitting the bottom at a certain location in a channel at a certain moment in time, can be divided into the steps below.

Under keel clearance (UKC)¹

The basic UKC is the UKC of a ship given the waterlevel, the draught of the ship and the squat².

Motion

After determining the basic UKC and taking squat into account, the effect of the motion of the ship can be determined. This is done by calling the OCTOPUS program. This program uses a description of the ship under certain conditions (a compiled hydrodynamic database (?)) to create a RAO function (response amplitude operator). This function is then used to calculate the ships response under a variety of conditions that could occur at the desired time and location:

1. Depth / draught ratio ³
2. Ship heading
3. He10 ⁴
4. Possible wave spectra
5. Wave direction

For each response the maximum significant vertical motion and corresponding motion period is stored. These results are then grouped per depth / draught ratio, heading and wave height, which can then be used to estimate the vertical motion at any circumstance.

Frequency of bottom touches

By taking the responses calculated with OCTOPUS the frequency of the number of bottom touches is derived:

Where:

• m(0): 0th spectral moment of the ship movements
• KC: calculated basic UKC
• T: mean period of the ship movements
• lambda: frequency of bottom touches

Probability of bottom touches

Finally it is assumed that the bottom touches follow a Poisson distribution. From this the probability of the number of bottom touches during a navigational route, T(pas) can be derived:

This probability can be used as the probability of hitting the bottom if during the whole navigational route the conditions (speed, water level and channel depth) stay the same.

Probability distribution analysis

By making draws out of the distribution of the water level forecast, the He10 expectation, the different possible wave spectra and a variance of the angle of incidence of the waves, we get an estimate of the probability density function chances that the the bottom is touched at one time at one location. We can use a test to analyze if the found bottom touch chances are significantly below the cut off safety criterion.

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1. The space between the bottom of the channel and the navigating ship in smooth water.
2. Increase of the draught of the ship because of the speed. As the water is pushed downward by the passing hull it accelerates and its pressure falls. The reduced pressure on the bottom of the boat sucks the boat slightly downward until the increased displacement counteracts the force generated by the reduced pressure.
3. The ratio between the amount of water and the draught of the ship. For channel- and tide-bounded ships the value lies between 1.1 and 1.5.
4. Height of the low frequency waves.