2.2 Theoretical background
From a theoretical point of view, the slamming phenomenon is not yet completely solved the main open problems being the effects of air entrapment in the water, the shape of the wave immediately before the impact with the structure, and the stiffness of local structure. All these effects significantly affects the value of slamming pressure exerted on the hull, its extension in both time and space as well as the resulting stresses induced on the hull structures. Despite considerable R&D efforts on the subject, see e.g. [4] for a survey of present status, use of model test results is still the most viable method to be used during ship design.
Model tests are necessarily limited to a few sea state conditions, therefore the problem arises on how to extrapolate the recorded values to the whole ship life.
The approach used to solve this problem is based on the assumption that the effects of ship forward speed and sea state intensity on the maximum slamming pressure, Pmax, is given by the relative vertical velocity of the ships and the water at the impact location, Vr. Hence, a slamming pressure coefficient can be defined [5] as follows:
Cpmax = 2 Pmax / (ρV2r) (1)
being ρ the water density.
By using equation (1) with the value of Vr corresponding to the maximum expected in the ship's lifetime, the design pressure is obtained.
In the approach used, Cpmax was derived from model tests and Vr was calculated by means of strip theory and long term statistical analysis.
2.3 Validation of the approach
In order to validate the approach, experimentally derived values of Cpmax and of relative ship motions were considered for the ship under analysis.
As far as Cpmax is concerned, results of model tests for 8 different combinations of sea state intensity and heading have been compared with the simplified formulation of Cpmax suggested in [4]:
Cpmx = 0.25π2 cotg2(β) (2)
where β is the flare angle.
Results of the comparison are shown in Table I where the average value of Cpmax obtained from model tests in three different panels are compared with equation (2).
Initially the agreement was not satisfactory: the reason was found to be the presence of "loners" in the measured pressures, i.e. in some cases the value of the maximum experimental pressure was found to be higher than twice the second highest recorded value. This is a not uncommon result when impact pressures model tests are carried out, due to the effects of air entrapment which is can not be properly scaled, see [6]. Exclusion of loners from experimental results resulted in fairly good comparison, see Table I .
As far as the relative ship speed with respect to the water at the impact locations, numerical results from linear strip theory were compared with experimental results from model tests. The agreement was found to be very good, see Figure I , showing that strip theory can be used for this type of analysis.
The overall conclusion was that the approach was sound and reasonably straightforward in view of application for the design of a cruise ship bow structure.
2.4 Application of the method
The method was applied during the design stage of a cruise ship of the last generation, whose main dimensions are as follows:
length between perpendiculars, LPP = 242 m.
beam, B = 36 m.
draught. T = 8.3 m.
displacement,Δ = 52500 m3
type of service: unrestricted navigation
design speed = 20 kn.
Typical results are shown in Figure 2 where the maximum slamming pressure recorded during model tests are compared with results of calculations and rule requirements.
Model test results refer to ship speed of 10 kn and sea state severity corresponding to 8 m, significant wave height. At the same speed, the maximum calculated pressure in the ship life is higher, this is due to the fact that sea state severity up to 14 m significant wave height can be encountered, although with a very low probability, during the ship life.
Moreover, the design pressure according to classification rules is to be evaluated at the ship design speed, for this reason calculations have been repeated also for a speed of 20 kn and are compared with rule requirements. The results show that rules tend to be over conservative.
In view of this conclusion, a comparison between rule requirements and extrapolated model test results was carried out for 4 cruise ships with length ranging from 200 and 240 m. Results (see Figure 3) were used to calibrate the following reduction factor for the rule slamming pressure on cruise ships:
c = 0.82 - 0.09 (z - T)/T (3)
where z is the vertical location of the panel with respect to the base line and T is the ship draught.
2.5 Design and operational benefits
From the design point of view, the use of the slamming pressures extrapolated from model tests as discussed in the above, allowed to optimise the bow's structural scantlings with a thickness reduction up to 20% with respect to traditional rule approach. This is a major result in view of the need to reduce the weight of a cruise ship.
A side result of the study was the possibility to draw indications on speed reduction in heavy weather, this is illustrated in Figure 4 where the maximum calculated slamming pressures vs. the ship speed are displayed. With this type of information the ship master can determine safe conditions of navigation even in rough seas.
3. LIMITING OPERATIONAL SEA STATES FOR HIGH SPEED CRAFT
3.1 General
High Speed Craft (HSC) are allowed to operate up to a maximum sea state severity which is identified by its significant wave height. The design parameter for an HSC is generally the vertical acceleration: passenger comfort is directly related to its value and wave induced loads are also generally expressed in terms of vertical acceleration along the craft hull.
The normal practice is to determine the maximum acceleration form model tests and to use simplified formulations for the other wave induced loads. However, these formulations are based on studies carried out some 15 years ago or more when HSC were considerably smaller and slower than at present.
