3.5 Background of the severe wind and rolling criterion (weather criterion)

  3.5.1.1 The severe wind and rolling criterion (weather criterion) is one of general provisions of the 2008 IS Code. This criterion was originally developed to guarantee the safety against capsizing for a ship losing all propulsive and steering power in severe wind and waves, which is known as a dead ship. Because of no forward velocity of ships, this assumes an irregular beam wind and wave condition. Thus operational aspects of stability are separated from this criterion, and are dealt with the guidance to the master for avoiding dangerous situation in following and quartering seas (MSC/Circ.707), in which a ship could capsize more easily than beam seas under some operational actions.

  3.5.1.2 The weather criterion firstly appeared in the IMO instruments as Attachment No.3 to the Final Act of Torremolinos International Convention for the Safety of Fishing Vessels, 1977. During the discussion for developing the Torremolinos Convention, the limitation of the GZ curve criterion based on resolution A.168(ES.IV) was remarked; it is based on experiences of fishing vessels only in limited water areas and it has no way for extending its applicability to other ship types and other weather conditions. Thus, other than the GZ curve criterion, the Torremolinos Convention adopted the severe wind and rolling criterion including a guideline of calculation. This new provision is based on the Japanese stability standards for passenger ships (Tsuchiya, 1975; Watanabe et al., 1956).

  3.5.1.3 Then, a similar criticism to the GZ curve criterion for passenger and cargo ships, resolution A.167(ES.IV), was raised at IMCO. At least resolution A.167(ES.IV) was claimed to be applicable to ships of 100 m in length or below because of the limitation of statistical data source. As a result, a weather criterion was adopted also for passenger and cargo ships as well as fishing vessels of 45 m in length or over, as given in resolution A.562(14) in 1985. This new criterion keeps the framework of the Japanese stability standard for passenger ships but includes USSR’s calculation formula for roll angle. For smaller fishing vessels, resolution A.685(17) in 1991 was passed. Here the reduction of wind velocity near sea surface is introduced reflecting USSR’s standard. When the IS Code was established as resolution A.749(18) in 1993, all the above provisions were superseded.

  3.5.2.1 The basic principle of the weather criteria is energy balance between the beam wind heeling and righting moments with a roll motion taken into account. One of the pioneering works on such energy balance methods can be found in Pierrottet (1935) (Figure 23). Here, as shown in Figure 3.1, the energy required for restoring is larger than that required for the wind heeling moment. Since no roll motion is taken into account, a ship is assumed to suddenly suffer a wind heeling moment at its upright condition. This was later used in the interim stability requirements of the USSR and then Poland, Rumania, GDR and China (Kobylinski & Kastner, 2003).

  3.5.2.2 In Japan the energy balance method is extended to cover a roll motion and to distinguish steady and gusty wind as shown in Figure 24. Then it is adopted as the basic principle of Japan’s national standard (Watanabe et al., 1956). The regulation of the Register of Shipping of the USSR (1961) also assumes initial windward roll angle as shown in Figure 24. The current IMO weather criterion of chapter 2.3 of the IS Code, part A, utilizes the energy balance method adopted in Japan without major modification. Here we assume that a ship with a steady heel angle due to steady wind has a resonant roll motion in beam waves. Then, as a worst case, the ship is assumed to suffer gusty wind when she rolls toward windward. In the case of the resonant roll, roll damping moment and wave exciting moment cancel out. Thus, the energy balance between restoring and wind heeling energy can be validated around the upright condition. Furthermore, at the final stage of capsizing, since no resonance mechanism exists near the angle of vanishing stability, the effect of wave exciting moment could be approximated to be small (Belenky, 1993).

  3.5.3.1 In the Japanese standard the steady heeling moment, M_w , is expressed as follows:

• V_w wind velocity

  3.5.3.2 Values of C_D obtained from experiments of passenger ships and train ferries ranges from 0.95 to 1.28. In addition, a wind tunnel test for a domestic passenger ship (Okada, 1952) shows that H/H₀ is about 1.2. Considering these data, the value of C_D(H/H₀) was assumed to be 1.22 on average. These formula and coefficients were adopted also at IMO.

  3.5.3.3 To represent fluctuating wind, gustiness should be determined. Figure 25 shows the ratio of gustiness measured in various stormy conditions. (Watanabe et al., 1955). Here the maximum is 1.7 and the average isHowever, these were measured for about 2 hours of duration but capsize could happen within half the roll natural period, say 3 to 8 seconds. In addition, reaction force could act on centre of ship mass because of such short duration. Therefore, in place of the maximum value, the average value of Figure 25 is adopted. This results in 1.5 as heeling lever ratio for gustiness as shown in the 2008 IS Code.

 In general, ship motion consists of surge, sway, heave, roll, pitch and yaw. In beam seas, however, only sway, heave and roll are dominant. Furthermore, the effect of heave on roll is negligibly small and coupling from sway to roll can be cancelled with roll diffraction moment (Tasai & Takagi, 1969). Therefore, the roll motion can be modelled without coupling from other motion modes if the wave exciting moment is estimated without wave diffraction. Consequently, considering nonlinear roll damping effect is taken into account, the amplitude of resonant roll in regular beam waves, φ (degrees), can be obtained as follows:

  3.5.4.1 Wave steepness

 Based on observations at sea, Sverdrup and Munk (1947) published a relationship between wave age and wave steepness as shown in Figure 26. Here the wave age is defined with the ratio of wave phase velocity, u, to wind velocity, v, and wave height, H _w , means significant wave height.

 If we use the dispersion relationship of water waves,

 this diagram can be converted to that with wave period, T, as shown in Figure 27. Further, since the ship suffers a resonant roll motion, the wave period could be assumed to be equal to the ship natural roll period. Here it is noteworthy that the obtained wave steepness is a function of roll period and wind velocity. In addition, because of possible spectrum of ocean waves, regions for the maximum and minimum steepness are modified from the original data.

  3.5.4.2 Hydrodynamic coefficients

 For using Equation (2), it is necessary to estimate the values of r and N. Since we should estimate wave exciting moment without wave diffraction due to a ship, it can be obtained by integrating undisturbed water pressure over the hull under calm water surface. Watanabe (1938) applied this method to several ships and developed an empirical formula, which is a function of wave length, VCG, GM, breadth, draught, block coefficient and water plane area coefficient. For simplicity sake, it is further simplified for 60 actual ships only as a function of VCG and draught shown in Figure 28. The formula used in the IMO weather criterion for r was obtained by this procedure.

 For estimating the N coefficient, several empirical formulae were available. However, in the Japanese stability standards, N=0.02 is recommended for a ship having bilge keels at the roll angle of 20°. Some evidence of this value can be found in Figure 29 (Motora, 1957).

  3.5.4.3 Natural roll period

 For calculating the wave steepness, it is necessary to estimate the natural roll period for a subject ship. In the Japanese standard, the value measured with the actual ship is corrected with Kato’s empirical formula (Kato, 1956). However, at the STAB Sub-Committee, this procedure was regarded as tedious and Japan was requested to develop a simple and updated empirical formula for the roll period. Thus the current formula was statistically developed by Morita, and is based on data measured from 71 full-scaled ships in 1982. As shown in Figure 30, all sampled data exist within ± 7.5% of error from Morita’s formula. More precisely, the standard deviation of the error from the formula is 1.9%. Furthermore, sensitivity analysis of C on required GM indicated that even 20% error of C estimation results in only 0.04 m error of required GM calculation. Therefore, IMO concluded that this formula can be used for weather criteria.

  3.5.4.4 Wave randomness

 While the wave steepness obtained from Sverdrup-Munk’s diagram is defined by the significant wave height in irregular waves, the resonant roll amplitude given by Equation (2) is formulated for regular waves. For filling the gap between two, the roll amplitude in irregular waves whose significant wave height and mean wave period are equal to height and period of regular waves was compared with the resonant roll amplitude in the regular waves. As shown in Figure 31, if we focus the maximum amplitude out of 20 to 50 roll cycles, an obtained reduction factor is 0.7.

  3.5.4.5 Steady wind velocity

 As explained above, the Japanese weather criterion introduced probabilistic assumptions for determining gust and roll in irregular waves. These make final probabilistic safety level unclear. Possible estimation error for wind heel lever coefficient, roll damping coefficient, effective wave slope coefficient, natural roll period and wave steepness added uncertainty to the required safety level. Therefore, Japan carried out test calculations for 50 ships, which include 13 ocean going ships as shown in Figure 32. Based on these calculated outcomes, the steady wind velocity was determined to distinguish ships having insufficient stability from other ships. In other words, for ships having insufficient stability the energy balance should not be obtained with the above procedure. As a result, the wind velocity for ocean going ships is determined as 26 m/s. Here a sunken torpedo boat (0-12-I), a sunken destroyer (0-13) and three passenger ships having insufficient stability (0-3, 7, and 9) are categorized as unsafe and 2 cargo ships, 3 passenger ships and 3 larger passenger ships are done as safe. It is noteworthy here that 26 m/s of wind velocity is only obtained from casualty statistics for ships and is not directly obtained from actual wind statistics. IMO also adopted 26 m/s as critical wind velocity. If we substitute V _w =26 m/s to Equation (1), the wind pressure in the current IS Code is obtained.

  3.5.4.6 Rolling in waves (USSR’s method)

 In the stability standard of USSR (USSR, 1961), the maximum roll amplitude of 50 roll cycles is estimated as follows:

 Here k is a function of bilge keel area, X₁ is a function of B/d, X₂ is a function of the block coefficient and φ _A is roll amplitude of the standard ship, which is shown in Figure 33. This formula was developed by systematic calculations for a series of ships utilizing the transfer function and wave spectrum (Kobylinski & Kastner, 2003).

 As mentioned earlier, IMO decided to partly use this USSR’s roll formula together with the Japanese criterion. This is because the USSR’s formula depends on hull forms for estimating roll damping while the Japanese does not. The proposed formula is as follows:

 Here C _JR is a tuning factor for keeping the safety level of the new criterion as the same as the Japanese domestic standard. To determine this factor, member states of a working group of STAB Sub-Committee executed test calculations of Japanese and new formulations for many ships. For example, Japan (1982) executed test calculation for 58 ships out of 8,825 Japanese flagged-ships larger than 100 gross tonnage in 1980. These include 11 cargo ships, 10 oil tankers, 2 chemical tankers, 5 liquid gas carriers, 4 container ships, 4 car carriers, 5 tug boats and 17 passenger or RoPax ships. As a result, IMO concluded that C _JR should be 109.