3.3 Background of the approximate formula for the minimum GM ₀ for small fishing vessels (part B, paragraph 2.1.5.1 of the 2008 IS Code)

  3.3.1 The approximate formula for the minimum metacentric height for small fishing vessels was developed using the method of regression analysis. In 1967 the Panel of Experts on Fishing Vessels Stability (PFV) of IMO recommended to develop an appropriate stability standard for small fishing vessels less than 30 m in length. The reason for this was the fact that for small fishing vessels quite often no drawings and stability data are available; therefore, the application of criteria of resolution A.168(ES IV) is not possible. It was proposed that a stability standard for those vessels could be developed in the form of a formula for GM _crit that could be compared with the actual GM₀ estimated on the basis of the rolling test. The value of GM _crit should correspond to the criteria of resolution A.168(ES IV).

  3.3.2 For the development of the appropriate formula, members of the Panel were requested to submit stability data for as many small fishing vessels as possible and also information regarding approximate formulae on GM _crit used in their countries, if any. Those formulae were later compared with the formulae developed by the regression analysis. The review of all approximate formulae revealed a rather wide scatter of values of GM _crit. This could be expected because it is obvious that the formulae do not take into account all parameters of the ship’s hull that are important from the point of view of stability. Therefore, none of the formulae were adopted by IMO and it was decided to develop a new formula based on a regression analysis of a larger number of data for small fishing vessels.

  3.3.3 The formula should provide results as close as possible to those provided by using IMO criteria included in resolution A.168(ES IV). As it would be impossible to take into account all criteria, it was decided that the representative criterion which should be satisfied was GZ ₃₀ = 0.20 m.

  3.3.4 Stability data was collected on 119 vessels of between 15 and 29 m in length and analysed [IMO 1968a].

  3.3.5 As the condition for GM_crit is GZ ₃₀ = 0.2 m, the following is valid (Figure 21):

  3.3.6 As MS₃₀ / B depends only on geometrical parameters of the hull, this parameter might be used not only to evaluate GM_crit but also to compare different hull shapes from the stability point of view.

  3.3.7 It is assumed that, in general,

 polynomial expressions of different

 type were tested with coefficients evaluated by regression analysis. The evaluation of errors while estimating GM _crit of those expressions with respect to the actual GM _crit of the analysed vessels showed, as expected, that for about 50% of the vessels the calculated GM _crit was smaller than the actual value. For another 50% it was greater than the actual value (Figure 22a) with the distribution of errors considered acceptable. To increase the safety, it was then decided that the calculated values of GM _crit should be increased by a certain amount, C_GM , in order to achieve a situation where about 85% of vessels were on the safe side (Figure 22b). This supplementary C_GM was evaluated by an iteration process and it was determined that the proper value is C_GM = 0.1250.

  3.3.8 The formula (4) was modified as follows:

  3.3.9 The final formula, as given in resolution A.207(VII), was:

 where: