Abstract: Over the last 30 years, there has been considerable research into the prediction of hydrodynamic derivatives in order to identify the various hydrodynamic forces for the purpose of predicting a ship's manoeuvring performance. There are a number of key works that now form the basis of many manoeuvring studies and theories commonly in use today and these are presented with reference to how todays mathematical models could benefit from taking derivatives from multiple sources. Two cases have been used to test this concept; the ESSO OSAKA due to the large number of full-scale and model test data available, and the GOLDEN PRINCESS, being typical of modern cruise ship hull forms and a vessel for which manoeuvring is an important design and operational issue. A comparison of the predicted forces and moments is given including Computational Fluid Dynamics and Systems Identification methods and an assessment of the sensitivity of standard and slow-speed 'harbour' manoeuvres to the different methods of predicting the hydrodynamic derivatives. Finally, the future direction of research at BMT is introduced with reference to the cost-effective gathering of full-scale data and the subsequent prediction of manoeuvring performance.

　

 British Maritime Technology (BMT) was formed in 1984 from the merger of the British Ship Research Association (BSRA) and the National Maritime Institute (NMI) and has a long history in the field of ship manoeuvring. In particular, this has included;

　

 In recent years, as the requirement for more accurate mathematical models has increased, BMT has sought to improve its theoretical models for ship manoeuvring including aspects such as bank effects and ship-ship interaction, as well as the foundation of all simulators; the 'own-ship' mathematical model.

　

 As part of BMT's on-going research and development program and combined with an important European Union (EU) research project, a study into the cost-effective prediction of hydrodynamic forces has been undertaken to address the needs of modern manoeuvring simulators.

　

1.1 Motivation and Objectives

　

 Over the last 30 years, there has been considerable effort into the prediction of hydrodynamic forces for the purposes of predicting the manoeuvring performance of surface vessels. Much of this work has been used successfully and today lives on in the experience and knowledge that those of us involved in ship manoeuvring still use. However, there is still much to learn about the hydrodynamics of manoeuvring ships, in particular the reliable (and cost effective) prediction of hydrodynamic forces and moments for the full range of ship types.

　

 As will be discussed later in this paper, of prime importance in our industry is accuracy. The mathematical modelling of ship manoeuvring for crew training, manoeuvre rehearsal, vessel/port familiarization all require accurate ship models. The foundation or 'building block' for this is the accurate representation of hydrodynamic forces and moments and it is important that we are able to accurately model the manoeuvring of a range of ships in all regimes of motion.

　

 The specific objectives of this study are therefore:

　

　

1.2 General Approach and Methodology

　

 As is natural with a study of this nature, we must first establish the current methods available for predicting the hydrodynamic derivatives. It is therefore necessary to examine a range of predictions for a single vessel, comparing the data with model test and fill-scale results where possible.

　

 This clearly points us the direction of the ESSO OSAKA and this vessel will therefore be used as our 'control case'. It is not proposed to assess all of the available prediction methods for this vessel as this is a subject in itself and is adequately described elsewhere. See references [1] and [2].

　

 A number of data sets for the ESSO OSAKA will be examined, including a comparison of simulated and full-scale manoeuvres and introducing some preliminary comparisons with CFD and SI predictions. In order to extend the boundaries of research into ship manoeuvring, we will also examine a modern cruise ship, the GOLDEN PRINCESS. For this vessel, we will primarily concentrate on slow-speed or harbour manoeuvres, as it is this regime of motion that is the most important to such vessels.

　

 In comparing the data from different sources, we will be examining predictions from a range of studies, assessing the measurement of hydrodynamic derivatives from model tests and the empirical (or semi-empirical) formulae commonly used to calculate derivatives for different vessels.

　

 An assessment will be made of the relative merits of using derivatives calculated by a single method or through a combination of approaches, the so-called multi-source approach.

　

 Finally we will introduce an important EC research project called SEA-AHED and how this project will allow us to use full-scale ship performance data to improve our prediction methods in the future.

　

 The prediction of hydrodynamic forces acting on a manoeuvring ship is generally undertaken using one of the following methods:

　

　

 Some significant advances have been made in the application of CFD and similar approaches to ship manoeuvring (see references [3] and [4]). It can be seen from these works that good agreement may be obtained at lower drift angles, but at higher drift angles. The agreement is less satisfactory. The calculations are generally limited to small drift angles and ultimately regimes of motion where the forward speed of the vessel is dominant, presumably due to difficulties in representing vortex shedding at higher drift angles. It is therefore fair to say that ship manoeuvring still presents CFD with its greatest challenge due to its inherent non-linearity and strong interaction with the environment [2].

　

 Systems identification methods, such as those demonstrated in [5] and [6] have received more attention as we try to learn from the full-scale performance of ships in order to improve our predictions. It seems that relatively good results can be obtained using these methods, given the appropriate modelling of all relevant terms and a detailed, accurate set of trials results. However, the full validity of the approach has not yet been assessed through the application of the 'identified' coefficients to different manoeuvres than those used in the identification process.

　

 It is the empirical approaches that currently demand our attention, as they provide a cost-effective method of estimating the hydrodynamic forces and moments and are therefore of particular use in estimating the performance at the design stage. They are equally important for those involved in creating ship models for marine simulators, where both accuracy and commercial issues such as cost are important.

　

 A review of the available literature on this subject shows that empirical formulae for the linear derivatives are far more common than those for the non-linear or acceleration terms, perhaps due to the easier identification of the linear derivatives from experimental data. The accurate prediction of non-linear coefficients is clearly more difficult and is limited to a few datasets.

　

 The available prediction formulae for the added mass terms differ slightly, in that whilst there are relatively few empirical formulae available in the public domain, results have been obtained using 'strip-wise' methods (i.e. slender body approaches) and hence this provides an alternative means that can be readily used in conjunction with the empirical formulae.

　

 Table 1 below, shows the number of formulae available for each of the derivatives. A full description of these methods, their applicability and an assessment of their relative accuracy is given in [7]. For the purposes of this paper, it is sufficient to highlight the key datasets in order that we may assess their use for the prediction of hydrodynamic forces.

　

　

 Table 1 is by no means an exhaustive list, but is sufficient to describe the general availability of prediction formulae for each derivative.

　

 The authors feel that the following datasets are 'key' to forming a benchmark from which to further develop our ability to accurately predict hull forces and moments. In keeping with the need for a test case, we have split the list into two areas;

　

　

2.1 Key Datasets-ESSO OSAKA

　

　

2.2 Key Datasets - General