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23rd International Towing Tank Conference

Proceedings of the 23rd ITTC – Volume I 153

1. GENERAL

1.1. Membership and Meetings

The following members of the 22nd ITTC left the Manoeuvring Committee: Dr. R. Barr, Dr. G. Capurro and Dr. M. Hirano. The mem-bers of the present Committee wish to express their appreciation for their effort during their term. The Committee appointed by the 22nd ITTC consisted of the following members:

Dr. Stéphane Cordier (Chairman), Bassin d’Essais des Carènes, France

Prof. Kazuhiko Hasegawa (till 2000), Osaka University, Japan

Dr. Masayoshi Hirano (from 2001), Aki-shima Laboratories (Mitsui Zosen) Inc., Ja-pan

Dr. Jakob Buus Petersen, Danish Maritime Institute, Denmark

Prof. Key-Pyo Rhee, Seoul National Uni-versity, Korea

Mr. Peter Trägårdh, SSPA, Sweden Prof. Michael Triantafyllou, Dr. Franz

Hover, Massachusetts Institute of Technol-ogy, USA

Prof. Marc Vantorre (Secretary), Ghent University/Flanders Hydraulics, Belgium

Prof. Zou Zaojian, Wuhan Transportation University, P.R. China

Following meetings were organised September 11, 1999: 22nd ITTC, Shanghai,

P.R. China May 3-4, 2000: MIT, Cambridge (Mass),

USA

October 12-13, 2000: ENSTA, Paris, France

April 5-6, 2001: SSPA, Göteborg, Sweden October 15-17, 2001: Akishima Laborato-

ries (Mitsui Zosen) Inc., Akishima, Japan January 14-16, 2002: DMI, Lyngby, Den-

mark

1.2. Tasks assigned by the Advisory Council

The Advisory Council defined the follow-ing tasks to be performed by the Committee.

Review the state-of-the-art, comment on the potential impact of new develop-ments on ITTC, identify the need for re-search and development in the areas of manoeuvrability. Monitor and follow the development of new experimental tech-niques and extrapolation methods.

Review the ITTC recommended proce-dures, benchmark data, and test cases for validation and uncertainty analyses and up-date as required. In particular, the following procedures should be reviewed:

▫ Manoeuvring Trials Code including IMO criteria, ITTC procedure 4.9-03-04-01

▫ Captive Model Test Procedure, ITTC procedure 4.9-03-04-03

Prepare a procedure for free-running model manoeuvring tests including con-ventional and unconventional propul-

The Manoeuvring Committee

Final Report and Recommendations to the 23rd ITTC

154 The Manoeuvring Committee 23rd International

Towing Tank Conference

sion/manoeuvring devices such as Z-drives and water jet propulsion.

Devise a validation procedure for manoeu-vring simulation models obtained from model and/or full scale data.

Develop procedures for the evaluation and documentation of manoeuvring and control characteristics of HSMVs.

Identify the requirements for new proce-dures, benchmark data, validation, uncer-tainty analyses and stimulate the necessary research for their preparation.

Procedures must be in the format defined in the ITTC Quality Manual and they should be included in the Committee report as separate appendices. Symbols and termi-nology should agree with those used in the 1999 version of the SaT List; if necessary, new symbols should be proposed.

Review methods for prediction manoeu-vring in shallow and confined waters.

Prepare an up-to-date bibliography of rele-vant technical papers and reports.

1.3. Structure of the Report

In Chapter 2, the efforts of groups of insti-tutions performing joint research on subjects related to manoeuvring are mentioned.

Chapters 3 through 7 cover the tasks con-cerning the state-of-the art review and the bib-liography, focusing on following subjects:

Hydrodynamic forces (Chapter 3); Simulation of dynamics (Chapter 4); Model test techniques (Chapter 5); Sea trials and validation (Chapter 6); Manoeuvring characteristics of autono-

mous underwater vehicles (Chapter 7).

In Chapter 8, an overview is given of the efforts of the Committee on the review of existing procedures, the development of new procedures and the review of methods for predicting manoeuvrability in shallow and restricted waters, the latter being incorporated in this Report as a separate Appendix. The

conclusions of the Manoeuvring Committee are formulated in Chapter 9.

2. SPECIAL GROUPS

2.1. RR74 (Japan)

In order to review the IMO Interim Stan-dards for Ship Manoeuvrability, the panel of RR74 Manoeuvrability WG was established by Japan Shipbuilding Research Association in 1995. In the first phase of panel activity, the propriety of the Standards has been exam-ined on the basis of the database of full scale manoeuvring trials developed mainly for newly built ships with modern hull forms.

Subsequently, a second phase of review of the Standards is underway by performing extensive simulator studies with the use of the modular type of mathematical model (MMG model). Revision of the criteria with respect to the second overshoot angle in 10/10 zigzag manoeuvre, the first overshoot angle in 20/20 zigzag manoeuvre and the stopping distance have been discussed.

2.2. Co-operative Research Ships (CRS) and others

The CRS MAN working group is pursuing the development of a simulation model adapted to twin screw ships and more recently Pod propulsion.

The manoeuvring and course keeping per-formance of podded ships is also being stud-ied as part of a Joint Industrial project, JIPOD, as well as a European Union project OPTIPOD.

A working group of specialist as been cre-ated in the North Atlantic Treaty Organisation to define manoeuvring criteria for naval ships.



3. HYDRODYNAMIC FORCES

To predict the manoeuvrability of ships it is essential to determine the hydrodynamic forces acting on the ships beforehand. Of re-cent years, while the traditional experimental and semi-empirical methods are still often used, numerical methods based on advanced numerical techniques or CFD (Computational Fluid Dynamics) are becoming more and more popular to be used for estimation of the hydrodynamic forces.

Flow around a ship in manoeuvring mo-tion and the hydrodynamic forces acting on the hull, propeller and rudder as well as the hydrodynamic interaction among them can be estimated with increasing accuracy by CFD techniques, based on either potential flow or viscous flow methods. The effects of forward speed and the restricted waterway on the hy-drodynamic forces as well as the environment influences can be taken into account.

Furthermore, numerical manoeuvring simu-lations using unsteady numerical methods that simultaneously solve the fluid flow and the ship motion equations using time-matching scheme. This application of CFD is treated as a simulation technique in section 4.6.

3.1. Hull Forces in Deep Water

Experimental and Semi-Empirical Meth-ods. Using the data for 15 ships, Kijima & Nakiri (1999) proposed the approximate for-mulae for hydrodynamic forces acting on a ship in manoeuvring motion taking into ac-count the effect of stern shape. Di Felice & Mauro (1999) carried out a series of experi-ments to analyse the shedding vortex system, arising from a bare hull in large drift condi-tion. Mean cross flow velocities were meas-ured using LDV. Beukelman (1998) carried out oblique towing test and forced horizontal motion test with a PMM for a surface-piercing wing-model in both deep and shallow water. Sadakane et al. (1998) conducted a constant

brake force test to study the lateral drag coef-ficients of a ship in the decelerating stage. Ki-jima et al. (2000a, 2000b) carried out captive model tests to measure the hydrodynamic forces acting on a disabled ship with trim and heel angles. Yumuro & Uchida (2001) carried out segmented model experiments in oblique flow. Petersen & Lauridsen (2000) developed a regression method based on a database of manoeuvring derivatives obtained from PMM tests. It was concluded that in order to obtain satisfactory regressions, the lateral forces and moment had to be non-dimensionalised by means of the lateral profile area instead of L×T, and that the stern shape parameter σA was identified as a less significant parameter.

Inviscid Flow. Sasaki (1998) proposed pre-diction method for the linear derivatives based on a hydrodynamic model for full ships. The hull is divided into three parts: entrance, paral-lel, and stern. The local hydrodynamic deriva-tives were investigated both experimentally and theoretically. Maekawa et al. (1999) pre-sented a method to calculate added mass coef-ficients of a ship’s superstructure by means of CFD. Nakatake et al. (2001) developed a method to calculate the flow field and forces around a ship hull in oblique and turning mo-tions using a surface panel method, SQCM.

Kijima et al. (1998) proposed a prediction method for the hydrodynamic forces acting on a ship hull based on slender-body theory. A parameter representing the initial position of vortex filaments shed from the separation points was introduced into the prediction model and the relationship between this pa-rameter and the principal particulars of ship was investigated.

Karasuno et al. (2000) presented a modi-fied modular-type mathematical model of hy-drodynamic forces derived from a simplified vortex systems model with ring vortex, horse-shoe vortex and cross-flow vortex. Kijima & Kishimoto (1999) presented a numerical method for estimation of the hydrodynamic forces acting on a disabled ship with large



trim and heel angles when towed. Kijima & Takazumi (1999) proposed a prediction method to estimate the hydrodynamic force acting on a ship hull in lateral motion based on method. Kijima & Kaneko (2000) investi-gated the hydrodynamic forces acting on three types of model ship with different stern shape by applying the slender-body theory with the discrete vortex model.

CFD Methods for Viscous Flow. Hydro-dynamic forces acting on a manoeuvring ship hull are caused by viscous effect, hence, nu-merical methods for viscous flow that have been developed recently, are better adapted and there have been many reports of such studies.

SR221 joint research project in Japan made extensive calculations and model tests to validate CFD results. The flow around two full ships with same fore body and different aft body were calculated in steady oblique course by Makino & Kodama (1997), and also in steady turning motion by Ohmori et al. (1998) and Miyazaki et al. (2000). Compari-son with experimental data of lateral force distributions and wake distribution showed good agreement (Figure 3.1, Figure 3.2, Figure 3.3).

Work has also been done based on the Se-ries 60 hull form at a drift angle. Campana et al. (1998), Alessandrini & Delhommeau (1998), Tahara (1999) used free-surface RANS computation and comparison with ex-perimental wave pattern and forces are gener-ally satisfactory (Figure 3.4).

Hochbaum (1998) presented a multi-block computational method that can deal with complicated configurations (e.g. hull with ad-ditional devices).

Levi & Wanderley (2001) presented a nu-merical solution of 3D viscous flow around slowly rotating ships in the presence of an in-cident flow.

Figure 3.1 Computed and measured lateral force distribution (Ohmori et al., 1998).

Figure 3.2 Computed and measured hydro-dynamic forces (Makino et al., 1997).

Zhang & Wu (2001) solved the 3D vis-cous flow around a ship hull in oblique mo-tion by using finite-analytic method. Hoshino et al. (1999) presented a viscous flow method for estimation of the hydrodynamic forces act-ing on a damaged and capsized ship. Yama-saki et al. (2001) described an application method of CFD to the ship manoeuvrability study at the initial stage of hull design.



3.2. Hull/Rudder/Propeller Interaction

The modelling of hull, propeller and rudder interaction by CFD is difficult because of the complexity of the topology. An approach fre-quently used is to calculate each part sepa-rately, incorporating interaction in iterative cal-culations. Although calculations for self-propulsion have been made, for a manoeuvring ship this method is still under development.

Figure 3.3 Measured and computed wake distribution (Miyazaki et al. 2000).

Figure 3.4 Computed and measured wave pattern for series 60 (Tahara, 1999).

Figure 3.5 Lateral force and yawing mo-ment, with and without propeller (Takada et al., 2000).

Takada & El Moctar (2000) performed hull-propeller interaction calculation in oblique tow, steady turning, and PMM mo-tion. This method is composed of a CFD hull flow calculation and an actuator disk propeller model (Figure 3.5).

On the interaction between propeller and rudder, El Moctar (1999) presented a CFD computation method. Multi-block computa-tion was adopted to deal with complicated configuration of rudder and propeller (Figure 3.6). Hydrodynamic characteristics of rudder, including stall, is well estimated (Figure 3.7).

Kawakita et al. (1999) developed a fortified solution method to deal with hull/propeller/rud-der interaction. Flow field around Esso Osaka tanker in straight course with constant rudder angle was computed (Figures 3.8 and 3.9).

Krüger (1998) presented a method for pre-dicting propeller-ship interaction. The thrust de-duction is computed by a panel code for the hull combined with a lifting-line propeller calcula-tion. Yang et al. (1998) proposed a method for predicting the hydrodynamic performance of a reaction rudder behind a propeller. The hydro-dynamics of the rudder was calculated by panel method and the performance of the propeller was predicted by the simple propeller theory. The interaction between rudder and propeller was determined by iterative procedure.



Figure 3.6 Computational grids on rudder and propeller surface (El Moctar et al., 1999).

Figure 3.7 Lift and drag of rudder (El Moc-tar et al., 1999).

Figure 3.8 Arrangement of multi-block computational grid (Kawakita et al., 1999).

Figure 3.9 Hydrodynamic forces on hull, propeller and rudder (Kawakita et al. 1999).



Sannomiya et al. (2001) estimated the effect of ship trim and displacement on the interaction coefficients and the characteristics of ship ma-noeuvrability, making use of ship trial data and model experiment results of PMM test.

Kataoka et al. (2001) investigated the hull-propeller-rudder interaction by calculating the flow corresponding to rudder angle test, where the hull and the rudder were repre-sented by a panel method and the propeller expressed by infinitely bladed propeller.

El Moctar (2001a, 2001b) presented a comprehensive numerical investigation on hull-propeller-rudder interaction for a ship in manoeuvring motion by using a RANSE code.

3.3. Forces by Means of Control

There exist not so many studies about CFD calculations on rudders. Chau (1997) computed the viscous flow around a model rudder by Comet CFD code and succeeded in capturing stall. El Moctar & Muzaferija (1998) conducted CFD calculations of the flow around a rudder in the propeller wake.

Söding (1998) compared the rudder force and stock moment results by panel method, RANS calculation and model experiments and discussed the limit of potential calculation for rudder flow prediction. Ahn et al. (1999) car-ried out model experiments and numerical simulations on the Coanda effect of a flapped rudder. Zhu et al. (1999) conducted the open water test of a Becker flap-rudder and com-pared its performance with a normal rudder. Ma et al. (1999) carried out a series of hydro-dynamic performance test research on a new type of flap rudders and derived some regres-sion formulae for the rudder hydrodynamic performance. Chen et al. (1999) presented re-gressive formulae of marine build-up rudder hydrodynamic coefficients. Yuda (1999) per-formed numerical calculation of hydrody-namic forces acting on a VecTwin rudder. Pyo & Suh (2000) applied a low-order potential based boundary element method to predict the

performance of flapped rudders as well as all-movable rudders in steady inflow. The calcu-lated results on forces and moments were compared with experimental data.

Son & Rhee (2000), Son et al. (2001) pre-sented an empirical formula to estimate the steering gear torque of a tanker with a horn type rudder. The hydrodynamic characteristics of the horn type rudder in the free-stream condition were calculated by using the modi-fied lifting line theory by proposed by Mol-land, and the interaction effects by propeller and hull were analysed by the regression analysis of the sea-trial data of 32 vessels.

Min & Chung (2000) carried out an ex-perimental study for the optimum rudder de-sign. Some practical useful design directions and conclusions were derived for the major characteristics section shape, platform and aspect ratio. Fukutani (2001) conducted vari-ous model experiments such as open water test, behind propeller test and self-propelled free running test using a new type of rudder with parallel auxiliary foils arranged to both sides of the trailing edge of main rudder.

Miyazaki et al. (2001) applied a NS code to compute flows around a ship with rudder in manoeuvring motion and compared the com-puted hydrodynamic forces and interaction between ship hull and rudder with experimen-tal values.

3.4. Interaction Effects

Based on the boundary element method, Zhang & Wu (1998) proposed a numerical method for hydrodynamic interaction forces between ships in meeting and passing condi-tions in shallow water and for hydrodynamic forces acting on a ship in the proximity of a non-uniform bank wall.

Varyani et al. (1999) investigated the ship interaction problem and presented empirical formulae for predicting peaks of forces and moments during interactions.



Li et al. (2001) carried out experiments on bank effects in extreme shallow water and near bank conditions with three ship models. The influence of propeller loading and the wave pattern during bank passage were also studied.

3.5. Hull Forces in Restricted Water

A discussion of existing methods for predict-ing the effects of restricted waters is presented in an appendix to this report. The following is a discussion of the more recent literature.

Based on the crude analysis of one-dimensional flow and slender body theory, Zheng (1999) presented a method to calculate the linear hydrodynamic derivatives for ships moving obliquely along the centreline of a narrow channel.

Gronarz (1999) used a semi-empirical formula for estimating the hydrodynamic co-efficients in shallow water and demonstrated that this is the simple and easy way for con-sideration of water depth effects in the ma-noeuvring simulation.

Yumuro (2001) examined the influence of the position of the single vortex on hydrody-namic forces on a turning ship in shallow water.

By applying the slender-body theory with dispersive vortex model, Kaneko & Kijima (2001) investigated the hydrodynamic forces acting on a ship hull in shallow water.

Based on some series calculations, Sada-kane et al. (2001) presented simplified formu-las for the ratio of the added mass and mo-ment of inertia in shallow water to those in deep water.

Shallow water problem is also tried to solve by CFD. Ohmori (1998) extended WISDAM code to shallow water condition and calculated steady oblique and turning motion

of Esso Osaka tanker. Results showed qualita-tive agreement with measured value in most case (Figure 3.10).

Berth et al. (1998) computed Esso Osaka in shallow water condition by Fluent CFD code.

Figure 3.10 Change of linear derivative due to water depth (Ohmori, 1998).

3.6. Non-Conventional Ships

Using a surface panel code, Turnock & Smithwick (1998) analyzed the hydrodynamic performance of underwater appendages and hull of the Reflex 28 yacht in upright and heeled conditions for a range of hull drift and rudder angles. Ikeda et al. (1999) measured the six components of hydrodynamic forces acting on the scale model of a planing craft in oblique towing condition. Tajima et al. (1999) measured the six components of hydrody-namic forces acting on the scale model of a planing craft by planar motion mechanism test for various planar motions and running atti-tudes. Iwasaki & Suzuki (1999) presented a numerical analyses of free surface flow around a sailing yacht in heeling condition. The hydrodynamic interactions between the main hull, the fin keel and the rudder were also studied.



3.7. External Forces

Ueno et al. (2000, 2001a, 2001b) pre-sented a calculation formula for predicting steady horizontal forces and moment due to short waves acting on ships in manoeuvring motion. Calculated results were compared with experimental data.

4. SIMULATION OF DYNAMICS

4.1. Simulation models

Developments in simulation of dynamics have concentrated on modelling special prob-lems. Some papers describe simulation using CFD either directly or using CFD calculated forces.

Miller et al. (2000) described the devel-opment of a simulator for operation of barges in a littoral environment. Mathematical mod-els are presented for an azimuthing water jet as well as for the behaviour of several lighters held together by flexural connectors in a sea-way. The simulator also includes a module for simulating the barge behaviour when landing at the beach.

Some papers describe mathematical models that are related to stopping manoeuvres. Ja-kobsen et al. (2000) describe a prediction method covering the whole propeller range from full ahead through wind-milling to full astern. Benvenuto et al. (2001) developed a method to simulate the propulsion system behaviour, which is compared with full-scale trials.

Munitic et al. (2000) developed a computing environment for modelling system dynamics, demonstrating it on a steam turbine model.

Senda & Kobayashi (2000) developed control algorithms for the deceleration (stop-ping) of ships, which were verified against simulator experiments. These take into ac-

count the distance to berth and the ship’s lat-eral deviation and heading deviation from planned route.

Szelangiewicz (1999a, 1999b) presents a mathematical model for simulating anchoring manoeuvres with up to four anchors. Simula-tions indicate that using a joystick positioning system improves the anchoring time signifi-cantly.

A mathematical model for simulating the behaviour of hydrofoil crafts is presented by Krezelewski (1999), which includes roll mo-tion as well as added masses of the foils.

Clarke & Kurniawati (2000) show that chaotic ship manoeuvres can be observed for sinusoidal rudder motion.

4.2. Validation of simulator models

Validation of simulation models is impor-tant in order to be able to trust their predic-tions. Gofman & Manin (1999, 2000), showed examples of simulation models where very unsatisfactory results are obtained using stan-dard simulators. The simulated standard ma-noeuvres compare very poorly with results from full-scale trials. It is stated that training and certification of deck-officers using these models could be a problem.

Ishibashi & Kobayashi (2000) presented a mathematical model for simulation of harbour manoeuvres in shallow water, based on cap-tive model tests in various water depths to draught ratios and validated against free sail-ing manoeuvres. Good agreement between the latter and simulated manoeuvres is found.

The 22nd ITTC Manoeuvring Committee recommended the Esso Osaka be used for the validation of force predictions and simulation models. One reason for this was the existence of well-documented trials in both deep and shallow water (Crane, 1979). Another reason



was that much work had already been made in the past for this specific ship, and models as well as drawings still exist. New work related to the validation of force predictions as well as manoeuvre predictions for the Esso Osaka is therefore as relevant as ever.

Figure 4.1 Trajectory and time history of drift angle for 35o starboard turning (10 knots).

Kim et al. (2001) performed a comparative simulation study, considering three different “whole ship” models based on captive model tests with appended Esso Osaka hulls at three different institutions. It is shown that similar manoeuvres are obtained from the three models, except for larger drift angles and yaw rates as experienced in the last part of the turning circle. This is illustrated in Figure 4.1, showing the predicted turning circle tracks and drift angle as

function of time for the three methods and the full-scale trials. Unfortunately, the drift angle in the full-scale turning circle was too contami-nated by current to obtain a valid reference.

Another paper by Ishibashi & Kobayashi (2001) compares results from simulations based on the MMG model. Here, different ef-fects, related to the model testing and the data analysis procedure, are investigated. First the influence of choosing different ranges of drift angles and yaw rates in captive tests using a 6 m model is investigated. Secondly, the influ-ence of using a bare hull or an appended model for deriving the hull forces is investi-gated for a 2.5 m model. For the appended model, the propeller was tested running at both the model and the ship self-propulsion points. It is shown that for the Esso Osaka, the range of drift angles and yaw rates in the tests clearly has a large influence on higher order derivatives. It is also shown that the propeller loading has little influence for the Esso Osaka hull form at the tested scale.

Send (2000) has made an assessment of the sensitivity of submerged body manoeuvres to changes in the hydrodynamic coefficients.

Because the ITTC community is involved in simulation model use and development, the 23rd Manoeuvring Committee was given the mandate to develop a procedure for validation of simulation models (see paragraph 8.4).

4.3. Combined manoeuvring and seakeeping

To be able to simulate the behaviour of a ship manoeuvring in rough weather including the effect of wind, current and waves is impor-tant for the prediction of the ship’s handling ability and for correcting trials for environ-mental conditions. Also in other situations the effect of the environment should be included, e.g. investigation of operability criteria, simula-tor studies and training in rough weather.

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Bailey et al. (2000) are developing a “uni-fied mathematical model” which is an attempt to merge seakeeping theory with manoeuvring models. Convolution is used to model both the first order linear manoeuvring derivatives as well as the radiation forces. Froude-Krylov forces are calculated at the instantaneous water surface around the hull. The theory is validated against seakeeping theory on a straight course in waves and against a calm water manoeu-vring model for a turning circle, using a Mari-ner type ship. Promising results are shown for a turning circle in regular waves where the ex-pected drifting in the direction of the wave propagation is observed. Lee (2000) and Lee et al. (1998) also use convolution integrals to solve the combined manoeuvring and seakeep-ing problem, validating their method using a zigzag manoeuvre in regular waves.

Iwamoto et al. (2001) developed a mathe-matical model of ship motions including roll in regular waves. The model was used to in-vestigate a course and roll controller using active fins and rudders. It is shown that an improved rudder and fin performance can be obtained using a coupled optimal controller.

4.4. System Identification

The problem of identifying a mathematical model based on results from free sailing model tests or full-scale ship trials has been a continu-ous research area for many years. Neural net-works have been used for this purpose in two different papers by Hess & Faller (2000) and Morawski & Rak (1999). Both papers show that non-linear simulation models can be obtained that accurately reproduce the manoeuvres that were tested. The model used by Hess & Faller (2000) also includes roll and pitch.

The results from full-scale trials are often corrupted by noise, which makes it difficult to identify parameters in mathematical models. Some authors applied system identification to determine parameters of well-known mathe-matical model structures. Zhuang & Jiang

(2000) identified parameters in a four-quadrant mathematical simulation model us-ing a “step-wise” extended Kalman filtering technique. Addition of noise to the simulated manoeuvres appeared to result into a reduc-tion of the number of identifiable parameters. Sung et al. (2000) presented simulations with an Abkowitz model and a MMG model using a system identification technique for identify-ing the derivatives. It is concluded that rea-sonable results are obtained from a considera-bly reduced number of dynamic test runs compared with a traditional approach.

Kim (1998) developed a method for esti-mating both the structure of and parameters in a mathematical model for submersibles, based on results from captive model tests. Kim (1999) also developed a method for ranking the identifiability of parameters in a linear model for submersibles.

4.5. Simulation of Tugs

Some effort has been put into modelling of tug assistance, either for salvage situation or for harbour manoeuvring.

Wulder et al. (2000) described the simula-tion of harbour manoeuvres of a large ship assisted by tugs. The large ship as well as the tugs are individually modelled in a real-time simulator and can thus be separately con-trolled by navigators. Interaction forces from pushing or towing lines as well as tug-to-ship and ship-to-tug interactions are modelled. Three different tug designs are discussed: conventional, Voith-Schneider and a Rotor tug. Also Waclawek (1999) describes a simu-lation model of a Voith-Schneider tug and a towed ship. The tug model is validated against model experiments for various drift angles and thrust vector angles.

Sohn et al. (2000) and Kijima et al. (2000a) investigate the stability of a system of a tug tow-ing a larger ship in various damaged conditions.



Also Varyani (1999) simulated the behav-iour of a tug towing two disabled vessels. Stable and unstable regions are identified using a tug autopilot. The wind is shown to be an important parameter in the system investigated.

4.6. IMO Res. A751 criteria

Yoshimura et al. (2000) analyse a database of full-scale trials in Japan with regard to the IMO interim manoeuvring standards (Res. A751, 1993). The paper states that the second overshoot angle in the 10-10 zigzag and the first overshoot in the 20-20 zigzag criteria are too severe, and that the theoretical back-ground for introducing these two criteria is limited. These conclusions are supported by simulator studies with pilots.

Rhee et al. (2001) also investigated a data-base of full-scale manoeuvring trial results. It is shown that more than 10% of the new-buildings do not satisfy the IMO criteria at the tested loading condition and that more than 25% of the ships do not meet these criteria after correction of the loading condition to the scantling draught. A real-time simulation study was carried out as well to relate the IMO criteria to safe navigation in realistic harbour or channel approaches. It is con-cluded that both the 1st and the 2nd overshoot angle in the 10-10 zigzag manoeuvre are re-quired as criteria. A ship fulfilling these crite-ria, however, is shown to meet the 1st over-shoot angle criterion in the 20-20 zigzag ma-noeuvre as well.

Lebedeva (2000) suggests that the adopted IMO Res. A751 interim standards can fail to identify ships with poor manoeuvring charac-teristics because the standards do not take into account the time between executes, which is suggested to be adopted as a criterion.

4.7. Dynamic stability

Introduction. The “classical” course stabil-ity problem has had little attention recently, and few papers deal with this subject. How-ever, a good understanding of the definitions and basic theoretical developments in this area is often required, and no recent reference provides an overview of this topic. Therefore, the 23rd ITTC Manoeuvring Committee con-sidered a review of the various stability crite-ria and the definition of the various parame-ters used in these criteria to be helpful. Note that all of the criteria defined here are valid for “whole ship models”, that is, models where rudder and propeller are mounted and the propeller is running at the estimated self-propulsion point.

Stability indices. The following linear dif-ferential equations in non-dimensional form for sway and yaw motions are considered:

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&& (6)

( ) vrrv NmYNYC ′′−′−′′= (7)



σ1,2 are the straight-line stability indices of the ship with zero rudder angle. Assuming that no external lateral forces or yawing mo-ments are acting on the ship, the sway velocity v and yaw rate r will approach zero with in-creasing time if (the real parts of) σ1,2 are nega-tive.

Stability levers. It can be shown that both stability indices are negative if C>0, or:

rr

r

v

vv Yum

N

Y

Nll ′≡

′+′′−′

<′′

≡′1

(8)

which implies that straight-line stability is ob-tained if the point of application of the forces due to sway should be located aft of the point of application of the forces due to yaw.

Nomoto’s controllability parameters (K, T). Assuming that the coupled inertia terms are negligibly small, i.e. 0== vr NY && , and intro-ducing forces and moments proportional to the rate of rudder angle change, following lin-ear differential equations for sway and yaw are obtained:

( ) ( ) δδ δδ ′′−′−=′′−′+′′−′+′′ && && YYrmYvmYvY rvv (9)

( ) δδ δδ ′′−′−=′′−′+′′+′′ && && NNrINrNvN zzrrv (10)

If terms in the second time derivative of the rudder angle are neglected, (9)-(10) can be transformed into the Nomoto equations:

( ) δδ ′′′′=′+′′+′+′′′ &&&& TK + Krr TTrTT 32121 (11)

( ) δδ ′′′′=′+′′+′+′′′ &&&& TK + Kvv TTvTT vvv 32121 (12)

These expressions are consistent with con-trol engineering practice, the coefficients be-ing expressed in terms of time constants (T'1, T'2, T'3, T'3v) and system gains (K', K'v). It can be shown that:

( ) rvrv

vv

NYmY N

YNNYK

′′−′−′′′′−′′

=′ δδ (13)

( )( ) rvrv

rrv NYmY N

NmYYNK

′′−′−′′′′−′−′′

=′ δδ (14)

11

1

σ ′−=′T ;

22

1

σ ′−=′T (15-16)

( )δδ

δδδYNNY

NYYNNYmT

vv

vvv

′′+′′−′′−′′+′′−′

=′&&&

3 (17)

( ) ( )( ) δδ

δδδNmYYN

YNNmYYINT

rr

rrzzrv ′′−′−′′

′′−′′−′+′′−′=′ &&&

3 (18)

Laplace transformation of (11) yields:

( )[ ] ( )( )( ) ( )

( )[ ]( )( )pTpT

rTTrTTpTT

ppTpT

pTKtr£

)()(

′′+′′+

′′′+′′+′+′′′+

′′′+′′+

′′+′=′′

−−

21

02102121

21

3

11

11

1

&

δ

(19)

The transfer function Y's(p) can be ex-panded in a Taylor series as follows:

( ) ( )( )( )

( )[ ]K+′′−′+′−′≅′′+′′+

′′+′=′′

pTTTK

pTpT

pTKpYs

321

21

3

1

11

1

(20)

For small values of p, i.e. for low fre-quency rudder motions, the transfer function can be replaced by a first order approxima-tion:

( ) ( ) [ ]K+′′−′≅′′+

′=′′ pTK

pT

KpYs 1

1 (21)

with K' given by (13), and T' by:

321 TTTT ′−′+′=′ (22)

In this way, second order yaw motion equation (11) is simplified to:

δKr rT ′=′+′′& (23)

The indices T' and K' represent ratios of non-dimensional coefficients:

tcoefficien damping yaw

tcoefficien inertia yaw=′T (24)

tcoefficiendampingyaw

tcoefficienmomentturning=′K (25)



If the rudder angle is suddenly put over from zero to δ0, the yaw rate and the change of heading are, respectively, given by

−′=′ ′

′−

T

t

e K r 10δ (26)

−′−′′= ′

′−

T

t

e Tt K 10δψ (27)

K' and T' can be interpreted as follows:

K' acts as a gain: a larger K' provides a smaller turning circle diameter and, therefore, a greater steady-state turning ability:

00

2

δ K

V D = (28)

T' acts as a time constant: a smaller T' provides a better responsiveness to the rudder, i.e. a quicker initial response to the helm and, therefore, good course-changing ability and good course-checking ability at the end of a manoeu-vre. A small, positive value for T also corresponds to good course-stability.

P index (Norrbin). A highly manoeuvrable ship, characterised by quick response to the rudder, good turning ability and course stabil-ity, will therefore have a small T and a large K value and, as a result, a large value for the Norrbin parameter P:

T

K

L

V

T

KP

2

2

2

1

2=

′′

= (29)

which is, approximately, the course change angle per rudder angle at one ship length travel after rudder execution:

( ) PT

KeTTK T

t =′′

≈

′+′−′= ′

−=′ 2

1

1

1ψ (30)

Norrbin (1965) proposed P>0.3 as a rea-sonable standard of course-changing ability. Later P>0.2 proved sufficient for large tank-ers.

Overshoot angle. According to Nomoto (1966), overshoot angles during zigzag tests are approximately proportional to K'T' (see Figure 4.2). A small overshoot angle can be the result of the combination of either good turning and fast response or good course sta-bility (large K, small T) or poor turning and slow response and or poor course stability (small K, large T).

For this reason, the overshoot angles basi-cally give no indication on turning ability and course stability, but on yaw-checking ability. However, the validity of this statement de-pends upon the magnitude of applied rudder angle: according to the recent research, the first overshoot angle in 10/10 zigzag manoeu-vre gives a good indication on the course-keeping ability.

Parameter P' introduced by Barr. Accord-ing to Barr (1987), a ship should have good handling properties (turning and course-checking) if

1370

630>

+′

′′

=′.

T

.T

K

P (31)

Indices proposed by Backero. Backero (1981, also 17th ITTC Manoeuvrability Committee, 1984) introduced new indices DG and AVC:

δ2sin2L

DDG = ; δ10.

L

AdAVC=

(32-33)

D and Ad being turning diameter and ad-vance, respectively; in (30), the rudder angle is expressed in degrees.



Figure 4.2 1st and 2nd overshoot angle dur-ing δ0/ψ0 zigzag test, calculated making use of Nomoto model, assuming rudder orders exe-cuted with dδ/dt =∞.

The indices DG and AVC, together with Norrbin’s P number and the width A of the hysteresis loop of the spiral manoeuvre, are proposed by Backero as a set of indices, inde-pendent of the rudder angle, which can be taken as representative of turning ability (DG), course and track changing ability (P, AVC) and course stability (A).

Index of ship manoeuvrability Q'. Bian-cardi and Dellwo proposed an index of ship manoeuvrability Q' where:

dr

dv

LQ

1=′ (34)

Q' measures the transient change in sway due to variations in yaw rate. It is smaller for ships which manoeuvre at a high rate of yaw with small changes in sway velocity than for ships that manoeuvre a high sway velocity and small yaw rate.

Recent research. Spyrou (1999) studied the effect of delayed control on a ship’s course-keeping capability. Stability criteria by Nomoto, Barr, Eda are treated.

From simulations using a mathematical model it has been shown by several authors, Oltmann (1996), Kijima & Furukawa (1998), that the course stability of fast displacement ships with low metacentric height can be a problem. In an analytical study Haarhoff & Sharma (2000) developed a course stability equation, which includes the effect of ship speed and GM:

[ ]0

2>

′′⋅

⋅′−′′+′−′′+′−′′+

′−′

GMm

FY

)xx(z)xx(z)xx(z

)xx(

nϕ

ϕβγγϕββγϕ

βγ

(35)

The equation reduces to the traditional stability criterion treated above as x′γ = l′r and x′β = l′ν for the case of slow speed and infinite metacentric height.

4.8. Prediction methods

Prediction of manoeuvring motion using empirical methods. More effort has been put into the simulation of the IMO standard ma-noeuvres using mathematical models to im-prove regression equations based on captive model test results.

Kijima et al. (2000) presented new im-proved regression equations for predicting the hull derivatives, the flow straightening factor and the wake fraction used in the MMG model, based on PMM tests. These equations are valid for both even keel and trimmed con-ditions. More advanced parameters which re-late to the shape of the aft body, are included. The turning circle and the 10-10 and 20-20 zigzag manoeuvres predicted for two ships which are not included in the database, agree well with manoeuvres obtained from simula-tions based on PMM test results on these two hulls. The method presented is valid for pre-dictions at model scale.

0

1

2

3

4

5

0 1 2 3 4 5K'T' δ0/ψ0

over

shoo

t ang

le /

ψ0

1st overshoot angle

2nd overshoot angle



Lee et al. (1998) used results from PMM tests for 12 low-speed high block coefficient ship models to derive a new regression for the estimation of parameters in the MMG model, which was shown to improve the prediction.

Lee et al. (1999) developed new empirical equations for the four linear derivatives in-cluding a stern profile parameter.

The type-ship concept, as described by Kose et al. (1996), was used by Lee and Shin (1998) to estimate the manoeuvrability for ships at different loading conditions.

Another prediction method is presented by Martinussen & Ringen (2000) who use a slen-der body theory and subsequent empirical cor-rections based on regression analysis and cross-flow theory for prediction of hull forces. The method is able to predict the different manoeuvring behaviour of a U-shaped aft body versus a pram stern shape.

Since the introduction of the IMO Interim Standards, Japan and Korea have each col-lected results from manoeuvring trials for new ships. The existence of this database has en-abled the development of methods that di-rectly predict the results of the IMO Res. A751 manoeuvres from basic ship parameters.

Haraguchi (2000, 2001) uses Nomoto’s equation and regression analysis on a database of full-scale trials to develop simple equations to estimate the results of standard manoeu-vres. The input parameters are simple ship characteristics and the output consists of over-shoot angles in zigzag manoeuvres and turn-ing circle parameters. The method produces good results for the turning circles but some improvement is needed for the 10-10 zigzag manoeuvre.

Estimation of manoeuvring motion using CFD. Manoeuvring motion can be estimated directly without using simulation models (lower-order force models) using unsteady

CFD techniques. Hydrodynamic forces are calculated by CFD and ship response by the equations of motion, and they are solved si-multaneously.

Akimoto (1997) performed the simulation of a sailing yacht using unsteady RANSE for the hull forces and lifting surface theory for rudder and keel forces.

Takada et al. (1999a) adopted a body-fixed grid system and introduced multi-block compu-tation to evaluate hydrodynamic force on the keel. Takada et al. (1999b) extended the method to 6-degrees of freedom motion of a submerged body with horizontal and vertical rudders.

Bellevre et al. (2000) calculated 6-DOF submarine manoeuvres using forces calcu-lated from RANSE code in steady conditions. McDonald (1996) and Davoudzadeh (1997) presented CFD manoeuvring simulation of a self-propelled submarine.

Izumi et al. (1999) combined hull force computation by a RANSE code and MMG-type representation of rudder and propeller forces. Results of simulated zigzag manoeu-vres with SR221 tanker hulls show qualitative agreement with measured results as seen in Figure 4.3.

Chen et al. (1999) carried out a berthing simulation by chimera multi-block CFD com-putation. Forces, which act on fender, are compared with the result of full-scale meas-urement. Figure 4.4 shows the pressure distri-bution around a berthing ship.

Ohmori (1998a) applied CFD code to un-steady problems by use of moving grid system to simulate PMM motions. Computed and measured time histories of hydrodynamic forces agreed well (see Figure 4.5).

Maekawa et al. (1999) estimated added mass by calculation of steadily accelerated motion using a RANSE code.



Figure 4.3 Time histories of a zigzag test by CFD and experiment (Izumi et al., 1999).

Figure 4.4 Pressure distribution around a berthing ship (Chen et al., 1999).

Figure 4.5 Computed and measured time histories of hydrodynamic forces (Ohmori, 1998).

5. MODEL TEST TECHNIQUES

5.1. Captive Model Tests

Review papers. Captive model test tech-niques are nowadays commonly used for pre-dicting ship manoeuvring characteristics. Tak-ing account of the variety of test types, the differences between and evolution of the con-cepts of the existing mechanisms and the large number of test parameters to be selected, at present each institution applies its own test methodology, mainly based on its own ex-perience and semi-empirical considerations.

In the frame of its tasks, the 22nd ITTC Manoeuvring Committee circulated a ques-tionnaire on captive model test techniques among the member organisations in order to acquire a thorough insight in present method-



ologies for selecting the experimental parame-ters. Thanks to the satisfactory response, the Captive Model Test Procedure, published in the ITTC Quality Manual, could be provided with quantitative data reflecting the present state-of-the-art.

A summary of the responses to the ques-tionnaire was given by the 22nd ITTC Ma-noeuvring Committee (1999). A more detailed overview was published by Vantorre (2000).

A major tool for experimental determina-tion of manoeuvring characteristics is the pla-nar motion mechanism. The installation of the CPMC (Computerised Planar Motion Carriage) at HSVA in 1975 is to be considered as a mile-stone in the history of ship model techniques. Oltmann (2000) describes the history of the creation of this facility and the modifications and improvements attained over the years.

Optimisation of experimental techniques. A captive manoeuvring test program should pro-vide all information required for determining a mathematical manoeuvring model. Sung et al. (2000) managed to obtain the full set of coeffi-cients of both Abkowitz and MMG type equa-tions by means of only six PMM runs, making use of a batch type least square estimator.

Test techniques involving six degrees of freedom. Captive model test techniques for determining a ship’s manoeuvring behaviour generally only focus on three or four degrees of freedom. In some situations, however, all six degrees of freedom have to be taken into account. In particular, this is the case for plan-ing craft; for this reason, a test program was executed with a fully captured model equipped with a six components load cell (Ikeda et al., 1999; Tajima et al., 1999).

Another application concerns the estima-tion of the manoeuvring performance of sub-merged body. In order to obtain roll-dependent coefficients, Rhee et al. (2000) de-veloped a coning motion device (see Figure

5.1), and discussed an experimental program composed of coning motion tests and horizon-tal PMM tests.

Figure 5.1 Apparatus of Coning Motion Test (Rhee et al., 2000).

Non-conventional captive tests. According to Eloot & Vantorre (2000), conventional harmonic PMM sway tests are not suitable for accurate low frequency tests, because the sway acceleration dependent force is rela-tively small compared to the sway velocity dependent force. Control inaccuracies may also affect the imposed maximum accelera-tion, especially at low frequency. Further-more, motions induced during PMM sway tests cannot be considered as very realistic. For these reasons, an alternative sway test was proposed (see Figure 5.2).

Figure 5.2 Alternative PMM sway test (Eloot and Vantorre, 1998).

A partly captured PMM test technique was developed by Katayama et al. (2000) in order



to measure unstable motions of a planing craft induced by periodic manoeuvring motion.

Ueno et al. (2001d) developed a new measuring system for steady wave forces and moment acting on a ship at zero speed. The system makes use of three torque motors ful-filling two functions: inducing restoring forces for surge, sway and yaw motion, and acting as counterweight for balancing steady wave forces and moment.

5.2. Free Sailing Model Tests

One of the tasks of the Committee con-sisted of preparing a procedure for free-running model manoeuvring tests (see paragraph 8.3).

In order to collect information about the present methods used for performing ma-noeuvring tests with free sailing – or free-running, that maybe is more common – mod-els, a questionnaire was put together and dis-tributed to 23 selected ITTC member organi-sations. As much as 15 responses were re-turned and a summary is given in Table 5.1 and Table 5.2.

The questions concerned the available test facilities, size of models, types of propulsion device, outfitting of model, type of tests car-ried out, etc. Correction of scale effects was of special interest to the committee.

Hull flow turbulence stimulation is used by all responding organisations. In some cases the rudder flow is stimulated as well. The methods are trip wire, studs or sand roughening strips.

In order to compensate for the excessive viscous resistance for the model the use of a towing force created by a fan or air-jet is sometimes used.

As an alternative method to correct for wake and viscous resistance scale effect, computer simulations may be used. Thus the results are corrected by means of simulation using the model test result to tune the simula-tion model and then simulating the full-scale predictions. This would be one way to predict the stopping distance provided that the full-scale engine and propeller characteristics are simulated reasonably well.

Appendages as bilge keels and bow thruster tunnels are always fitted when applicable.



Table 5.1 Summary of questionnaire responses.

Organisation 1 2 3 4 5 6 7 8

Basin 1 L (m) 300 65.5 110 - 56 - 69 40 B (m) 18 26 73 - 30 - 46 27.6 H (m) 6 3.5 6.4 - 4.5 - 4 2 Carriage Speed (m/s) 8 - 7.7 - - - 4 2 Model Speed (m/s) 4 - 2 4 2 Length (m) <10 4-6 1-7 - 2-4 - <4.5 <3

Displacement (m3) <5 0.5-1.5 <1.4 - 0.1-1 - <0.8 -

Basin 2 L (m) - - 3000 1800 2000 4000 220 80 or lake B (m) - - 1500 1300 500 700 190 80 H (m) - - 20 35 8 20 10 4.5 Model Speed (m/s) - - 2 3.5 Length (m) - - 1-7 - 2-5 3-9 <4.5 <3

Displacement (m3) - - <1.4 - 0.1-1 0.6-3.5 <0.8 -

Trim angle y n n y y s y y Measure-ments Roll angle y y y y y s y y Yaw rate y y s y y n y y Propeller thrust y n n y s s n y Rudder force y n n y s s y y Calibration 2/year b b&a daily 1/year b&a b b&a Sampling rate (Hz) 20 50 20 5 10 40 10 20 Time between runs (min) 20 0 5 0 15 - 3 10

Shallow water n n s n s n y s Bilge keels n y y y y y y y Tunnel thruster y y y y y y y - Turbulence stimulation y y s y y s y y Towing force s n s n n n s n

Tests Turning n y y y y y y y

Accelerated turn n - n n n n n y

Pull-out n y y y n y y n Zig-zag y - y y y y y y Stopping n - n n y y y y Direct spiral n - y n y y y n Reversed spiral n - n y y n n y Bow thruster n - y n n n y n Crabbing n - n n n n y n

(y = yes; n = no; s = sometimes; b = before tests; a = after tests)



Table 5.2 Summary of questionnaire responses (cont.).

Organisation 9 10 11 12 13 14 15

Basin 1 L (m) 25 35 88 150 170 80 64 B (m) 25 22 39 30 40 50 40 H (m) 1.25 3 0-3.2 5 5.5 0-9.5 2.5 Carriage Speed (m/s) 2.8 - 3.5 5 6 5 - Model Speed (m/s) 3 1.5 3.5 3.5 3.5 5 2.5 Length (m) <6.5 1.5-2.5 5 (1-7) <5 2-10 1.5-6 3-4.5

Displacement (m3) <2 0.03-0.1

0.8 (.1 - 4) <0.8 0.1-3

0.075-3.5 -

Basin 2 L (m) - - 4000 >3000 220 - - or lake B (m) - - 500 >2000 16.75 - - H (m) - - 7 >60 0-1.1 - - Model Speed (m/s) 2.5 6 <5 3 - - Length (m) - 1.5-2.5 6 (2-9) <8 2-12 - -

Displacement (m3) -

0.025-0.1 1 (0.1-4) <1.3 0.1-1.5 - -

Trim angle y s y y y s y Measure-ments Roll angle n s y y y y s Yaw rate y s y y y y y Propeller thrust y s y y s s s Rudder force s s y y s s y Calibration - - 1/year b 1/year b&a b Sampling rate (Hz) 100 analog 50 20 50 40 10 Time between runs (min) 20 - 10 - <30 10 10

Shallow water y n y n y s s Bilge keels - y y y y y y Tunnel thruster y y y y s y y Turbulence stimulation y y y y y y y Towing force s n s n n y s

Tests Turning y y y y y y y

Accelerated turn y y y - y y y

Pull-out n y y y y y y Zig-zag y y y y y y y Stopping y n y y y y y Direct spiral y y n y y y y Reversed spiral y y y y y y - Bow thruster y y y - n y - Crabbing n y y - n y -

(y = yes; n = no; s = sometimes; b = before tests; a = after tests)



6. SEA TRIALS AND VALIDATION

In general, ship manoeuvrability at design stage is estimated using theoretical methods, model experiments or both, but there is no guarantee that the ship will behave identically at sea, because of errors and uncertainties such as scaling and environmental distur-bances. Consequently, the predicted manoeu-vre should be validated by comparison with full-scale trials.

6.1. Sea Trials

Measuring System and Trial Data. Since the IMO has adopted Resolution A. 751(18), “Interim Standards for Ship Manoeuvrabil-ity”, most shipyards have been collecting their sea trial manoeuvring data in a more quantita-tive way, by using advanced navigational equipment and technology, although there are still many uncertainties to be revealed. To-ward this end, data on manoeuvring tests have been collected by the Ministry of Transport in Japan, and an up-to-date manoeuvring per-formance database has been created from this resource (Haraguchi et al., 1998).

Foremost among the available systems to-day, Global Positioning System (GPS) or dif-ferential GPS (DGPS) technology is used to accurately provide a ship’s position, course, heading and ground speed in sea trials. Light-body (1998) introduced a highly accurate GPS-based trial management and reporting system, which employs DGPS and other inte-grated data to produce a complete graphical report. Also, Kim, H.S. et al. (2000) devel-oped a sea trial measurement and analysis sys-tem. The stability of a DGPS signal can be checked by a stationary test; Figures 6.1 and 6.2 show typical data points from DGPS and GPS systems. The scatter of the DGPS data is clearly less than 1.0 m, compared with about 12 m for GPS. In Kim’s analysis, the time his-tory of other signals such as engine rpm and power, rudder angle, heading angle, ship speed, yaw rate and environmental conditions

(e.g. wind speed and direction) are recorded as well. The complete set of data provides good insight into the ship’s manoeuvring.

Satellite navigation and especially DGPS far outperform most traditional methods for position measurement. As an example, turn-ing trajectories of a 230K GT Ore Carrier as measured by the so-called chip log method, and by DGPS, are shown in Figure 6.3 (Ko-bayashi et al., 2000).

Figure 6.1 Stationary test results with refer-ence signal (Kim et al., 2000).

Figure 6.2 Stationary test results without reference signal (Kim et al., 2000).

Figure 6.3 Comparison of measured turning trajectories (Kobayashi et al., 2000).

-0.4

-0.3

-0.2

-0.1

0

0.1

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

latitude(m)

longitude(m)

-2

0

2

4

6

8

10

12

14

-1 0 1 2 3

latitude(m)

longitude(m)



Environmental Effects. As an effort to in-vestigate environmental effects on manoeu-vring motions, an experiment for measuring steady wave forces and moments acting on a VLCC model was carried out by Ueno et al. (2001a, 2001b). The authors used a system that enables the measurement of steady forces while the model’s periodic motion in waves remains unconstrained. Figure 6.4 shows that the model is free to pitch, roll and heave, while the other degrees of freedom are controlled by servomo-tors. The experimental data are compared with calculated results, by applying Ohkusu’s meth-ods for calculating added resistance in short head waves, to manoeuvring conditions that include oblique trajectories, turning, and both. The experimental results confirm that the cal-culation method provides practical prediction of steady short wave forces and moments act-ing on the model.

Forces and moments caused by wind are normally estimated from experimental results obtained in wind tunnel tests, since ship pro-files above the waterline are not simple. Fuji-wara & Ueno (2001) proposed a new estima-tion method for wind forces and moments, that uses the stepwise method in linear multiple re-gression analysis. Wind tunnel data for various ships built in recent years were collected as samples; the estimation method is examined by comparing with the method of Isherwood, Ya-mano and Yoneta. The longitudinal and lateral wind force coefficients [CX, CY], and yaw and roll wind moment coefficients [CN, CK] on a VLCC are shown in Figure 6.5 along with ex-perimental results and other estimates.

In order to estimate the effect of wind on trial manoeuvres, the 23rd ITTC Manoeuvring Committee performed simulations of the IMO standard manoeuvres in varying wind condi-tions with a container feeder (LPP=152 m) model, which included roll effects. Each stan-dard manoeuvre was made for four wind speeds (0, 5, 10, 15 m/s) and eight wind direc-tions (0, 45, 90, 135, 180, 225, 270, 315 deg) relative to the initial heading. The derived IMO criteria of advance, tactical diameter and

overshoot angles were calculated for each manoeuvre. Figure 6.6 shows the tactical diameter as a function of wind speed for the eight wind directions; it varies from 2.0 LPP to 2.6 LPP at the highest speed. Figure 6.7 shows the first overshoot angle in the 10-10 zigzag manoeuvre, varying from 7 to 16 degrees at the highest wind speed.

6.2. Validation

Ship handling simulators, based on mathe-matical modelling of ship motion, are widely applied, for example, to train seafarers, check the manoeuvrability of new ships, and design new harbours. Effective validation of a ship handling simulator is carried out by direct comparison of full-scale and corresponding simulated ship manoeuvres. Since the valida-tion of all ship manoeuvres is impossible, the problem of the validation on the whole is often reduced to the comparison of summary indices.

Validation of a complete modelling proce-dure is ideally achieved through (1) generation of hydrodynamic forces and

moments from captive model test data, to construct a mathematical model,

(2) comparison of simulated trajectories from the mathematical model with free running model test data, and

(3) further comparison of simulated trajec-tories from the mathematical model with full scale trial results.

Figure 6.4 General profile of a system for measuring steady wave load and ship motions in waves (Ueno et al., 2001a, 2001b).



Figure 6.5 Comparison of experimental results and predictions of wind force and moment coeffi-cients (Fujiwara et al., 2001).

Ueno et al. (2001c) have successfully exe-cuted this process, with captive and free run-ning model tests at a 1/24.5 scale, and actual ship trials. The simulation model was con-structed based on the captive model tests, and then validated through the free running model tests. At sea trials of the training ship, data on ship speed, propeller rpm, wind speed and di-rection, current speed and direction, etc. were collected, later allowing for a realistic simula-tion of the trials. In Figure 6.8, results of the free running model tests are shown in com-parison with the simulated results, for 35-degree rudder turns to port, and model speed corresponding to ship speed of 10 knots. The simulation model describes the manoeuvring motion of the test model quite well. On the other hand, the full-scale trial data of the

training ship are compared with those ob-tained by the numerical simulation in Figure 6.9. Even though the validated simulation model is used, its predicted trajectory differs from that of the sea trial, because of wind and current disturbances. Overall, however, the turning trajectory looks similar.

Full-scale and model tests of a 35000 dwt shallow-draft full-form bulk carrier were car-ried out by Zheng & Zhang (1998) to find ways of improving manoeuvrability. The simulation calculation, which has been com-pared with model and full-scale results, in-cludes the effects of a stabilising fin and fish-tail rudder with swash plate; also, two of the full scale tests were performed in the fully loaded condition.



Figure 6.6 Tactical diameter as a function of wind speed and direction for a loaded con-tainer feeder model.

Figure 6.7 First overshoot angle in the 10-10 zigzag as function of wind speed and direction for a loaded container feeder model.

Figure 6.8 35-degree port turning trajectory of free-running model and simulation (Ueno et al., 2001), showing x-y position, speed, drift angle, yaw rate, and thrust.

The propulsive performance and manoeu-vring characteristics of a cruise ship with an Azipod propulsion system were tested during sea trials, and comparisons were made with model test predictions by Kurimo (1998). Specifically, the manoeuvrability of the Azi-pod-equipped ship was compared with that of her sister ship using conventional diesel-electric propulsion.

300

310

320

330

340

350

360

370

380

390

400

0 5 10 15Wind speed (m/s)

Tac

tica

l Dia

met

er (

m)

0 45 90 135180 225 270 315

initial relative wind direction (deg)

5

10

15

20

0 5 10 15Wind speed (m/s)

1st o

vers

hoot

10-

10 (

deg)

0 45 90 135180 225 270 315

initial relative wind direction (deg)



Nielsen et al. (2001) compared predicted IMO manoeuvres for a 160000 dwt Suezmax tanker by five different methods: two predic-tions, two PMM test series, and one free-sailing test series. It was concluded that al-though all methods showed that the IMO In-terim Standards were met, the spread in re-sults is unsatisfactory.

Gofman & Manin (2000) discuss an analy-sis method in which elements of the modelled forces are validated independently with full-scale data.

Figure 6.9 35-degree port turning trajectory of ship (Ueno et al., 2001).

7. AUTONOMOUS UNDERWATER VEHICLES (AUV)

7.1. Introduction

The manoeuvring performance of un-manned underwater vehicles is an evolving field, even though there are at least several hundred different vehicles of the tethered and untethered varieties currently in operation. The relative immaturity of knowledge in ma-noeuvring follows from the two main types of missions performed by current vehicles: large-scale survey and low-speed inspection. In this review, the two mission types are referred to simply as “survey” and “inspection”, with the implication that most vehicles are created for one task or the other; there are only a few ve-hicles that are intended for both. The ma-noeuvring performance of a given vehicle, especially if the vehicle is designed from sound engineering principles, may play only a small part in typical survey and inspection missions.

Towed vehicles are not considered in this review, except a few which incorporate posi-tioning thrusters.

Survey Vehicles. Several fundamental and crucial problems have received the most at-tention, in the area of surveying, or long-range, vehicles. These pertain first to naviga-tion, typically handled through dead-reckoning, or with a long-baseline acoustic system (LBL). Other issues relate to the spe-cific system components which comprise a vehicle capable of executing missions of use-ful length, gathering meaningful images and data, and surviving the ocean environment. Hence, the following topics are described in many sources: batteries and power systems, propulsion design and performance, high-level mission control, sensor fusion, and im-age mosaicking, to name a few. High-level or mission control is, for the purposes of this re-



view, considered to be a separate task from flight control and manoeuvring.

In general, untethered vehicles intended for long survey work are of a conventional shape, having a simple cross-section, e.g., cir-cular, and possessing rudder and elevator con-trol surfaces, with a minimum of propellers. These attributes derive from the need for long-duration missions, and a controllable ve-hicle. As might be expected, the manoeuvring problem for these vehicles is not dissimilar to that for large submarines and aircraft. Several variations on the common geometry have been in use, however, specifically for in-creased manoeuvring capability, and they are discussed below.

Inspection Vehicles. Unlike survey vehi-cles, those designed for inspection or low-speed work are usually equipped with redun-dant propeller actuation which permits full six degree-of-freedom control at near-zero speed. Because the vehicles move comparatively slowly, the majority of inspection vehicles are tethered, allowing higher power and payloads, and, as a result, these vehicles often carry one or more manipulator arms, and high-performance lighting and camera systems. The main topic discussed below relating to inspection vehicles is low-speed positioning performance, which depends on accurate models and effective control strategies for non-linear thruster response.

The problem of manoeuvring for un-manned underwater vehicles can be developed from coefficient based modelling (Lewis, 1988), and is commonly studied using simula-tion and the same techniques for surface ves-sel simulation. With regard to the actual ma-noeuvring performance of vehicles, we note that a large portion of the available literature on manoeuvring is given in the context of control system design. As a result, presenta-tion here mixes pure hydrodynamic studies with some results from vehicles under closed-loop control.

7.2. Streamlined Vehicles at Low Speed

Streamlined vehicles which need low-speed capability are subject to two unique phenomena: cross-body thrust reversal due to reattachment, and dive-plane reversal due to buoyancy stiffness.

Cross-Body Thrusters. Beveridge (1971, 1972) performed some of the first tests with cross-body thrusters in submarine applications. Low-speed water jets created by thrusters are able to reattach to the faired body downstream, creating a reversal effect at the low-pressure region. There exist conditions in which the re-attachment degrades the effectiveness of the thruster by eighty percent or more, hence mak-ing it useless for manoeuvring and control of the vehicle. One specific solution suggested is the use of high-velocity, low-area jets, which are less likely to interact with the hull. How-ever, for realistically sized thrusters, significant cross-currents may require that a particular an-gle of attack not be exceeded, due to both the large drag force presented laterally across a ve-hicle, and due to reattachment (Watkinson et al., 1995). In general, faired vehicles employ-ing through-hull or cross-body thrusters are subject to the same design considerations as larger vessels, e.g., Carlton (1994). A proposed solution for bow thrusters is a simple ventila-tion tube, which allows pressure to equalize on either side of the hull; this approach can be ap-plied to submersibles.

A few current faired vehicles employ a cross-body thruster arrangement, for example the Proteus AUV (Whitney & Smith, 1998) and Cetus (Trimble, 2000). Proteus has a cy-lindrical cross-section, with small horizontal and vertical jets; Cetus has a flattened hull-form with three vertical jets only.

Dive-Plane Reversal. The inability of dive planes at low speeds to induce a sufficient moment to pitch a vehicle has been under-stood for some time in the context of larger submarines. The effect derives from passive



pitch stability, which does not scale with speed; the gain which maps elevator deflec-tion to depth rate undergoes a sign change at diminishing forward speeds, and limit cycling due to a Hopf bifurcation occurs with or with-out a closed-loop control operating (Papoulias & Papadimitriou, 1995).

Fin Arrangement. The presence of fore-aft asymmetric stabilizing fins in a hovering ve-hicle leads to strong coupling in all the direc-tions of motion; Strumpf (1967) developed guidelines for tail-stabilized survey-type vehi-cles which must also hover. In particular, such vehicles are highly unstable during hovering in a stern-to-bow current. One practical solu-tion proposed is the use of bow-stern symmet-ric control surfaces, i.e., large bowplanes. In addition to restoring stability, bow-planes add to manoeuvrability, and have been imple-mented on many more modern vehicles, nota-bly the Naval PostGraduate School (NPS) ve-hicle, Marius, and VORAM, discussed below.

7.3. Control

Survey vehicles often succeed in their mission with linear modelling and control sys-tem design, the linearization being made about a nominal forward speed. The vehicles employ control surfaces and streamlined bod-ies, both of which have a good linearization up to moderate angles of attack.

In inspection vehicles, passive roll and pitch stability may be very high, since the ve-hicles are often physically tall and thus have a good separation of buoyancy and weight cen-tres. In this case, only four degrees of freedom are controlled: yaw, depth (heave), surge, and sway. Coupling of sway, surge, and yaw mo-tions remains critical, however, and can be alleviated to some extent by proper layout and thruster location. As with dynamic positioning systems in surface vessels, a primary tool is the thrust allocation matrix, which translates between vehicle-frame forces and moments

and the thrust developed at each controller. Tethered vehicles which are operated manu-ally often map joystick (or equivalent) user commands through a similar matrix to drive the vehicle thrusters.

One of the few comprehensive texts in the area of control for marine vehicles is Fossen (1994).

Linear Control. Almost all underwater survey vehicles are designed to be controlla-ble through simple control logic, e.g., the in-dustrial PID-type control. An excellent exam-ple of this approach is the NDRE craft (Jalv-ing, 1994). This vehicle has a classical cruci-form arrangement of elevators and rudders forward of a single prop; the vehicle has rea-sonable roll and pitch stability, which allows the speed, depth, and heading loops to be de-coupled. During propulsion, the static roll an-gle is designed to be near zero, and a clean linear analysis of each decoupled system al-lows for conventional control system design (PID). The NDRE control system was suc-cessfully demonstrated in extremely long du-ration missions, wherein the command changes were small and slow enough that the near linearity of the vehicle was maintained. Similarly, gains were chosen to be small enough that actuator linearity held, i.e., no saturation or stalling occurred. The vehicle, with 4.31 m length, and speed 2.1 m/s, exe-cutes ten-degree heading changes without overshoot in about five seconds; it completes a 50 m depth change in about three minutes at a maximum pitch angle of 18 degrees.

A multivariable, self-tuning control algo-rithm was developed for a ROV by Goheen & Jeffreys (1990); the control law is linear, but contains an adaptation on its own parameters and is hence ultimately non-linear. Two schemes are developed both of which depend on favour-able open loop properties of the vehicle. First, an implicit scheme is considered, for which no model of the plant is asserted or created; the controller adjusts so that the observed output



follows some nominal dynamics, e.g. a damped second-order response. An explicit scheme uses and updates a simplified model of the vehicle, i.e., a time constant and gain mapping every in-put to every output. Simulations show that both approaches can accommodate long-term varia-tions in the vehicle response, such as would be caused by fouling of propellers.

The linear control of survey vehicles also makes frequent use of inner-outer loop de-signs. Specifically, a survey vehicle with rud-der and elevator achieves a steady-state turn-ing rate which scales with rudder position, and a pitch angle (for small angles) scaling with elevator position; the buoyancy moment will prevent the vehicle from pitching freely. Hence yaw and pitch angles of the vehicle are easily controlled directly through rudder and elevator. Next, considering that the yaw and pitch closed-loop dynamics are fast, they may each be incorporated into an outer loop, ser-voing cross-track error (in the case of an abso-lute navigation capability), and depth. In a typical inner-outer loop cross-track controller, the desired heading angle is the heading of the desired trackline, perturbed by a gain multi-plied by the cross-track error. Similarly, the pitch command can be perturbed by a gain multiplied by the depth error. In both cases, what enables the inner-outer approach is that the bandwidth of the outer loop is signifi-cantly slower than that of the inner loop. The below equations indicate the control laws for cross-track and depth servoing:

( )( )referencedesired

referencetracklinedesired

zzk

yyk

2

1

−=−+=

θφφ

(36)

where y represents the cross-track location, and z the depth of the vehicle; heading is φ and pitch is θ. The “desired” values pertain to the inner (fast) loops; the “reference” values pertain to the outer (slow) loops.

Robust Nonlinear Control. Low-speed ve-hicles can be controlled effectively by making use of various methodologies, including the

sliding mode technique (Slotine & Sastry, 1983); this was first applied to underwater ve-hicles by Yoerger et al. (1985, 1986). A Ben-thos RPV-430 was modelled as a simple inertia and a quadratic drag; the two model coeffi-cients were determined from step responses to thrust commands. The significance of the slid-ing mode approach is that it explicitly involves feed-forward action to eliminate the non-linear effects, and coupling to a PD-type of feedback to create a nearly linear closed-loop system.

Higher-level non-linear control, including adaptation of parameters during closed-loop operation, has been developed and imple-mented in other vehicles as well. Cristi et al. (1990) describes an approach wherein the dominant dynamic response is carried in a lin-earized model and controlled with a linear feedback law; but then this is augmented by a second control component, based on the slid-ing mode technique. This second term takes the form of a discontinuity that follows the sign of an aggregate error vector, i.e., distance to the so-called sliding surface. The advan-tages of this approach are first that the design of the linear control part can proceed from classical approaches, and second that the dis-continuous term provides robustness to the non-linearities and other uncertainties and dis-turbances. The sliding mode approach was also developed for underwater vehicles by Fossen & Sagatun (1991).

Healey (1992) presents a related strategy in which the linearized plant is used to de-velop optimal trajectories off-line, according to a quadratic penalty function; these trajecto-ries are again augmented by a non-linear part derived from sliding control. Application of a sliding mode approach was made to a realistic vehicle model by Healey & Lienard (1993); the vehicle described has forward and aft ele-vator and rudder pairs, leading to four plant inputs; the speed, depth, and heading control algorithms, however, were independent. Fi-nally, an experimental implementation of a sliding mode control law for the TATUI ROV is given by da Cunha et al. (1995). Track fol-



lowing tasks in the horizontal plane are con-sidered, which involve forward and sway mo-tions, concurrent with heading changes.

Other Control Issues. Fuzzy-logic and neural network approaches often have to their advantage simple, linguistic implementation, straightforward integration into mission-level program logic, self-adaptation to the point of good fault tolerance, and the ability to work without any model structure (Yuh & Lakshmi, 1990, 1993; Smith et al., 1995).

Insofar as streamlined vehicles cannot manoeuvre easily in the sway direction, one may consider the problem of path planning to have a non-holonomic constraint, which can be addressed using specific control formula-tions (Canudas de Wit & Sordalen, 1992, Sordalen et al., 1993).

7.4. Manoeuvring of Existing Vehicles

Observed Turning of Streamlined Vehi-cles. Odyssey-class vehicles have been em-ployed in an integrated Autonomous Ocean Sampling Network (AOSN), which involves remote docking to deep-water moorings. Re-sponse of these vehicles during docking gives a good indication of manoeuvrability; the streamlined vehicle is 2.1 m in length, with a nominal forward speed of 1.4 m/s. In one case (Feezor et al., 1997), the vehicle completes a 180-degree turn with about 20 m cross-track deflection, measured by acoustic navigation. In another test, the vehicle completes a 180-degree turn in approximately fifteen seconds; the dead-reckoned turning diameter is about 15 m (Singh et al., 1997).

Similar docking experiments with the Re-mus vehicle show comparable results; Remus has a minimum length of 1.35 m, and a long-range speed of 1.5 m/s. The turning circle dur-ing homing has a diameter of approximately 20 m (Stokey et al., 1997).

Inspection Vehicles. Detailed hydrody-namic tests were made with the Dolphin 3K vehicle (Nomoto & Hattori, 1986); this vehi-cle is representative in geometry and layout of many tethered inspection vehicles. Static tests indicate that relatively simple streamlining steps, such as rounding flotation block corners and using structural members of circular cross-section, have significant impact. Table 7.1 lists the reported coefficients, non-dimensionalised with ρ/2 and the projected areas (for Cd) or the volume of the vehicle’s envelope (other coefficients). The coupled added mass terms were found to be negligible.

Table 7.1 Dolphin 3K vehicle: hydrody-namic data.

Cd (forward) 0.67 Cd (backward) 0.74 Cd (side) 0.98 Cd (upward) 0.81 Cd (downward) 1.58 A'11 0.07 A'22 0.077 A'33 0.131 A'44 0.08 A'55 0.123 A'66 0.085 K'p|p| 0.133 M'q|q| 0.288 N'r|r| 0.243

Another ROV which has been character-ised hydrodynamically is the ROMEO ROV, Caccia et al. (2000). This vehicle has signifi-cant thruster-hull interaction effects, and the experiments were made using a free vehicle and system identification techniques. Table 7.2 gives the coefficients, in MKS units. The vehicle has a height of one meter, a width of 0.9 m, a length of 1.3 m, and an in-air weight of 450 kg. Eight thrusters provide for posi-tioning, but they interact with the hull and with each other to reduce the effectiveness compared to thrusters in open water. The rela-tive efficiency of the thrust action in each di-rection is given in the table as η. A series of control tests conducted using gain scheduling, wherein the vehicle model is linearized about an operating point and interpolations are made between different linear controllers, was made for the ROMEO vehicle (Caccia & Veruggio, 2000).



The VORAM vehicle has a single vertical cross-body thruster, and elevators in the wake of two main propulsors, presenting a highly non-linear system for control (Lee et al., 1999). The vehicle is 2.8 m in length, with a flattened cross-section. Development of a non-linear, discrete-time control system leads to closed-loop depth changes of about 1 m in ten seconds.

Survey Vehicles. A brief study of an unusu-ally-shaped vehicle was made by Anderson (1992); the vehicle was an early form of the Autonomous Benthic Explorer (ABE), currently operated by Woods Hole Oceanographic Institu-tion. This vehicle presents three streamlined cy-lindrical hulls, connected together by struts to form a V-shape, as seen from the front. Drag and lift coefficients of the hull are given in Table 7.3; the drag data are based on the projected area in the direction of motion. The lift value, rele-vant for motions in the pitch/depth plane, is based on the planform area of the vehicle, and is thought to be dominated by lift forces on the struts. Additionally, the lift value given is an av-erage, as the vehicle exhibits a localised stall behaviour in the range α = 5÷20°.

Table 7.2 Coefficients of the ROMEO ve-hicle.

Zw -44.7 ηN 0.60

Zw|w| -430.3 Xu -46.9 (forward)

ηZ 0.56 -57.9 (reverse)

Nr -20.5-23.8

(low speed)

Xu|u| -306.2-331.4

(forward) (reverse)

Nr|r| -49.5-30.8

(low speed)

ηX 0.730.80

(forward) (reverse)

Table 7.3 ABE model: Hydrodynamic data.

Cd (forward motion) 0.024

Cd (backward motion) 0.048

Cd (side motion) 0.076

Cd (upward motion) 0.077

Cd (downward motion) 0.080

Sideslip lift slope 8.5/rad

Table 7.4 Marius vehicle: hydrodynamic data.

X'u|u| -534 (fwd) M'w 6200 (stat)X'u|u| -844 (rev) 6450 (dyn)X'vv -1400 (stat) M'δe -474 -800 (dyn) M'δa 760X'δrδr -1100 M'w' -1730X'δaδa -1000 M'q -2400X'rr 512 M'q' -420Y'v -3800 (st/dyn) N'v -1580 (stat)Y'v|v| -7300 (stat) -1410 (dyn) -12900 (dyn) N'v|v| 1510 (stat)Y'δr 1450 1940 (dyn)Y'v' -4450 N'δr -895Y'r 1330 N'v' 822Y'rrr 3570 N'r -833Y'r' 347 N'rrr -191Z'w -24900 (stat) N'r' -245

-24500 (dyn) m' 5820Z'δe -842 I'yy 360Z'δa -5190 I'zz 364Z'w’ -11500 X'g -5220, 0, 5000Z'q 7960Z'q' -1490

(Note: primes in subscriptsindicate time derivatives)

PMM experiments with Marius, a “flat-fish” type vehicle, provide a more compre-hensive set of linear manoeuvring coefficients (Egeskov et al., 1994, Aage & Smitt, 1994, Aage & Larsen, 1997). It should be pointed out that this vehicle has as actuators: two large forward control surfaces (“ailerons”, δa), three vertical and one lateral cross-body thrusters, a large elevator aft (δe), and twin shrouded propellers aft, each with a rudder in the wake (δr). Comparatively, Marius repre-sents an extremely well-actuated vehicle. Co-efficients are given in Table 7.4; the vehicle was originally considered to be open-loop un-stable in both pitch and yaw.

PMM experiments were also conducted for the AUV-HM1, revealing an unstable yaw mode (Chiu et al., 1997). The Aqua Explorer 2 vehicle (Kojima et al., 1997) is a stream-lined vehicle designed for relatively low-



speed inspection of underwater cables. This vehicle has forward elevators, and two main propulsors, separated along the sway axis, for heading control. A one meter step change in depth for this vehicle is demonstrated to settle (with small overshoot) in about twenty sec-onds, for a forward speed of 1 m/s. Finally, we note a fairly large AUV, the R-1 device, with a diesel engine for long-term power (Ura & Obara, 1997), which performs depth changes of 40 m in about five minutes.

Behaviour in waves. Autonomous vehicles are performing many missions near the shore-line and in shallow waters, which can provide a highly energetic wave environment in com-parison with very deep water. In still water, it has been known for some time that large submarines are affected by the free surface and that extra trim is usually required for op-eration in its proximity. A very large AUV, the LSV 1, was used to experimentally cor-roborate these effects, and the data provide a basic description of free-surface effects (Humphreys et al., 1999).

A potential flow numerical analysis and experimental investigation of wave forces on a lightly-damped, submerged body (Musker, 1985) shows the following effects of waves. First, in regular waves, a neutrally-buoyant, streamlined cylindrical body, with center-line located z = 0.18L below the surface, and being towed at U = 0.09(gL)½ into head seas, the heave motion is approximately 25% of the wave height, for λ/L = 1.75; the heave is very small for λ/L ≤ 0.75. In a Bret-schneider wave field, with modal λ/L = 2.0, z = 0.20L, and U = 0.12(gL)½, a similar body undergoes a depth standard deviation of about 0.03z.

More recently, a boundary integral method has been developed for the purpose of charac-terizing vehicle motions in a wave field (An-anthakrishnan & Zhang, 1998). These calcula-tions involve a stationary vehicle. For the con-ditions of z = 0.5D, λ/L = 2.0, H/L = 0.18

(wave height), and d = 2.0L (depth) one ob-tains, per unit beam of the vehicle, suction and surge force amplitudes, respectively, for a following wave:

22 00500250 gL.X;gL.Z ρρ == (37)

With z = 0.25L, these forces are

22 00600400 gL.X;gL.Z ρρ == (38)

This reference also shows that during operations near a flat bottom, the vehicle tends to “squat”, with Z ~ 0.001 ρU2L2 for an altitude of 0.15L; this force decays rapidly with increasing distance from the bottom.

An estimation of the wave field from the motions of a vehicle, and a subsequent predic-tive surge controller has been suggested by Riedel & Healey (1998).

A controlled wave experiment with a free-swimming vehicle was performed at the David Taylor Model Basin, using an Explorer series vehicle (An & Smith, 1998). The re-sponses were obtained with the vehicle under closed-loop fuzzy attitude control, not at-tached to any carriage, in regular following, head, and beam seas. With a vehicle depth of z = 0.94L, and U < 0.33 (gL)½, H/L = 0.19, the vehicle undergoes significant pitching mo-tions of near four degrees, particularly in fol-lowing seas; in beam seas, coupling of roll and pitch occurs, with several degrees of mo-tion on each axis. Worst-case surge accelera-tions are 0.07g in the case of a following sea; significant sway and heave accelerations also occur for beam sea conditions.

7.5. Non-Traditional AUV’s

This section describes some departures from the traditional composition of propellers and control surfaces. A number of these vehi-cles are biomimetically-derived, that is, they borrow their form or motion, or both, from



living animals. It is a generally accepted fact that most biological swimmers are far supe-rior to the traditional vehicles, perhaps in the area of propulsive efficiency, and clearly in the area of manoeuvring (Sfakiotakis et al., 1999). A systematic classification of fish ma-noeuvrability and speed was carried out by Bandyopadhyay et al. (1997), along with an experiment with manoeuvrable fish in a maze. The authors report that for a given turning ra-dius, non-dimensialised with body length, lat-eral accelerations are about one order of mag-nitude less than those of existing small un-derwater vehicles.

The tuna and dolphin are extremely high-performance swimmers, and this fact has moti-vated at least several robotic versions (Trian-tafyllou et al., 1996; Anderson et al., 1997; Na-kashima & Ono, 1999 (dolphin)). While the MIT robot (Triantafyllou) is constrained to swim in a straight line, the Draper VCUUV (Ander-son) and the dolphin robot are autonomous de-vices, for which flight controllers have been im-plemented. The VCUUV is 2.4 m in length, mimicking a tuna in both shape and motion, and systematic series of manoeuvring tests were per-formed. The vehicle achieves longitudinal accel-erations of 0.06g; a hard tail turn from straight-line swimming near 1 m/s achieved a near 180-degree turn in 12 s; the peak turning rate is above 70 degrees per second.

Fish which inhabit reefs, wave zones, and close waters such as streams typically employ pectoral fins as well as other fins and append-ages for high manoeuvrability. Among spe-cies, the fins may be highly articulated, and employ either or both a lift-based stroke (e.g., a bird wing), and a drag-based stroke. A vehi-cle employing drag-based pectoral fins has been developed by Kato (1999, 2000), who demonstrated a fuzzy-logic control algorithm capable of driving the fish along paths in the horizontal plane. Lift-based flapping foil pro-pulsion has been considered in detail by Read et al. (2001) for a rectangular foil in this ex-periment, the net manoeuvring forces (normal

to the incident flow) are about twice as large as can be obtained with an equivalent zero-camber wing at a static angle of attack. A spe-cific application of flapping foils to vessels is discussed in Yamamoto et al. (1995).

Another novel vehicle which has been un-der development for some time is the Pilot-fish, from Nekton Technologies (Hobson et al., 1999). This craft is an oblong ellipsoid with four actuated fins arranged around the minimum circumference. Each fin is driven harmonically near 20 Hertz, about a twist axis by large motors; the fins are constructed of a compliant material such that thrust can be generated through the twisting, which couples the fluid and the resonant structure. The vehi-cle is controllable and reasonably uncoupled in all six degrees of freedom, due to the fact that each fin essentially provides vectored thrust of variable magnitude.

8. PROCEDURES AND REVIEW TASKS

8.1. Manoeuvring Trial Code

This procedure has been rewritten based on the 14th ITTC trial code. An effort was made to associate manoeuvres with handling characteristics and some manoeuvres added.

Validation data: Full scale trials of the Esso Osaka are referenced.

8.2. Captive model test procedure

Minor changes have been made to this procedure which still requires the addition of circular motion tests.

Validation data: Time trace of the meas-ured forces in PMM tests need to be identi-fied.



8.3. Free sailing model test procedure

This procedure is completely new. Its de-velopment was supported by questionnaire.

Validation data: Esso Osaka data base is referenced.

8.4. Validation procedure for manoeuvring simulation models

This procedure is completely new. It has been difficult to develop because of the com-plexity of the structure of mathematical mod-els. The development process needs to be pur-sued.

8.5. Procedure for evaluation and documentation of HSMV manoeuvrability

This procedure is completely new. Its development has been inspired by conventional ship methods with attention to specific problems (e.g. dynamic effects, speed range, …).

Validation data: no such data has been identified. The issue of validation data is more difficult due to the diversity of HSMV architecture.

8.6. Review of methods for predicting manoeuvring in shallow and confined waters

Methods described in literature for pre-dicting the manoeuvring behaviour of ships navigating in areas characterised by limita-tions in depth and width are described in Ap-pendix A. Following aspects are covered:

Shallow water effects; Effect of muddy bottoms; Horizontal restrictions of the waterway; Ship-ship interaction; Squat effects.

A short, general description is given of each of the discussed effects. As a main ob-jective, however, an attempt was made to give an overview of published practical methods and formulations, and to provide a selection of validation data, if available, which can be used to assess the reliability of the various methods.

By creating a separate appendix, the Ma-noeuvring Committee suggests that the review would be corrected, extended, updated and provided with (new or existing) validation data by the following Committees.

One alternate way to maintain this infor-mation up to date is to transform it in a rec-ommended procedure for predicting shallow water effects on manoeuvring performance.

8.7. New requirements

All procedures – as well as the review on manoeuvring prediction methods for shallow and confined water – should be updated and completed.

Given the increase in the capability of CFD, a procedure for CFD applications in manoeuvring field might be of interest. This procedure would have strong similarities with CFD procedures in the resistance field.

9. CONCLUSIONS

Forces Use of CFD, particularly viscous flow

simulations, is more widespread and more complete in the description of the flow (free surface) and the complexity of the geome-try (hull/rudder/propeller interaction)

Potential flow methods are still being de-veloped and used for restricted water appli-cations, transient manoeuvres (e.g. berth-ing)…



Simulation Use of unsteady CFD for simulation of ma-

noeuvres is developing Regression models are being developed to

take into account the hull shape in the after-body

Tugs and towing simulations have received more attention

Not much progress (at least not published) on 6dof models (combining manoeuvring and seakeeping)

Model test techniques Few noteworthy developments in new test-

ing techniques A test method using the coning motion of

submarines has been developed to measure roll-dependent coefficients

Very few new published data showing evi-dence of scale effects. Most published comparisons show reasonable agreement between full scale and model scale results.

Sea trials and validation, IMO There is little change since the last ITTC in

terms of availability of accurate full-scale data for validation use (trial results + de-tailed ship information). This data is clearly insufficient.

Large efforts are being made in Japan and Korea to collect full scale trial results on the IMO criteria.

The accuracy of the prediction of IMO ma-noeuvres at design stage needs to be im-proved.

The application of the IMO criteria requires that methods for correcting for loading con-ditions be developed

The application of the IMO criteria requires that methods for correcting for environ-mental conditions be developed

AUV The prediction of AUV manoeuvrability

requires that similar experimental ap-proaches be applied to AUV as is the case for surface ships.

Full scale trials procedure Much work is required in order to develop

correction methods for environmental con-ditions, e.g. by on-line simulations…

Captive model test procedure This procedure needs to be further im-

proved, in particular by addition of a sec-tion on circular motion tests

This procedure requires a set of validation data for captive model tests in form of time traces of forces for a given ship and a given motion history (i.e. PMM).

Free-sailing model test procedure Validation data for other hull forms than

Esso Osaka are required.

Validation of simulation models procedure Although this is a particularly difficult

topic, a first draft of the procedure has been written which outlines the general philoso-phy. However, several issues remain out-standing in the validation process.

HSMV procedure This procedure lacks validation data.

9.1. Recommendations to the Conference

Adopt the amended Procedure “Manoeu-vring Full Scale Manoeuvring Trials Procedure” 4.9-03-04-01,

Adopt the amended Procedure “Manoeu-vring Captive Model Test Procedure” 4.9-03-04-03,

Adopt the Procedure “Manoeuvring Free-sailing Model Test Procedure” 4.9-

Adopt the Procedure “Manoeuvring Evaluation and Documentation of HSMV Procedure” 4.9-

Adopt as an Interim Procedure “Manoeu-vring Validation Procedure for Manoeu-vring Simulation Models” 4.9-



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APPENDIX A. MANOEUVRING IN SHALLOW AND CONFINED WATERS

A.1 Introduction

A ship’s behaviour in general, and her manoeuvrability in particular, depends on the depth h of the navigation area. A rather arbi-trary distinction can be made between (PIANC, 1992):

deep water h/T > 3.0 medium deep water 1.5 < h/T < 3.0 shallow water 1.2 < h/T < 1.5 very shallow water h/T < 1.2

The effect of depth restrictions can be no-ticed in medium deep water, is very signifi-cant in shallow water, and dominates the ship’s behaviour in very shallow water.

The effect of water depth on ship manoeu-vrability is very often illustrated by comparing standard manoeuvres at different values of wa-ter depth. Actually, such a comparison is mostly based on simulations, as standard ma-noeuvres are always carried out in deep water; trials in shallow water are so rare that the ships involved have become legendary (e.g. Esso Osaka). Indeed, water depth restrictions not only affect the ship’s manoeuvring behaviour; moreover, they are mostly related to other ap-plications. Deep water manoeuvring is mainly investigated for assessing course stability, op-timising ship control, predicting standard ma-noeuvres. Studies of ship behaviour in shallow water, on the other hand, are often related to conditions for which a ship is not particularly designed: course keeping in access channels and canals, swinging, berthing, unberthing in harbours, tug assisted manoeuvres, slow and reversed speed and/or propeller rate. Studies of ship manoeuvring in shallow water are more often carried out in the frame of harbour design or pilot training, while deep water manoeu-vring is more a concern for ship designers. This polarisation is even more explicit if manoeu-vring in horizontally restricted navigation ar-eas is considered.

A description of a ship’s manoeuvring be-haviour in (horizontally and vertically) re-stricted water is therefore not only more com-plex due to the occurrence of additional pa-rameters such as depth to draft ratio and bank clearance, but also due to the fact that several parameters determining a ship’s kinematics (forward speed, drift angle, rate of turn) and control (rudder angle, propeller rate) belong to a more extended range.

In this review of methods for predicting the effect of geometrical restrictions of the navigational areas on ship manoeuvrability, the emphasis is laid on practical formulations. Following aspects will be focused on:

effect of depth restrictions (A.2); effect of fluid mud layers (A.3); effects of horizontal restrictions (A.4); forces excited by other ships (A.5); squat effects (A.6).

A.2 Effect of water depth restrictions

Effect of water depth on standard ma-noeuvres. Data of full-scale manoeuvring tri-als with large ships in shallow water are so scarce that the few existing examples have become legendary. The most complete pub-lished set of trial results concern the Esso Osaka experiments carried out in 1977 (Crane, 1979). The main conclusions were summarised by the 16th ITTC Manoeuvrabil-ity Committee (1981):

In shallow water, turning circle tactical di-ameters increase by as much as 75% with 20% under keel clearance, while drift angle and related speed loss reduce relative to turning in deep water. With 50% bottom clearance, the changes from deep water turning were much less.

Checking and counter turning ability are reduced as water depth decreases from deep water to an intermediate depth (50% bot-tom clearance) and then increase again at more shallow depths, becoming better than in deep water at 20% under keel clearance



in these trials. This phenomenon is closely related to the apparent reversal in controls fixed course stability shown by the trial re-sults, where stability first decreases when moving from deep to medium water depths and then increases again as water depth be-comes very shallow.

The greatest effect of decreasing water depth on the stopping of this single-screw tanker from slow speed, is an increase in heading deviation to starboard, which var-ies from 18 to 50 and then to 88 degrees in deep, medium and shallow water, respec-tively. Stopping distance is substantially in-dependent of water depth.

Effect on lateral force and yawing mo-ment: overview. Several authors proposed formulae for the shallow to deep water ratio of the linear hull force derivatives. This im-plies the availability of a set of expressions of estimating the deep water derivatives, the formulation of which is mostly based on slen-der-body strip methods making use of the dis-tribution of the two-dimensional horizontal added mass coefficient along the length of the hull.

Most of the formulae accounting for the shallow water effect are therefore based on an analytical approach of the influence of the presence of a bottom on the two-dimensional horizontal added mass coefficient of circular, elliptical and rectangular body sections.

Following (semi-)empirical formulations will be discussed in this review:

formulations based on expressions by Sheng (1981) for the added mass of two-dimensional elliptical sections: linear de-rivatives according to Clarke et al. (1983, 1997), and water depth corrections by Ankudinov et al. (1990), covering a greater range of water depths, manoeu-vring coefficients and ship parameters;

expressions for coefficients occurring in the MMG mathematical manoeuvring model,

according to Hirano et al. (1985), Kijima et al. (1990), Kobayashi (1995);

empirical formulae for added inertia coeffi-cients proposed by Li & Wu (1990).

Formulations based on Sheng’s formulae. Sheng (1981) showed that for elliptical sec-tions the deep to shallow water ratio of the added mass can be represented by

2

210

++=

∞ T

BK

T

BKK

C

C

H

H (A1)

where

1 with

1

22

31

211

1

30

20

0

F

aK

T

hF

F

c

F

b

F

aK

F

b

F

aK

=

−=++=

++=

(A2)

with following values for ai, bi, ci:

a0 = 0.0775; b0 = -0.0110; a1 = -0.0643;

b1 = 0.0724; c1 = -0.0113; a2 = 0.0342.

After integration, Clarke et al. (1983) ob-tained following deep to shallow water ratios for the derivatives:

2

210

2

210

2

210

2

210

2

210

2

210

3

1

2

1

15

8

3

2

15

8

3

2

105

24

5

2

15

8

3

2

++=

++=

++=

++=

++=

++=

∞

∞

∞

∞

∞

∞

T

BK

T

BKK

'N

'N

T

BK

T

BKK

'Y

'Y

T

BK

T

BKK

'N

'N

T

BK

T

BKK

'Y

'Y

T

BK

T

BKK

'Y

'N

T

BK

T

BKK

'Y

'Y

r

r

r

r

v

v

v

v

r

r

v

v

&

&

&

&

(A3)



Clarke (1997) revised this method and published corrected values for ai, bi, ci:

a0 = 0.0774; b0 = -0.0151; a1 = -0.0125;

b1 = 0.1674; c1 = -0.0199; a2 = 0.0431.

In both cases, the expressions are applica-ble for 1.25 < h/T <∞.

Ankudinov et al (1990) published a water depth correction matrix based on (A3), but extended to a greater range of water depths (1.085 < h/T < 5) and ship parameters (CB ≤ 0.85). Shallow water effects on hull coeffi-cients are summarised as follows:

Linear sway-yaw terms:

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) fnrN

Nfnv

N

N

fyrY

Yfyv

Y

Ygnr

N

N

gvN

Ngv

Y

Ygv

Y

Y

r

r

v

v

r

r

v

v

r

r

v

v

r

r

v

v

=′′

=′′

=′′

=′′

=′′

=′′

=′′

=′′

∞∞

∞∞∞

∞∞∞

;

;;

;;

&

&

&

&

&

&

&

&

(A4) Non-linear sway-yaw terms:

( ) ( )

( ) ( )

( ) ( )

( ) ( ) gnrN

N

N

N

gvN

Nfnv

N

N

fyvY

Y

Y

Y

fnrY

Yfnv

Y

Y

vr

vr

vrr

vrr

rr

rr

vv

vv

vr

vr

vrr

vrr

rr

rr

vv

vv

=′

′=

′

′

=′

′−=

′

′

=′

′=

′

′

=′

′−=

′

′

∞∞

∞∞

∞∞

∞∞

;4

5

4

9

;4

5

4

9

(A5)

Surge terms:

( ) ( )

( ) ( ) frvX

X;frv

X

X

gnrX

X;gv

X

X

vv

vv

vr

vr

rr

rr

u

u

=′′

=′′

=′′

=′′

∞∞

∞∞&

&

(A6)

with

21

21

10 15

8

3

2

++=T

BK

T

BKKgv

2

12

110 105

40

15

8

++=T

BK

T

BKKgnr

5051 .fnv.fyv −= 2

12

110 105

24

5

2

++=T

BK

T

BKKfyr

2

12

110

++=T

BK

T

BKKfnv

21

21

10 3

1

2

1

++=T

BK

T

BKKfnr (A7)

where

B

T

F

.K:

T

Bfor;

F

.K

F

.

F

.

F

.

F

.K

F

.

F

.

F

.K

13704

03420

00007650011300724006430

000068001100077501

22

5321

5320

=>=

+−+−=

+−+=

2

1 1;1with

+=−=

L

BBCB

T

hF B (A8)

Formulations based on the MMG model. For the velocity derivatives occurring in the MMG mathematical model, Inoue et al. (1981) proposed empirical formulae for the deep water case, where forces and moments are non-dimensioned by means of ½ρL2U2 and ½ρL3U2, respectively. For the linear de-rivatives, following formulae were proposed in deep water:

( )L

Tk'Y

L

Tkk.'N

L

Tk'N

L

T

L

BC.k'Y

rr

vBv

4540

412

2 π

π

=−−=

−=

+−=

(A9))

while the non-linear derivatives for the deep water case were approximated by:



( )

( )L

TC

B

T.Y

L

T.C

B

T.C

B

TY

L

T.C

B

T.Y

L

TC

B

T.Y

Bvrr

BBvvr

Brr

Bvv

−−=′

−+

−=′

−=′

+−=′

1955

2081262114

0703430

2

1152

2

( ) ( )

L

T.C

B

T.N

L

T.C

L

B.C

L

B.N

L

T.C

L

B.N

L

T.C

B

T.C

B

TN

Bvrr

BBvvr

Brr

BBvv

−=′

−+

−=′

−=′

−−−

−=′

050500

72222350120

08904730

2081019178

2

2

(A10)

Hirano et al. (1985) have included the shallow water effect in semi-empirical expres-sions for the linear velocity derivatives. In the latter, the effective aspect ratio of the hull in deep water, k = 2T/L, is replaced by an effec-tive ship aspect ratio in shallow water:

λππ

+

=

h

Tcot

h

T

h

Tk

kke

222

(A11)

in which the coefficient λ has to be adjusted experimentally. Values proposed are λ = 2.3 for Y'v, λ = 1.7 for N'v, λ =0.7 for Y'r and N'r.

Kobayashi (1995) proposed following ex-pressions for the linear derivatives:

( )L

BpCk

L

BpC

h

Tk

h

Tk

Y

Y

B

B

q

v

v

+

+

+

=′

′

∞2

2cot

2

1

1

2

1

π

ππ

π

(A12)

( ) ( ) ( )

1

22

1

1

q

r

r

r

r

v

v

h

Tcotk

h

TN

N,

Y

Y,

N

N

+

=′′

′′

′′

∞∞∞ ππ

(A13) where p has to be determined for each ship model from the results of captive model tests in deep water, and

q1 = 3

q2 = 1.4 for N'v; = 1.2 for Y'r; = 0.5 for N'r

For the added mass and added moment of inertia in shallow water, following formula-tions were proposed:

( ) ( )4

21 3

q

rzz

rzz

v

v

h

Ttanq

NI

NI,

Ym

Ym

+=

′−′′−′

′−′′−′

∞∞

π&

&

&

&

(A14) with

q3 = 0.21 and q4 = 1.2 for vYm &′−′ q3 = 0.15 and q4 = 1.2 for rzz NI &′−′

Starting from formulae (A9) and (A10) for the derivatives in deep water, Kijima et al. (1990) proposed following corrections for shallow water conditions:

deepshallow Dh

TfD

= (A15)

For D = Y'v, Y'vv, Y'vrr, N'v, N'r, the correction factor f is suggested to be:

h

T

h

Th

Tf

n−

−

=

1

1 (A16)

with

51147

4250

801132

741260

400

.k.nNDT

BC.nND

.T

BC.nYD

.T

BC.nYD

T

BC.nYD

r

Bv

Bvrr

Bvv

Bv

+−=⇒′=

=⇒′=

+−=⇒′=

+−=⇒′=

=⇒′=

(A17)



For the other derivatives, following correction factors are assumed:

3

3

2

211

+

++=

h

Ta

h

Ta

h

Ta

h

Tf (A18)

with ( )

−+

−=

+−

=

−+

−=

⇒

′−′−′=

25019738

23018537

5312655

2

3

2

2

2

1

T

BC

T

BCa

T

BC

T

BCa

.T

BC

T

BC.a

XmYD

BB

BB

BB

ur &

(A19)

( )( )( )

−⋅−=−⋅=−⋅−=

⇒′=55

552

551

1102813

110161

1101560

B

B

B

rr

C.a

C.a

C.a

YD (A20)

( )B

vvr

CB

Twith

..a

..a

..a

YD

−=

−⋅+⋅−=−⋅+⋅−=+⋅−⋅=

⇒′=

1

14001055210089

2741075010084

2201048010152

4243

4242

4241

τ

ττττττ

(A21)

( )( )

( )

+−⋅−=−−⋅=

+−⋅−=⇒′=

467110981

413110771

57110240

33

32

31

B

B

B

vv

C.a

C.a

C.a

ND (A22)

( )B

rr

CB

Twith

.a

.a

.a

ND

−=

−+⋅−=+−⋅=−+⋅−=

⇒′=

1

1372650102161

1462720102221

25448101960

243

242

241

τ

ττττττ

(A23)

−=

+−=

−=

⇒′=

143508

144515

2591

3

2

1

B

TCa

B

TCa

B

TCa

ND

B

B

B

vvr (A24)

−=

+−=

−=

⇒′=

678312

645295

8840

3

2

1

T

BCa

T

BCa

T

BCa

ND

B

B

B

vrr (A25)

Added inertia coefficients. Li & Wu (1990) formulated the shallow water effect on added inertia coefficients as follows:

−=

++

+=

++

+=

−−++=

∞

∞

∞

1with

005540019204130

1

0129003204130

1

43323301417731

820

2

66

66

820

2

22

22

30111

11

T

hF

F

T

B.

T

B..

m

m

F

T

B.

T

B..

m

m

F

C.T

L.

T

B..

m

m

.

.

.

B

(A26)

Sadakane et al (2001) suggest following expressions:

−+= 11 h

T

deepshallow eDDβ

α (A27)

with

++−=

++−=⇒=

+−−=

++−=⇒=

+−−=

++−=⇒=

4054750

023200010020

072211

00980070020

8280

705005050

.CB

T.

.C.B

T.

ND

.C.B

T.

.C.B

T.

YD

.C.B

T

.C.B

T.

XD

B

B

r

B

B

v

B

B

u

β

α

β

α

β

α

&

&

&

(A28)



Resistance and propulsion. For the estima-tion of hull resistance in shallow water, fol-lowing formula has been introduced by Mill-ward (1989, see also Kobayashi, 1995):

721

6440.

deepshallow h

T.kk

+= (A29)

where kdeep and kshallow are form factors for resistance in deep and shallow waters.

Making use of following standard SNAME expression for the resistance and propulsion contributions to the longitudinal force:

( )222

2

1 ηηρ PPP cbauL ++ (A30)

η being the relative propeller advance ratio (η=1: self-propulsion, η=0: propeller stopped, η=∞: bollard pull), Ankudinov et al. (1990) published following expressions for water depth dependency of the coefficients aP, bP, cP:

8

7fnr

8

1

c

c

b

b;

4

3fnr

4

1

a

a

P

P

P

P

P

P +==+=∞∞∞

(A31)

Propeller wake velocity terms are corrected as:

6

5

6

11

+=

∞ fnrCU

CU (A32)

So-called “η” terms, expressing variations of hydrodynamic coefficients (such as Xvv, Yr, Yv, Nr, Nv) due to deviations from the self-propulsion condition, are affected by water depth as follows:

( ) gvf

f=

∞η

η (A33)

Asymmetry terms due to propeller/hull inter-action are expressed by so-called “star” terms:

( )2222

2

1DncunDbuaYL UUU* ++′ρ (A34)

and similar for N. For the coefficients Y'* and N'*, following correction is proposed:

frndfnrN

N

Y

Y

*

*

*

* =+=′′

=′′

∞∞ 12

11

12

1 (A35)

while the propeller wake velocity term cU is corrected as follows:

6

5

6

11

+=

∞ fnrc

c

U

U (A36)

Based on model experiments with single propeller and single rudder, Yasukawa (1998) proposed following formula for the shallow water effect on the wake factor, which in-creases significantly with decreasing under keel clearance:

( )( )

50201 .h

Tfor.

h

TCa

w

w bCb

Bh >

−+=

∞ (A37)

where

( ) ( ) 2.24.5;0.76.6 −=−= BBBB CCbCCa (A38)

Expression (A38) is not valid for ships with low block coefficient.

Effect on rudder induced forces. In the MMG mathematical model, rudder-induced forces and moment are expressed as follows:

( )( )( ) δ

δδ

cosFxaxN

cosFaY

sinFaX

NHHRR

NHR

NXR

+−=+−=+−=

1

1

(A39)

where the rudder normal force FN can be writ-ten as:

RNRRN sinCUAF αρ 2

2

1= (A40)

αR and UR = (uR2 + vR

2)½ being the effective rudder inflow angle and velocity, respectively.

According to Yasukawa (1998), the nor-mal force coefficient is not affected signifi-cantly by water depth variations. On the other hand, rudder induced forces and moments are affected by shallow water effects due to the influence on the hull force factor aH, which increases significantly with decreasing water



depth, and the longitudinal co-ordinate xH of the application point of the hull force, which tends move forward when h/T decreases (see Figure A.1).

The water depth also influences the rudder inflow velocity. If uR and vR are expressed as

( )rlvfUvJ

Kuu RR

TPR ′′+′=+= ;

81

2πκε (A41)

Figure A.1 Influence of water depth on hull-rudder interaction (Hirano et al, 1985).

Kobayashi (1995) proposes formulae for the shallow water effect on f (v' + l'R r'), ε andκ:

( )( )

6

51q

deep

shallow

h

Tq

tCoefficien

tCoefficien

+= (A42)

with q5 = 1.4; q6 = 3 for f (v' + l'R r'),

q5 = 0.8; q6 = 3 forε,

q5 =-1.2; q6 = 3 for κ

In the approach by Ankudinov et al (1990), rudder terms are corrected for shallow water influences as follows:

( ) frndfnrf

f

rud

rud =+=∞ 12

11

12

1 (A43)

The inflow velocity at the rudder is ex-pressed as follows

2222ppR DgnfunDeuu ++= (A44)

with corrections for the coefficients e, f and g:

6

5

6

111

1+

===∞∞∞ fnrg

g;

frndf

f;

e

e (A45)

Experimental methods. Gronarz (1999) proposed a power law function for dealing with the shallow water influence on the hy-drodynamic coefficients f occurring in a ma-noeuvring mathematical model:

n

n h

Tccf

+= 0 (A46)

in which c0, cn and n have to be determined experimentally.

Validation data. Figures A.2 and A.3 com-pare a selection of empirical formulae for hull coefficients with experimental data. In gen-eral, the Ankudinov formulae appear to result into a fair approximation; for Nur and rN & , Kobayashi’s expressions perform very well for slender ships.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

T/h (-)

a H

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1

T/h (-)

x'H

tanker (exp) LNGC (exp)

tanker (cal) LNGC (cal)



Figure A.2 Effect of water depth on ma-noeuvring coefficients for Esso Osaka, (h/T)ref = ∞: experiments vs. empirical formulae (Pe-tersen, 1999). Figure A.3 Next page: Effect of water depth on manoeuvring coefficients for con-tainer carrier model (LPP=3.88 m, B=0.54 m, T=0.18 m, CB=0.60, (h/T)ref=1.32): experi-ments vs. empirical formulae (Vantorre, 2001).

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1T/h

Yuv

/Yuv

,ref

- 1

ExperimentClarkeAnkudinovKobayashiKijimaHirano

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1T/h

Yv|

v|/Y

v|v|

,ref -

1 ExperimentsAnkudinovKijima

0

2

4

6

0 0.2 0.4 0.6 0.8 1T/h

Yur

/Yur

,ref

- 1

ExperimentClarkeAnkudinovKobayashiHirano

0

2

4

6

0 0.2 0.4 0.6 0.8 1T/h

Yr|r

|/Yr|r

|,ref -

1

ExperimentAnkudinov

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1T/h

Yvd

ot-Y

vdot

,ref -

1

ExperimentClarkeAnkudinovKobayashi

0

2

4

6

8

0 0.2 0.4 0.6 0.8 1T/h

Nuv

/Nuv

,ref

- 1

ExperimentsClarkeAnkudinovKobayashiKijimaHirano

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1T/h

Nur

/Nur

,ref

- 1

ExperimentClarkeAnkudinovKobayashiKijimaHirano

0

1

2

3

4

0.0 0.2 0.4 0.6 0.8 1.0T/h

Nr|r

|/Nr|r

|,ref -

1 ExperimentAnkudinov

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1T/h

Nrd

ot/N

rdot

,ref -

1

ExperimentClarkeAnkudinovKobayashi



0

2

4

6

8

10

1 1.1 1.2 1.3 1.4 1.5h/T

Yuv

/Yuv

,ref

experimentsClarkeHiranoKijimaAnkudinovKobayashi (p=0)Kobayashi (p=5)

0

1

2

3

4

5

1 1.1 1.2 1.3 1.4 1.5h/T

Yv|

v|/Y

v|v|

,ref

experimentsKijimaAnkudinov

0

1

2

3

4

5

1 1.1 1.2 1.3 1.4 1.5h/T

Nuv

/Nuv

,ref

experimentsClarkeHiranoKobayashi (p=0)KijimaAnkudinov

-20

0

20

40

60

80

100

1 1.1 1.2 1.3 1.4 1.5h/T

Nv|

v|/N

v|v|

,ref

experimentsKijima

0

0.5

1

1.5

2

1 1.1 1.2 1.3 1.4 1.5h/T

Nur

/Nur

,ref

experiments Clarke

Hirano Kobayashi

Kijima Ankudinov

0

0.5

1

1.5

2

1 1.1 1.2 1.3 1.4 1.5h/T

Nr|

r|/N

r|r|

,ref


0

5

10

15

1 1.1 1.2 1.3 1.4 1.5h/T

Yur

/Yur

,ref

-4

-2

0

2

(Y

ur-m

+Xud

ot)/

(Yur

-m+X

udot

) ref

experiments (Yur)ClarkeHiranoKobayashiAnkudinovexperiments (Yur-m+Xudot)Kijima

0

1

2

3

4

5

1 1.1 1.2 1.3 1.4 1.5h/T

Yvd

ot/Y

vdot

,ref

-2

-1

0

1

2

3

(m -

Yvd

ot)/

(m -

Yvd

ot,r

ef)

experiments (Yvdot)ClarkeLi&WuAnkudinovexperiments (m-Yvdot)Kobayashi

0

1

2

3

4

5

1 1.1 1.2 1.3 1.4 1.5h/T (-)

Nrd

ot/N

rdot

,ref

-2

-1

0

1

2

3

(Izz

-Nrd

ot)/

(Izz

-Nrd

ot,r

ef)

experiments (Nrdot)ClarkeLi&WuAnkudinovexperiments (Izz-Nrdot)Kobayashi

0

1

2

3

4

5

1 1.1 1.2 1.3 1.4 1.5h/T

Yr|

r|/Y

r|r|

,ref




A.3 Effect of muddy bottoms

Introduction. Many navigational channels have bottoms that are covered with fluid mud suspensions, characterised by low density (1050-1300 kg/m³) and weak shear strength. In such conditions, the bottom level and, therefore, the depth are not clearly defined, as traditional survey techniques appear to be not adequate. In muddy areas, it is appropriate to introduce the nautical bottom concept, de-fined as the level where physical characteris-tics of the bottom reach a critical limit beyond which contact with a ship’s keel causes either damage or unacceptable effects on controlla-bility and manoeuvrability. For more informa-tion about this concept reference is made to PIANC-IAPH joint working group 30 (PIANC/IAPH, 1997). The present report will only focus on the influence of mud deposits on a ship’s manoeuvrability, as a result of two kinds of phenomena:

the rheological properties of the mud, which are particularly important in case of contact between the mud and the ship’s keel;

the presence of a two-layer system, so that undulations are not only generated in the air-water interface, but also in the water-mud interface. This effect also may affect ship behaviour if no contact occurs.

The present knowledge on interaction be-tween ships and fluid mud layers is based on (Vantorre, 1994):

model tests above mud-simulating layers at Marin (Sellmeijer & van Oortmerssen, 1983), Flanders Hydraulics (Vantorre & Coen, 1988; Wens et al., 1990; Vantorre, 1991; Ferdinande & Vantorre, 1991; Van Craenenbroeck et al., 1991) and Sogreah (Brossard et al., 1990a, 1990b);

full-scale tests in Rotterdam (van Bochove & Nederlof, 1979; Sellmeijer & van Oort-merssen, 1983), Nantes-Saint-Nazaire (Brossard et al., 1990a) and Zeebrugge (Kerckaert et al., 1988; Van Craenenbroeck et al., 1991);

theories (Ferdinande and Vantorre, 1991; Zilman et al., 1994) and numerical calcula-tions (Tulin et al., 1993; Wu, 1993; Avital and Miloh, 1994; Miloh, 1995).

Interface deformation. The effect of fluid mud layers on a ship’s behaviour mainly de-pends on the deformation of the interface caused by the pressure field around the mov-ing hull. These vertical interface motions are influenced by the ship’s forward speed (Figure A.4):

At very low speed, the interface remains undisturbed (1st speed range).

At intermediate speed, an interface sinkage is observed under the ship’s entrance, which at a certain section changes into an elevation. This internal hydraulic jump is perpendicular to the ship’s longitudinal axis and moves towards the stern with increas-ing speed (2nd speed range).

At higher speed, the jump occurs behind the stern (3rd speed range).

In general, the effect on ship behaviour is most important in the 2nd speed range. The transition velocity between 2nd and 3rd speed ranges can be estimated as (Vantorre, 1991):

−=

2

11 1

27

8

ρρ

ghU crit (A47)

Propulsion and resistance. The effect of interface deformation on the propulsive prop-erties of a ship is clearly illustrated by the re-lation ship speed-propeller rate. In the 2nd speed range, a given propeller rpm results in a significantly lower speed compared to a solid bottom situation; it appears to be difficult to overcome the critical speed. In the 3rd speed range, the effect of the muddy bottom is prac-tically nil (Figure A.5). The transition be-tween 2nd and 3rd speed range is very clear at an under keel clearance of 0.1 ÷ 0.2 T relative to the interface, but is smoother with decreas-ing under keel clearance.

There are indications that the speed reduc-tion in the second speed range is not caused



by increased resistance, but by obstruction of the flow to the propeller due to contact be-tween the ship’s keel and the risen interface. An important increase of the thrust coefficient is observed in these conditions, indicating an increase of the wake factor.

Figure A.4 Ship induced water-mud inter-face motions. Above: 2nd speed range, below: 3rd speed range (Vantorre, 2001b).

Figure A.5 Model tests above and in mud- simulating layers: typical speed-propeller rate relationships (Vantorre, 2001b).

Manoeuvrability. A mud layer appears to affect dynamic behaviour as follows (Sellmei-jer & van Oortmerssen, 1983).

A ship becomes more sluggish if the under keel clearance is reduced, until the latter is 3-5% of draft. Further reduction makes the ship less slow in her manoeuvres.

The effect of mud on manoeuvres is larger at slow speed (3 knots) than at high speed

(up to 7 knots). Steady motions are generally slackened

(forward speed, drift and rate of turn are lower), while dynamic motions are acceler-ated (smaller overshoot in zigzag tests).

Rudder action is affected in several ways: The force induced by rudder action in-

creases, while its application point shifts forward.

At small rudder angles, instabilities may occur: rudder induced forces and moments act in the wrong sense if the keel is in con-tact with both water and mud. Such insta-bilities take place if the keel is in contact with both water and mud, especially if the contact zone is located near the stern.

Controllability may be heavily affected if a ship’s keel is in contact with a plastic consoli-dated mud layer. She tends to follow her own way; at the same time, it is practically impos-sible to decrease speed, although the latter is only 1 or 2 knots. Such phenomena were ob-served during full scale tests and confirmed by pilots and crew of inland vessels.

A.4 Effect of horizontal restrictions

Introduction. In restricted waters, a ship’s behaviour is affected by the presence of the lateral limits of the navigation area, such as banks and quay walls. These restrictions may influence the hydrodynamic forces and mo-ments acting on the ship hull, due to effects of different origin. Following distinction is made:

bank effects due to a ship’s motion parallel to the bank causes and/or propeller action;

cushion effect: the lateral force acting on a ship hull moving laterally at constant speed towards a solid boundary increases with decreasing bank clearance;

lateral restrictions influence a ship’s fre-quency domain characteristics and, there-fore, hydrodynamic memory effects occur-ring in case of large accelerations or decelerations (e.g. contact with fenders).

0 20 40 60propeller rate (rpm)

spee

d (k

n)

2

4

6

8

2nd speed range

Solid bottom

Muddy bottom

Muddy bottomh1/T = 1.20

3rd speed range

h1/T = 1.20

h1/T = 0.96



Bank effects. Several experimental studies on ship-bank interaction were reported: Fujino (1968), Eda (1971), Norrbin (1974, 1985), Fuehrer & Römisch (1974), Dand (1981), Ch’ng et al. (1993), Vantorre (1995), Li et al. (2001). This list is incomplete, and should be extended with theoretical/numerical studies.

For a given ship, bank effects depend on several parameters:

ship-bank distance: generally, the lateral force Y and yawing moment N increase with decreasing bank clearance, although the yawing moment may decrease if the clearance becomes very small;

forward speed u: Y, N are approximately proportional to u²; especially in shallow water, the effect of u is more important;

depth-draft ratio: if h/T exceeds a critical value, located in the range 1.1–1.25, a towed ship is attracted to the bank, while at low h/T, repulsion takes place. N in-creases significantly at very low h/T;

propeller action: positive propeller rpm results in an attraction between the stern and the bank; at very low h/T, bank re-pulsion at zero rpm can be changed into bank attraction due to this effect;

bank geometry (slope, surface piercing, flooded).

Only a very few semi-empirical methods allowing calculation of ship-bank interaction forces as a function of relevant parameters are available. The formulation published by Norrbin for a specific tanker model (L = 5.024 m, B = 0.852 m, T = 0.339 m, CB=0.821, pro-pelled) is often referred to (see Figure A.6):

Figure A.6 Norrbin (1974, 1985): bank configurations.

for vertical banks (Norrbin, 1985):

+−=

+=

2

02

2

02

0755000250

372009250

h

T..LBTuCN

h

T..BTuCY

B

B

ηρ

ηρ

(A48) for sloping banks (Norrbin, 1985):

+−

+−=

−+

++=

=

=

33

2

0

0

33

2

0

0

0195003310

88175001

0988006730

531937701

kh

T.k.

kgL

u.k.

NN

kh

T.k.

kgL

u.k.

YY

k

k

η

η

(A49)

for flooded banks (Norrbin, 1974):

1

1

1

2

)0(hh

h

h eYY −−

== (A50)

Ch’ng et al. (1993) proposed a formulation for bank-induced sway force and yaw moment based on tests on two MarAd Series hull forms (L = 1.698 m, B = 0.340 m, T = 0.077 m, CB = 0.85; bulbous and cylindrical bow) and a container ship model (L = 1.750 m, B = 0.254 m, T = 0.095 m, CB = 0.57):

222

313

39

37335

22

00060110

2

11000

TB

TBB

nBBnBB

CF

y.C

F

y.

F

ya

F

Fya

F

yaFyya

LU

Y

+++

++=ρ

(A51)

222

23

16

233

1423

1333

832

0044000090

2

11000

TBB

TBnB

BBBBB

CF

yy.C

F

y.

F

Fyb

F

yyb

F

yb

F

yyb

LU

N

−++

++=ρ

1with −=T

hF (A52)

hT

B/η0 B/ hη

h

ηB/ 0

1hh

kh



with a5 = –59.3 +34.7 CB B/T a7 = 1.87 +0.382 CB B/T a9 = –0.896 –3.22 CB B/T a13 = 0.0145 –0.234 CB B/T b8 = –1.1 +0.389 CB B/T b13 = –0.159 +0.0191 CB B/T b14 = 0.0379 –0.0413 CB B/T b16 = –4.21 –1.69 CB B/T

(A53)

yB and yB3 are defined as (see Figure A.7):

stbport

112

1

yy

ByB

+= ;

stb3port3

3 112

1

yy

ByB

+= (A54)

Figure A.7 Ch’ng et al. (1993): symbols.

CT is the thrust coefficient:

22

2

1A

PT

VD

TC

ρ= (A55)

TP being the propeller thrust, VA = (1-w)U the speed of advance and D the propeller diameter.

Cushion effects. A ship hull moving later-ally at constant speed towards a solid boundary (e.g. quay wall) undergoes a lateral force that increases with decreasing bank clearance. For modelling this cushion effect, following ex-pression is proposed by Vantorre & Laforce (1998):

B

qk

Th

Bq

B

Th

Bq

C

MM

M

eA,,n,'YLv

,,n,Y

−

∞→=±==

=

02

2221 πβρ

β

×

−+

−BMq

nke1 (A56)

( )),,0n,(Y),,n,(Y Th

BMq

Th

BMq ∞→=−∞→× ββ

qM being the lateral clearance between the ship’s side and the quay wall. A similar ex-pression can be formulated for the yawing moment NC. The first term formulates the in-crease of lateral resistance with decreasing clearance; the second term accounts for the effect of propeller action. The latter induces two kinds of effects, counteracting each other.

Figure A.8 Lateral bank suction force on a panamax bulkcarrier model at zero speed due to propeller action: influence of h/T (u=0, v=0) (Vantorre & Laforce, 1998).

Figure A.9 Lateral force on a panamax bulkcarrier model moving laterally towards a vertical quay in function of quay clearance and depth to draught ratio (n=0) (Vantorre & Laforce, 1998).

T T

yp ys

yp3 ys312

0

1

2

0 2 4 6qM/B (-)

Y' (

-)

h/T = 1.1

h/T = 1.2

h/T = 1.5

-0,2

0

0,2

0,4

0,6

0,8

1

0 1 2 3 4 5qM/B (-)

Y/T

(-)

h/T = 1.1

h/T = 1.2

h/T = 1.5



The hydrodynamic forces and moments acting on a swaying ship model in open water are influenced significantly by propeller ac-tion; in the vicinity of a bank, however, pro-peller action results into an attraction of the stern towards the bank. This bank suction force significantly increases with decreasing water depth (Figure A.8).

The factor A, being the ratio between the lateral cushion force Y*

C0 for zero quay clear-ance and the lateral force Y*

O due to pure sway in open water, strongly depends on h/T, as can be derived from Figure A.9. An ap-proximate value for k appears to be 2; kn var-ies between 0.5 and 1.0, depending on h/T. Exact values for these coefficients can be de-termined experimentally.

Hydrodynamic memory effects. If a ship undergoes relatively large accelerations or de-celerations, so-called hydrodynamic memory effects cannot be neglected. These effects are caused by the presence of a free surface: a sudden acceleration causes denivellations, which affect the hydrodynamic forces acting on the hull during some time interval after the event. This implies that a quasi-stationary ap-proach is no longer valid.

Such effects occur during berthing manoeuvres, in case of contact between the ship and (fendered) jetties or quay walls. Also in collision situations, manoeuvres assisted by tugs or anchors, and even sudden rudder and machine manoeuvres, non-stationary phenom-ena may affect a ship’s behaviour, and should be implemented into the mathematical simula-tion model.

As non-stationary hydrodynamic forces are caused by wave effects, they are influ-enced substantially by the boundaries of the navigation area. There is not only an import-ant effect of the water depth, but in the vicin-ity of quays, banks or other closed boundaries, memory effects depend on the relative posi-

tion between the ship and these boundaries as well.

Several methods are available in literature in order to represent non-stationary hydrody-namic forces, although most of them are origi-nally not meant for real-time applications. Taking account of the possible way of implementation of these methods into a ma-noeuvring simulator’s algorithm, these mathematical models can be divided in two categories:

models requiring no modifications to the simulator’s integration scheme, as non-stationary forces are calculated in a sepa-rate module;

models introducing a set of time depend-ent parameters fulfilling supplementary differential equations, to be integrated simultaneously with the original equa-tions of motion.

In models of the first category, non-stationary hydrodynamic forces are calculated by means of impulse response functions (IRF). Models based on IRF techniques are applied rather currently for determining a ship’s kinematic and dynamic time history in case of contact with fixed constructions (Pe-tersen & Pedersen, 1981; Blok et al., 1984; Fontijn, 1987, 1988), collisions with another ship (Petersen, 1982), moored ships in waves (van Oortmerssen et al., 1974, 1976, 1986; Remery, 1974). These functions, denoted hkj(τ), represent the time history of the hydro-dynamic force acting in mode k caused by a velocity pulse in mode j and are grouped in a n×n-matrix [h]:

( )[ ] ( )[ ] ( )[ ] τττ d-t t-

xhFh &∫∞

∞=

[ ] ( )[ ] [ ] ( )[ ] ( )[ ] ( )[ ] τττ d-tttt

-

xKxλxµ &&&& ∫∞

++=

(A57)



Figure A.10 Added mass and hydrodynamic damping for a swaying rectangular block near a ver-tical wall, h/T = 1.167 (Fontijn, 1988).



[µ] and [λ] denote the high-frequency lim-its for added mass and hydrodynamic damp-ing coefficients, while [K] denotes the matrix of retardation functions, which are time do-main characteristics. Compared with a quasi-stationary approach, the low frequency limits for added mass and damping are replaced with the high-frequency limit, and an integral is added in order to incorporate memory effects.

IRF techniques appear to be very suitable for implementation into a manoeuvring simu-lator program with modular structure, but re-quire rather lengthy numerical operations. At each time step, retardation functions must be calculated, multiplied with the recent kine-matic history and integrated. As a con-sequence, the use of an IRF method is only feasible if an algorithm is available for calcu-lating the retardation functions taking account of the ship’s relative position to the bounda-ries of the navigation area.

The retardation functions, which can be considered as the time domain characteristics of the manoeuvring ship, are related to the frequency domain characteristics:

( )[ ] ( )[ ]∫∞

∞−= ωω

πω det tiTK

2

1 (A58)

T(ω) is a complex transfer function, defined as:

( )[ ] ( )[ ] [ ]( ) ( )[ ] [ ]( )λbµT −+−= ωωωω ai (A59)

which can be calculated by means of appro-priate numerical techniques. Expressions for the lateral force and the yawing moment based on a slender body approximation are formulated by van Oortmerssen (1976), Peter-sen (1982), Vantorre (1992).

In the vicinity of a quay wall, the fre-quency domain characteristics and, therefore, the retardation functions are influenced sub-stantially. In case the ship is parallel with the quay wall, this influence is mainly concen-trated in a narrow frequency range, character-ised by an important increase of the damping coefficient. The added mass curve consecu-

tively reaches a maximum and a minimum in this range. Even negative values for added mass occur, which means that the water mass between quay and ship acts as a spring at these frequencies (see Figure A.10). The in-fluence of the presence of a quay on the lateral force acting on a decelerated ship is illustrated in Figure A.11.

L

gtt )( 3−

Figure A.11 Captive quay wall approach tests with panamax bulk carrier model (h/T = 1.2, u = 0, n = 0): lateral force during and af-ter deceleration phase. Influence of quay clearance qM (Vantorre & Laforce, 1998).

Vantorre & Laforce (1998) proposed follow-ing approximation for the elements of [T(ω)] in the vicinity of a quay wall:

( ) ( ) ( )( )

( ) ( ) ( )∑∑= ++

===

N

jj

jN

j

j

j AAii

BitTT

0 012

1

0 ωω

ωω (A60)

leading to following expressions for added mass and hydrodynamic damping coefficients:

( ) ( )( ) ( )( )

( )( ) ( )∑=

+−

−+=

N

jj

jjj

j AA

ABa

02

1222

0

201

ωω

ωµω (A61)



( )( ) ( )

( )( ) ( )∑= +−

=N

jj

jj

j AA

ABb

02

1222

0

211

ωω

ωω (A62)

while following expression is obtained for the retardation function:

( ) ( ) ( )∑=

=N

j

j tKtK0

(A63)

with

( ) ( ) ( ) ( )

( ) ( )( )

( ) ( ) ( )

( )( ) ( ) ( )

( ) ( )( )

( ) ( ) ( )

<

−

=−

>

−

⋅

⋅= −

2

000

0

2

0

2

000

0

1

1

jjjj

jj

jjj

jjjj

jj

tjj

Aiftsinhtcosh

Aift

Aiftsintcos

eBtKj

αωωαω

αα

αωω

αω

α

(A64)

where

2)()(0

2)(0

)(1

)( ;2

1 jjjjj AA αωα −== (A65)

T(0) is the transfer function for laterally un-restricted, shallow water conditions. The trans-fer function parameters ξ(j), A0

(j), A1(j), B1

(j) (j=1,…,N) depend on the position of the ship referred to the quay wall, i.e. on distance and orientation. With N = 2 to 4, a fair agreement with experimental results can be obtained.

Direct time approach (DTA) and state variables (SV) methods belong to the second category. The difference between both is situ-ated in the nature of the parameters. In a DTA, the latter are characterised by a clear relation-ship with the physical reality. In a SV method, the parameters are grouped in an artificial “state vector” without physical meaning, ful-filling differential equations selected according to purely mathematical conventions. A typical example of a DTA is the long-wave approxi-

mation, applied by Middendorp (1981). A two-dimensional rectangular section performs a lat-eral motion in shallow, but laterally unre-stricted water, causing denivellations of the water level which move away from the ship with velocity cw=(gh)½. It is assumed that the lateral hydrodynamic force acting on this sim-plified hull form can be expressed as a function of five parameters: the denivellations on port and starboard, the lateral fluid velocity on port, on starboard and under the keel. Five differen-tial equations are added to the equation of mo-tion in lateral direction: continuity and mass conservation on both port and starboard, and momentum conservation under the keel. Elimi-nation of four of these parameters leads to a system of two differential equations with two unknown time functions: the lateral position x2 of the ship and the fluid velocity vb in the un-der-keel area:

( ) ( )[ ]

( )( )[ ]

( )LBT

(t)FxvLT

TxT-hvxc

c

LBT

2g

TxT-hvx+c

T-hvTc

xc

c

BT

g2x

2b

b

w

w

bw

bw

w

w

ρργ

=−−

+−

+

+−

−+

2

2222

22

2

222

222

&

&

&

&&&

&&

(A66)

( )[ ]

( ) 02

12

2

2

222

2

=

−

−+

+−−

+

xvTh

TxThvxc

c

B

gv

b

bw

wb

&

&&

&

ργ

(A67)

γ being a proportionality coefficient for the

shear stress in case of laminar flow (= νωρ in case of oscillating flow).

Fontijn (1988) developed a DTA for the lateral motion of a rectangular vessel parallel with a vertical wall. For this purpose, three simplified differential equations with three unknown time functions were used: the longi-tudinal fluid velocity distribution and the free surface elevation in the quay clearance, and the ship’s lateral position.



The use of SV for the calculation of non-stationary hydrodynamic forces on floating vessels is theoretically developed by Schmiechen (1973, 1974), who applied the technique to the case of two ships in a colli-sion situation. The horizontal motions of a moored tanker were simulated making use of SV by Jiang et al. (1987).

The hydrodynamic forces in (A57) can be considered as a functional:

[ ] [ ][ ] [ ][ ] ( )[ ] ( )[ ]

( )[ ]( )[ ] tτ

d-t

t

-

≤<∞−≡

++= ∫∞

,τ

τττ

vP

xKxλxµFh &&&& (A68)

This formulation is replaced with a system of recursive relationships containing a set of state variables [s0],[s1],...,[sn]. If this system is assumed to be linear, it can be formulated as:

( )[ ] [ ][ ]( )[ ]( )[ ] [ ] ( )[ ] [ ] ( )[ ]

[0] ][ and 0,1,..., with 1

01

==−−=

=

+

+

n

kkn-k

n-kn-kn-k

nk

ttt

,t

svBsAs

vsQs

&

&

(A69)

[ ] [ ] ( )[ ]( )[ ] [ ] [ ] ( )[ ]ii

m

0=i

ij , vCsvsRFh ∑+== 0 (A70)

(i) denoting the i-th time derivative. A suitable formulation for the hydrodynamic forces is obtained if m=1 in (A70), with:

[ ] ( )[ ] [ ] [ ] ( )[ ] [ ] µaCλbC =∞==∞= 10 ; (A71)

so that [s0] expresses the non-stationary part of the hydrodynamic forces in (A68):

[ ] ( )[ ] ( )[ ] τττ d-tt

-

xKs &∫∞

=0 (A72)

The other state variables [s1],...,[sn] can be considered as memory parameters, as they must be known in order to calculate [s0].

Making use of the frequency response characteristics [a(ω)] and [b(ω)], the scalar elements of matrices [Ak] and [Bk] can be es-timated as follows. The set (A69) of n+1 first-

order differential equations is rewritten as one differential equation of order n+1. After Fou-rier transform and elimination of [s0], follow-ing set of algebraic equations is obtained:

( ) [ ]knk

n

0=k

i B1−−∑ ω (A73)

( ) [ ] ( )[ ] [ ]( ) ( )[ ] [ ]( ){ }

( )[ ] [ ]( ) ( )[ ] [ ]( ){ }λbµ

λbµA

−+−=

−+−

− ∑

ωωω

ωωωω

ai

aii kk

n

0=k

If numerical data for [a(ω)] and [b(ω)] are available for a (equidistant) set of pulsations ω, an optimal estimation for the matrix ele-ments Ak and Bk can be found by means of a least square method.

In the marginal case n=0 only one SV, [s0], is introduced. Elimination of the latter leads to:

[ ] [ ][ ] [ ][ ][ ] [ ][ ]( )[ ] [ ][ ] [ ]( )[ ] 0000

0

=++++++

vBλAvµAλvµFAF hh&

&&&

(A74)

For uncoupled sway, (A74) is equivalent with a simplified long-wave approximation if µ=0, λ=-B0/A0≠0, a(0)=-B0/A0

2, so that:

0 = v A

B - Y A + Y hh && 20

00 (A75)

Hence, an acceptable approximation for the frequency response characteristics can only be guaranteed for relatively low frequencies, as this approach results in high frequency limits for added mass and damping which are in contradiction with experimental and theoreti-cal data. If rather moderate frequencies are expected, the method can be used for simulat-ing memory effects in laterally unrestricted water, a fair approximation of a ship’s fre-quency characteristics near a quay wall cannot be obtained.

n should at least be 1 for a realistic approximation of added mass and hydrodynamic damping coefficients (see



damping coefficients (see Figure A.12). Even an approximation of the typical shape of the frequency response characteristics of a ship near a closed boundary can be obtained, al-though n=2 to 4 is advised.

Figure A.12 SV method, n=1: frequency response characteristics.

A.5 Ship-ship interaction

Overview. There are few published data from experimental research on interaction be-tween ships. Newton (1960) investigated in-teraction effects during overtaking manoeu-vres with two ship models in deep water (L1 = 4.51 m, B1 = 0.63 m, T1 = 0.18 m, CB1 = 0.61; L2 = 3.46 m, B2 = 0.43 m, T2 = 0.18 m, CB2 = 0.71; h = 2.74 m). Müller (1967) studied both overtaking and meeting of ships in a narrow canal, Remery (1974) the interaction forces on a moored vessel due to the passage of another ship. Dand (1981) carried out overtaking and head-on encounter tests between two ship models (L1 = 3.32 m, B1 = 0.47 m, T1 = 0.17 m, CB1 = 0.70; L2 = 3.96 m, B2 = 0.51 m, T2 = 0.21 m, CB2 = 0.76; h = 0.23-0.56 m) on par-allel courses. Comprehensive test series with ship models of both equal and different length in overtaking and encountering manoeuvres are described by Vantorre et al. (2001).

Other authors have developed numerical methods to calculate interaction forces theoreti-cally, e.g. Tuck & Newman (1974), Kijima (1987), Kaplan & Sankaranarayanan (1987).

There are very few semi-empirical ap-proaches, resulting in an estimation of the time histories of forces and moments in the horizontal plane due to interaction with an-other ship as a function of geometry, speeds and environment parameters. Brix (1993) pre-sents a method to estimate the forces and moments acting on a ship during overtaking. The influence of water depth not taken into account, and the ratio of ships’ lengths is lim-ited. Varyani et al. (1999) present empirical formulae for predicting the peaks of the lateral force and the yaw moment during encounter manoeuvres. The cases in which one of the ships has zero speed are not covered, and the length ratio is limited.

General observations. The general pattern of the time histories of the longitudinal and lateral force components and of the yaw mo-ment acting on the own ship mainly depends on the ship lengths ratio and the ship speeds ratio.

Interaction forces between two ships of approximately the same length can be charac-terised as follows

Head-on encounters:

▫ X: consecutive decrease and increase of the ship’s resistance

▫ Y: initial repulsion, followed by at-traction between both ships, and fi-nally repulsion again;

▫ N: consecutive actions of bow repul-sion, bow attraction, bow repulsion and bow attraction.

However, a different pattern is observed if the target’s ship speed is zero:

▫ X: a general resistance increase;

▫ Y: the first repulsion phase is missing;

▫ N: no clear pattern.

ω

b

µ

0A 0A

1

1

A

B

ω

a

0

1

A

B



Figure A.13 Ship-ship interaction: symbols and conventions.

Target ship overtakes own ship:

▫ X: consecutive resistance increase and decrease;

▫ Y: comparable to encounter manoeu-vres;

▫ N: only two extremes, consecutive bow repulsion and bow attraction.

Own ship overtakes target ship:

▫ X: slight resistance decrease, followed by increase;

▫ Y: consecutive attraction and repulsion; ▫ N: consecutive bow attraction and bow

repulsion.

For X and N, the first phases disappear with decreasing target ship’s speed.

If the length of both ships is significantly different, these patterns may be different.

Head-on encounters:

▫ X, Y: the general pattern remains valid, although some higher harmonics may be introduced;

▫ N: the general pattern remains valid for the longest ship, while the smallest ship undergoes a larger number of ex-tremes.

For overtaking manoeuvres, the general pattern for ships of equal length is, to

some extent, also applicable, although higher harmonics can be distinguished.

Empirical formulae. Brix (1979, 1993) pre-sented a semi-empirical approach to estimate forces and moments acting on a ship during an overtaking manoeuvre. The maximum values of the longitudinal force, the transverse force and the yawing moment can be approximated by (see Figure A.13):

( )( )( ) mmm

mmm

mmm

TLVN

TLVY

TLVX

2221

max

221

max

221

max

0.0070.004

0.0300.025

0.0170.014

ρ

ρ

ρ

÷=

÷=

÷=

(A76)

where Lm=½(LO+LT); Tm=½(TO+TT); Vm= ½(VO+VT). The smaller values have to be used for LT/LO > 1.5.

The values in (A76) are valid for a standard passing distance ycc0 = 0.35 Lm. The influence of the spacing ycc between the ships’ centre-lines can be included as follows:

ycc < 0.6 Lm : ∝ ycc-1

0.6 Lm < ycc < 1.6 Lm : ∝ ycc-2

ycc > 1.0 Lm : ∝ ycc-3 ÷ ycc

-4

The curves of these interactions as func-tions of relative ship position ξ may be con-structed using Table A.1.

TARGET

OWN

yo

xo

LTBT

ybbycc ycb

yooyoT

12

(L o +L T )

L oBo

To

TT

h

Vo VT



Table A.1 Interaction forces and moment on overtaking ships in function of relative ship position (Brix, 1993).

ξ -1.000 -0.750 -0.500 -0.250 0.000X/Xmax -0.289 -0.690 -1.000 -0.850 -0.250Y/Ymax 0.289 0.345 -0.060 -0.595 -0.935N/Nmax 0.264 0.706 1.000 0.873 0.221

ξ 0.000 0.250 0.500 0.750 1.000X/Xmax -0.250 0.590 0.980 0.810 0.330Y/Ymax -0.935 -0.982 -0.637 -0.250 -0.089N/Nmax 0.221 -0.682 -0.927 -0.706 -0.424

Table A.2 Lateral force on meeting ships: co-efficients and exponents (Varyani, 1999).

i 1 2 3 Yi

ms 1.20 -2.00 1.01 Yi

md -0.85 -0.85 -0.85 Yi

mu 0.434 0.492 0.626 αi -5.50 -4.80 -6.00 βi -0.90 -0.96 -0.94 δi -2.19 -2.19 -2.19

Table A.3 Yaw moment on meeting ships: coefficients and exponents (Varyani, 1999).

I 1 2 3 4 Ni

ms 0.305 -0.81 0.95 -0.21 Ni

md -0.85 0 0 -0.85 Ni

mu (UT>UO) 0 1.585 7.059 0 Ni

mu (UT<UO) 0 0.839 3.926 0 εi -5.00 -8.00 -10.00 -5.00 ϕi -0.75 -1.00 -1.20 -0.90 δi -2.19 -2.19 -2.19 -2.19

Varyani et al. (1999) present empirical for-mulae for predicting the peaks of the lateral force and yawing moment due to interaction between two meeting ships:

−+

+

+=

O

OTmui

T

Omdi

O

O

ccmsiOOTOi

V

VVY

L

LY

T

h

L

yYTBVVY

i

i

1

121

δβ

α

ρ

(A77)

(i=1: bow-bow; i=2: midship-midship; i=3: stern-stern)

−+

+

+=

O

OTmui

T

Omdi

O

O

ccmsiOOOTOi

V

VVN

L

LN

T

h

L

yNTBLVVN

i

i

1

121

δϕ

ε

ρ

(A78)

(i=1: bow-bow; i=2: immediately before mid-ship-midship; i=3: immediately after midship-midship; i=4: stern-stern)

Values for the constants and exponents are given in Tables A.2 and A.3.

Validation. Figures A.14 and A.15 compare experimental data (Vantorre et al, 2001) with the results of (A77-A78). The following is con-cluded.

The formulae proposed by Varyani et al. (1999) for the lateral force and yawing moment lead to results in the same order of magnitude as the measured data in the case of an own ship with full shapes. This is the case for several types of target ships: slender (Figure A.14) and full (Figure A.15a) ships the length of which is compa-rable to the own ship’s length, and a full ship with a significantly smaller length (Figure A.15b). Nevertheless, the lack of the influence of the target ship’s draft in the latter can be observed, while the effect of the own ship’s draft appears to be over-estimated.

The lateral interaction force acting on a slen-der ship during encounter manoeuvres with full ships of comparable length is clearly un-derestimated by (A77), see Figure A.15c. The first peak of the yawing moment is un-derestimated by (A78); the other peaks may be either under- or overestimated.

In comparison with the experimental obser-vations mentioned by Vantorre et al. (2001), Brix’ method results into an important underes-timation of the forces acting on an overtaking ship. It should be born in mind, however, that Brix (1993) is valid for deep water only.



▲ □ ◊ ∆ ▫ ■ ●

ref,O

O

T

T 0.66 1.00 1.00 1.00 1.00 1.00 1.24

ref,T

T

T

T 1.00 1.00 1.00 1.00 1.11 0.86 1.00

OT

h 1.68 1.20 1.48 1.10 1.20 1.20 1.20

-120

-100

-80

-60

-40

-20

0

-120 -100 -80 -60 -40 -20 0Y2 (N) - experiments

Y2

(N)

- V

arya

ni

0

10

20

30

40

50

0 10 20 30 40 50N1 (Nm) - experiments

N1

(Nm

) -

Var

yani

Figure A.14 Ship-ship interaction, lateral force (Y2) and yawing moment (N1): comparison between experimental data (Vantorre et al., 2001) and empirical formula by Varyani et al. (1999). Own ship: Esso Osaka model (LO = 3.824 m, BO = 0.624 m, TO,ref = 0.207 m); target ship: container carrier (LT = 3.864 m, BT = 0.550 m, TT,ref = 0.180 m).

▲ □ ◊ ∆ ▫ ■ ● ▲ ∆ □ ◊ ∆ ▫ ● ● ▲ □ ◊ ∆ ▫

ref,O

O

T

T

0.66 1.00 1.00 1.00 1.00 1.00 1.24 0.66 0.66 1.00 1.00 1.00 1.00 1.24 1.24 0.86 1.11 1.00 1.00 1.00

ref,O

O

T

T

ref,T

T

T

T

1.00 1.00 1.00 1.00 1.11 0.86 1.00 1.42 1.00 1.00 1.00 1.00 1.42 1.00 1.42 1.00 1.00 1.00 1.00 1.00

ref,T

T

T

T

OT

h 1.68 1.20 1.48 1.10 1.20 1.20 1.20 1.68 1.68 1.20 1.48 1.10 1.20 1.20 1.20 1.60 1.24 1.71 1.38 1.27

OT

h

Figure A.15 Ship-ship interaction, lateral force (Y2): comparison between experimental data (Vantorre et al., 2001) and empirical formula by Varyani et al. (1999).

(a) Own ship: Esso Osaka model (LO = 3.824 m, BO = 0.624 m, TO,ref = 0.207 m); target ship: bulk carrier (LT = 3.984 m, BT = 0.504 m, TT,ref = 0.180 m).

(b) Own ship: Esso Osaka model (LO = 3.824 m, BO = 0.624 m, TO,ref = 0.207 m); target ship: small tanker (LT = 2.210 m, BT = 0.296 m, TT,ref = 0.125 m).

(c) Own ship: container carrier (LT = 3.864 m, BT = 0.550 m, TT,ref = 0.180 m); target ship: Esso Osaka model (LO = 3.824 m, BO = 0.624 m, TO,ref = 0.207 m).

-140

-120

-100

-80

-60

-40

-20

0

-140 -120 -100 -80 -60 -40 -20 0Y2 (N) - experiments

Y2

(N)

- V

arya

ni

-60

-50

-40

-30

-20

-10

0

10

-60 -50 -40 -30 -20 -10 0 10Y2 (N) - experiments

Y2

(N)

- V

arya

ni

-120

-100

-80

-60

-40

-20

0

-120 -100 -80 -60 -40 -20 0Y2 (N) - experiments

Y2

(N)

- V

arya

ni



A.6 Squat

Definition of squat. Squat is the combined effect of sinkage and trim due to the forward velocity of the ship. Tuck (1995) defines squat as follows: “Squat is not a change of draft (...). It is an overall lowering of the ship together with the water in the neighbourhood of the ship. Hence it is almost unseen in the open sea, where it is nevertheless present. However, squat is mainly of concern in re-stricted water (...)”.

Slender body theory. Tuck (1966, 1967) and Tuck and Taylor (1970) developed ex-pressions for sinkage and trim making use of a slender body theory considering one-, two- and three-dimensional flow for both subcriti-cal and supercritical speeds. In the subcritical range, following expressions are obtained:

2

2

1100100

h

hss

PP

Ms

Fr

FrC

L

sC

−== (A79)

2

2

1100100

h

hT

PP Fr

FrC

L

tC

−==τ (A80)

In these expressions, sM and t denote midship sinkage and trim, respectively; Frh is the Froude depth number:

gh

UFrh = (A81)

Css and CT are given by:

αβα

−−

=1

MFss

CCC ;

αββ

−−

=1

FMT

CCC

where

( )( )∫

∫=dxxB

dxxxB

L

1α ; ( )( )∫

∫=dxxBx

dxxxBL

2β (A82)

( ) ( )

( )∫

∫∫ −−=

dxxB

dxdxd

dS

dx

xdB

LCF

ξξξξ

π

log

2

1 (A83)

( )( ) ( )

( )∫

∫∫ −−=

dxxxB

dxdxd

dS

dx

xxBd

CM 2

log

2

1ξξ

ξξ

π(A84)

Another way of representing sinkage and trim makes use of following notation:

2

2

2h

h

PPZM

Fr1

Fr

LCs

−

∇= ;2

2

2h

h

PP Fr1

Fr

LCt

−

∇= θ

(A85)

Squat calculation based on one-dimensional theory. A semi-empirical theory to predict sinkage and trim with reasonable accuracy was developed by Dand and Fergu-son (1973). Application of the continuity equation and Bernoulli’s equation in the case of a ship with sectional area A(x) and beam B(x) moving with speed U in a canal of rec-tangular cross-section area Ach=W*h yields following equation for the relative water ve-locity U1(x):

( ) ( ) ( )01

U

xUFrxm

U

xUFr 12

h

32

h =+

+−−

2

11

2

1 1

(A86)

m(x) being the local blockage factor:

( )chA

xAxm

)(= (A87)

This results in a water level ζ(x) near the ship:

( ) ( )

−

−= 1

U

xUFr

2

1

h

x2

12h

ζ (A88)

Integration of the water level variations over the ship length yields sinkage and trim coeffi-cients:

( ) ( )( )∫

∫==dxxB

dxxBx

LL

sC

PPPP

Ms

ζ1001001 (A89)

( ) ( )( )∫

∫===dxxxB

xdxxBx

LL

tC

PPPP21

100100100

ζττ

(A90)



Figure A.16 Effect of self-propulsion on trim (Dand & Ferguson, 1973).

This approach can be applied to the case of shallow water of infinite width if an effective channel width is assumed. Dand & Ferguson (1973) propose an effective width W = 0.975 LPP, and to apply following correction factors to the results of equations (A89-A90):

( )

( ) w..CCC

Cw

w..CCC

Cw

n

sss

sn

71400560 ; 1

1

44411961 ; 1

1

1

1

−=+

==

−=+

==

τττ

τ δδ

β

δδ

α

w denoting an affective width parameter: 2

hPP

Fr1L

Ww −=

so that

2

2

h

1n

h

1ssn

Fr1696.0056.2

CC

Fr1408.1196.2

CC

−−=

−−=

ττ

The subscript n refers to the naked hull; the effect of self-propulsion is accounted for as follows:

nhp

snsp

CT

h,FrC

CC

ττ γ

=

=1.1

γ being deduced from model tests and shown in Figure A.16.

Squat formulae for practical use. A reli-able estimation of squat effects is of impor-tance for evaluating the water depth required for safe navigation. For this reason, several authors proposed practical methods for calcu-lating squat based on general ship characteris-tics. An overview of these methods will be given in chronological order; many of them can be found in the review carried out by PIANC/IAPH Joint Working Group No. 30, Dimensions of channels and fairways – a practical guide (PIANC, 1997).

Soukhomel & Zass (1958) proposed:

2m

2m

kVsT

h

Vh

Tks

T

h

12.961.4

12.961.4

=⇒≤

=⇒≥ (A91)

with



95.3for 0143.011.1

≤≤

=

−

B

L

B

Lk PPPP

(A92)

It is assumed that sAP ≥ sFP, which is only the case for slender ships; the sinkage of the ship’s stern is given by:

mAPPP

mAPPP

mAPPP

ssB

L

ssB

L

ssB

L

10.10.90.7

25.10.70.5

50.10.55.3

=⇒<≤

=⇒<≤

=⇒<≤

(A93)

Hooft (1974) makes use of formulation (A85), proposed by Tuck & Taylor (1970), with CZ = 1.4÷1.53 and Cθ = 1.0 for a wide range of ship forms.

The National Ports Council (Dand, 1975) published a graphical “squat estimation chart” (Figure A.18, next page) for full-bodied ships.

Huuska (1976) formulated the bow squat sb in a similar way and introduced a blockage factor Ks:

2

2

22.4

h

h

PPsb

Fr1

Fr

LKs

−

∇= (A94)

with

030for 1

030for 760457

1

11

.sK

.s.s.K

s

s

≤=>+=

(A95)

1

11

KA

As

ch

s= (A96)

K1 is a correction factor (Figure A.17); As and Ach denote the ship’s midship section area and the wetted cross sectional area of the channel or canal, respectively (Figure A.17). For open water (small s1, Ks = 1), the formula was adopted by ICORELS (1980).

Eryuzlu & Hausser (1978) proposed fol-lowing expression, valid for 1.08 ≤ h/T ≤ 2.78, based on model tests with three VLCCs with bulbous bow at self-

propulsion point:

1.80.27

0.113 hb FrT

hB s

−

= (A97)

Barrass (1979a) tentatively proposed fol-lowing empirical formula:

g

V

V

V

AA

ACs

smc

mBb

275.3

275.0

−= (A98)

based on squat results from different full scale and model test observations of ships with 0.5 < CB < 0.9 both in open water and in restricted channels for 1.1 < h/T < 1.5. For laterally unrestricted water the effective width Weff of the waterway is equal to

BCW WP ])(145[7.7 2eff −+= (A99)

Barrass (1979b, 1981) modified and sim-plified his initial formula to:

[ ]( )2.083

2

knots30

1V

AA

ACs

mc

mBmax

−

=

(A100)

Figure A.17 Correction factor K1 used by Huuska’s model for confined channels (PIANC/IAPH, 1997).



Figure A.18 Graphical method for prediction of squat of full-bodied ships (Dand, 1975).



Figure A.19 Cross-section of channel/canal: definitions (PIANC/IAPH, 1995)

which can be simplified to: ▫ in confined water, 1.1 < h/T < 1.2:

[ ]( )2max knots

50

1VCs B= (A101)

▫ in open water (0.06 < Am/Ac < 0.30):

[ ]( )2knots100

1VCs Bmax = (A102)

Fuehrer & Römisch (1974), reviewed by Römisch (1989), represent the bow and stern squat as fractions of critical values which are the values at the upper limit of the sub-critical speed range:

+

−

=

=≡

0.06250.584

crit

2

crit

critcrit

V

V

V

V

s

s

s

sC

,AP

AP

,FP

FPV

(A103) with:

TT

hs

TL

BC

T

hs

,AP

PP

B,FP

0.155

100.155

crit

2

crit

=

=

(A104)

and following critical speed values: ▫ unrestricted shallow water (m<0.167,

W/LPP > 3):

ghB

L

T

hV PP

0.125

crit 0.58

=

(A105)

and following critical speed values: ▫ canal with rectangular or trapezium-

shaped cross section (m>0.167, LPP/W<3):

ghKV c=crit (A106)

Kc being a function of Ac/Am:

Ac/Am 1 6 10 20 30 ∞

Kc 0.00 0.52 0.62 0.73 0.78 1.00 ▫ restricted channels:

mTT

cT

ch ghh

hK

h

hKV

+

−= 1crit

(A107) with

0.125

0.58

=

B

L

T

hK PP

ch (A108)

−−=

h

hhhh m

TmT 1 (A109)

Millward (1990) developed an expression for maximum bow squat in laterally un-restricted water based on model tests with various hulls (0.44 ≤ CB ≤ 0.83) in length to depth ratios L/h = 6 to 12:

1000.910.5515.0

2PP

h

h

PPBb

L

Fr

Fr

L

BCs

−

−=

(A110) Millward stated that his formula would “likely overestimate the squat and there-fore err on the side of safety”.



Millward (1992) derived a second em-pirical formula using Tuck’s basic for-mat:

2

2

1000.661.7

h

hPP

PPBb

Fr1

FrL

L

TCs

−

−=

(A111)

Eryuzlu et al. (1994) undertook thorough model tests with general cargo ships and bulk carriers with bulbous bow (CB ≥ 0.8, L/B = 6.7÷6.8, B/T = 2.4÷2.9) in laterally non-restricted water with restricted depth (1.1 ≤ h/T ≤ 2.5). The effect of channel width on squat was investigated in sup-plementary model tests carried out in a channel (height of dredged underwater trench hT = 0.5 h, bank slope n = 2). An empirical formula, valid for both chan-nels and canals, was obtained and evalu-ated by means of full scale squat meas-urements.

bb K T

h

gT

V

T

h s

=

2.972-2.2892

0.298

(A112) with

61.9when 1

61.9when 1.3

≥=

<=

B

WK

B

W

B

WK

b

b

(A113)

Kijima & Higashi (1995) propose follow-ing approximate formulae for sinkage and trim:

2

2

1 h

hs

M

Fr

FrC

L

s

−= ;

2

2

1 h

ht

Fr

FrC

L

t

−=

(A114) where

αβα

−−=

1MF

sCC

C ;

αβα

−−

=1

MFs

CCC

(A115)

( )

+−−×

×

+×

×∇=

PWPW

B

PWF

CCCC

CL

B

L

T

LCCC

754032

208.2253.21488

2

1

2

3π

A(116)

−

−+×

×

−

×

×∇−=

∗

∗∗∗

∗

2

32

39

452420

173.210.15233

4

1

WW

WPPWWPP

B

PWW

M

Ci

CCiCiCi

CL

B

L

T

LCCKC

π

(A117)

2

; ; ∗

∗∗∗ ====

W

WWP

K

ii

L

LCF

L

LCBi βα

(A118)

WW C

K105

4

28

32−=∗ (A119)

Ankudinov et al. (1996) proposed follow-ing method for predicting average sink-age:

▫ in deep water:

( )( )

−−

∞+=

B

LCFr

PAR_HULLKFrS

PPBL

SPL

10.05

1

4

2DEEP

(A120) ▫ in shallow water:

( )

( )

−−−

+

=

+

1010

SHALLOW

0.951

110.005

))((

))((1

h

PPBh

h

SP

FrB

LCFr

1CH_PARFr_PAR

T/HPARHULLs_PARK

S

(A121) ▫ hull effect:



++

−

=∞

2

2

0.2

0.060.8

PPPP

PPB

B

L

BT

L

T

B

LC

C

HULL_PAR

(A122)

22

004.07.1_ BPP

B CL

BTCHULLsPAR +=

(A123) ▫ propeller effect:

0.20.13:twin

0.10.1:single

00 :prop. no

======

TP

SP

TP

SP

TP

SP

KK

KK

KK

(A124) ▫ Froude depth number effect:

86

40.41.80

0.90.7

0.5

hh

hhFr

hh

FrFr

FrFrFr_PAR

++

+= +

(A125) ▫ channel effect:

( )h

hhh

S2CH_PAR

SSS1CH_PAR

51

11.5101 0.5

−=+−+=

(A126) S being the blockage factor (ship sec-tion / channel area), and Sh = S/(h/T).

For the trim, following method is proposed: ▫ in deep water:

( )( )

( )T/B_PARB

LC1Fr

01.0

TRIM_KHULL_PARFr

TRIM

PPBL

L

DEEP

−+

∞−=

=

4

22.5

(A127)

( )Tin

TTR

TB

TPB KKKKC

TRIM_K

++++−= 0.152

(A128) ▫ in shallow water:

( )( )( )( )

( ) ( )

−−+

−=

+10

10

0.95110.005

2

2.5

h

PPBh

h

SHALLOW

Fr

T/HPAR

B

LCFr

CH_PART/H_PAR

TRIM_KFr_PARHULLs_PAR

TRIM

(A129) ▫ bulb effect:

0:bulb no

0.1:bulb

==

TB

TB

K

K (A130)

▫ depth-draft ratio effect and depth-propeller effect on trim:

2

0.351

+=+ h

TT/HPAR (A131)

−

−= hFrT

h

eT/H_PAR

112.5

1 (A132)

▫ B/T effect:

2

0.10.201

−+=

T

B

T

BT/B_PAR

(A133) ▫ transom stern effect:

B

BK TRT

TR 0.1= (A134)

BTR being the transom stern breadth; ▫ non-zero initial trim effect:

FPAP

FPAPTin

TT

TTK

+

−= 5.0 (A135)

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Proceedings of the 23rd ITTC – Volume III 685

I. DISCUSSIONS

I.1. Discussion on the Report of the 23rd ITTC Manoeuvring Committee: Hydrodynamic memory effect

By: Masataka Fujino, University of Tokyo, Japan

First, I would like to appreciate great ef-fort of the Manoeuvring committee, and wish to make a brief comment on the hydrody-namic memory effect, to say, effect of fre-quency dependence of hydrodynamic coeffi-cients. This was one of the important issues discussed on the occasion of 14th ITTC, 1975, if my memory is correct.

In manoeuvring field, the quasi-stationary approach has been widely and long used. Ex-actly speaking, however, the hydrodynamic coefficients such as added mass and hydrody-namic damping coefficients are dependent on the frequency of motions. Therefore, the main discussion point at the former ITTC meeting was concerning the appropriateness of quasi-stationary approach.

Speaking more definitely, the frequency dependence of hydrodynamic coefficients should be considered in predicting the ma-noeuvring motion even in deep and/or unre-stricted water: this controversy was raised mainly by seakeeping people.

Replying to this controversy, several im-portant contributions were made by many per-sons including Prof. Bishop, Prof. Price, Prof. Nomoto, myself and so on.

I would like to suggest the Manoeuvring Committee to pay attention to those former discussions, and to refer to them in an appro-priate way.

I.2. Discussion on the Report of the 23rd ITTC Manoeuvring Committee: Validation of theoretical results through full-scale test data

By: Michael Schmiechen, Germany

Concerning squat I would like to draw the attention of the Conference to a very large project contracted by the German Wasser-strassen-Direktion Nord at Kiel in the early nineties with the goal to obtain a sound basis for decisions on designing and utilizing wa-terways. In view of the more than ill-defined traditional ‘formulae’ full scale squat meas-urements have been carried out with five Con-tainer ships on the River Elbe in five measur-ing sections, each two kilometers long.

VWS, the Berlin Model Basin, in fact I personally was in charge of the formidable task of the overall evaluation of the vast amount of data and finally was permitted to publish some of the results in a Squat-Workshop held at the Fachhochschule Olden-

The Manoeuvring Committee Committee Chair: Dr. Stéphane Cordier (Bassin d’Essais des Carènes)Session Chair: Dr. Arne Hasle Nielsen (Force Technology-DMI)



burg/Elsfleth in November 2000. The paper and its presentation, both in German, are to be found on my website. The essential result is that the full scale results confirm Tuck’s theo-retical results. After careful elimination of systematic effects the evaluation included not only the establishment of confidence ranges, but checks of statistical distributions.

I.3. Discussion on the Report of the 23rd ITTC Manoeuvring Committee: On the prediction method

By: Katsuro Kijima, Kyushu University, Ja-pan

The first of all, I would like to say con-gratulation for very interesting committee re-port, and also for effort of the committee members to investigate the problems in all fields of ship manoeuvrability.

I have a comment on Chapter 4, section 4.8 “Prediction Methods”. As everybody knows well, several kind of the prediction methods for ship manoeuvrability has already developed, but these methods have still some problems relating to accuracy.

From the practical point of view in ship design, we need to have a simple and high accurate method. Because we have to inspect the ship manoeuvring performance with the criteria of IMO Standards of Ship Manoeu-vrability.

Generally speaking, I suppose we have not so much full time to estimate the ship ma-noeuvring characteristics for inspection of the IMO criteria at design stage. Then it will be necessary to develop a simple, reliable and high accurate prediction method as possible.

As my personal opinion, I expect ITTC also should support to develop those predic-tion methods. Then I would like to ask the committee members to improve its accuracy

and to develop a simple, reliable and useful prediction method at design stage.

I.4. Discussion on the Report of the 23rd ITTC Manoeuvring Committee: On the squat prediction

By: Tao Jiang, VBD, Germany

First of all I want to congratulate the committee members for their comprehensive work. I have a comment to the squat predic-tion. In you report, many empirical formulae are listed for predicting ship’s squat and trim. For the practical applications they are often limited by large speed and complex bottom topography. So I would like to suggest to use the CFD tools, for instance, based on the ex-tended shallow-water approximations.

We have developed in Duisburg such a computer program. Numerical results show that it is efficient and reliable. Particularly, it works for arbitrary geographical configuration and can also be applied in the transcritical and supercritical speed range. Therefore, I wish the Committee would draw more attention to the CFD prediction of the ship’s squat and trim.

II. COMMITTEE REPLIES

II.1. Reply of the 23rd ITTC Manoeuvring Committee to M. Fujino

The committee wishes to thank Dr. Fujino for emphasizing the so-called memory effects in maneuvering simulations. The committee has concentrated its work on the tasks out-lined by the Advisory Council and hence has not considered this topic specifically. Fur-thermore, the literature survey has found little evidence of this research specifically oriented towards this topic, hence it has not been brought up in detail.


Proceedings of the 23rd ITTC – Volume III 687

II.2. Reply of the 23rd ITTC Manoeuvring Committee to M. Schmiechen

The committee wishes to thank Prof. Schmiechen for bringing up to the attention of the ITTC the existence of a data base on squat. The committee encourages Prof. Schmiechen to publish this work in an Inter-national Conference or publication.

II.3. Reply of the 23rd ITTC Manoeuvring Committee to K. Kijima

Thank you for your question. Yes, you are right, the ship designer needs a tool for pre-diction of ship manoeuvring at the ship design stage.

Now we know that the IMO manoeuvra-bility criteria are no longer interim, they will take effect as from next year. In the Commit-tee we think that the most reliable methods for manoeuvring predictions today are captive model testing or free sailing tests. For reliable

predictions at the design stage we will have to wait until the CFD methods become reliable and easy to use. In the meantime we can only try to improve the various regression methods that are being developed and refined at vari-ous institutions.

But, as said many times before, we still need more sets of benchmark data before any manoeuvring prediction method can be vali-dated satisfactorily.

II.4. Reply of the 23rd ITTC Manoeuvring Committee to Tao Jiang

The committee wishes to thank Prof. Jiang for pointing out the capability of CFD in computing maneuvering forces of ships in re-stricted waters. The report of the committee has emphasized the importance of these devel-opments which will constitute in the future a real alternative to classical simulation models.

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