SHIP MANOEUVRING
UNDER
HUMAN CONTROL
a n a l y s i s of the h e l m s m a n ' s
control b e h a v i o u r .
wim veldhuyzen
//2>i9 / 53 ^
00 o 00 M CD 0>
SHIP MANOEUVRING UNDER
HUMAN CONTROL
ANALYSIS OF THE HELMAN'S CONTROL BEHAVIOUR
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. DR. IR. H. VAN BEKKUM, VOOR EEN COMMISSIE, AANGEWEZEN DOOR HET COLLEGE VAN
DEKANEN, TE VERDEDIGEN OP WOENSDAG 16 JUNI 1976 TE 14.00 UUR DOOR WILHELMUS VELDHUYZEN , , , r / / J> è scheepsbouwkundig ingenieur geboren te Oegstgeest BIBLIOTHEEK TU Delft P 1138 1336 "O UI W O' 00
Dit proefschrift is goedgekeurd door de promotoren: LECTOR DR. IR. H. G. ST ASSEN
1
The research reported in this thesis has been executed v/ithin the Man-r%chine Systems Group of the Laboratory for Measurement and Control, Department of Mechanical Enp*ineerini? of the Delft Univer-sity of Technology. The research was sponsored by the Delft Uni-versity Foundation and by the Netherlands Organization for the Advancement of Pure Research (ZWO). The sim.ulator experiments were nade possible financially by the Netherlands Ship Research Centre
(TNO). In particular I will acknov/ledge the help of the sta^f members of the Institute TNO for Mechanical Constructions, who cooperated in running the experiments. The Royal Netherlands Naval College contributed in putting the training ship "Zeefakkel" at the disposal of the Man-Machine Systems Group. Many collaborators of the Delft University of Technology contributed in one or another way to this thesis. In particular I like to acknowledge Ir. C.C. Glansdorp of the Shipbuilding Laboratory for his contribution in the set-up of the experim^ents, Mr. J.F. Zegwaard of the Hybrid Computer Centre for his enthousiastic and valuable assistance in computer programming and data processing, and finally the students Mr. H.B.M. van Rooyen, Mr. P.O. van Holten, Mr. D.H.P. Snel, Mr. H.V/.J.M. van Gendt, and Mr. R.E. Schermerhorn, who each contributed with their Master of Science work partially to the total research program.
CONTENTS
page
CHAPTER I GENERAL INTRODUCTION
1.1 1.2 1.3 1.4 1.5 Problem statement 9 Modelling the helmsman: A review of literature 10
System identification 12 Outline of the thesis 15 Definition of symbols 16
CHAPTER II: SHIP DYNAMICS
2.1 2.2 2.3 2.4 2.5 Introduction
Models of ship manoeuvring The model selected
Parameter values
Ship motions due to waves
20 20 22 23 26
CHAPTER III: SHIP MANOEUVRING IN CALM WATER
3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.3 5.3.1 3.3.2 3.3.3 3.4 Introduction Experimental set up
The manoeuvring simulator Ship dynamics
Displays and controls
The ordered headings: The test signal Subjects
Experimental programme Data collection
Modelling the helmsman's control behaviour Preliminary analysis of the experiments Linear modelling •lonlinear modelling Parameter estimation 31 31 31 32 33 34 35 35 36 36 36 41 42 47
page
3.5 3.6
Results
Discussion and conclusions
49 56
CHAPTER IV: SHIP MANOEUVRING IN WAVES
4.1 4.2 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 4.4 4.4.1 4.4.2 4.5 4.6 Introduction 65 Extension of the nonlinear helmsman's model 66
Experimental set up 68
Ship dynamics 68 Displays and controls 70
The ordered headings: The test signal 72
Subjects 72 Experimental programme 72 Data collection 73 Prediction of scores 73 Model structure 73 Parameter values 76 Results 78 Discussion and conclusions 8I
CHAPTER V: 5 5. 5. 5 5 5 5 5 5 5 5 1 2 2 . 2 . 2 . . 2 . .2 .2 .3 .4 .5 1 2 3 4 5 6
FULL SCALE EXPERIMENTS WITH A SMALL SHIP
Introduction
Experimental set up Ship dynamics
Displays and controls
The ordered headings: The test signal Subjects
Experimental programme Data collection
The analysis of the experimental data Results
Discussion and conclusions
85 85 86 86 87 87 87 87 88 '89 93
-6-page CHAPTER VI: CONCLUDING REMARKS AND FURTHER RESEARCH
6.1 Results achieved , 97
6.2 Further research 100
SUMMARY 101
CHAPTER I: GENERAL INTRODUCTION
1.1 Problem statement
Progressively larger ships have been built during the last twenty five years [l]; the modern crude carriers often possess a length of more than three or even four hundred metres. As a consequence, the manoeuvring properties of these ships may differ from the conventional freighters. For instance, the very slowly responding supertankers
can be directionally unstable, which means that they tend to start turning to either starboard or port when the rudder is kept amid-ships. In particular this phenomenon was felt undesirable. There-fore, a lot of research has been devoted to the principle factors which influence mainly the handling quality of ships.
One of the first papers with a more theoretical approach on this subject was written by Davidson and Schiff [2], since that time many other studies were published [3, 4, 5, 6j. In particular, much attention was paid to the manoeuvring properties of large tankers
[7, 8, 9].
In trying to describe the handling quality of a ship it is important to state that the dynamic behaviour of a ship is not only determined by the dynamics of the ship itself, but also by those of the con-troller, i.e. the helmsman or autopilot. The system- Controller-Ship is a closed loop system; in order to obtain an optimal performance the dynamics of the ship and the controller must be known. In many
cases automatic controllers are applied to keep èhips on the de-sired course or the dede-sired track. Many authors treated the design of autopilots for course keeping [lO, 11, 12, 13, l4] ; also the design of controllers to steer ships along a prespecified track got rather much attention [l5, l6, 17]. At this m.oment emphasis is laid on automatic steering of ships in those circumstances where the dynamical behaviour is not constant, but time varying, so that an adaptive autopilot has to be preferred [l8].
Apart from the design of autopilots it is desirable to focus the attention on the human controller, as in rather dangerous circum-stances this controller is preferred to automatic steering. An example is a large tanker sailing in restricted water with an intensive traffic density. Not much is known about this manual
control of slowly responding systems (which are often unstable too). In particular data about the abilities of man to control slowly responding systems are unknown. Wagenaar performed a series of experiments to investigate the influence of auxiliary equipment, e.g. a rate of turn indicator, on the performance of helmsmen
controlling ships with different dynamical properties [l9]. However, this study does not yield information of the dynamical behaviour of helmsmen. Stuurman published the results of a study to model the helmsman's control behaviour; however, he only studied rather small and thus relatively fastly responding ships [.20, 21^.
But as stated before, to design a ship, which is optimal with res-pect to handling quality, information of the helmsman's control behaviour must be available. The study reported in this thesis is therefore aimed to obtain at least a part of this information. To restrict this wide area of research, the scope of this study is mainly limited to the helmsmen's behaviour during the control of a ship along a prescribed heading. The manual control of the ship's position, where often more people are involved, e.g. an officer, has not been studied. The investigations reported may be considered as a first attempt and should be followed by more extensive studies.
-9-For practical reasons a manoeuvring sim.ulator has been used. It could be adapted to well defined goals, because the ship dynamics and disturbances acting on the ship could be m.ade as desired in a relatively simple and cheap way. This is generally not the case with full scale trials, or tests with ship models [22, 23]. During the simulation the manoeuvring dynam.ics of the ships were represented by a mathematical m.odel. As the helmsman adapts his behaviour to the ship dynamics, the dynamic behaviour of ships, and the models des-cribing this behaviour constitute an essential part of the study. Using the results of the simulator tests an attempt has been made to develop a m.athematical model of the control behaviour of the helm.sman. In literature many human operator models are given. The literature reviewed is given in Ch. 1.2. To model the helmsman's behaviour a m.odel has to be selected on the base of certain
selection criteria. V/hen a model, suitable to analyze the helms-man's behaviour is chosen, the parameters of this model have to be estim.ated by means of param.eter estim.ation methods. In Ch. 1.3 an introduction is given to the identification of systems, as well as to the m.ethods, which can be used to estim.ate the model param.eters.
1.2 Modelling the helm.sman; A review of literature
Starting in the forties much attention has been paid to manual control problems. The function of the human operator therein v/as considered to be that of a controller; an element that has to close the loop in a certain optim.al v;ay. The manual control theory thus developed has resulted into a number of useful models, which will be shortly reviev;ed in this paragraph.
Based on linear system, theory the output of the human operator can be divided into two parts, one part which corresponds v;ith the response of an equivalent linear system, the describing function, and another part, the remnant, which represents the difference
between the response of the actual system, and the equivalent linear
element. The model is called the describing function model.
The hum.an operator adapts his control behaviour to the system under control in such a way that a stable and well dam.ped closed loop performance is achieved. McRuer has summarized many studies and recognized that the open loop describing function H^H,, near the crossover frequency can be approxim.ated by an integrator and a time delay; where Kp means the human operator describing function, H(, represents the controlled element dynam.ics, and where the crossover frequency is the frequency for which the open loop gain (HpH^,) eauals 1. In this way McRuer's well-knov/n crossover model has been obtained
[24, 2 5 ] :
HpHc = 3^ e-J'^^e, (1.1)
with H = human operator describing function; H^ = controlled element transfer function; (jü(, = crossover frequency;
Tg = effective time delay including neurom.uscular dynamics. Here it should be mentioned again that the describing function model is only based on stability considerations. It was developed to describe the human operator's behaviour in controlling relative-ly fastrelative-ly responding systems, such as aircraft,space vehicles, cars and bicycles. Applications of the crossover theory in the field of slowly responding systems could not be found in literature.
Another model, also originating from linear system theory is the optimal control model [26], This model is based on the assumption that the human operator behaves in a certain optimal way within his inherent limitations: He cannot observe without introducinp-noise; he cannot position the controls infinitely precisely, and finally he also needs a certain tim.e for data processing. This model, consisting of a Kalman filter, a predictor to compensate
for the human time delay, an optimal controller and observation and motor noises, is based on the assumed knowledpe the human
operator has about the system dynamics. Though this model is mostly used to describe the human operator in controlling fastly responding systems, it may be expected to be useful in relation to slowly
responding systems. No examples hereof are reported in literature as far as known.
Besides these two im.portant models m.any other models have been developed such as the decision model [27, 28], and many nonlinear models, which are mostly extended linear models [29, 30, 31, 32]. The decision model, based on statistical decision theory, describes the behaviour of the human operator in a system with abruptly
changing dynamics during the adaptation phase. When the human
operator has adapted his behaviour to the changed system dynamics, his behaviour can be described again with the crossover m.odel. The nonlinear models were often developed to obtain model outputs, which correspond better with the actual human operator output than the output of a linear model. The nonlinear elem.ents were mostly chosen rather intuitively, the applicability of these nonlinear models is restricted to the situation for which the model was developed.
All these models show one com.mon aspect: In order to provide a successful control behaviour the human operator needs some mation of the dynam.ics of the system, to be controlled; this infor-mation should also include knowledge of the disturbances actinr on the system. This knov;ledge is called an Internal Model, that is an internal representation of the knov/ledge the human operator has
[33]. The existence of such an internal model is implicitely true for the crossover model [24, 25], where the human operator adapts his control to the dynam.ics of the controlled element and to the band width of the system input; it is very clearly true for the optim.al control m.odel [26j and the decision model [27, 28], Some nonlinear models are based on the internal model concept too. Besides the many studies executed by control and system engineers as mentioned above, a number of studies have been reported by
psychologists. Some of these papers are related to specific situat-ions [33, 34J, other papers deal with the behaviour of the human operator in a more general way [35, 36]. The models are all more or less based on the internal model concept.
kn important aspect of the behaviour of the human operator con-trolling a slowly responding system, is his monitoring behaviour
[33]. The quantity to be observed is often changing so slowly that the human operator does not watch the indicators continuously, but in an interm.ittent way. Som.e studies on the human's monitoring behaviour can be mentioned [37, 38, 39] ; again these studies are based on the internal model concept.
To summarize the literature the following remarks can be made;
-11-• With a few exceptions, less attention has been paid to the human operator as a controller of slovrly responding systems. However, an increasing interest in the field of human control of slow response systems exists [4o].
• All models describing the human operator are more or less based on the internal m.odel concept. VJhen the internal model is an
explicit part of a system engineering m.odel, m.ostly the internal model contains all the information with respect to the controlled system, whereas the human operator may have less knowledge of the system dynamics.
• The following criteria to use a particular type of model to des-cribe the human operator's behaviour in a particular situation were found:
• The usefulness of the model to predict the human operator's control behaviour in terms of stability and damping of the system for conditions different from the test conditions. • Measures indicating how well the model output fits the human
operator output.
• The applicability of the model in practical situations such as display design. As an example the optimal control m.odel can be mentioned [4l].
• The character of the model output compared with the character of the human operator output. Sometimes nonlinear elements are used in connection with a linear m.odel to obtain a more
realistic model output [29, 30, 31, 32].
e The simplicity of the model: A simple model with only a few parameters describing the human operator's behaviour in a reasonable way often yields more consistent results than a multi parameter model [42]; moreover it is more convenient to apply in analyzing the human operator's behaviour.
1.3 System identification
An important part of this thesis is concerned with models describing the helmsman's control behaviour, where linear models as well as non-linear models are applied. To explain the problem.s encountered in the developm.ent of the models som.e introductory remarks about the identification of systems should be made.
As mentioned before the output of a non-linear system can be divided into two parts, one part which corresponds with the response of an equivalent liner system, the describing function, and an additional noise, the remnant (Fig. 1.1).
FlGURE 1.1:
Time domain representation of a system consisting of a linear model and a remnant.
The describing function is obtained by minimizing the variance of the error between system output and describing function output, the remaining error is then the remnant; it can be proven that the rem-nant and the input of the system or the describing function are un-correlated in the case of an open loop system. To identify the describing function, several methods are available, which can be divided into two main groups [43]:
• Methods without any a-priori knowledge. • Methods with certain a-priori knowledge.
In the case that no a-priori knov/ledge is available about the system to be identified, the identification should be achieved on the basis of general methods such as the determination of Bode or Nyquist plots from the analysis of deterministic test signals or spectral density functions of stochastic processes. For instance, in an open loop, the human operator describing function denoted by H(v) can be determined by the following well-known relation:
S (v) uy'
H(v) S (v). uu ^''' • (1.2)
In closed loop systems, however, the noise n(t) is correlated with the systems input e(t) due to the feed back loon (Fig. 1.2.a)
[^3, 45].
U(V) E{V)mv)
H ^ ( V J ^ Y(V) Z(V) H j f V ) N(l/) U(VI• ;
UHj(l/)H2(V)| H,(»/. 1 UHj(V)H^(»/)j ^v. N,(»/) f J Y(V) FIGURE 1.2:Trans formation of a closed loop system into an open loop system.
Therefore the determination of the describing function by minimi-zation of the variance of the error between system output and describing function output v;ill lead to a biased describing func-tion.
-13-However, by transforming the closed loop system, into an equivalent open loop system (Fig. 1.2.b), the method explained just-before can be applied again, hence it follows:
S (v) ue
(1.3)
In determining the describing function, estimated of the cross spectral densities S (v) and S (v) as well as of the auto spec-tral density Suu(v) ^Kould be^a\^lilable. Methods to determine these estimates S^y(v), Sue(^^) and S„^(v) of the spectra Suy(v), Sye(v) and Suu(v) abe given in the literature [44].
In the case that the structure of the linear system is known, para-meter estimation methods can be used. These m.ethods are based on the concept of minimization of an error criterion E(e,T) v.'ith
respect to the unknown parameters (Fig. 1.3). The general criterion to be minimized is:
E(e,T) = /^|e(t)1^ w(e-t) dt, e-T
(1.4) ;vhere e(t)
q
difference between system output and model output; factor indicating the influence of the magnitude of e(t);
w = v;eighting function to take into account the time his-tory of the error e(t).
u(t)
r»
stem linear modelT
SL
y(t)_1
linear | y ( > ' ^ f ^ ' ^ model minimizaiicn of E(-5,T) porameters FIGURE 1.3:Block diagram of system identification by means of parameter estimation.
The block diagram of Fig. 1.3 shows the method for an open loop system. In Fig. 1.4 a block diagram of a parameter estimation method, applied in a closed loop situation, is given; here the controlled elem.ent dynam.ics have to be known. It can be proven that this method results into consistent estimates in closed loop systems.
controlled system
•itJ
FIGURE 1.4:
Block diagram of a closed loop parameter estimation method.
Analoguous to the methods of linear modelling,the output of an open loop nonlinear system can be divided into a part resulting from a nonlinear model, having the same input as the nonlinear system, and an additional noise. As the number of possible non-linear elements, as well as the structures of a model built up with these elements, is unlimited, it is from the practical point of view not possible to conclude to a certain configuration by minimization of the variance of the error signal between m.odel output and actual system output. Therefore,this structure has to be chosen on the basis of a-priori knowledge of the system dynamics. To estimate the parameters of the nonlinear model, a general theory is not available. The parameter estimation m.ethods developed with respect to linear models can also be used in the case of nonlinear models. However, an analytical derivation of the estimators of the parameters to be determined, is not possible in general.
1.4 Outline of the thesis
This thesis deals mainly with the manual control of large ships. After giving an introduction into and a definition of the problem, a review of human operator models and some introductory remarks on system identification, the outline of the thesis and the definition of the symbols used are given in Ch. 1.
To study the helmsman's control behaviour in relation to the dyna-mics of ships, knowledge of the manoeuvring characteristics of ships should be obtained. Moreover the application of simulator tests
requires the choice of a mathematical model, describing the
dynamics of the ships to be simulated. To be able to analyze the test results, this model should be as simple as possible. In Ch. 2 some models will be discussed, a simple mathem.atical model will be selected, and for several ships, for which data could be found in literature, the parameters of the model chosen will be given. Ch. 3 summarises the results of a large number of tests with a manoeuvring simulator. To analyze the helmsm.an's control behaviour two types of models were used, viz. a linear model and a nonlinear model. This nonlinear model results from a prelim.inary analysis and from the literature reviewed in Ch. 1.
-15-Ch. 4 deals with a study of the influence of additional displays on the behaviour of the helmsm.an steering a ship in waves. The nonlinear m.odel, described in Ch. 3, had to be extended to be able to interprete the results of this study.
During the simulator studies (Ch. 3 and Ch. 4) attention vras focussed mainly on rather large ships. Fortunately, the Royal Netherlands Naval College m.ade it possible to conduct a
full scale trials with a rather sm.all ship. In this way of simulator tests, viz. linear and nonlinear m.odelling could be evaluated with respect to a small ship. In Ch. tests and the results obtained are described.
Some concluding rem.arks are made in Ch. 6; this chapter also gives some guidelines with respect to further research work in this field
series of the results results, 5 these
1.5 Definition of symbols
In Fig. 1.5 a block diagram is given of a ship under hum.an control.
disturbances » helmsman I — » steering | 6 ( t ) gear
i
ship FIGURE 1.5:Block diagram of the ship steered by a helmsman.
V^(t)
Using the steering v/heel, of which the position is denoted by <Sd(t), the helmsman controls the rudder position fi(t), by v.'hich the heading angle of the ship i(j(t) can be controlled. The heading angle is the angle between the longitudinal axis of the ship and the xo-axis of a right handed, orthogonal system, of coordinates fixed relatively to the earth: Ox y^z^ (Pif. 1.6).
FIGURE 1.6:
The X Q direction can be the south-north direction for example . The ordered heading is denoted by i|)(j(t). The positive direction of the heading is clockwise, just as for the rudder angle and the course ijj(t). The rudder angle is the angle betv/een the longitudinal axes of the ship and the rudder; the course angle is the anp-le between the direction of the ship velocity vector V and the x^-axis.
A second right handed and orthogonal system of coordinates Gyvz is defined, fixed relatively to the ship, having its origin at the ship's centre of gravity. The x-direction coincides with the ship's longitudinal axis. The components of the ship's velocity vector V in X- and y-direction are denoted by u and v respectively. In thTs study it is assum.ed that the ship's centre of gravity is constrained to the horizontal Oxoyo pla^^e, and that this plane coincides with the Gxy plane at all tim.es.
REFERENCES •" ' ' 1. Koele, L.A.,
Behaviour of larf^e tankers in shallow water in relation to the dimensions of an approach channel.
Proc. Symp. on Offshore Hydrodynamics.
Public: Netherl. Ship Model Basin, Vfapeninpen, 1971, Mo. 375, pp. 12,1 - 12,20.
2. Davidson, K.S.M.; Schiff, L.I.,
Turning and course keeping qualities.
Trans, of the S.N.A.M.E., Vol. 5t (igl^ö), pp. 152-200. 3. Nomoto, K.; Taguchi, T.; Konda, K.; Hirano, S.,
On the steering qualities of ships. I.S.P. Vol. iJ (1957) No, 35, pp. 35')-370.
H. Abkowitz, M.A. ,
Lectures on hydrodynamics.
Report: Lyngby (Denmark), Hydro og Aerodynamisk Laboratorium., 1964, 113 p. No. Hy-5.
5. Eda, H.; Crane, C.L.,
Steering characteristics of ships in calm water and waves. Trans, of the S.N.A.M.E. Vol. 73 (1965), pp. 135-177. 6. Norrbin, N.H.,
Theory and observations on the use of a m.athematical model for ship m.anoeuvring in deep and confined waters.
Public: Gothenburp:, SSPA, 1971, No. 68, 117 p. 7. Glansdorp, C O . ; Buitenhek, V.,
Manoeuvring trials with a 200,000 tons tanker.
Report:.Delft, Shipbuilding Laboratory, 1969, No. 248, 31 p. 8. Glansdorp, C . C ,
Simulation of full scale results of manoeuvring trials with a 200,000 tons tanker with a simple mathematical model.
Report: Delft, Shipbuilding Laboratory, 1971, No. 301, 24 p. 9. Clarke, D.; Patterson, D.R.; Vfooderson, R.K.,
Manoeuvring trials with the 193,000 tonne deadweight tanker "Esso Bernicia".
Paper: Spring Meeting of the Royal Inst, of Naval Architects, 1972, No. 10, 14 p.
10. Hozos, A,; Thaler, G.J.,
Automatic control of directionally unstable ships.
Proc Fourth Ship Contr. System.s Symp., Royal Netherl. Naval College, Den Helder, 1975, Vol. 3 pp. 30-41.
11. Bech, M.I.,
Some aspects of the stability of automatic course control of ships. Proc. Int. Symp. on Directional Stability and Control of Bodies Moving in Water, Journ. Mech. Engineering Science, Vol. 14 (1972) No. 7, pp. 123-131.
12. Winkelman, J.E.W.,
Analyse en synthese van stuurautomaten.
Symp. Modelvorming voor scheepsbesturing. Delft, 1970, 17 p. 13. Horst, J.A.M, ter,
Vergelijking van stuurautomaten.
14. Koyama, T.,
Some notes on the auto-pilot of an unstable ship.
Report: Delft, Shipbuilding Laboratory, 1971, No. 327, 23 p. 15. Zuidweg, J.K.,
Automatic guidance of ships as a control problem. Diss.: Delft, 1970, 136 p.
16. Koyama, T.; Kimura, Y.,
An application of Kalnan Filter to the discrete time route trackinr of ships.
Proc Fourth Ship Contr. Systems Symp., Royal Netherl. Naval College, Den Helder, 1975, Vol. 1 pp. 170-184.
17. Canner, W.H.P.,
The accuracy requirements of automatic path guidance.
Proc Fourth Ship Contr. System.s Symp., Royal Netherl. Naval College, Den Helder, 1975, Vol. 1 pp. 141-151.
18. Amerongen, J. van; Udink ten Cate, A.J.,
Model Reference Adaptive Autopilots for Ships. Autom,atica, Vol. 11 (1975), pp. 441-449.
19. V/agenaar, V.'.A.; Paymans, P.J.; Brummer, G.M.A.; Wijk, V.'.R. van; Glansdorp, C.C Auxiliary equipment as a compensation for the effect of course
instability on the perform.ance of helmsm.en.
Com.munication Netherl. Ship Research Centre TNG, Delft, 1972, No. 28 S, 21 p.
20. Stuurman, A.M.,
Modelling the helmsman: A study to define a mathematical model describing the behaviour of a helmsman steering a ship along a straight course.
Report: TNO-IWECO, Delft, 1969, No. 4701, 59 p. 21. Stuurman, A.M.,
Human transfer function in ship steering; the effect of feel in the wheel.
Proc Fourth Ship Control Systems Sym.p., Royal Netherl. Naval College, Den Helder, 1975, Vol. 6, pp. 112-130.
22. Brug, J.B. v.d.,
Simulation of ship manoeuvring qualities.
Report of the post graduate course: Design and economical considerations on shipbuilding and shipping.
Wapeningen, Veenman, 1969, pp. 315-333. 23. Wagenaar, W.A.; Michon, J.A.,
The effect of contracted time scales in scale model manoeuvring. Report: The Institute for Perception, Soesterberg, 1968,
No. IZF-1968-C3. 24. McRuer, D.T.; Jex, H.R.,
A review of quasi-linear pilot models. IEEE-trans, on Human Factors in Electronics, Vol. HFE-8 (1967), No. 3 (Sept.), pp. 231-249. 25. McRuer, D.T.; Krendel, E.S.,
Mathematical models of human pilot behaviour. Report: NATO-AGARD, No. 188, 72 p.
26. Kleinman, D.L.; Baron, S.; Levison, W.H.,
A control theoretic approach to manned-vehicle systems analysis. IEEE-trans, on Autom.. Contr.
Vol. AC-16 (1971), No. 6 ( D e c ) , pp. 824-832. 27. Elkind, J.I,; Miller, D.C.,
On the process of adaption by the human controller.
Proc Third IFAC congress on automatic and remote control, London, June 1966, Vol, 1, book 2, paper 30A, 13 p.
28. Elkind, J.I.; Miller, D.C.,
Adaptive characteristics of the human controller of time-varying systems. Springfield, NTIS, 1968, 191 p. AD-665-455.
29. Diamantides, N.D,,
A pilot analog for airplane pitch control,
Journ, Aeronautical Sci, Vol. 25 (1958), pp. 361-370. 30. Costello, R.G.,
The surge m.odel of the well-trained human operator in simple manual control,
IEEE-trans, on Man-Machine Systems, Vol. r'MS-9 (I968), No. 1 (March), pp. 2-9.
31. Pitkin, E.T.,
A non-linear feedback m.odel for tracking studies. Proc. Eighth Conf. on Man. Contr., Ann Arbor, 1972, AFFDL-TR-72-92, pp. 11-22.
32. Phatak, A,V.; Weir, D.H.,
On the dynamic response of the human operator to transient inputs. Proc Fourth Conf. on Man. Contr., Ann Arbor, 1968,
NASA-SP-192, pp. 383-392. 33. Cooke, J.E.,
Human decisions in the control of a slow response system. Diss.: Oxford, 1965, 403 p.
34. Bainbridge, L.,
The nature of the mental model in process control.
Paper presented at Symp. on Man-Machine Systems, Cambridge (U.K.), 1969, 10 p,
35. Kelley, C.R.,
A psychological approach to operator modelling in manual control. Proc, Third Annual Conf, on Manual Control, Los Angelos, 1967, NASA-SP-126, pp. 165-180.
36. Kelley, C.R.,
Manual and autom.atic c o n t r o l . New York, Vfiley, 1968.
37. Senders, J,W.,
The human operator as a monitor and controller of multidegree of freedom system.s,
IEEE-trans, on Human Factors in Electronics, Vol. HFE-5 (1964), No, 1 (Sept.), pp. 2-5. 38. Smallwood, R,D,,
Internal models and the human instrument r.onitor, IEEE-trans, on Human Factors in Electronics, Vol, HFE-8 (1967), No. 3 (Sept.)., pp. 181-I87. 39. Rouse, W.B.,
A model of the human in a cognitive prediction task, IEEE-trans, on Systems, Man and Cybernetics,
Vol. SMC-3 (1973), No. 5 (Sept.), pp, 473-477, 40. Int, Symp. on Monitoring behaviour and supervisory control.
Berchtesgaden, 1976. To be published. 41. Kleinman, D.L.; Baron, S.,
Analytic Evaluation of Display Requirements for Approach to handing, Report: Cambridge (U.S.A.)', Bolt Beranek and Newman, NASA CR-1952. 42. Johannsen, G.,
The design of a non-linear multi-parameter model for the human operator.
In: Displays and Controls, Proc. Adv. Study Institute, Berchtesgaden. Amsterdam, Swets and Zeilinger, 1972, pp. 249-367.
43. Lunteren, A. van; Stassen, H.G.,
Annual Report 1969 of the Man-Machine Systems Group.
Report: Delft, Dept. of Mech. Engineering, 1970, WTHD 21, 102 p. 44. Jenkins, G.M.; Watts, D.G.,
Spectral Analysis and its Applications, Holden Day, I969.
45. Lunteren, A. van,
Systeem identifikatie en parameter schatting in open en gesloten ketens.
CHAPTER II: SHIP DYNAMICS
2.1 Introduction
To perform, simulator experiments a mathematical model describinfr the behaviour of a ship had to be selected. Keeping in mind the objectives of this study, the following requirements viith respect to such a model should be form.ulated:
• The responses of the model to any rudder angle inout must be as realistic as possible.
• To be able to analyze the test results the model should be as simple as possible. As the study is only concerned with the
behaviour of helmsm.en steering a ship alonr prescribed headings, only the relation between rudder angle and heading is iriportant. By a sim.ple model is meant, a model simple with respect to its structure and with a sm.all amount of parameters.
• The tests should provide information about the im.portance of different manoeuvring properties such as sluggishness and course instability.
• It should be possible to introduce also the influence of v:aves in the simulation.
Before the model used can be selected, a brief review of mathem.a-tical models describing the m.anoeuvring behaviour of ships will be given.
2.2 Models of ship manoeuvring
The steering of ships has been studied already for many years, but the more scientific approach started just in the forties. In 1946 Davidson and Shiff published a method to analyze the behaviour of ships, which can be regarded as the base of all later research on this subject [l] .
From elem.entary mechanics the equations of Euler for a sym.metric ship moving in the horizontal plane are known:
X = m (Ü - vr) ; (2.1-a) . Y = m (v + ur) ; (2.1-b)
N = 1^2^ , (2.1-c) where X = hydrodynamic force in x-direction;
Y = hydrodynamic force in y-direction; N = hydrodynamic moment;
m = ship's mass;
Izz = ship's m.om.ent of inertia about the z-axis; r = dij;(t)/dt = angular velocity.
Referring Un, r-n"^» Vn = 0 and 6^=0 as the nominal conditions, the following linearized equations of motions can be derived:
(X^^-m)u + X^Au ( Y . - m ) v + Y v + Y*f + V v r N'V + N V + (N'-I )f + V V r zz = 0 ^-m.u^)r = -Yg5
V =
-^6^
( 2 . 2 - a ) ( 2 . 2 - b ) ( 2 . 2 - c )In Eqs. (2.2) the subscript means the partial derivative with respect to the specific variable, and the quantity u^ denotes the constant forward speed. This model, consisting of three equations of which two equations are coupled, is based on the following assumptions:
• The ship is a rigid and sym.metric body.
• Only the motions in the horizontal plane are considered.
• The centre of gravity is considered to be situated in the Ox y plane, which is the water plane. ° °
• The X, y, and z-axes are the ship's principle axes of inertia. • The influence of external disturbances such as wind, v;aves or
current is neglected.
• The ship is sailing in unrestricted viater.
• The propeller is kept at a constant num.ber of revolutions. • The perturbations of the variables around the equilibrium, are
small.
To include also larger variations of the variables the model has to be extended v;ith nonlinear term.s. In this v;ay many different models have been suggested [2, 3, 4 ] . However, these m.odels have a rather large number of param.eters. To study the behaviour of a helmsm.an a much siripler miodel is to be preferred.
By elim.inating the drift speed v from, the Eos. (2.2-b) and (2.2-c) a single differential equation is obtained, knov/n as Nom.oto's
second order model [5]:
T^T2^(t) + (T^+T2)if(t)+iI^(t)=K[T^(5(t) + 6(t)], (2.3) where the parameters T., Tpj and T, are called time constants and
K is a gain factor. These parameters are functions of the partial derivatives in the Eqs. (2.2). If the rudder m.otions are low
frequent, this equation can be replaced by a simple first-order differential equation in the rate of turn [5, 6 ] :
Ti|}(t) + ii)(t) = K6(t). (2.4) Some authors extended these two miodels to obtain
with full scale test results [6. 7, 8, 9 ] . They r i|i(t) by a nonlinear function H[i|i(t)], for which o polynomial is,used. Wellknown models in this resp of Bech [7] :
T^T2'ii.'(t) + (T^+T2)i(}(t)+H[iI»(t)]=K[T^é(t) + 6(t and of Nomoto - Norrbin [6, 8 ] :
T if(t) + il»(t) + a
a better agreemient eplaced the term ften a cubic
ect are the model
)] (2.5)
[Ht)]^ = K6(t).
No simple mathem.atical model describing the manoe in waves has been found. Mostly a sum of sine v;a noise, is added to the output of the model descri of the ship in calm, water, in such a way that the output of the model obtained m.eets the actual spe motions of a ship in waves (Fig. 2.1).
(2.6) uvring of ships ves or a coloured bing the behaviour
spectrum of the ctrum. of the ö(t) model of shipdynamics in calm water V^l») ship motions due to waves • u * mt) FIGURE 2.1:
Model describing the behaviour of a ship in waves.
-21-2 . 3 The m.odel selected
On the basis of the requirements Fiven in Ch. selected. Nomoto's first-order m.odel (2.4) ha and is one of the sim.plest models developed t m.anoeuvring properties. The stationary charac between the rudder angle and the rate of turn is linear. However, from full scale experimen this stationary characteristic often is nonli shape of this curve might influence strongly our, also ships with different characteristic This mioans that a nonlinear m.odel had to be u of Bech or Norrbin [7, 8 ] . As Norrbin's model cribes the behaviour of ships viith characteri Pig. 2.2 rather well, this model had to be ch
2.1 a model has been 5 only two param.eters o describe ship
teristic - the relation in the steady state -ts it is known that near [10] . As the the helmsman's
behavi-s had to be behavi-simulated. sed, e.g. the models
is simpler and des-stics as shown in osen.
FIGURE 2.2:
Stationary characteristics of a directionally stable and an directionally unstable ship.
However, twin screw ships with one rudder situated at the ship's centerline can show a stationary characteristic different from Fig. 2.2, but one like Fig. 2.3.
Ö [deg]
FIGURE 2.3:
Stationary characteristic of a twin screw ship with one rudder situated at the shiv's
To be able to simulate also this type of ships the Norrbin model was extended with a second nonlinear term:
Tgi(;(t)+a^iJ^(t)+a2['l'(t)]^+a^[iKt)]^^^ = K^6 (2.8)
Model (2.8) was finally used during the simulator experiments. It has been chosen mainly because of its simplicity, although also the three remaining requirements were fulfilled. In paragraph 2.4 a review is given of ship data in terms of this model as found in literature. It was hoped that those data were sufficient to choose the model parameters in such a v;ay that realistic sim.ulations could be obtained.
To control the rudder position often a hydraulic servo-system is used. Som.e models describing such a system are given by Bech and Brummer et. al. [lO, ll] . Though the actual dynamics are much more complicated, the dynam.ic behaviour can be approxim.ated in a reason-able way by m.eans of a first-order differential equation. Because of the lim.ited capacity of the oil pumps, the angular velocity of the rudder is lim.ited. The following model is thus obtained:
Tj 6(t) + 6(t) = <S^(t) ; (2.9-a)
|5(t)| < 6^ , (2.9-b)
•
v;here T 5 is a time c o n s t a n t and 6^ is t h e m a x i m u m r u d d e r a n g u l a r v e l o c i t y . In F i g . 2.4 t h e b l o c k d i a g r a m of t h e s t e e r i n g g e a r , a p p l i e d d u r i n g the e x p e r i m e n t s , is g i v e n .
öd(t)
FIGURE 2.4:
Block diagram of the steering gear.
2.4 P a r a m e t e r v a l u e s As m e n t i o n e d b e f o r e , t h e d y n a m i c s o f t h e s h i p s t o b e s i m u l a t e d should b e as r e a l i s t i c a s p o s s i b l e . In o r d e r t o o b t a i n d a t a to imiprove s u c h a sim.ulation, t h e l i t e r a t u r e o n s h i p s t e e r i n g v m s t h e r e f o r e r e v i e w e d . A t e c h n i q u e u s e d by m a n y a u t h o r s t o m o d e l ship d y n a m i c s is b a s e d o n s p e c i a l t e s t s o r z i g - z a g t e s t s . T h e s e d a t a , h o w e v e r , had t o b e t r a n s f o r m e d in t e r m s o f t h e n o n l i n e a r m o d e l . T h e r e s u l t s o f t h e s p i r a l t e s t s w e r e used to estim.ate t h e m o d e l p a r a m e t e r s a ^ , 32, S-j, and Kg b y m e a n s o f a l e a s t s a u a r e d e r r o r m e t h o d . T h e r e s u l t s o f t h e z i g z a g t e s t s w e r e u s e d to e s t i -m a t e t h e para-m.eter T 3 . As only a r o u g h e s t i -m a t i o n w a s n e e d e d , so-me a p p r o x i m a t i o n s w e r e i n t r o d u c e d in e s t i m a t i n g Tg ( F i g . 2 . 5 ) : e T h e r u d d e r e n g i n e d y n a m i c s w e r e n e g l e c t e d . o T h e h e a d i n g ^(t) w a s c o n s i d e r e d t o b e a s i n u s o i d a l s i g n a l . • T h e n o n l i n e a r e l e m e n t s w e r e approxim.ated by t h e i r d e s c r i b i n g f u n c t i o n s .
I — » J 5(t)dt
ö(t) 2 3-•%n «0 ^ 0
1
1 öitJ 1 Ks 4 1 1 i * tnoaei shipdynamicsL
1f
J
V'\
1 s ^^ " 1 V^f'l . J FIGURE 2.5:Block diagram of the model during a zig-zag test.
In this way the following formula could be obtained:
T 6 / ilJ,^ - 6 ^ T.^ s o ^1 o 1
7
TT^ ii^
(2.10)where 6 = actual rudder amplitude;
i)^ - am.plitude of the heading;
T. = period of one oscillation.
The results of the parameter estimations are given in Table 2.1. VJith respect to this- table the following remarks can be made:
9 A relatively small amount of full scale tests has been performed The larper part is related to larp-e ships.
© Not any ship with stationary characteristic like Fig. 2.2 has been found, except the railroad ferrv when sailing backwards
[11].
o In accordance to Norrbin [8] and Bech [?] the coefficient a^ was kept equal to 1 or -1 depending on the fact that the ship was stable or unstable. Some m.arginally stable ships v/ere found where B.^ is equal to zero. In these cases the parameter values were__norm.alized v/ith respect to Kg which was kept eoual to -.05
sec -1
A large number of ships were examined by Nom.oto [25] . Based on zig-zag tests v.'ith about seventy ships, the parameters of
Nomoto's first-order m.odel v/ere calculated. As this model
approximates the stationary characteristic by a straight line, Nomoto's data do not provide inform.ation about the actual shape of the stationary characteristics of the ships.
The literature reviewed does not provide enough information to choose the model param.eters of a range of ships to be sim.ulated.
TABLE 2.1: Summary of the manoeuvring properties of different ships, found in literature.
Kind of ship Railroadferry Passenger and Cargo Liner Cargo Liner Container ship Tanker Loaded Ballasted Tanker Loaded Undeep water Ballasted Undeep water Bulkcarrier Bulkcarrier Tanker Tanker Unknown Unknown Cruise ship Pilot boat Trainingship Deadweight tons 42 900 200 000 193 000 69 250 3 200 80 000 50 000 SHIP Length m 139.6 134.0 135.6 273.0 310.0 304.9 242.8 62.8 221.0 313 307 106 59 41 DATA Breadth m 17.4 20.0 18.9 32.2 46.9 47.2 32.2 15.3 29.6 48.2 48.2 10.6 7.5 Draught m 5.9 5.4 7.8 8.1 18.9 dj- 7.3 djj-11.0 18.1 dj- 7.8 d^-10.8 12.8 4.9 12.5 19.4 19.4 3.7 2.2 Displ. m' 9 100 7 300 13 170 238 000 106 000 215 000 3 800 65 089 250 251 250 750 382 Speed Knots 19.8 23 16.5 20 15 15.5 10.5 13.8 14 12 10 8 12 8. PARAMETERS MODEL ^s sec 51 28 25 33 264 46 135 89 — 234 --207 76 208 185 28 20 18 25 •'s sec-1 -.22 -.10 -.05 -.04 -.05 -.04 -.05 -.05 -.04 -.04 -.05 -.09 -,14 -.06 -.07 -.05 -.05 -.05 -.12 -.92 -.63 -.26 -.25 -.10 »1 -0.156 -1. .125 -1. -1 . -0.046 -0.042 -0.23 "2 « ! • ) ' .72 .49 .47 4.12 16.5 24.3 3.6 4.9 20.0 20.0 26 39. 6. 63. 3.8 5.3 7.4 10. ,22 1.07 1.59 2.10 .13 .04 "3 c-i»)*"' .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 1 REF. 11 12 13 14 15 15 9 15 9 16 17 18 19 20 21 21 22 23 24
2 .5 Ship m.otions due to waves
To study the control behaviour of a helmsm.an steering a ship in a sea-way, the behaviour of ships in waves had to be known. As this study was mainly based on fixed base sim.ulator experiments (Ch. 3 and 4 ) , only the yawing motions had to be considered. To introduce the disturbances in the sim.ulations, a signal simulating these yawing motions had to be available.
In calculating the ship motions in irregular sea, often a linear model based on the potential theory is applied [26, 27]. The re-sults hereof show a fair agreem.ent between predictions and measure-m.ents [28]. The random, sea surface, denoted by ^ ( X Q , V Q , t ) , is assumed to be composed of an infinite number of sinusoidal compo-nents with different am.plitudes, frequencies and phases. Formulas describing the spectral density of the sea waves as function of the circular frequency '^ are given by Neumann [29], and by Pierson and Moskowitz [30] . The dynam.ic of a ship can be described just as the sea surface, by statistical methods. V.'hen the spectral density of the sea surface is denoted by S?c('^p), and the ship's responses are given by the transfer function H,jj^(^Wg)j the spectrum of the
can be calculated bv: ship's yawing m.otions S^.^ C^p)
s^^(%) =
iH^^(^e) ; (" ) .^C^ e^
(2.11)
It should be noted that the spectrum and the transfer function depend on the frequency of encounter ^ . The wave spectrum based on the wave frequency ^ has to be transform.ed to a v;ave spectrum based on the frequency of encounter Wg. The relation betvjeen oj and ü3g follovjs from, classical wave theory and is given by:
U) |(o -ülJi cos y| cj^V
g
(2.12)
where V = ship speed;
g = acceleration of gravity;
y = angle between the ship's velocity vector V and the wave velocity c (Fig. 2.6).
V ^
\ \ \ \ \ \ \ \ \ \ \ \ \ FIGURE 2.6:A ship sailing in a regular sea; V - ship speed;
c_ = wave velocity;
The spectral density of the waves as function of wg can be computed from the spectral density based on u by means of the following
formula:
==U<"e) - Sec'"' % • (2-">
where du/dcog can be computed using Eq. (2.12). However, the fre-quency ID is not a uniquely function of I>)Q. T O transform the wave spectrum S (OJ) into S^^((Dg) the spectrum S^^(a)) should be divided into parts^for which the relation between u and Wg is unique. Each of these parts result in a part of the spectrum S55((jL)g), which m.ay coincide with the other parts. The spectral density S^^(ue) is obtained by adding for each Wg the densities resulting from, the transformation of each part.
The ship's responses to the wave exerted m.oments are given by the following differential equation:
where I = ship's moment of inertia; Nr = damping coefficient;
NÏ = added mass;
N^ = hydrodynamic mom.ent.
The transfer function can be written as:
H, (joj ) = -, rrf w \ • rr—r • (2.15)
The hydrodynamical coefficients N.. and N^ can be estimated using the so called strip theory [27, 31, 32]. Starting points are the known two-dimensional solutions for the cross-sections, which can be computed by means of conform.al mapping. By integrating the cross-sectional values the result for the three dimensional ship is found [28] .
The right hand side of Eq. 2.l4, the wave exerted mom.ent, can be approximated by the assumption that the presence of the ship does not influence the pressure in a wave. This pressure, known from wave theory, can be integrated over the ship's hull, where a
correction is needed to take into account the relative motion of the ship. In this way the moment exerted by one wave component can be calculated. As a liner theory is used a linear transfer function Hj^r(jü)g) can be defined, describing the moments acting on the ship in regular as well as irregular waves. The spectral density of the ship's yawing motions then can be estimated by the formula:
^^^'^e^ -- l % ^ > e ) • "nS^J'^e^l^ h^^'^e?' ^^.16) To perform the computations described above the Delft Shipbuilding
Laboratory has completed a number of com.puter program.s. Using these programs the motions of a ship in regular waves, i.e. the transfer functions Hjor(ü3g), can be computed, and using the wave spectra as given by Pierson and Moskowitz [30] Sr^(we) can.be calculated as described above.
-27-The calculation of the ship m.otions in waves is based on frequency domain methods. However, as stated before a signal to be added to the output of the model describing the ship's responses to rudder actions, v;as required. An approxim.ation of such a signal can be obtained by a sum of a large, but finite number of sine v.'aves, with properly chosen amplitude, phase and freauency. Therefore, the calculated spectrum S..(tüg) is divided in small bands with ;
bandwidth Aw (Fig. 2.7). a
>^^(We'
FIGURE 2.7:
Approximation of the continuous spectrum by a discrete spectrum.
The sine waves are chosen in such a way that the frequencies eauals the central frequencies of each of the bands. The amplitude of each component is selected in such a way that the power of a particular component equals the power within the corresponding band. Finally the phases are chosen randomly.
REFERENCES
1. Davidson, K.S.M.; Schiff, L.I.,
Turning and course keeping qualities.
Trans, of the S,N,A,M.E. Vol. S't (.19'iè), pp. 152-200. 2. Abkowitz, M.A.,
Lectures on hydrodynamics.
Report: Lyngby (Denmark), Hydro og Aerodynamisk Laboratorium, 1964, 113 p., Hy-5.
3. Eda, H.; Crane, C.L.,
Steering characteristics of ships in calm water and waves. Trans, of the S.N.A.M.E., Vol. 73 (1965), pp. 135-177. 4. Norrbin, N.H.,
Theory and observations on the use of a m.athematical model for ship m.anoeuvrinp in deep and confined waters.
Public. Gothenburg, SSPA, 1971, 117 p.. No, 68, 5. Nomoto, K,; Taguchi, T.; Honda, K.; Hirano, S,,
On the steering Qualities of ships, I,S,P, Vol, 4 (1957) No, 35, pp. 354-370. 6. Nomoto, K.,
Problems and requirements of directional stability and control of surface ships.
Proc. Int. Sym.p. on Directional Stability and Control of Bodies Moving in Water, Journ. N'ech. Engineering Science, Vol. l4 (1972) No. 7, pp. 1-5.
7. Bech, M.I.; Wagner Smitt, L.,
Analogue simulation of ship manoeuvres based on full scale trials or free-sailing model tests.
Report: Lyngby (Denmark), Hydro og Aerodynamisk Laboratorium, 1969, 24 p. No. Hy-14.
8. Norrbin. N.H.,
On the design and analysis of the zig-zag test on base of quasi-linear freauency response.
Proc. Tenth Int. Towing Tank Conf. 1963, pp. 355-374, 9. Glansdorp, C . C ,
Simulation of full scale results of manoeuvrinr trials with a 200,000 tons tanker with a simple mathematical model.
Report: Delft, Shipbuilding Laboratory,' 1971, 24 v., No. 301, 10. Bech, M.I.,
Some guidelines to the optimum adjustment of autopilots in ships. Proc. Symp. fodelvorm.ing voor scheepsbesturing. Delft 1970, 32 p. 11. Brix, J.; Fritsch, M.,
Eisenbahnf"ahrschiff "Deutschland". Modellversuche und Bordmessungen. 372. Mitteilung der Ham.burgischen Schiffbau Versuchanstalt.
Schiff und Hafen, Jahrg. 24 (1972) Heft 11, pp. 791-795. 12. Enkvist, E.; Saarikangar, K.,
"Finlandia" Finish-built Passenger and Car Liner
Some Design Considerations. Shipping V.'orld and Shipbuilder Vol. 160 (1967) No. 3811 (Sept.) pp. 1500-1513.
13. Lindgren, H.; Norrbin, N.H.,
Model tests and ship correlation for a cargo-liner.
Trans, of the Royal Inst, of Naval Architects. Vol. 104 (1962), pp. I4l-l8l.
14. Containerschiff "Bremen Express". HANSA
Jrg. 109 (1972) STG-Sondernumm.er II (Nov.) pp. 2043-2076. 15. Glansdorp, C . C ; Buitenhek, V.,
Manoeuvring trials with a 200,000 tons tanker.
Report: Delft, Shipbuilding Laboratory, 1969, 31 p.. No. 248. 16. Clarke, D.; Patterson, D.R.; Wooderson, R.K.,
Manoeuvring trials with the 193,000 tonne deadweight tanker "Esso Bernicia". Paper presented at Spring meeting 1972 of the Royal Inst, of Naval Architects, No. 10, 14 p.
17. Chirila, J.V.,
Sea trials of the "Sighansa". Part I. Pronulsion and Manoeuvring tests. Shipping World and Shipbuilder. Vol. 156 (1965) No. 3773 (Dec.)
pp. 533-541.
18. "Mini Luck" Japanese-built mini bulk carrier.
Shipping World and Shipbuilder. Vol. 162 (1969) No. 3834 (June) pp. 817-Ö21.
19. Lehmkuhl, J.; Chirilia, J.V.; Gerbitz, U.; "arx, K.H., Turbinentankschiff "Altanin".
Schiff und Hafen, Jrg. 16 (1964) Heft 11 (Nov.) pp. 1033-1061. 20. Clarke, D.,
Manoeuvring trials with the 50,000 tons deadweirht tanker "British Bom.bardier".
Report:. BSRA, 1966, No. NS-142, 21. Fujino, M.; Motora, S.,
On the modified zig-zag manoeuvre and its anplication. In: Selected papers SNA Japan, Vol. 9 (1972) pp. 133-148. 22. Hebecker, 0.,
Das Manover "Mann über Bord".
Schiff und Hafen, Jrg. 15 (1963) Heft 10, pp. 963-966. 23. V.'inkelman, J.E.V.'.; Am.erongen, J. van,
Verslag van de metingen verricht aan boord van de loodsboot "Capella" van 040472 tot 180472.
Report: Delft, Laboratorium voor Regeltechniek, nn. 1-10. 24. Verstoep, N.D.L.,
Verslag van de metingen verricht aan boord van de "Zeefakkel" van 221073 tot 241073.
Report: Delft, Laboratorium, voor Pegeltechniek, pp. 1-8. 25. Nomoto, K.,
Analysis of Kempf's standard manoeuvre test and nronosed steering quality indices.
Proc. First Symp. on Ship Manoeuverabilitv.
Report: David Taylor Model Basin, I960, No. l46l, pp, 275-304, 26. St. Denis, M.; Pierson, K.J.,
On the motions of ships in confused seas.
Trans, of the S.N.A.M.E., Vol. 6I (1953) pp. 280-357. 27. Gerritsma, J.,
Behaviour of a-ship in a sea-way.
Report: Delft, Netherlands Ship Research Centre TNO, 1966 , No. 84s, 20 p.
28. Gerritsm.a, J.; Beukelman, W.,
Com.parison of calculated and measured heaving and pitching motions of a series 60, CK= 70 ship m.odel in regular longitudinal waves. Report: Delft, Shipbuilding Laboratory, 1966, l6 p. No. 139. 29. Neumann, G.,
On "Ocean wave spectra and a new method of forecasting wind-generator sea".
Technical Memoranium: Beach Erosion Board, No. 43, 30. Pierson, V.'.J.; Moskowitz, L.,
Proposed spectral form for fully developed wind seas.
Report: New York University, Geophysical Sciences Lab, 1963, No, 63-12.
31. Vugts, J.H.,
The hydrodynamic coefficients for swaying, heaving and rolling cylinders in a free surface.
Report: Delft, Shipbuilding Laboratory, 1968, No. 194, 115 p. 32. Vugts, J.H.,
The hydrodynamic forces and ship motions in waves. Diss.: Delft, 1970.
CHAPTER III: SHIP MANOEUVRING IN CALM V.'ATER
3.1 Introduction
To gather information about the helmsm.an's control behaviour in re-lation to the ship dynam.ics, a series of experiments were performed, To structure the information obtained in this way a model of human behaviour has been developed. On the basis of some preliminary ex-periments linear as well as nonlinear models were formulated; the usefulness of the different models, being an im.portant part of this study, was analyzed.
The test conditions were chosen in such a way that a simple, well defined experiment could be executed, so that the results obtained could be analyzed and interpreted in an understandable v/ay. It was assumed that:
• Only the heading of the ship had to be controlled by the helms-man, the position of the ship had not been taken into account. • The helmsman steered the ship by means of the steering wheel
only. The engine telegraph was not used. o The ship dynamics were constant.
o The disturbances v/ere as sm.all as possible; that is, the influ-ences of waves, current, wind, etc., and also the presence of other people on the bridge, partly engaginr the helmsm.an's attention could be neglected.
To achieve these goals the simulation on a manoeuvring simulator was preferred to the execution of full scale tests, because then the test conditions can be controlled as desired. Moreover, full scale tests are very expensive. However, it should be noted that a validation of the simulator test results by means of full scale tests will be necessary (see Ch. 5 ) .
3.2 Experimental set up
3.2.1 The manoeuvring simulator
The simulator of the Institute TNO for Mechanical Constructions at Delft was used to perform the tests. This simulator has been des-cribed extensively by Brummer and Van V/ijk [l] . Therefore, only a brief description will be given. Fig. 3.1 shows a block diagram, of
desiied state projecrion environmemoili ' 2 " " " ^ display I I I »
rp
indicating instruments! instiuciions I ^ helmsman I — ^nF5^^
controls ship's dynamics [ wheel house analogue I j computerFIGURE 3.1: Block diagram of the TNO simulator.
-31-t h e s i m . u l a -31-t o r . The m.ain p a r -31-t s a r e -31-t h e v.'heelhouse, -31-t h e p r o j e c -31-t i o n system and t h e analojrue computer. F i g . 3.2 shows a p h o t o r r a p h of t h e sim.ulator d u r i n g a s i m u l a t e d harbour a p p r o a c h .
FIGURE 3.2:
The ship research and manoeuvring simulator of the Institute TNO for Mechanical Constructions at Delft.
On the computer the dynamics of the ship to be simulated have been program.med. The com.puter generates the sirnals to control the
environmiental display system and the indicating instruments, "^he sim.ulator is a fixed base simulator, hence the helmsman obtains only inform.ation from, the environmental display and the indicati'nr-instrum.ents .
3.2.2 Ship dynam.ics
The tests should provide information about the importance o^ diffe-rent mianoeuvring properties, such as sluggishness and course insta-bility, in relation to manual steerin,--. As the results of the
literature study shov.-ed a rap v/ith respect to certain types cf ships, the param.eters of the model chosen to simulate the ships, could not be selected on the base of Table 2.1. Therefore an other and systemiatic approach had to be follov.'ed.
Using the extended version of Norrbin's m.odel (En. 2.8):
tv/o im.portant aspects can be distinguished, viz. the shape of the stationary characteristic, in particular the slope of this curve at zero rudder angle, and the sluggishness. These nuantities vrere varied system.atically: Three values of T^ v.'ere chosen, viz. 10, 50 and 250 seconds, corresponding with small, normal and large ships respectively. For each of these values the shane of the stationary characteristic was varied: Stable v.'ith a more or less linear characteristic, unstable, and stable with the characteristic simulating a dead zone. The m.odel parameters used are given in
Table 3.1
TABLE 3.1: The selected parameters of the model used to simulate the ships Ship Nr. 1 2 3 4 5 6
I
9" 10 11 12 13 14 15 Characteristic (see Fig. 3.3) I II III IV V VI Parameters model Ts Sec 10 50 250 10 50 10 50 250 10 50 10 50 250 10 50 K s Sec-^ -.05 -.05 -.05 -.05 -.05 -.05 -.05 -.05 -.025 -.025 -.1 -.1 -.1 -.05 -.05 H 1 1 1 0 0 -1 _^ -1 -1 ^2 /sec>2 M e g ' 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 ^3 (deg)2/3 sec' 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1To show the stationary characteristics of the ships Fig. 3.3 is given.
Besides the parameters of the ship dynam.ics the parameters of the steering gear had to be chosen as well. Some indications about actual values of the maximum angular velocity 6^ and the tim.e constant Tg could be found in literature [2, 3] . Based on these data the follov/ing values were chosen:
6 = 3 deg/sec;
Tj. = 1 sec.
3.2.3 Displays and controls
The displays used were a com.pass and a rudder angle indicator. Moreover, the subject could obtain information from a projection screen, displaying the ship sailing in unrestricted water; that means the helmsman only perceived the sea, the sky and the front part of the ship. No coast line v;as displayed.
-33-5 [deg/sec] -24 -16 char. I -24 -16 -8 / char.H 8 16 24 -.4^-^-^Ö[deg] 6 peg/sec] ..2 8 16 24 ^ Ö[deg] -.6 -2 8 16 24 Öfleg] -24 -16 -Sr" char.nZ .6 [deg/sec] char.31 6 [deg/sec] FIGURE 3.3:
The six stationary characteristics used in the ship simulations.
In these first series of experiments rate of turn indicator v;ere used, as the influence of additional displays cators of the simulator, such as v.'at which were not im.portant with respec the helmsman, were out of use. The o by means of a digital counter; when auditory signal was given.
The helmsman controlled the ship's h wheel, which could easy be turned wi physical effort.
, no additional displays like a it vras the intention to study lateron. The remaining indi-er depth indicator and speedlog, t to the task to be executed by rdered heading was displayed a new heading was ordered, an
eading by m.eans o,f a steering th only a small am.ount of
3.2.4 The ordered headings: The test signal
The helmismen were instructed to headings. The sequence of these or test signal, was a periodic one period, v;ith a random.ly cho a test depended on the tim.e con time constant T_ 10 sec, 20 m Tg = 250 sec, since in steering helm.sm.an needs m.ore time to exe a small and fastly responding s signal for a test with a large
steer the sh headings, de signal. Each sen starting stant Tg of t in for Tg = 5 a slowly res cute a manoeu hip. A tim.e h ship is shown ip along prescribed noted by input signal test consisted of just point. The duration of he ship: 10 min for a 0 sec and 40 miin for ponding ship the vre than in steering istory of the test
[deg] 2 o -2 -4 -6 400 800 1200 1600 2000 2400 2800 I [*«] FIGURE 3.4:
Time history of the test signal of a forty minutes test.
Tests were performed using the test signal with am.plitudes as indi-cated in Fig. 3.4, and with am.plitudes twice as larrre. In the first case the test signal is indicated by TS S, in the last case by TS L.
3.2.5 Subjects
Four subjects, trainees of the School of Navigation at Amsterdam, were used to analyze the helmsmian's behaviour. None of them was experienced in steering ships larger than 10,000 tons. To become familiar with the dynam.ic behaviour of large ships, each subject controlled about one hour the large unstable ship (Ts=250 sec. Char. Ill) before starting the experim.ents. The subjects were instructed to steer the ships just as they normally did. To keep them motivated small rewards were paid, but in spite of this fact a decrease of their m.otivation during the experim.ents could be observed. The com.ments m.ade by the subjects supported this fact. To keep the num.ber of tests the subjects had to perform; as small as possible, each of them, steered only a certain num.ber of all the ships simu-lated. The subjects Al and A2 steered the ship with the stationary characteristics I, III and IV, the subjects Bl and B2 the ships with the characteristics I, II, V and VI.
3.2.6 Experimental programme
In Table 3.2 a survey of the tests to be executed with the TNO sim.ulator is given. It was intended to execute two tests v;ith each subject and each condition, hence the total number of experiments was 144.
-35-TABLE 3.2: Summary o'" the tests with the TNO simulator, Ship Charact. I II III IV V VI data Tg(sec) 10 50 -10 - 50 10 50 -10 - 50 10 50 -10 - 50 250 250 250 S/L S/L S/L S/L S/L S/L Subjects Al A2 El B2 El B2 Al A2 Al A2 Bl B2 Bl B2 3.2.7 Data collection o 0 o o o
;he following signals were recorded on miagnetic tape: The desired headin,-- ijj.,(t);
The heading ,!;(t) ; ^ The rate of turn i|;(t);
The steering wheel position 6^(t) The rudder angle 6(t).
3.3
Modelling the helmsrian's control behaviour3.3.1 Preliminary analysis of the experim.ents
By the Figs. 3.5 and 3.6 some exam.ples are given of the tim.e histo-ries of the desired ship heading lijd(t), the actual heading i|)(t), and the position of the steering wheel ^^{t) as recorded durinr-the tests.
P«g] \
Öj{t)40.
[deg]20
FIGURE 3.5:
Time histories of the signals T^ ,(t), \lj(t), and^n(t). Subject A2, TS S, T = 250 sec. Char. Ill (unstable char.).
ÓdCUO
feg]20 O
FIGURE 3.6:
Time histories of the signals ii^(t), ip (t), and 6j(t).
Subject Al, TS S, T = 250 sec. Char. Ill (unstable char.).
s
The following remarks can be m.ade with respect to the records: • In all cases the records of the steering v.'heel position 6(j(t)
show that the helmsman generates a steering wheel position which consists m.ore or less of discrete steps. In p-eneral the number of rudder calls a helmsman uses to change the heading of the ship decreases with the training.
• A change of heading often consists of four phases. Durinp* the first phase the helmsm.an generates an output in order to start the ship rotating, then during the second phase, the rudder is kept am.idships. During the third phase, the helmsman stops the rotating motion of the ship and when the desired heading is achieved with only a small rate of turn (the desired state) the fourth phase starts (rudder angle zero). If the rate of turn is not small enough, there will be an overshoot and to achieve the desired state the cycle is repeated starting with the first phase again. This behaviour can be showed clarly by means of the phase-plane: the rate of turn of the ship lii(t) plotted against the heading error ^e{t) - ^{t) - ^(^{t) . An example of such a phase-plane plot is shown in Fig. 3.7.
FIGURE 3.7:
Phase-plane trajectories recorded during a test with a large unstable ship.
-37-As the ship the rate of zero. During the like a rect during the In some cas a short per generated b stop the m.o In Fig. 3.8 a
was unstable in this case, during the second phase turn increased with the rudder angle 6(t) equal to
first phase the output of a helmsman is often shaped angular pulse v;ith only a few rudder calls, v/hereas third phase the num.ber of rudder calls is much larger. es when there will be an overshoot, som.etim.es during iod of tim.e a peak in the steering v/heel position is y the helm.sman. It looks as if the man prefers it to tion by large rudder am.plitudes to avoid overshoots. set of estimated squared spectral density functions
SV'dV^d'^' [LOG]-»-^ -2.1 -4, [LOG] -' -I -3. -4. -5. .01 V[HZ] .01 V[HZ]' ^2 '.OOj
RtlV^e'»"
0.50aoo
.001 .01 V[HZ] V[HZ] FIGURE 3.8.Estimated squared spectral density functions and squared coherency
spectra of a test with a stable ship; T - 50 sec; Char. I;
Subject A^, TS L.
and estimated squared coherency spectra of a test with a stable ship (Char. I, Tg = 50 sec) are shown. From the estimated coherency ri|j^4jg(v) it can be concluded that the feedback loop does not con-tain components with frequencies higher than .01 Hz.
