SHIP MANOELJVRING UNDER HUMAN CONTROL analysis of the helmsman's control behaviour.
Wim Veldhuyzen Proefschrift
Rapportnr.
460-P
16 juni 1976Deift University of Tòchnology
SHIP MANO.EUVRING
U/JIIJER
H
HUMAN CO/if TROL
analysis of
the helms ma n's
control
behavour.
wim veIdhuyzen
SHIP MANOEUVRING UNDER
HUMAN CONTROL
ANALYSIS OF THE HELMAN'S
CÓ:ÑTROL BEHAVIOUR
PROEFSCH RIFT
TER VERKRIiJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE
HOGESCHOO.L DELFT, Qp :GEZAG VAN DE RECTOR
MAGNIFICUS PROF. DR. IR. H. VAN BEKKUM, VOOR EEN
COMMISSIE AANGEWEZEN DOOR HEI COLLEGE VAN
DEKANEN, TE VERDEDIGEN OP WOEÑSDAG 16 JUNI 1976 11E 14.00 UUR
DOOR
WILHELMUS VELDHUYZEN scheepsbouwkundig ingenieur
Dit proefschrift is goedgekeurd door 'de promotoren: LECTOR :DR. IR.H.G. SASSEN
STELLINGEN
Studies v-an het menselijk regelgedrag zouden bij voorkeur gebaseerd moe-ten zijn op het Intern-Model-concept.
Lit.: Dit proefschrift.
0m een mens-machinesysteem te optimaliseren is een gedegen kennis omtrent de informatieuitwisseling tussen mens en machine van groat belang. Hier-bij dienen twee vragen beantwoord te worden, nl.: "Over welke informatie dient te mens te beschikken, teneinde een machine zo goed mogelijk te
kunnen besturen?", en "Hoe dient deze informatie te worden gepresenteerd?".
Het is te betreuren, dat het overgrote deel van het mens-machineondezQek gericht is op het verkrijgen van een antwoord op de laatste vraag, tervijl
.juist de eerste vraag van veel groter belang geacht moet worden.
Voor de beschrijving van het gedrag van de mens als regelaar van relatief trage systemen kan met vrucht gebruik gemaakt worden van de reeds ontwik-keLle lineaire modeltheorie met betrekking tot de regeling van relatief
snelle systemen.
Lit.: McRuer, D.T; .Jex, H.R.
A review of quasi-lineair pilot models. IEEE-trans. on Human Factors in
Electronics, Vol. HFE-8 (1967), No. 3(Sept.), pp. 231-2149.
Door Wagenaar et.al. is experimenteel de inyloed van koersstabiliteit op de prestaties van roergangers bepaald, waarbij verschillende
informatie-presentatie systemen zijn onderzocht.
Het door hen uitgevoerde onderzoek zou sterk in waarde hebben gewonnen indien de onderzoekers hun resultaten op basis van een model ter
beschrij-ving van het gedrag van de roerganger zouden hebben verklaard. Lit.: Wagenaar, W.A.; et.al.,
Auxiliary equipment as a compensation
for the effect of course instability on the performance of helmsmen. Communication Netherl.. Ship Research Centre TNO, Deift, 1972, No. 28 S,
2lp.
Door Johannsen is een methode aangegeven orn systemen opgenomen in een ge-sloten keten m.b.v. niet-lineaire modellen te identificeren. De. door Johannsen gesuggereerde algemeenheid van deze methode is aanvechtbaar.
Lit.: Johannsen, G.,
Development and Optimization of a Nonlinear Multiparameter Human
Operator Model.
BIj fundamenteel onderzoek naar het gedra van de mens als bewaker/ regelaar van een systeem is het gebruik van een door een digitale reken-machine gestuurde simulator te verkiezen boyen het gebruik van een door
een analoge rekenmachine gestuurde simulator.
De aandacht die thans besteed wordt aan het mondeling- en schriftelijk rapporteren tijdens de voor-kandidaatsstudie voor werktuigkundig
Inge-nieur is volstrekt onvoldoende.
Met het ontbreken van de mogelijkheid. tot doubleren op de door de
Minis-ter van Onderwijs en Wetenschappen voorgestelde middenschool ontbreekt 00k een belangrijke mogelijkheid tot het opdoen van levenservaring voor
de scholier.
Het verschil tussen de doelstelling van de systeemtheoretisch geschoolde ergonoom en de doelstelling van de experimenteel psychologisch geschool-de ergonoom ten aanzien van ongeschool-derzoek op het gebied van geschool-de mens-machine-Systemen resulteert in een totaal verschillende opzet van uit te voeren experimenten. Dit verschil in experimentele condities vormt een sterke belemmering voor de noodzakelijke samenverking van beide disciplines. Een doelmatiger muziekonderricht bij het basis onderwijs en het
voortge-zette ondervijs kan een belangrijke bijdrage leyeren tot een grotere
belangstelling voor de serieuze muziek van deze eeuv.
Werd vroeger het onderwijs nadelig beinvloed door de zekerheid van de juistheid van het bestaande onderwijssysteem, tegenvoordig is het juist de onzekerheid die het ondervijs nadelig benvloed.
The. research reported in this thesis has been executed within the Man-Machine Systems Group of the Laboratory for Measurement and Control, Department of Mechanical Engineering of the Deift Univer-sity of Technology. The research was sponsored by the Deift Uni-versity Foundation and by the Netherlands Organization for the Advancement of Pure Research (ZWO). The simulator experiments were
made possible financially by the Netherlands Ship Research Centre
(TN0). In particular I will acknowledge the help of the starf
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 o.f the Shipbuilding Laboratory for his contribution in the set-up of the experiments, Mr. J.F. Zegw.aard 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 Rooyerì, Mr. P.C. van Holten, Mr. D.H.P. Snel, Mr.
H.W.J.M. van Gendt, and Mr. R.E. Schermerhorn, whO each contributed with their Master of Science work partially tó the total research
CONTENTS
CHAPTER I: GENERAL INTRODUCTION
1.1 Problem: statement 9
1.2
Modelling the helmsman: A review of literature 101.3 System identification 12
111 Outline òf the thesis 15
1.5 Definition of symbols 16
CHAPTER II: SHIP DYNAMICS
2.1
Introduction 202.2
Models of ship manoeuvring 20.2.3
The model selected 222.11 Parameter values 23
2.5
Ship motions due to waves 26CHAPTER III: SHIP MANOEUVRING IN CALM WATER
3.1
Introduction 313.2
Experimental set up 313.2.1
The manoeuvring simulator 313.2.2
. Ship dynamics 323.2.3
Displays and controls 333.2.14
The ordered headings: The test signal 3113.2.5
Subjects . . 353.2.6
Experimental programme 353.2.7
Data collection 363.3
. Modelling the helmsman's control behaviour 363.3.1 Preliminary analysis of the experiments . 36
3.3.2
Linear modelling 1413.3.3 Nonlinear modelling 42
3.11 Parameter estimation . 117
3,5
Results t493.6
Discussion and conclusions 56CHAPTER IV: SHIP MANOEUVRING IN WAVES
Introduction
65
4.2
ExtenSion of the nonlinear helmsmants model66
4.3 Experimental set up 68
4.3.1
Ship dynamics .68
4.3.2
Displays and controls70
4.3.3
The ordered headings: The test signal72
4.3,4
Subjects72
4,3.5
Experimental programme72
4.3.6
Data collection 734,4
Prédiction of scores73
4.4.1
Model structure73
;k,k.2 Parameter values . 76 14.5 Results 7814.6 Discussion and conclusions 81
CHAPTER V: FULL SCALE EXPERIMENTS WITH A SMALL SHIP
5.1
Introduction 855.2
Experimental set up 855.2.1
Ship dynamics 865.2.2
Displays and controls .5.2.3
The ordered headings: The test signal87
5.2.4
Subjects ..
87
5.2.5
Experimental programme87
5.2.6
Data collection .87
5.3
The analysis of' the experimental data.88
5.4
Results .89
5.5
Discussion and conclusions . 93
CHAPTER VI: CONCLUDING REMARKS AND FURTHER RESEARCH 6.1 Results achieved 6.2 Further research SUMMARY pa ge 97 loo 101 SAMENVATTING 103
CHAPTER I: GENERAL INTRODUCTION
1.1 Problem statement
Progressively larger ships have been built during the last twenty five years [i]; the modern crude carriers often possess a length of
more thah 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, .i4, 5, 6]. In particular, much attention was paid to the manoeuvring properties of large tankers
I,
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 helmsmañ 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 ships on the
de-sired course or the dede-sired track. Many authors treated the design
of autopilots for course keeping [io, ii, 12, 13, 114]; also the design of controllers to steer ships along a prespecified track got
rather much attention [15,16, 17]. At this moment emphasis is laid
ön àutbmatic 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
ji8].
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 isa 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 toò). In particular Gata about the abilities of man to control slowly
responding systéms 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 [1.9]. 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 lastly 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 re.ported 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 st.udy 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 simulator has been used. It
could be adapted t.o well defined goals, because the ship dynamics and disturbances acting on the ship could be made as desire,d 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 dynamics of the ships were represented by a mathematical model. 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 develo.p a mathematical model of the control behaviour of the helmsman. In literature many human operator models are given. The literature reviewed is given in Ch. 1.2. To model the helmsman's
behaviour a model has to be selected on the bas:e of certain selection criteria. When a model, suitable to analyze the
helms-man's behaviour is chosen, the parameters of this model have to be
estimated by means of parameter estimation methods. In Ch. 1.3 an introduction is given to the identification of systems, as well as
to the methods, which can be used to estimate the model parameters.
1.2 Modelling the helmsman.: A review ofliterature
Starting in the forties much attention has been paid to manual control problems. The function of the human operator therein was
considered to be that of a controller; an element that has to close the loop in a certain optimal way. The manual control theory thus developed has resulted into a number of useful models, which will
be shortly reviewed in this oaragraph.
Based on linear system theory the output of the humañ operator can be divided into two parts, one part which corresponds with the response of an equivalent linear system, the describing function, and another part, the remnant, which represents thedifference
between the response of the actual system and theequivalent linear
element. The model is called the
de8cribing function model.
The humanoperator adapts his control behaviour to the system under
control in such a way that a stable and well damped closed .loop
performance is achieved. McRuer has summarized many studies and
recognized that the open loop describing function HpHc near the crossoyer frequency can be approximated by an integrator and a time
delay; where H means the human operator describing function, H represents the controlled element dynamics, and where the crossover frequency is the frequency for which the open loop gain (HpHc) equals 1. In this way McRuer's well-known crossover model has been obtained
[2L, 25]
HpHc
eJWTe,
(1.1)with H human operator describing function; = controlled element transfer function;
crossover frequency;
te = effective time delay including neuromuscular 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
Another model, also originating from linear system theory is the
optimal control mode'l [26]. Thismodel is based on the assumption that the human operator behaves in a certain optimal way within
his inherent limitations: He cannot observe without introducinR
noise; he cannot position the controls infinitely precisely, and finally he also needs a certain time for data processing. This
model, consisting of aKalman filter, a predictor to compensate for the human time delay, an optimal controller and observation and motor noises, is based on the assumed knowledge the human
operator has about the system dynamics. Though this model is mostly used to describe the human operator in controlling lastly respondinp
systems, it may beexpected to be useful in relation to slowly responding systems. No examples hereof are reported in literature
as far as known. .
Besides these two important models many other models have been developed such as the decision model [27, 28], and many nonlinear model8, 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 model. 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 elements 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 common aspect: In order to provide a
successful control behaviour the human operato.r.needs some mation of the dynamics of the system to be controlled; this
infor-mation should also include knowledge of the disturbances acting on
the system. This knowledge is called an Internal Model, that is an
internal representation of the knowledge the human operator has [33]. The existence of such an internal model is implicitely true
for the cro:ssover model [2t, 25], where the human operator adapts
his control to the dynamics of the controlled element and to the bandwidth ofthe system input; it is very clearly true for the optimal control model [26] and the decision model [27, 28]. Some nonlinear models are based on the internal model concept too. Besides the. maiy stüdi,es executed by control and system engineers as mentioned above, a number of s.tudies have been reported by
psychologists. Some:of these pape.rs are related to specific situat-ions [33, 314], other papers deal ,ith 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..
An 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 i,s often changing so slowly tha.t
the human operator does not watch the indicators continuously, but, in an intermittent way. Some studies on the human's monitoring
behaviour can be mentioned [37, 38, 391; again these studies are
based on the internal model concept.
To summarize the literature the following remarks can be made:
-11-.0 With a few exceptions, less attention has been paid to the human.
operator as a controller of s1owly responding systems. However, an increasing interest in the field of human control of slow response systems exists [140]
Ail models describing the human operator are more or less based
on the. internal model cnc.ept. When the internal model is an,
explicit part of a system engineering model, mostly 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 differènt from the test conditions,. Measures indicating how Well the model outpu.t fits the human operator output.
The applicability of the model in practical situations such as
display design. As an e.xample the optimal control model can be
mentioned [141].
o The character of the model output compared with the character
of the human operator output. Sometimes nonlinear elements are
used in conne.ction with a linear model to obtain a more realistic model output [29, 30, 31, 32]
o The simplicity of the. model: A simple model with only a few
parameters describing the human operator's behaviour in a reasonablé way often yields möre consistent results than a
multi parameter model [142]; 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 encountered in the, development of the models some 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 sys.tem, the describing function, and an additional noise, the remnant (Fig. 1.1). .
u(t) I ylt)
,LsYstem
F'GURE 1.1:
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
[Lt3]:
Methods without any a-priori knowledge. Methods with certain a-priori knowledge.
In the case that no a-priori knowledge 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 1-1(v) can be determined by the following well-known relation:
s(v)
H(v) Suu (y). (1.2)In closed loop systems, however, the noise n(t) is correlated with the systems input e(t) due to the feed back loop (Fig. 1.2.a)
[43, 45].
NR')
U (V)
4
FIGURE 1.2:
Trana formation of a closed loop system into an open loop system.
Therefore the determination of the describing function by
minimi-zation of the variance ofthe error between system output and
describing function output will 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 Tollòws: S (y)
H1()
S(v)
(1.3)In determining the describing function, estimated of the cross spectral densities S (y). and S () as well as of the auto
spec-tral density S(v)
4ould beailable. 1ethods to determine these
estimates S(v), Sue(v) and S11('v) of the spectra
Suy(V),
ue(v) and Suu(V) ae given in the lierature [144].In the case that the structure of the linear system is known,
para-meter estimation methods can be used. These methods are based on the concept of minimization of an error criterion E(e,T) with
respect to the unknown parameters (Fig. 1.3). The general criterion
to be minimized is:
E(O,T)
.f°c(t)w(O_t)
dt, (1.14)O-T
where c(t) = difference between system output and model output; q = factor indicating the influence of the magnitude of
w weighting function to take into account the time his-tory of the error c(t).
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 lodp system. In Fig. 1.4 a block diagram of a parameter estimation method, applied in a closed loop situation, is given; heré the controlled element dynamics have to be known. It can be proven
that this method results into consistent estimates in closed
u(t) efl) porameers linear model ImIn,mizanonhI w.
O1ET.
y (t) z(t)*
controlled z sys rem FIGURE 1.4:Block diagram of a closed loop parameter esti'mation method.
Analoguousto the methods of linear n'iodelling,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 model 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 methods developed with respect to linear models can also be. used in the case of nonlinear models. However, an analytical derivation of the estimatòrs of the parameters to be determined, is not possible in general.
i.L Outline of the thesis
This thesis deals mainly with the manual control of large ships. After giving än 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 thesi1s 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 mathematical 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 surnmarises the results of a large number of tests with a
manoeuvring simulator. To analyze the helmsman's control behaviour two types of models were'used, viz, a linear model and a nonlinear
model. This nonlinear model results from a preliminary analysis
and from the literature reviewed in Ch. 1.
15
-linear
Jcontrolled
Ch.. 14 deals with a study of the influence of additional displays
on the behaviour of thè helmsman steering a ship in waves. The
nonlinear model, 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. k) attention was
focussed mainly on rather large ships. Fortunately, the Royal
Netherlands Naval College made it possible to conduct a series of full scale trials with a rather small ship. In this way the results
of simulator tests,, viz, linear and nonlinear modelling results,
could be evaluated with respect. toa small ship. In Ch. 5 these
tests and the results obtained are described.
Some concluding remarks are made in Ch.
6;
this chapter also givessorne guidelines with respect to further research work in this field.
1.5 Definition of symbols
Ïn Fig. 1.5 a block diagram is given of a ship under human control.
disturbances
dW steersng 6(t)
ø helmsman ship
FIGURE 1.5:
Block diagram of the ship steered by a helmsman.
Using the steering wheel, of which the position is denoted by 6(t), the helmsman controls the rudder. positiön 6(t), by which
the heading angle of the ship ip(t) can be cont.rolled. The heading
angle is the angle between the longitudinal axis of the ship and
the x0-axis of a right handed, orthogonal system of coordinates fixed relatively to the earth: 0x0y0z0
(Fig. 1.6).
o X
FIGURE 1.6:
The x0 direction can be the south-north direction for example. The ordered heading is denoted by d(t). The positive direction of the heading is clockwise, just as for the rudder angle and the course
p(t). The rudder angle is the angle between the longitudinal axes
of the ship and the rudder; the course angle is the angle between
the direction of the ship velocity vector V and the x0-axis. A second right handed and orthogonal syste of coordinates Gx
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 y respectively. In thTs study it is assumed that.the ship's centre of gravity is constrained to the horizontal 0x0y0 plane, and that.. this plane coincides with the Gxy plane at all times.
REFERENCES .
Koel, L.A.,
Behaviour of large tankers in shallow water in relation to the dimensions of an approach channel.
Proc. Syinp. on Offshore Hydrodynamics.
Public.: Netherl. Ship Model Basin, Wageningen, 1971, No. 375, pp. 12,1 - 12,20.
Davidson, K.S.M.; Schiff, L.I.,
Turning and course keeping qualities.
Trans. of the S.N.A.M.E., Vol. 514 (19146), pp. 152-200.
Nomoto, K.; Taguchi, T.; Honda, K.; Hirano, S., On the steering qualities of ships. I.S.P. Vol. 14 (1957) No. 35, pp. 3514-370.
¿4 Abkowitz, M.A.,
Lectures on hydrodynamics.
Report: Lyngby (Denmark), Hydro og Aerodynami.sk Laboratorium,
19611, 113 p. No. HY-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. Norrbin, N.H.,
Theory and observations on the use of a mathematical model for ship manoeuvring in deep and confined waters.
Public.: Gothenburg, SSPA, 1971, No. 68, 117 p. Glansdorp, C.C.; Buitenhek, M.,
Manoeuvring trials with a 200,000 tons tanker.
Report:.Delft, Shipbuilding Laboratory, 1969, No. 2148, 31 p. 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, 211 p. Clarke, D.;.Patterson, D.R.;.. Wooderson, 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, 114 p.
Hozos, A.; Thaler, G.J.,
Automatic control of directionally unstable ships.
Proc. Fourth Ship Contr. Systems Symp., Royal Netherl. Naval College,
Den FIelder, 1975, Vol. 3 pp. 30-111.
Bech, M.I.,
Some aspects of the stability of automatic coürse control of ships. Proc. mt. Symp. on Directional Stability and Control of Bodies Moving in Water, Journ. Mech. Engineering Science, Vol. 111 (1972)
No. 7, pp. 123-131. Winkelman, J.E.W.,
Analyse en synthese van stuurautomaten.
Symp. Modelvorming voor scheepsbesturing, Delft, 1970, 17 p. Horst, J.A.M. ter,
Vergelijking van stuurautomaten.
Symp. Modelvorming voor scheepsbesturing, Delft, 1970, 30 p.
-17-1. Koyama, T.,
Some notes on the auto-pilot of an unstable ship.
Report: Deift, Shipbuilding Laboratory, 1971, No. 327, 23 p. Zuidweg, J.K.,
Automatic guidance of ships as a control problem. Diss.: Deift, 1970, 136 p.
Koyama, T..; Kimura, Y.,
An application of Kaiman Filter to the discrete time route, tracking of ships.
Proc. Fourth Ship Coritr. Systems Symp., Royal Netherl. Naval College, Den Heider, 1975., Voi. 1 pp. i7o-i84.
Canner, W.H.P.,
The accuracy requirements of automatic path guidance.
Proc. Fourth Ship Contr. Systems Symp., Royal Netherl. Naval College,
DenHeider, 1975, Voi. 1 pp. 11-151.
i8. Amerongen, J. van; Udink ten Cate, A.J.,
Model Reference Adaptive Autopilots for Ships.
Automatica, Vol. 11 (1975), pp. 1411-14149.
Wagenaar, W.A.; Paymans., P.J.; Brummer, 0.M.A.; Wijk, W.R. van; Glansdorp, C.C., Auxiliary equipment as a compensation for the effect of course
instability, on the performance of helmsmen.
Communication Netherl. Ship Research Centre PMO, Delft, 1972,
No. 28 s., 21 p.
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, Deift, 1969, No. f1701, 59 p. Stuurmam, A.M.,
Human transfer function in ship steering; the effect of feel in. the wheel.
Proc. Fourth Ship Control Systems Symp., Royal Netherl. Naval College, Den Heider, 1975, Vol. 6, pp. 112-130.
Brug, J.B. v.d.,
Simulation of ship manoeuvring qualities.
Report of the post graduate course: Design and economical considerations on shipbuilding and shipping.
Wageningen, Veenman, 1969, pp. 315-333. Wagenaar, W.A.; Michon, J.A.,
The effect of contracted time scales in scale model rianoeuvring. Report: The Institute for Perception, Soesterberg, 1968,
No. IZF-1968-C3.
2i. 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. 23l-29.
25 McRuer, D.T.; Krendel, E.S.,
Mathematical models of human pilot behaviour. Report: NATO-AGARD, No. 188, 72 p.
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 (Dec.), pp. 82L4_832. 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. Elkind, J.I.; Miller, D.C.,
Adaptive characteristics of the human controller of time-varying systems. Springfield, NTIS, 1968, 191 p. AD-665-55.
Diamantides, N.D.,
A pilot analog for airplane pitch control.
Journ. Aeronautical Sci. Vol. 25 (1958), pp. 361-370. Costello, R.G.,
The surge model of the well-trained human operator in simple manual control.
IEEE-trans. on Man-Machine Systems, Vol. MMS-9 (1968), No. 1 (March), pp. 2-9.
Pitkin, E.T.,
A non-linear feedback model for tracking studies. ?roc. Eighth Conf, on Man. Contr., Ann Arbor, 1972, PFFDL-TR-72-92, pp. 11-22.
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. Cooke, J.E.,
Human decisions in the control of a slow response system. Diss.: Oxford, 1965, l03 p.
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. 165-180o
Kelley, C.R.,
Manual and automatic control. New York, Wiley, 1968,. Senders, J;W.,
The human operator as a monitor and controller of multidegree of freedom systems.
IEEE-trans. on Human Factors in Electronics. Vol. HFE-5 (19611), No. 1 (Sept.), pp. 2-5. 36. Smallwood, RiD.,
Internal models and the human instrument monitor. IEEE-trans. on Human Factors in Electronics. Vol. HFE-8 (1967), No. 3 (Sept.), pp. 181-187.
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. 1173_477. I0. mt. Symp. on Monitoring behaviour and supervisoí'y control.
Berchtesgaden, 1976. To be published. 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.
Johannsen, G., .
-The design of a non-linear multi-parameter model for the human operator.
In: Displays and Controls, Proc. Adv. Study Institute, Berchtesaden. Amsterdam,' Swets and Zeilinger, 1972, pp. 21l9367
43. Lunteren, A. van; Stasseri, H.G.,
Annual Report 1969 of' the Man-Machine Systems Group..
Report: Delft, Dept. of Mech. Engineerinp, 1970, WIRD 21, 102 p.
1111. Jenkins, G.M.; Watts, D.G.,
Spectral Analysis and its Applications. Holden Day, 1969.
115. Lunteren, A. van,
Systeem identifikatie en parameter schatting in open en gesloteri ketens.
Rapport: Delft, Lab. voor Werkt. Meet- en Regelt., 1976, N-114, 109 p.
-19-CHAPTER II: SHIP DYNAMICS
2.1 Introduction
To perform simulator experiments a mathematical model describing the behaviour of a ship had to be selected. Keeping in mind the objectives of this study, the following requirements with respect
to such a model should be formulated:
The responses of the model to any rudder angle input must be
as realistic as possible.
o To be able to analyze the test results the model should he as simple as possible. As the study is only concerned with the
behaviour of helmsmen steering a ship along prescribed headings, only the relation between rudder angle and heading, is important. By a simple model .is meant, a model simple with respect to its.
structure and with a small amount of parameters.
The tests should provide information about the importance of different manoeuvring properties such as sluggishness and course
instability.
It should be possible to introduce also the influence of waves
in, the simulation.
Before the model used can be selected, a brief review of mathema-tical models describing the manoeuvring behaviour of ships will be
given.
2.2 Models of ship manoeuvring
The steering, of ships has been studied aiready for many years, but
the more scientific approach started just in the forties. In 19L6
Davidson and Shiff published a method to analyz.e the behaviour of ships, which can be regarded as the base of' all later 'research on this subject [1].
From elementary mechanics the equations of Euler fora symmetric
ship moving in the horizontal plane are known:
X = m (i - vr) ; ' .' (2.1-a)
Y m + ur) ; : '
(2.1b)
N = I'
, ' (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 moment of inertia about the z-axis; r = dp(t)/dt = angular velocity.
Referring
U,
r0, v=O and 5n0 as the nominal conditions, the
following linearized equations of motions can be derived:
(X_m)ú +.X1u
= O (2.2-a)(Y,-m)" + Yvv + Y;i' + (Yrmun)r = (2.2-b)
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 niodel,' consisting of three equations of which two equations are coupled, is based on the foilowinr assumptions:
e The ship is a rigid and symmetric body.
s Only the motions in the horizontal plane are considered.
e The centre of gravity i considered to be situated in the Ox y
plane, which is the water plane. O O
The x, y, and z-axés are the shipts principle axes of inertia. The influence of external disturbances such as wind, waves or
current is neglected.
The ship is sailing in unrestricted water.
The 'propeller is kept at a constant 'number 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 with nonlinear terms. In this way many different models have been suggested [2, 3, 4]. However, these models have a rather large number of' parameters. To study the behaviour of a helmsman a much simpler model is to be preferred.
By eliminating the drift speed y from the Eqs. (2.2-b) and (2.2-c) a single differential equation is obtained, known as Nomoto's
second order model [5]
T1T2(t)+(T1+T2)(t).+(t)=K[T3(t)+6(t)]
, (2.3)where the parameters T1, T2, and T. are called time constants and
K is a gain factor. These parametes are functions of the partial derivatives in the Eqs. (2.2). If the rudder motions are low
frequent, this equation can be replaced by a simple first-order differential equation in the rate of turn [5, 6]:
T(t) +
(t)= Kt).
(2.)
Some authors extended these two models to obtain a better agreement with full scale test results [6 7, 8, 9]. They replaced the term i(t) by a nonlinear function H[1i(t)], for which often a cubic
polynomial is.üsed. Wellknown models in this respect are the model of. Bech [7]
(2.5) and of Nomoto - Norrbin [6, 8]:
T (t) +
(t)+ a[(t)]3
K(t).
(2.6)No simple' mathematical mode.l describing the rrianoeuvring of ships
in waves has been found. Mostly a sum of sine waves or a coloured
noise, is added to 'the output of the model describing the behaviour of the ship in calm water, in such a way that the spectrum of the output of the model obtained meets the actual spectrum of the motions of a ship in waves (Fig. 2.1).
oc,) shp motions du In waves model of I V((t) shipdynam.cs in calm water
J
FIGURE 2.1:Model describing the behaviour
of
a shipin waves.
-21-2.3 The model selected
On the. basis o:f the requirements given in Ch. 2.1 a model has been selected. Nonioto's first-order model (2.4) has only two parameters
and is one of the simplest models developed to describe ship
manoe.uvring properties. The stationary characteristic - the relation
between the rudder angle and the rate of turn in the steady státe
-is linear. However, from full scale experiments it -is known that
this stationary characteristic often is nonlinear [10]. As the
shape of this curve might ihfiuence strongly the helmsman's behavi-our, also ships with different characteristics had to be simulated.
This means that a nonlinear model had to be used, e.g. the models
of' Bech or Norrbin 7, 8]. As Norrbin's model is simpler and
des-cribe.s the behaviour of ships with characteristics as shown in Fig. 2.2 rather well, thi.s model had to bechosen.
FIGURE 2.2:
Stationary characteristics
of
a directionally stable and andirectionally unstablé 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.
w
[deg/sec]
FIGURE 2.3.:
Stationary characteristic
of
atwin screw ship with one rudder
situated at the shin's
center-line.
TTT
To be able to simulate also this type of ships the Norrbin model was
extended with a second nonlinear term:
Tß(t)+a1i'(t)+a2{iT(t)]3+a3[(t)]1"3 (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 oaragraph 2.14 a review is given of shio data in terms of this model as found in
literature. It was hoped that those data weresufficient to choose
the model parameters in such a way that realistic simulations could be obtained.
To control the rudder position often a hydraulic servo-system is used. Some models describing such a system are given by Bech and
Brummer et. al. [io, li]. Though the actual dynamics are much more
complicated, the dynamic behaviour can be appróximated in a reason-able way by means of a first-order differential equation. Because of the limited capacity of the oil pumps, the angular velocity of the rudder is limited. The following model is thus obtained:
T ¿(t) + (t) d(t)
I(t)I <
= m'
where T is a time constant and Ó is the maximum rudder angular velocity. In Fig. 2.14 the block diagram of the steering gear,
applied during the experiments, is given.
6d ()
FIGURE 2.4:
Block diagram of the steering gear.
2.14 Parameter values
As mentioned before, the dynamics of the ships to be simulated should be as realistic as possible. In order to obtain data to improve such a simulation, the literature on ship steering was therefore reviewed. A technique used by many authors to model ship dynamics is based on special tests or zig-zag tests. These data, however, had to be transformed in terms of the nonlinear
model. The results of the spiral tests were used to estimate the model parameters a1, a, a3 and K5 by means of a least squared
error method. The results of the zig-zag tests were used to
esti-mate the parameter T. As only a rough estimation was needed, some
approximations were introduced in estimating T5 (Fig. 2.5): The rudder engine dynamics were neglected.
The heading *'(t) was considered to be a sinusoidal signal.
The nonlinear elements were approximated by their describing
functions.
Jt3d
ö(t)
(2.9-a)
(2.9-b)
60 -60
Ib
modI IshipdynamicsL---.
T3 SFIGURE 2.5:
Block diagram of the model during a aig-zag teat.
In this way the following formula could be obtained:
T5
_K560/i2 _62'T2
, (2.10)
7T
where 60 actual rudder amplitude; amplitude of the heading; T1 period of one oscillation.
The results of the parameter estimations are given in Table 2.1. With respect to this table the following remarks can be made:
o A relatively small amount of full scale test.s has been performed;
The larger part is related to large ships.
o Not any ship with stationary characteristic like Fig. 2.2has
been found, except the railroad ferry when sailing backwards
[ii].
o In accordance to Norrbin [8] and Bech [7] the coefficient a
was kept equal to i or -1 depending on the fact that the ship was stable or unstable. Some marginally stable ships were found where a1 is equal to zero. In these cases the parameter values were normalized with respect to K5 which was kept equal to -.05
sec
o A large number of ships were examined by Nornoto [25]. Based on
zig-zag tests with about seventy ships, the parameters of Nomoto's first-order model were calculated. As this model
approximates the stationary characteristic by a straight line,
Nomoto's data do not provide information about the actual shape
of the stationary characteristics of the ships.
o The literature reviewed does not provide enough information to
choose the model parameters of a range of ships to be simulated. o¿d KS
TABLE 2.1: Summary of the manoeul)ring propertiee of different shipa found in literature.
-25-4
SHIP DATA PARAMETERS MODEL REF. Kind of ship Deadweight Length Breadth Draught Dispi. Speed T5 K5 a1 a2 a3
tons in a in a3 Knots sec sec'
(4j..)2 Railroadferry 139.6 17.4 5.9 9 100 19.8 51 -.22 1. .12 .0 11 Passenger and 134.0 20.0 5.4 7 300 23 28 -.10 1. .49 .0 12 Cargo Liner 135.6 18.9 7.8 13 170 16.5 25 -.05 1. .47' .0 13 Container ship 42 900 273.0 32.2 8.1 20 33 -.04 1. 4.12 .0 14 Tanker 200 000 310.0 46.9 18.9 238 000 15 15 Loaded 264 -.05 -0.156 16.5 .0 15 -- -.04 -1. 24.3 .0' 9 Ballasted df 7.3 d flfl 106 000 46 -.05 1. 3.6 .0 15 a -- -.05 1. 4.9 .0 9 Tanker 193 000 304.9 47.2 18.1 215 000 16 Loaded 135 -.04 -1. 20.0 .0 Undeep water d - 7.8 89 -.04 -1. 20.0 .0 Ballasted d 10 8 a -- -.05 .125 26 .0 Undeep water -- -.09 -1. 39. .0 Bulkcarrier 69 250 242.8 32.2 12.8 15.5 234 -.14 1. 6. .0 17 Bulkcarrier 3.200 62.8 15.3 4.9 3 800 10.5 -- -.06 -1. 63. .0 18 Tanker 80 000 207 -.07 1. 3.8 .0 19 Tanker 50 000 221.0 29.6 12.5 65 089 76 -.05 -0.046' 5.3 .0 20 Unknown . ' .313 48.2 19.4 250 251 13.8 208 -.05 -0.042 7.4 .0 21 Unknown 307 48.2 19.4 250 750 14 185 .05 -0.23 10. .0 21 Cruise ship 106 28 -.12 1. .22 .0 22 Pilot boat 59 10.6 3.7 12 -- -.92 1. 1.07 .0 23 10 20 -.63 1. 1.59 .0 8 18 -.26 1. 2.10 .0 Trainingahip 41 7.5 2.2 382 12 25 -.25 1. .13 .0 24 8. -- -.10 1. .04 .0
2.5 Ship motions due to waves
To study the control behaviour of a helmsman 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 simulator experiments (Ch. 3
and 1!), only the yawing motions had to he considered. To introduce the disturbances in the simulations, a signai 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-suits 1erçof show a fair agreement between predictions and measure-ments 28J. The random sea surface, denoted by t(0, y9, t), is
assumed to be composed of an infinite number of sinusoidal compo-nents with different amplitudes, frequencies and phases. Formulas
describing the spectral density of' the sea waves as function of'
the circular fçeqency are given by Neumann [29], and by Pierson
and Moskowitz 130]. The dynamic of a ship can be described just as
the sea surface, by statistical methods. When the spectral density
of the sea surface is denoted by S(We), and the ship's responses
are given by the transfer function
H(We), the spectrum of the
ship's yawing motions S(We) can be calculated by:
S(W)
IH(We)I2 S(We)
(2.11)It should be noted that the spectrum and the transfer function
depend on the frequency of encounter We The wave spectrum based
on the wave frequency U) has to be transformed to a wave spectrum based on the frequency of encounter The relation between w
and We follows from classical wave theory and is given by:
e
:1w
cas Pl,(2.12)
where V ship speed;
g acceleration of gravity;
angle between the ship's velocity vector
Vand the wave
velocity e (Fig. 2.6). \ \ \ \ FIGURE 2,6:A Bhip eailin?' in a regular Bea; V = ship speed;
C = wave velocity;
The spectral density of the waves as function of We can be computed from the spectral density based on w by means of the following
formula:
S(We)
8(W)
dw (2.13)where dw/dwe can be computed using Eq. (2.12). However, the
fre-quency w is not a uniquely function of We. To transform the wave
spectrum S
(w) into S(We) the spectrum S(w) should be divided
into partsor which the relation between wand We is unique. Each of these parts result in a part of the spectrum S(we), which may coincide with the other parts. The spectral density S(we) is
obtained by adding for each We the densities resulting from the transformation of each part.
The ship's responses to the wave exerted moments following differential equation:
(I-N)
(t) - N i(t) = N (t), (2.111)where = ship's moment of inertia; damping coefficient;
= added mass;
hydrodynamic moment.
The trasfer function can be written as:
i
3We[zzp) jWeN]
The hydrodynamical coefficients N? and Np can be estimated using
the so called strip theory [27, 3, 32] . Starting points are the
known two-dimensional solutions for the cross-sections, which can be computed by means of conformal mapping. By integrating the cross-sectional values the result for the three dimensional ship
is found [28]
The right hand side of Eq. 2.111, the wave exerted moment, 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
correôtionis needed tó 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
H(jW) can be defined, describing the moments acting onthe ship
in regularas well as irregular waves. The spectral density of the
ship's yawing motiöns then can be estimated by the formula:
) 1H (jWe) '
Hn(j:we)I2 S().
e
are given by th
(2.15)
(2.16)
To perform the computations described above the Deift Shipbuilding Laboratory has completed a number of computer programs. Using
these programs the motions of a ship in regular waves, i.e. the transfer functions H(We), can be computed, and using the wave spectra as given by Pierson and Nloskowitz [30] S(we).canbe
calculated as described above.
-27-The calculation of the ship motions 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, was required. An approximation of such a signal can be
obtained by a sum of a large, but finite number of sine waves,
with properly chosen amplitude, phase and frecuency. Therefore, the calculated spectrum S,i(We) is divided in small bands with a
bandwidth A(Fig. 2.7).
'Sp(W
FIGURE 2.7:
Approximation of the conti.nuous spectrum by a discrete spectrum.
The sine waves are chosen in such a way that the frequencies equals 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
Davidson, K.S.M.; Schiff1 L.I.,
Turning and course keeping qualities.
Trans. of the S.N.A.M.E. Vol. 5i (191i6), pp. 152-200. Abkowitz, N.A.,
Lectures on hydrodynamics.
Report; Lyngby (Denmark), Hydro og Aerodynamisk Laboratorium, 1964, 113 p., Hy-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.
14 Norrbin, N.H.,
Theory and observations on the use of a mathematical model for ship manoeuvring in deep and confined waters.
Public. Gothenburg, SSPA, 1971, 117 p., No. 68. Nomoto, K.; Taguchi, T.; Honda, K.; Hirano, S.,
On the steering qualities of shipB. I.S.P. Vol. ¡4 (1957) No. 35, pp. 35I4370.
Nomoto, K.,
Problems and requirements of directional stability and control of surface ships.
Proc. mt. Symp. on Directional Stability and Control of Bodies Moving in Water, Journ. Mech. Engineering Science, Vol. (1972)
No. 7, pp. 1-5. 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.
Norrbin. N.H.,
On the design and analysis of the zig-zag test on base of quasi-linear frequency response.
Proc. Tenth mt. Towing Tank Conf. 1963, pp. 355-3711. Glansdorp, C.C.,
Simulation of full scale results of manoeuvrinp trials with a 200,000 tons tanker with a simple mathematical rodel.
Report: Delft, Shipbuilding Laboratory, 1971, 211 p., No. 301. Bech, N.m.,
Some guidelines to the optimum adjustment of autopilots in shins. Proc. Symp. Nodelvorniing voor scheepsbesturing. Deift 1970, 32 p. ii. Brix, J.; Fritsch, M.,
Eisenbahnf"ahrschiff "Deutschland". Modellversuche und Bordmessungen. 372. Mitteilung der Hamburgiachen Schiffbau Versuchanstalt.
Schiff und Hafen, Jahrg. 24 (1972) Heft 11, pp. 791-795. Enkvist, E.; Saarikangar, M.,
"Finlandia" Finish-built Passenger and Car Liner
Some Design Considerations. Shipping World and Shipbuilder Vol. 160 (1967) No. 3811 (Sept.) pp. 1500-1513.
Lindgren, H.; Norrbin, N.H.,
Model tests and ship correlation for a cargo-liner.
Trans. of the Royal Inst. of Naval Architects. Voi. 1014 (1962),
pp. 1141_181.
111. Containerschiff "Bremen Express". HANSA
Jrg. 109 (1972) STG-Sondernummer II (Nov.) pp. 20113-2076. Glansdorp, C.C.; Buitenhek, N.,
Manoeuvring trials with a 200,000 tons tanker.
Report: Delft, Shipbuilding Laboratory, 1969, 31 p., No. 2148. 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.
Chirila, J.V.,
Sea trials of the "Sighansa". Part I. Propulsion and Manoeuvring tests. Shipping World and Shipbuilder. Vol. 156 (1965) No. 3773 (Dec.)
pp. 533-541.
"Mini Luck" Japanese-built mini bulk carrier.
Shipping World and Shipbuilder. Vol. 162 (1969) No. 38311 (June) pp. 817-821.
Lehmkuhl, J.; Chirilia, J.V.; Gerb±tz, U.; Marx, K.}I., Turbinentankschiff "Altanin".
Schiff und Hafen, Jrg. 16 (19614) Heft 11 (Nov.) pp.. 1033-1061. Clarke, D.,
Manoeuvring trials with the 50,000 tons deadweir-ht tanker "British Bombardier".
Report:. BSRA, 1966, No. NS-1142.
Fujino, M.; Motora, S.,
On the modified zig-zar manoeuvre and its application. In: Selected papers SNA Japan, Vol. 9 (1972) pp. 1331148. Hebecker, O.,
Das Manöver "Mann über Bord".
Schiff und Hafen, Jrg. 15 (1963) Heft 10, np. 963-966.
Winkelman, J..E.W.; Ar!lerongen, J. van,
Verslag van de metingen verricht aan hoord van de loodsboot
"Capelia" van 0140472 tot 1801172.
Report: Delft, Laboratorium voor Regeltechniek, pp. 1-10. 214. Verstoep, N.D.L.,
Versiag van de metingen verricht aan boord van de "Zeefakkel"
van 221073 tot 2141073.
Report: Delft, Laboratorium voor Regeltechniek, pp. i-8. Nomoto, K.,
Analysis of Kempf's standard manoeuvre test and proposed steering quality indices.
Proc. First Symp. on Ship Manoeuverablli.ty.
Report: David Taylor Model Basin, 1960, No. 1461, pp.. 275-3011. St. Demis, N.; Pierson, W.J.,
On the motions of ships in confused seas.
Trans. of the S.N.A.M.E., Vol. 61 (1953) pp. 280-357. Gerritsma, J.
Behaviour of aship in a sea-way.
Report.: Deift, Netherlands Ship Research Centre TNO, 1966 No. 84s, 20 p.
-29-Gerritsma, J.; Beukelman, W.,
Comparison of calculated and measured heaving and pitching motions
of a series 60, Ct? 70 ship model in regular longitudinal waves. Report: De].ft, Shipbuilding Laboratory, 1966, 16 p. No. 139. Neumann, G.,
On "Ocean wave spectra and a new method of' forecasting wind-generator sea".
Technical T4emoranium: Beach Erosion Board, No. f43. Pierson, W.J.; ?4oskowitz, L.,
Proposed spectral form for fully developed wind seas.
Report: New York University, Geophysical Sciences Lab. 1963, No. 63-12.
Vugts, J.H.,
The hydrodynamic coefficients for swaying, heaving and rolling cylinders in a free surface.
Report: Delft, Shipbuilding Laboratory, 1968, No. 1914, 115 p. Vugts, J.H.,
The hydrodynamic forces and ship motions in waves. Dise.: Delft, 1970.
CHAPTER III: SHIP MANOEUVRING IN CAL1 WATER
3.1 Introduction
To gather information about t'he helmsman's control behaviour in
re-lation to the ship dynamics, a series of experiments were performed. To structure the information obtained in thi,s way a model of human behaviour has be:en 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 important part of this study, was analyzed.
The test conditions were chosen in such a way that a simple, well
defined experiment could beexecuted, so that the results obtained
could be analyzed and interpreted in an understandable way. It was assumed that:
Only the heading of the ship had to be çontrolled by the helms-man, the position of the ship had not been taken into account. i The helmsman. steered the ship by méans of the steering wheel
only. The engine telegraph was not used. The ship dynamics were constant.
o The disturbances were as small as possible; that is, the influ-ences of waves, currént, wind, etc., and also the presence of other people on the bridge, partly engaging the helmsman'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. Noreover, 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 lVTechanical Constructions at Deift was used to perform the tests. This simulator has been des-cribed extensively, by Brummer and Van W.ijk [i]. Therefore, only a brief description will be given. Fig. 3.1 shows a block diagram of
r
V ship's¡flfl,sheZo}.conoIs
'nmics
ianologui IFIGURE 3.1: Block diagram
of
the TNO Bimulator.
I.I
stafe
L!!!. house
-31-the simulator. The main parts are -31-the wheelhouse, -31-the projection
systerr and the analogue computer. Fir. 3.2 shows a nhotocranh of' the simulator durinp a simulated harbour approach.
Ak
FIGURE 3.2:
The ship research and manoeuvrini ßirnulator of the Institute TP/O for Mechanical Constructions at Deift.
On the computer the dynamics of the ship to he simulated have been programmed. The computer generates the sirnals to control the
environmental display system. and the indicatinr instruments. The simulator is a fixed base simulator, hence the helrsran obtains
only information from the environmental disnlay and the indicatinr
instruments.
3.2.2 Ship dynamics
The tests should provide information about the importance of
diffe-rent manoeuvring properties, such as sluggishness and course insta-bility, in relation to manual steering. As the results of the
literature study showed a gap with respect to certain types of ships, the parameters of' the model chosen to simulate the ships, could not be selected on the base of Table 2.1. There4'ore an other and systematic approach had to be followed.
Using the extended version of Norrbin's model (En. 2.8):
two important aspects can be distinguished, viz, the shape of' the stationary characteristic, in .particulár the slope of this curve at zero rudder angle, and the sluggishness. These nuantities were varied systematically: Three values of' T5 were 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 with a mrore or less linear characteristic, unstable, and stable with the characteristic simulating a dead zone. The model parameters used are given in
Table
3.1
TABLE 3.1: The selected parameters
of
the model used to simulate the shipsTo show the stationary characteristics of the ships Fig.
3.3 is
given.
Besides the.. parameters of the ship dynamics the parameters of the steering gear had to be chosen as well. Some indications about
actual values of the maximum angular velocity and the time constant Tó could be found in literature
[2, 3].
Based on these data the following values were chosen:= 3 deg/sec;
T i sec.
3.2.3
Displays and controlsThe displays used were a compass 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 was displayed.
-33-Ship . Pärareters model
T5 K. a1 a2 a3
Nr. Characteristic
(see Fig. 3,3) Sec . -i
Sec. (__.)sec 2 (____)deg 2/3 i . 10 . -.05 1 5 . .0, 2 50 -.05 1 5
-0.
3 . 250 -.05 1 II... 10 -.05 .0 5 0 5. 50 -.05 0 5 0 6iii
10 -.05 -1 5, 0 7 . 50 -.05 -1 5 0 8 . 250 -.05 -1 5 0 9 IV 10 -.025-i
5 0 10 . 50 -.025 -1. 5 0 11 V 10-.1
-1 5 1 12 - 50-.1
-1 5 1 13 250-.1
-.1 5 1 14 . VI 10 -.05 -1 5 1 15 50 -.05 -1 5 16 [deglsec] [deg/sec]
-24 -16 -B_2 8 16 24 -24 -16 -8 - 8 IS 24
char.I
_...L
ö[deg] char.]I ö[deg]
[degisec] sec]
.4
-I i i I i I i i i i
1---24 -16
-8 (-.2 8
16 26 -24 -16 -8e-' -.2 16 24char.JIL ö[deg) char.IZ
*.6 [deg/sec] .6 [deg/sec]
-.4
-.2
-.2
¡ I i
'-
I I I-24 -16 -B
-\ 8
16 24 -24 -16 -8:::N.!24
chav.Z
--.4\,[deg]
char. --.6 öteg]FIGURE 3.3:
The
Bis
stationary characteristics used in theBhip
simulations.In these first series of experiments, no additional displays like a rate of turn indicator were used, as it was the intention to study
the influence of additional displays lateron. The remaining indi-cators of the simulator, such as water depth indicator and speedlog,
which were not important with respect to the task tobe executedby the helmsman, were out of use. The ordered heading was displayed by means of a digital counter; when a new heading was ordered, an
auditory signal was given.
The helmsman controlled the ship's heading by means of a steering wheel, which could easy be turned with only a small amount of
physical effort.
3.2»4 The ordered headings: The test signal
The helmsmen were instructed to steer the ship along prescribed headings. The sequence of these headings, denoted by input signal or test signal, was a periodic signal. Each test consisted of just one period, with a randomly chosen starting point. The duration of a test depended on the time constant T5 of the ship: 10 min for a
time constant T 10 sec, 20 min for T5 = 50 sec and 4O min for Ts 250 sec, since in steering a slowly responding ship the
helmsman needs more time to execute a manoeuvre than in steering a small and fastly responding ship. A time history of the test
400 BOO 1200
IP
[_oo
2400FIGURE 3.4:
Time history
of
the te8t signal of a forty minutes test.Tests were performed using the test signal with amplitudes as indi-cated in Fig. 3.11, and with amplitudes twice as larpe. 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 Pmsterdam, were used to analyze the helmsman's behaviour. None of them was
experienced in steering ships larger than 10,000 tons. To become familiar with the dynamic behaviour of' large ships, each subject controlled about one hour the large unstable ship (T5=250 sec, Char. III) before starting theexperirnents. 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 motivation during the experiments could he observed. The comments made by the subjects supported this fact. To keep the number of tests the subjects had to perform as small as possible, each of them steered only a certain number of all the ships simu-lated. The subjects Al and A2 steered the ship with the stationary
characteristicsI,:III and IV, the subjects Bi and B2 the ships with
the charactèristics I, II, V and VI.
3.2.6 Experimental proramme
In Table 3.2 a survey of the tests to.be executed with the TNO simulator is given. It was intended to execute two tests with each subject and each condition, hence the total number of experiments was 1111$.
[Sec] 2800
-35-TABLE 3.2: Summary of the testa with the TNO simu'ator.
3.2.7 Data collection
The following signals were recorded on magnetic tane: o The desired heading pd(t);
o The heading p(t);.
o The rate of turn ip(t);
o The steering wheel position 6d(t); o The rudder angle 6(t).
3.3 !"ïodelling the helmsman's control behaviour 3.3.1 Preliminary analysis of the experiments
By the Figs. 3.5 and 3.6 some examples are given of the time
histo-ries of the desired ship heading ,j,(t), the actual heading p(t),
and the position of the steering wheel 6d(t) as recorded during
the tests. (t) g [deg]
+1
[deg]20 o -20 -4067
1200 21.00 t[sec] !4QQ t eC]FIGURE 3.5:
Time hietoriee
of
the si7nale *d(t), p (t), and 6,(t).Subject A2, TS S, T8
= 250
Bec, Char. III (unstable char.).Ship data TS Subjects Charact. P8(sec) I lo - 50 - 250 SIL Al A2 Bi B2
II
10-50
SIL B152III
10 - 50 - 250
S/L Al A2 IV10-50
S/L A1A2 V10 - 50 - 250
S/L Bi B2 VI10-50
S/L B152G
W(fl3
IegO
FIGURE 3.6:
trime histories
of
the, signals d(t), (t), and tSd(t).Subject Al1 TS S, T3 = 250 sec, Char. III (unstable char.).
The following remarks can be made with respect to the records: In all cases the records of the steering wheel position d(t) show that the helmsman generates a steering wheel position which consists more or less of discrete steps. In general 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. During the first phase the helmsman generates an output in order to start the ship rotating, then during the second phase, the rudder is kept amidships. During the third phase, the helmsman stops the rotating motion of the ship and when the desired heading is achieve,d with only a small rate of turn (the desired state) the fourt'h.phase starts (rudder angle zero). If the rate of turn is nôt small enough, there will be an overshoot and to achieve the désired 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 t) plotted against.the heading error I'e(t) p(t) - p(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.
