Li Meijing Mariner Design and Research Institute of Cliina
\Vu Xiuheng Wuhan University of Water Transportation Engineering . China
1. INTRODUCTION
Simulation calculation on ship maneuvering motions arid iiiaiieuvcrahility assessment criteria are two of thc most impor-tant suhecis in maneuverability research.
In tite simulation calculation, i/frano ci011tt-t6l have csta-bushed various mathematical modcls to calculate some normal manctivering motions such as zigzag. turning at normal satling sitcI. Soute of these models arc capable of evaluating env iron-inertial influences on ship maneuvering motions. However, it scern that so far there is riot such a versatile mathematical
rinde! that can deal with most maneuvering motions, including íigiiiiz. turning, backing, stopping arid man-in-loop maneuver-mu, let alone to consider environmental influences of wind. wave, current and water depth at the sanje time. Tite most knn!tv problem in developing such a mathematical model is perhaps how to evaluate hydrodynamic forces acting on a ship while tite ship is stopping or backing. Another difficulty is how Lo estimate forces induced by wave and current.
In this paper, by applying system identification method to irnilyi.e experiment data, some of which were front our own tests carried out on two ship models at four water depUtes, oth-rs vere from hundreds of captive or semi-captive rondel tests available to us, we have established practical formulas to esti-irate four qu:idrants forces. To facilitate calculation, we have Itirtirer introduced concepts of equivalent ship length and cultivaIent velocities in calculating formulas concerning wave forces and non-uniform cttrrcnt forces.
In ship maneuverability assessment research, most of
)TC'iOiLÇ work was devoted to expressing maneuverahilities precisely and detailedly as possible. At least tens of rnaneu-cerahility criteria have been suggested. Even so, it is still 'Jifliculi to use those criteria to properly a.ssess a ship's maneu-er:ibility. Indeed, since Ute course keeping stability_and the
ABSTRACT
In this paper, we present a practical mathematical model that can be used to calculate roost ship maneuvering motions, including zigzag, turning. stopping, backing and even man-in-loop maneuvering, under cnvironntental influences of wind, wave, current and water depth. Systentatie formulas have been developed to estimate four-quadrants hydrodynamic forces at different water depthes as well as other forces caused by wind, wave and current. A comprehensive assessment method is proposed to quantitatively assess a ship's nianeuverabilitiesafter its essential maneuvering characteristics are known. Numerical results show that Ute mathematical model and comprehensive assessment method presented in titis paper arc easy to calculate and applicable to conventional ships. They also have potential applications in ship optimum design, sail-plan making, sailing feasibility study and waterway dredging.
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turning ability of a ship arc often contradictory to each oilier. they arc exclusive in assessing a ship's nr;irreuverahihitics.
Other contradictions can also he fotindi in ship inherent manen-verahilities.
Wc believe lita t envi ron irr enta I i n liii erices and h titir tn control are equally important in assessirtg a ship's inaneuvcra-hilities. Miller etc. 191 have analyzed more tht:irt 8(b) sea accidents. They pointed out thai although a ship's inherent mancuverahihities affect greatly on ship safety, oilier two fac-tors, Ute ship's sailing environment and the ship's operator. have also played important roles. Therefore, in tins piper. unlike many oilier researchers, we have establish three criteria to comprehensively assess slop ntaneuver:thil itics. \Vc call diese three criteria as shop's inherent maneuvering quality, ship's relative maneuvering quality and ship's mao-in-Inuit maneuver-ing quality, cacit of them stressmaneuver-ing one of tite three factors riten-tinned above.
2. THE MATHEMATICAL MODEL FOR SIMULATION CALCULATION
In titis section, we will present tite ni itheoratical niodel for simulation calculation of ship maneuvering ululions.
According to the momentum theory, tite equations for describing ship maneuvering motions in a horiztintal plane cari
Inertia ninmcntum and added inertia momentum a.csociatcd with the situ) and propcllmg system. [X,Y,N,QJ dcnote longitudinal lorec, laicral forcc, moment and torquc. The subscripts HV, I IR, P, R, a, c and w indicate respectively forces caused by vi.ccosity, wave radiation, rudder, propeller, wind, current, and wave, u, y, r represent longitudinal, lateral, and yawing
veloci-Icc of the ship, n rotation speed of the propeller. Brief dcscrip-lions ;thotit tite calculation of these forces will be given in tite Itiliowing subsections and their details can be reviewed in refer-ence IDI. 1111.
2.1
TUE CALCULATION OF FOUR QUADRANTS
VISCOUS FORCES X1,.,,, Y,,.,,, N,,.., AND THE ADDED MASSES mO
Looking into four quadrants force curves of several ships in deep\vaicr and shallow water of different water depthes. we noticed thai tite four quadrants forces X,,.,,, Y,,.,,, Nm, can be approximated as functions of either synunctric or anti-symmetric with regard to the velocity u. Therefore, we use the following formulas to estimate four quadrants forces:
x,,v=x,u iv t +x,,,,u u i+x,,,,,, 3+x,,,,,,,,u lu i
1'uv= Y,,,tu ir+Y,,,,iu iv+Yv ivi (2)
N,,N,,,uv+N,,iiuIv+N,,,iuir
Our ituiticrical comparisons suggest that nonlinear termsin the
Nm, calculation are relative insignificant, and hence they are
omitted ti) simplify the calculation. Consequently, it is possible. on tite hais of available captive model test data, to formulate c:ich coefficient in equation (2).
Here, we use
Hirano's approach to calculate Y. Y. N andNa,:Y pLTK r O.7Cß1?
= --
+ L2 T y,,, = ..LpL2TKan(l+O8) N,,,=_+pL2rK,a i-0.27--'
N,,,= -pLTK,,4 -O.54n+ 1-1.25* K,4 (l+O.3t')'Flic remaining coefficients K,
and Y. X,,,
are re-analyzedbased on hundreds of available experiments data
(3)
t' =tíT 'ris¿lieship trim 2Ï/L. - K,1(0.51t+OE7CI3/'1) 2T/L K,,= T2 itT itT
+
ilLd-
21/ 211 X12,34 = (1 845, 1.708, 0.540, (1.853 =pLTCÇ1.350-32.I 2C5+45.S6C-2 I .s3c:) [l_6.l69e"-3.560c"
+22.30e3°'1 pLT [(I1/T_l)°7+l.263+o.xwonr1'] 2(1/IT-I)05
'(1.025-0.1651/ /T0.66211 2/JL) (l .233-1.162C5-O.740C,)Tite added ¡nassesPn9 ai different water dcpthes in
cqua-ti on (1) are al so formulated throug h opt mmm all i lyses on corresponding test data:
22-in22 (1/IT-I )0.2 I)0.82413+0.0320/) /'/'+i).i)129(//l.1.)2] Fn (,I_. m
-(i/ITi )0.82 LI/IT-1)082+0.413+0.0192///1.4 ts)554(lt i.!.))] ,,1 mit -(I/IT-I)''30 [(1/ir- 1)1.30+3.77+1.14///'r-o.233Lcr_3.43cnJWhere rn 22. mn a,.. and 'ni.. are lite added nt:tsscs o filie ship in deep water. They can he estimated with cnipirical for-mulas proposed in reference[4J.
To evaluate drag coefficients X,,,,, X,,,, X,,,,, ill formula (2). Ayre method for deep water and Scitiiching method for shallow water can he used.
2.2 THE CALCULATION OF RUDDER AND PROPELLER FORCES XE?, YR? andNR?.
In evaluating rudder and propel lcr forces. the most difficult problem is how to estimate the interferences among tite rudder, the propeller and the ship finii, especially while tite ship is stopping or backing. Here, we use u,,, u,, 12. 8 and r11 to describe such interferences at any working conditions of the rudder and the propeller:
XE= -(1-/R)--pARfi,,lu I usin28
X = au+bun+c,n
YE,.= YR+YP = _(I+aIi)+pARfa(u,,U'i'tiFn)
[(u,,u+uncin ()co.r8+(y1 7a181)(v+X,r)]
NR? NR+N? = (X,,+s/1a/j)Yp/(l+o/1)
(6)
(7)
Unlike other researchers who used very complicated method to calculate independently the lateral forc f,. caused
(in+m )ti-(m +m22)vr -(m +,nX,)r2 =X;,v-i-X,15 +XR +X+X +X+X, (,n+m,2)+(,n+m ii )ur+(,n +mX1) =Y,,,+Y/,R+YR+Yp+Y+Y+Y,, (J+m )i+(mS2+inKg)(+W') =N/N-+N,/R +NR +N+N +N+N
2n(,+J,);i
=QP+QE+QfrtWhere in, in0, i ,n J,, J,, arc mass,
(1)
I licpropeller reversing, we simplyincorporate Yp in the
cal-ciilatiun of tiic rudder force by using an equivalent rudderangle
. This greatly reduccs calculations both in system
it len i fi ca tionand in si ni ul a Lion.
In order lo establish fomlulas to estimate intcrfcrencc
coefficients through systcm identification, various
maneuvcra-bilitv tests, including turning. zigzag, stopping and backing with diflcrcnt rudder angics and propeller rotating speeds, were
carried 0111 on two ship models at four water dcplhes. After
careful siudy on the experiment data obtained, the following formulas arc reached:
f
=6.13?/(2.2.5+X)14,, = l.29KD\/lK10l1
14, =(l_dl)J)(l.1Kx+0.9S3Kx1K1pI./\JIK,oi.)
a11= (0.ó79-i.5lC5+l.44C)
.061-0.61ST/il +2.15o(T///)2J
X,,= -(0.4+0. lCß)Eo.99&+o.os1ST/Il-I .031 (Tul)21L
= 0.474+0.479C8+(l .28&-2.95 IC )(T/il) nO = I2.09-14.33C,1-(l 10.7-1S9.2C8)Ç1///) +(l4$.&-261.8C3)(T//l)2 n<0 .( =-0235+0.951 Ca+(0.75O+0.O37Ca)(T/Il) nO '(2 = -26.40+35.54Ca+(15. 1 857.37C8)Ç/Il) +(Sb.33-32.SSCR )ÇliIl)2 n <0, rightward = -3.354+3.7l3C+(1.8l0-43.13C8)(T//I) +(35 .S7-.8.225C)Ç/Il)2 n <0, left ward
Iii formulas (7) - (8), a), b» c1, K1,1,
(j
= 1, 2, 3. 4represent four situations. i.e.: u0, n0; u0, n<0; u<0, n0; and u<t), n<0) are determined by using existing four quadrants characteristic charts of propellers.
2.3 TI E CALCULATION 0F WIND FORCES X,,, Y,,. N,,.
There are many approaches available to estimate wind
forces let ng on aship, two of the most popular ones are Isher.
method and Tao11,method . However, we use Tao's
iiellitid in estimating wind normal pressure coefficient cR,,, pressure angular rs,, and pressure center coefficient C,,.
2.4 TI lE CALCULATION OF CURRENT FORCES Xr. Yr Nr. In this paper, the viscous effects of uniform current are cilnRiclered in the calculation of hydrodynamic forces by using relative velocity method. Therefore, only inertia influences are included in the calculation of Xr, Yr and N
= T VcSin(WOc)(fniim) = T Vccos(WUc)(m22-.-,nii) N = 7 Vccos(W-Oc)(m-m62)
A qualitative method is suggested to account the
in Il ucnce of non-uniform current:
Assume that V(x) and O(x) are the velocity and the angle of current distributing along the center plane of the Shill. We
define equivalent velocities vj and cqutvalcnt angular
velo-citync as follows ¡.12 ufr
i
f VCOS0dZ L L/2 LIZ Vj* f Vsiri9dx
-L/2 LIZ _!... f VSinex4x L -L12Superposing u1, v and on tlìc ship moving velocities
u, y and r enables us to generate an equivalent uniform current to evaluate the influences of the non-utiifuriit current.
2.5 THE CALCULATION OF 'NAVE RADIATION FORCES
X11, 1//R. N/rn.
By applying linear wave theory, the equal ions lar calcu-latingX/1R, Y/IR and N,1p can he derived
a,R R X,/R = PJ1
- n
Lat axayj
s Y/IR= - fJ [a bR *ÖR i r òxòyj
S I. R bì» N/jR = PJS L at sòyj
where, = +VCOS(5)I_O) 'ci = 'c-Vsin(V-9) =In (15). si is the ship course angle and Ç (j = 1. 2. 6) arc amplitudes of surging. swaying and yawing al tite ship. [3v applying strip theory, tite velocity potential oJ) should satisfy the following equations:
_aZQ(fl+2io'c,,.,Ci>+'cj2,,(J)_gQ,,(J)I, = = r) or
j=2,6 (16)
By using the multipolar expansion methxl. we can sol ve the velocity potential Q from equation (16) ( for convenience,
(12) the superscription (j) will he omitted thereafter ):
N
Q= A0Q0+ (17)
02m 2m0r2"
Q,,, =
sin(2m+l)Or"+-g 2(m+n) sin 2(rn+n)Or'}
-2
Vf_L_..cos(2,n+l )0r"+(2,n
+1 )sin2(m +1 )Or"g gm
lit equaLion (18),
where,
y-b I-*Lr (y-fb)+ix = -b)2+x2 +b)2+2
_LPV.SK
[KK,
K-K2--i- iti 1K2e-K2(.j b)oK2 K ieKl
=
_L.\'g2._jg
2g
-
/,D ao,,0"/0 = _p--+p(iryr)
Those forces caused by P, are called Froudc-Krylov forces and itose caused by P0 arc called diffraction forces. In order to integrate the above equation analytically, we equate the
ship to
a box with the same width B and height T, but
ccjsiivalent length L' = C503L. Then, by using the Haskind-Newman formula and medium value theorem of intcrgration, it Is possible to calculate Froudc-Krylov forces and diffraction krccs with the fol1owin analytical expressions:
sin!?,,, = 2jiII,,,g (1-e _KT)si,1L=sm(i,t.
sinL,,, Y,,,,, = 2p/I.,g (1_e_AT sinll,,,sincs,z
KL coso ¡ N,,,, = pIIg (1-e1'7) K B2sinL_(BcosB,,-sinB,,tJfl2 -L' 2sirìL,jL,,,cos/3,,,-sinL,j/L,,,,2 (18) (19)
Thc cocfficicnts A,,, (ni = 0, 1,..., N) in equation (17) arc determined in accordance with the boundary condition in equa-LiOn (16).
2.6 TI lE CALCULATION OF WAVE FORCES X,,,. Y,,,, N,,, According to lincar wave theory, the wave forces X,,,, Y,,, and N,,, can be calculated with:
X 55 (Pj+P0)n1dc=X1+X
=JI (P,P)n2dr =
N =55 (P+P0)(xn2-yn1)th
=N+N
Whcrc, K, ci arc the wave number and tite natural frc-(20) qucncy, and x. ci, arc the encounter angle and Use encounter
fre-quency. They arc related with each other n the fornì:
(21) (22) (23) ci,, ciu/,,,sinL,,, Y,,,0-L,,, .{ inXcOSBe_TK12m22+Sin {Dsin}eTm32']cIrìci1
--
[sin}eTnì2 ]cosci/}
r LcosL,,,-sinL,,, sinL,,,N0 = II,,,ci lci,L +vo
2L
jinXcosße_TK52m2+sin
[BsinXJen2Jcoso/
K+ stncos13,,,e n22+sin --ßsin e p132 SIriCi,1
3. THE MATHEMATICAL MODEL FOR COMPREHENSIVE ASSESSM ENT
(24)
(25)
I'vlost of previous researches about siìiJ) ritaneuveralsility criieria is concentrated on Lrylng to epres every tilaneilvera-bility precisely. To serve titis purpose. several criteria have been proposed, such as stability index T. turning ability index K, maneuverability index P, inertia criterion w,. etc. Each of these criteria specifies one particular maneuvering performance of the ship under consideration. However, there exist three problems in such "precise criteria". The first problem is that the existing criteria are too variform and sometimes even contradic-tory to each other. Tite second problem is that although each criterion de,ccribcs one aspect of ship maneiiverahilities, their contribution to a slop's overall maneuvering performance is not clear. The third problem is that the existing criteria do not con-sider influences of environment and human control which play an important role in ship maneuvering. Therefore. with existing criteria, it is uneasy to choose appropriate criteria to evaluate ship maneuverability, difficult to compare niancuverahilitics between two different ships and impossthle IC) consolent ade-quately on a ship's maneuverability under tite environmental influences and human control. In this paper, by means of fuzzy mat!wrnajicsb)h, we establish three consprcltensive
assess-ment criteria, ship's inherent maneuvering csiality, ship's rda-Live maneuvering quality and ship's man-in-1001) nianeoveroig q u al i t)', in an a tieni Pt to Ilse sol 'e the ti tree I roble OiS titen t itined above.
=
ci, = o-Ku:côs+Kvzsin'g (26)
and D,,,, L,, are defined as:
R_4 --KsinX
(27)
3.1 TI E SI lIP'S INHERENT MANEUVERING QUALITY licre, lite ship inherent maneuvering quality implies ship's mancuvcrabilitics excluding thc iníluenccs from both cnvironmcnt and human control.
If we can find a consistent and continuous function J
which project each maneuverability criterion set U1 on the
region of certain comment such as "Good","Poor", e.g
--410.11 (28)
lien, tite second problem mentioned above will be solved. We
tise fuzzy mathematics to set upsuch functions. Here,
f
as a luriction, is called membership function of criterion set U about ute comment C. u is an clement in the set the value off ati.e.. f(u,) is called membership value.
As for the difficulty for assessment caused by the first
)rohlcm. we suggest to USC comprehensive assessment method
tu solve it. Thus, a comprehensive criterion M,, or "ship inherent maneuvering quality", is established to measure the sluji inherent mancuverabilities:
Where, N is tise number of essential factors considered in the comprehcnsivc assessment, andu the element of the ith essen-dii factor lIi,
f
is the membership function of the dli essential factor about certain comment.i lacing studied many previous researches about ship u:ini.'siverability criteria, we think five (that means N takes value of five ) essential maneuverahilities should be considered in the situp comprehensive assessment. They arc course keeping tahihty, course changing ability, turning ability. stopping abil-ttv and low velocity steering ability which arc respectively expressed by tite criteria residual yawing velocity r initial yawing Linie ¡,, rel:tiive turning diameter D relative stopping J stances ¡t';, as well as tite nsiniinum velocity s4 requ red to
keels tise riikk'r cfl'ective. We usc index system u (i=l,2,3,4,5 to refer theist in the above stated sequences.
lo order to set up the membership functionsf.. we did a nsant'uverahility survey among over two thousands captains across Cluna. By means of fuzzy mathematics and optimization techniqui.'s such as Marquardt and Guass methods, we have csttililihcd a group of membership functions about different cousinlcnts. Asan example, we only list out the membership functions of five essential maneuverability criteria about tIse c(smnient "acceptable lo sail
.f (r) =0.5+0.Ssin l0.44(r'-0.143)1 3.73r'Sl0.9l
f2(t,) =0.5-0.5sin [1.15(z1 .74)] 0.3S1 3. I iX
f3(I)) =
D0.98
=0.5+0.Ssin lO.29(R,+3.72)1 l.6sI?;,12.48
f5(u)
=0.5O.5xin l6.99(ut-0.24O)1 0.019ujO.470Figure I shows one of comparisons of calculation resuhs :ihout itiembership values with investigation ones,
3.2 TI lE SI lIP'S RELATIVE MANEUVERING QUALITY "Ship's relative maneuvering quality" is designed to represent the ship mancuverabilities related to ils navigation environment. Similar to the previous discussion, the ship rela-tive nlancuvcririg quality MR is subjected to:
(30)
(4
Figure 1. Themembershipfunction of stopping distance about 'acccpiablc to sail"
N =
¿«I
N
= I
Where, u refers to the total effect combined witis wind,
wave, current and water depth in a typical situation:
= (K1u1)V(K2uu2)V(Ksu3)V(K4uu4)V(Ksu,)
i= 2,3,4,5 (32)
In equation (31), the weight coefficients a, indicate importance of the associated essential tn:weiivcr:iÌsility. "lucy are dependent on tise ship's satling environment. \Vc rtt:idc great effort to obtain the values of tite appropriate wcigist coefficients a by solving the following fttzi.y relationship cqtia. lions
ROA =B
O (ata 2a 3aaa 5) =O (33)
a;O ¡=1,2,3,4,5
In equation (33), A = (ai. a2. a , a4,as) is tite weight coefficient set; B =(h1, b2, b3, b,,b3)' is sise consolent set; and
R is tite fu7.zy assessment set. Its elements ri)=I? (X1 u,)
represent niembership values of tite jilt essential nianetiverahil. ity criterion of the itlt sitip. O (ata 2a 3a4a ) is tite pertltutatiort order of a, a2, a , a4, a5 from large Lo small, wlticit should be
equal to Ilse investigation one O . Tite symbol is a calctil:itiosi operation set in futzzy nsathent:titcs, It can stand for
+ ), ( A ,V), ( V , A ), (.' A ) and ((titer calculation opera.
tion,s with tite properties of coriliitutitv, otonotottosts increase, and positive definition.
lt should he pointed out tisai tite soltttiort set of equation (33) is always either a multi-elements Set, or an ctttp' set. For the former, we take iLs maximutrn or mediutii element; for tite latter, we take iLs "closed soltition" so called in tite fuzzy
ni a tltensat ics. In ca Ictil a ti ng the closed sol ut ioni, tise II ato uni i rig
formula is used to evaluate the closeness between two sets:
N,,(A 8)=
_L
I ,t (u1)ß (ui) (34)Rit
(31)
3.3 TIlE SlllP'S MAN-IN-LOOP MANEUVERING
QUAL-ITY
As we have known thai the economy and safety of ship
sai ing not only depend (Sn ship inherent nsaneuvcrahility and
cllvirnnlllcnt, hut also depend on the human steering skills. Therelore, we establish another comprehensive criterion called 'ship's man-in-loop maneuvering quality' M, to express the chip nanetiverability (Inder tise control of human being in con-Junctiun to the environmental influences:
Aie =G1 (a2G,,,2+a3S,,,+a4T,,,+a5D,,,+a6T,,,,) (35)
Where G,,,, G,,,2, S,,,, T,,,, D,,, and Ti,,, arc membership
Thc calculated rcsulis of wcight cocflicicntso are listed
n table I. Taking ocean ships for example, their code is 4 (code1)--! (code2), whcrc the stability weight coefficient a1 is
biggest, which tells that for ocean ships, the stability is most important. Therefore, with the help of fuzzy mathematics, we arc able to quantitatively assess qualitative StatCmenLS regarding to ship mancuverabilities. At present, such assessment approach is lar from perfcct. Nontheless the concept behind this approach tiiidosibily reveals a new philosophy in ship maneuverability
assessment.
able 1. 1hc wcgh cocfíicicnts of certain kinds of ships
e'°
fo = (L+L1)/2 S.fs,j= I S<r01
_v,(s_vo)2
¡=1,2 (4!)
In the above equations, SS and 1 are tite actual sailin
distance and the time required to complete this distance. &,,, t,, are the mean rudder angle and the steering frequency. S,,, ¡,, are theoretical ones for SS and t. n) is the number of olstacles that should be avoid to prevent colliding. stiels as other ships and reefs, and n the number of objects which should he approached, such as piers and buoys. L and L, arc principal lengthes of the ship and obstacles. S is the minimum distance between the ship and the obstacles, V is the SlliI) pcd.
4. EXAMPLES FOR CALCULATION SIMULATION AND COMPREHENSIVE ASSESS1ENT
13aced on t hic ns :11 licosa ti ca I nu cIcl s i resc 011.1 I abo ve,
codes llave been developed for situ ijlatiors calculaI ions of ship maneuvering nsotinns and conipreliensive :Lcscssllscnts on shi1)
nianeuverahiliiics. Extensive graphic techitliques Ire adopte(l Lo
give a vivid real Linie view of ship nl:IneLls'cring nsotintss during the calculation process.
For four ship models listed in table 2. we c:irricd out V arious simula tïon calcul at ioits, isc I ud ng zig/ag, t orni ng. spiral, hacking. stopping, approaching to or departing froni piers under different environmental conditions of wind, wave, current and water depth. Some results of the titinierical calcula-Lions arc shown in ligure 2 - bigure 10. \Ve also applied tue comprelsensive assessment method in tins paper to a few full size ships as well as ship models, l'art (mf these results were
ineltided in table 3 and table 4 and ligure 11. Finally, as an
integrated caictilation example, we perforoied a complete numerical calculation on the ship model 'Mariner'. TIle
calco-Iation consists of two parts. At the first part. siniulatiors calcula-tionS were carried out to obtain five needed values about essen-tial maneuverability criteria. The calculat ns included rudder returning. 7.igzag. turning, stopping 311(1 low velocity course keeping under four environmental conditions. Based on tIte data supplied by tise s ini ti latin rs cal cui a t ion, tite IO mdl vera bili y
assessment was fulfilled in the second part. The results are shown in table 5.
Table 2. The dimensions of four ship models
code1 code, a1 a? a1 a4 a9 tank ers 3 0313 0.106 0.2 18 o 223 0.I40
cargo 5111159 3 2 0.207 0.220 0.2 14 0.222 0.138 pas.scngcr ships 3 0.107 0381 0.279 0.19 6 0.049 passcflgcr cargo 3 4 0.102 0.291 0,223 0.206 0.17 9 tu gho14 3 5 0.08i 0.225 0.210 0.1 (.9 0.316 tour ships 3 6 0.074 0.2.49 0.144 0.157 0.375 (gaian ships 4 0.246 0.16 I 0.213 0.228 0.13 2 rivcrships 2 0.126 0.251 0.202 0.202 0.219 sca ships 4 3 0.137 0.267 0.226 0.203 0.167 Largc C11 ships 11 0.239 0.151 0.2.15 0.213 Ois 3
mediumC, ships lt 2 0.l93 0,254 0.19 I 0.234 0.126
small C11 ship.s Il 3 0.115 0.267 0.211 0.193 0.224
Ship name Ma rifler Sh a nella i t 'ha ncchc:mg L '('C
I (rim) 3.219 3.4 51) 3,270 3(0)0 It(os) 0.4(,4 0.566 5.1(5 0.537 T(n) 0.149 0.135 0,137 CR 0.613 0.746 0911 0.547 GP 0.620 0.7 59 0.1(1 (, 0.559 It(os) 0.153 0.154 0.13 8 0.156 L,(rn) 0,081 0.090 0.11149 0.133 D(m) 0.134 0.1 20 0.103 0.1)95 P.R 1.038 0.650 0(60 0.775 EAR 0.365 0.5110 0.590 0.565 S ca Ic so 511 50
values :1171)111 smp safety, economy and cornporiness. They are evaluated with the following formulas:
S,,, = t (SSS,,,,Ì)/S,,,1 (36) S,,,=0 r,,, = SS>2S,,61 t," = o (37) I),,,= t D,,, =0.5+0.5cm l0.42(,,,+3.26)] 0.49'c,,,7.98 (38) I),,. = (1 T,,,, = SO.12} (39) 1=,=e 1,,>0.l2 G,,,1 _min(l-fatj'f,,i)
j
= 1.2,3...m G,,,2=minj
= 1,2,3...n (40) fvt -C JV = I VV0 "<vo ¡=1,2 (42)lal)lc 3. 'Ihe comprckicnsivc asscocmcnt rcsulta for some ships' irtherent rnaneuvcrabjljt its
lahlc 4. 'l'ho comprehensive assessment results for some ships' relative maneuverabilitics (ocean ships
'l'aule 5. The comprchcnsivc assessment results on inherent and relative maneuverahilities of "Manner"
Figure 2. The turning characteristic curves of "Mariner' at different waler depthes
lo 20 30 40 50 c,1. cal. litt claVa) o rIcadi.)
Figure 5. 'l'he velocity history curves of "Mariner" while inertia stopping
o Irr. .63
Figure 3. 'l'ue wrning charactertslic curve of 'Chaiigcherig' with deep Waler
-y(ca)
Figure 4. The turning trajectory of "Mariner" with right 33i rudder angle
11)7' 2.) i
ship code fj
f'
fi
¡4 Is ocom M129 2.003 0.88)2 0999 0.867 0.846 1 0.920 25 .0(8) 0.999 0.562 0.999 0.822 1 0.877 27 I OCX) 0.853 0.802 0.760 0.830 I 0.9.49 28 2.0(8) 0.827 03)9 0.78.4 0.876 1 0.001 9 2.0(6') 0.394 0.798 0,952 0,720) I 0.773 44 IO(0) 1.0(8) 0689 0.612 0.478 1 0.756 2(, 2.00) 0.912 03)9 0.424 0.877 1 0.747 7 1.003 0.390 0.845 0.890 0.594 1 0.744 9 1.0(0) 0.999 0.372 0.4.85 0.788 I 0.729 .2 1,0(6') 037.8 0.69.9 0.410 0,967 1 0.7)9 30 2.018) 0343 0.822 0.699 0.337 2 0,682 (, 1.0(6) 0.422 0.478 0.654 0.849 2 0.651 34 1 0)5) 0.0(9) 0.772 0.608 0.935 3 0.663 lO 2.0(8) 0397 0.775 0.176 0.725 2 0.655 3 2.0(5) 0.382 0.054 0.569 0.710 2 0343 3 0992 0.410 0437 0.162 0.655 2 0311 45 04)5 0.673 0.471 0.957 0.329 2 0.509 4! 1.0(53 0.589 0.022 0.336 0.478 2 0.485 5 2.0(5) 03(1 0.312 0.015 0.453 2 0.469 37 0.776 0480 0054 0926 0,0)0 4 04.45
Slip coilc 1
/
,1I
R ori coin M144 (,(8)0 1,0(4.) 0.689 0.612 0,479 I 0.764 (8)0 0999 0.372 0485 0.789 1 0.7)8 7 1.0)10 0.390 0.s45 0.290 0394 0.722 4 1.18)0 0,322 0.689 0110 0.967 1 0.679 31) 2.118) 0.5.43 0.822 0.699 0.337 2 0.667 (, 1.18)1) 0.422 0479 0.654 0.849 2 0.632 (0 1.14.10 0397 0.775 0.176 0.723 2 0.622 5 1.1)00 0361 0.322 0.025 0.453 2 0.436 35 0.0(7 0.552 0.366 0.694 0,236 2 0.420 l'I 5.125 0279 0.613 0326 0.224 2 0384 I i'i,i (1) (2) (3) (4) V(tn/s) 0.0(8) 0.1(0) 0.15)0 0.0(10 V, (nr Io) 0,0(X) 4.000 0.600 7.220 Il,,(irz) 0.0(X) 0.010 0.600 0.600 I (ri) 13(5) 23(8) 0.243 0,243 25.740 17.250 10.990 16.020 r» 0.0(9) 6.824 0.8)0 2,024 2,260 2.4(8) 2.720 2.490 i.); 4420 4.470 3.980 5.980 3.820 4.220 3.020 3.7)0 U,> 0.2.80 0.320 0.320 0.344 ft 1.0(X) 0.893 1.28)0 1.28)0 ¡2 0.557 0.477 0.299 0.42.5 ¡3 0.156 0.137 0.0)0 0.0)0 ¡4 0.997 0.967 2.1)00 0.991 ¡5 0343 0.329 0.319 0.200 a2 0.260 0.24.6 0.137 0.126 a2 0.218) 0,282 0.267 0.251 a3 0.2(X) 0.223 0.226 0.202 24 0.20(1 0.228 0.203 0.202 a3 0.229) 0,232 0.167 0.219 M11 O ((49 0.558 0.473 0.477
30
Figure 6. The bucking Luming trajectory of 'Marincr" with left 29° ruddcr angic
io 20 30 40 so 60 70 io 20 30 40 30 60 70 y(u)
Figure 7. The turning trajectory of "Marincr" with right 25°
ruddcr angle in the unifonn wind
( V, = I0.2,nfs, O,, = 90", Wo = 30°
o1o4000* «mi
0-0---0----0---0 «ml io 20 30 40 caL Im, o iirr.I0 y(m)ligure 8. The backing turning trajectory of "Mariner'
with cli 35° rudder angle in the uniform current = 0.2,n/s, O, = 135°. 'Vo = 2W"
V = 02m/s
rigire 9. 'nie coinparis of velocity history cuz-ves of "Mariner" while crash stopping in different current situations
io 20 30 40 SO 60 ')"> ,nc,hod n p.n nhod n Ihia p.n yin)
Figure 10. The turning trajectory of "Mariner" with left 35°
rudder angle in the wave ( II,,, = 0.05
oao oibo' 'i")
o
a*jtjpnentrnuii
C,,3=032e), 6,2 0.772, S, = 0)110
r)") T,, = 0.443, t).,, = 0.10)0, T,, = 0.9)9
= 0.539
Figu re I I - 'lhc ¡11 an -in 'kxp in aneuvc rin g t r:ijec ury (If '' M ir inc r" under cc nain envi roninci) Lii COil (I) 3)1)0
V,,= 3.0,n/s, V0 = Olin/c, Ii,.,= 001m
O,, = 90°, O = 90". 0,, = 90',c = 5
From the resuRs, we can see tiott.
( i ). For turning. zig/ag ato! crash sto3ping OhiOlonc at dillercnt water depUtes, the calculation results arc very cori-Sistcnt wii,h tite experimental ones,
For inertia sL)))ping, lite c;ilciii)ion rcsliltÇ of 'Cli)-city history curves and stopping dit;tnccs li;ivc t 'in1il corrt'la
tion witi cxpernicnial data. The di (Tez-ence of the sliijt ito" rig
trajectory between calculation antI test is noticeable, lt sliottid
he pointed out that inertial stopping is very Sensitive tu hiC
slop's environmental conci i Lions. Sometimes, even the restiI 13 rif rcpatcd tesLs themselves arc quite diilcrcnt froto each other.
The simulation on ship hack ¡ng motions at different water depUres is in general successful.
Comparing our results wi tir others' (ines for crulcitlat-ing the influences of wind and current on tire oht turncrulcitlat-ing tuotionS, no remarkable differences arc found.
11 is encouraging to lind some plrenotnicna ol 5101)
moving in waves arc consistent with what were trhscrvcd. Ftir
example, the stability and the backing ability will be
deteriorated under the influences of waves; tire switying
phenomenon will happen easily if tire slop is moving ahrnig tire wave direction; it will be very di hlictilt to irr ake ir tunn of the ship when wave length is about tite ship length anti wave height greater tItan half of tire sinip draft.
(6). Table 3 and table 4 show some (If the c;ulcttlatiorr
results of inherent maneuvering qual uy M, anti relative maneuvering quality M for firll si/e ships. TIte ciat;u I. 2, 3. 4. and 5 in the column "ori_coni'' titean live grades un colirrucilts: "good''. "above medium", ''mediutni'', ''below rmucchitrit'' arid "poor" which carne from tite captains surveyed. Ihasicly. our assessments on sitip maneuverabihities here reilect tite ctnrveycci
7°
results, Iiowcvcr, ours give more detailed and clearer quantita-tive assessments. It is also possible to apply the comprehensive method in this j5aper to ship optimum designs and waterway drcdgings by establishing functions of relationship betweenM, and Ship main dimensions as well as between MR and water-way dimensions through series computations; or to apply the method to sail-plan making and sailing feasibility study by comparing the MR values of the same ship under different environmental influences. Taking the ship "Mariner' for
exam-ple, as shown in table 5, obviously, the environmental condition (4) has the worst influence on this ship's maneuverability. Therefore, it is wiser not to sail Mariner ship at very shallow
waterways.
(7). The simulation calculations with man-in-loopshown in figure II are still at the initial stage of its kind. Its applica-tion. however, can be extended to any maneuverability study where Ituman effort is involved. For example, by using the the slop's man-in-loop maneuvering quality Mc proposed here, we will he able to weave together the ship's inherent maneuvera-hihiv, the sailing environment as well as the skill and experi-ence of its captain, therefore we will be able to make a well-conceived ship navigation plan or analyze the steering skills of captains or trainees on ship simulators.
5. CONCLUSION
In this paper, the formulas of estimating four quadrants hydrodynarnic forces acting on ships were given by using system identification method; and forces caused by wave
and current were also formulated.
The mathematical model and program for calculating ship maneuvering motions , examined with hundreds of calculation examples, can be used to predict most ship maneuvering motions in wind, wave, current and shallow water. These maneuvering motions include zigzag, turn-ing, spiral, backturn-ing, stoppturn-ing, course keeping steering as
well as man-in-loop steering.
Three classes of comprehensive assessment criteria were established by means of fuzzy mathematics: ship's inherent maneuvering quality, ship's relative maneuver-ing quality and ship's man-in-loop maneuvermaneuver-ing quality. The assessment method in this paper can offer a clear quantitative, rather than just qualitative, assessment on ship mancuverahilitics. It can also be expected to be used in ship optimum design, sailing feasibility study, water-ways dredging, ship-steering training, steering skill analysis and sail-plan making.
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