Advanced weather routing of sail-assisted vessels

(1)

P

ARCH

EF

-1-Lab

y.

Schespsbouwkunde

Technische isdioo

Deift

ADVANCED WEATHER ROUTING OF SAIL-ASSISTED MOTOR VESSELS

Hidèki iÁIWAA

( Tokyo University of Mercantile Marine )

1. INTRODUCTION

In recent years, many sail-assisted mötor vessels have been operated

with remarkable advantages in saving, passage time and fuel oil and in

damping ship's motions in a seaway. In order to operate. those vessels

more effectively in ocean-crossing voyages, it is necessary tö develop

the advanced weather routing system. To accomplish the advanced

weather routing, the following requirements should be fulfilled

accurate forecast of environmental conditions ( wind, sea, swell

and.ocean current ) föra sufficient prediction period ;

good predictïon of ship's speed, drift angle and engine power under various conditions of environment, draught and trim;

practical computation of a (sub) optimum route for various demands

of shipmaster/owner. In this study., the methods to meet requirements

(ii) and (iii) are proposed, and the simulations are performed toverify the effectiveness of those methods.

2. MINIMUM TIME/FUEL.ROUTING 2.1 Minimum Time Routing

T

perform the effective minimum time routing, the practical method

-which is called the modified isochrone method by the author - has been

developed.

/1/

Let a ship depart from departure point X0 at time to and sail to the. destination Xf at the maximum ( constant ) number of

propeller revolutions. In the modified isochrone methOd, the isöchrone

( i.e. the outer boundary of attainable region from X0 ) at time t0+ (i+

l)it i's calculated as follows.

The ship is sailed for t hours from each point constructing the

isochrone {'X} at time t0+ iAt, following discretized headings around

the initial course of the great circle route from X. to Xf. ( Fig.l )

In each heading, the arrival point X.4.1 at time t0+ (i+l)Lt is calculated by Mercator's sailing.

X.1

f( ) (1)

where X ₌ ₍ _cp x )T U, ₌ ₍ V.

)T,

(2)

+ ( v

cos(

e.+

) +

} Lit

/ R(4.)

V. sin(

e1

c ₎ + E1

+ {

mp(1)

- mp()

v + c. ) + N1

ei

ship's heading at time t0+ iLit,, : latitUde, A.1 : longitude

V : ship's speed tirough the water, a1 drift angle ( leeway )

northerly component of ocean current

E1 : easterly component of ocean current

R(41) local radius of meridian,

mp(.)

: meridional parts

Then the sublane set {L(.k)} is defined on both sides of the great

çircle route between X0 and Xf. The lateral deviation D+i of arrival

point X1from the great circle route identifies the sublane L(k) to be

assigned to each X.1. From all X..1 included iñ each sublane L(k),

the, X+1(k) is selected with minimum great circle distance to Xf.. The

isochrone at time t0+ (i+1)Lit is obtained as a set of X+i(k) and is

represented by {X1}. Repeating this procedure, the isochrones are

successively constructed.

Whenthe isochrOne {Xn} at t0+ nLit approaches the destination Xf

sufficiently, the passage time Lit1 between each X and Xf along rhumb

line. is calculated. =

R(1)

- n secO

{f

V

cos( e+

) + N, 2 +

[

V sin(

_{O+ a}

) +

E]2Y1"2

(3)

where the ship's heading from Xn to Xf is given by

tan{( Af - A

)

/ [ mp() - mp() ]}

(4)

The passagé time T between X0 and Xf is

T n Lit + Lita =

T( XUnWn )

(5)

The minimum passage time Tmin is selected frOm the passage times of

all routes constructing the isòchrone {X}. Using X giving that

min

as a starting point and tracing the isoòhrones memorized in a computer backwards, the minimum time route from X0 to Xf can be obtained.

2.2 Minimum Fuel Routing

Consider a ship leaving departure point X0 at time to and arriving at destination Xf at time tf.and let us minimize the total fuel consumptiOn

during the voyage. In this case, the arrival time tf is specified and

the passage time T = tf - to is fixed. The minimum fuel routing by the

(3)

modified isochrone method is as follows.

First, a suitable number of propeller revolutions is assumed, and the

minimum time route and minimum passage time Tmin are calculáted by using

the.modified isochrone method. Then the number of propeller revolutions

is corrected so as to get close to the specified passage time T.

Using the corrected number of propeller revolutions, the minimum time

route and minimum passage time Tmjn are recalculated. If _Ii

-becomes small enough, the calculation is stopped. Otherwise, the above

procedures are repèated.

The obtained minimum time Ñute can be regarded as the minimum fuel

route for a specified passage time. The minimum fuel route calculated by this algorithm is not an optimum from the mathematical viewpoint, but it may be acceptable from the practical viewpoint.

3. ESTIMATION OF THE STANDARD DEVIATIONS OF PASSAGE TIME AND FUEL CONSUMPTION

For the shipmaster/owner, it is very important tó evaluate the

reliability of calculated optimum route. Namely, they are eager to

know the degree of uncertainties of calculated passage time, fuel

consumption, etc.. To meet this desire, the practical method to estimate the covariance matriçes of ship's positions and the standard deviations

of passage time and fidel consumption has been developed.

In equation (1), the vector U. may be regarded as, a function of ship's

heading 0, number of propéller revolutions ni and environmental

conditions ( wind, sea and swell ). Using the vector C. for representin,g

environmental conditions, U. can be written as

U= U( C,O1,n

) --- (6)

Since the fuel consumption G between t0+ it and t0+ (i+l)t is a

function of and ni, it may be written as G( ). The accumulated

fuel consumption F1 from to until t0+ (i+l)t is given by

F1

= F + G( ) '(7)

in equations (l),(6) and (7), as C. and W. are the random variables

distributed around their mean ( predicted ) values, U, X., G1, F

and also become random variables.' Expanding the right-hand sides

of (1),(6) and (7). around the mean values in a Taylor series and

(4)

f Xj + f

+ f AW.

ui= u

= + G

where AX etc. represent the prediction errors and f,, etc.

denote af/X. af/aiJ

etc.

Now, we regard and as the

gauss-markov randOm sequences produced by the following shaping filters.

= .

+

Wi+l

= w ¿W1 +

where AC1 and

are gaussian purely random sequences; and

are matricés representing the degree of correlation. The covariance

-4-.

is given by equation (15), an error ellipse of a ship's position can be

calculated by usin.g its eigenvalues and eigenvectors.

In order to estimate the standard deviations of passage time and fuel consumption, suppose that the ship's position Xn at time t+ nt

matrices of and are the functions of prediction period and

location in the ocean; and

w are the functions of time interval t,

sailed distance during t and location in the ocean.

Combining eqúations (8) through (12), we have

x fuUc Xi O O

*

0 1 _GvVc O O O We wi+l simply write o o o o o o (13) as ¿wi

Ï

O O I (13) =

A(i) M +

_{( 14)}

The covariance matrix Of is calculated as

P(f+l) A(i) P(i) A(i)T +

Q(j+]) BT

(15)

where P(i+l), P(i) and Q(i+l) are covariance matrices of , ÈY. and

1 1 respectively. -Q(i+l) where P(i+l), W.11 and

The matrix Q(i+l) can be obtained by

P(i+1)

- o

.0 _PW(i+1)

Pd(i)

i]

and are covariance matrices of

respectively. When the covariance matrix of

(5)

approaches the destination Xf sufficiently. The passage time T between

X0 and Xf is given by (5). We represent the füel consumption between

XandXfas

Gn = G( ₎ (17)

The total fuel consumption Ff between X0 and Xf becomes

Ff F _{+ G( Vn,nntn )} (18)

Expanding the right-hand sides of (5) and (18) in a Taylor series, wè have

=

+ T

U,.1

+ l

(19).

,Ff = AF _{+ G} _{+ Gt} T (20)

wherè

lu' G and Gt denote aT/aUn 3T/Wr 3G/aV and

G/at

respectively. Combining (19) and (20) with shaping filters for

Cf and Wf We havè LT J

[

T, o

-

o o

*

f I I

G1Ç

1

GV+ GtTUUC

GtT AF o o Cf (21)

LCf

O O O + I O Wf

J

t

O O O O

I

We simply write (21) as Yf = A(n) + B (22)

The covariance matrix of Yf can be calculated as

P(f) A(n) P(n) A(n)T + B Q(f) ßT (23)

where P(f), P(n) and Q(f) are covariance matrices of Mf and

respectively. Fróni (23), we can estimate the standard deviations of

passage time and total fuel consumption.

4. PREDICTION 0F SHIP'S SPEED, DRIFT ANGLE, RUDDER ANGLE AND ENGINE POWER To predict the ship's speed, drift angle, rudder angle and engine

power of a sail-assisted motor vessel, the method based on the equilibrium between forceS and moments acting on the ship has been develOped. /11,12/

For a sail-assisted motor vessel proceeding in aseaway at constant speed, the 1önitudinal forces X, the lateral forces Y and the yawing

moments M around center of gravity should be ba1anced. ( Fig..2 )

Xs + X + Xh + Xr + Xw + X 3

+

a + 'h + 'r = O

M +M +M +M =0

(6)

where

X,

_{'' M} : aerodynamic forces and moment due to sails

Xa _{'a' Ma} : aerodynamic forces and moment due to hull and superstructure

Xh _h' Mh : hydrodynamic forces and moment due to hull

Xr YrMr :

hydrodynamic forces andmoment induced by rudder

Xw : added resistance due to waves X : propeller thrust

In equations (24),(25) and (26), when the ship's heading, number of

propeller revolutions, draught, trim and environmental conditions are

given, the ship's speed V., drift angle a and rudder angle 6 become the

unknown variables. Thus V, a and 6 are obtained as follows.

Assuming a suitable value to V, a and 6 are calculated by (25) and (26).

Using those V, a and 6, the.léft-hand side of (24) is calculated. Then

V is corrected so as to make it close to z ro. Repeating this procedure,

we can find V, a and 6 satisfying (24),(25) and (26).

Given the number of propeller revolutions n and the ship's speed V, the engine power P can be calculated as

P = 2ïr Kq(VnD)

p D5 n3 / r m (27)

where

Kq(VnD)

torque coefficient : density of sea water

D : propeller diameter relative, rotative efficiency

mechanical efficiency of shaft bearings

Fig.3'shows an example of ship'.s speed and engine power calculated by (24) through (27). The mathematical model ship used here is 40,000 DWT

product tanker with 808 m2 sail area. _{( Fig.4 )} In Fig.3, the equivalent

motor vessel ( EQ MV ) denote the same ship as the sail-assisted motor

vessel ( S-A MV ) without sails. It can be found that, for true wind

directions larger than 20°, S-A MV can sail faster with smaller engine

power than EQ MV.

5. EXAMPLES OF THE SIMULATIONS Of MINIMUM TIME/FUEL ROUTING

Using the methods described in section 2,3,4 and the model ship

depicted in Fig.4, the simulations of minimum time/fuel routing were. performed. The wind, sea, swell and ocean current data were prepared from the global-band data set published by the Fleet Numerical

OceanOgraphy Center of the U.S. Navy.

Fig.5 shows the minimum time route ( MIR ) and the great circle route

( GCR ) of S-A MV from San Francisco to Tokyo. In this simulation,

since the forecast data were not available, the actual ( analyzed )

environmental data were used as the forecast data. For the covariance

(7)

-6-matrices and correlation -6-matrices of predicted environment, the dummy

data obtained from another environmenta.1 data set were used.

In Fig.5, the one-sigma ( 39 % ) error ellipses of the ship's positions

constructing the isochrone for 24 hours time interval are drawn. The

standard deviations of passage time, average speed and fuel consumption

are shown after th ± signs. We can find that the standard deviations

on the MIR are much less than those on the GCR.

From Fig.5, it is also found that compared with the GCR, the _passage

time and fuel oil were saved by 47.9 hours ₍ 12.3 % ) and 110.0 tons

( 19.2 % ) on.the MIR. _{In another simulation using EQ MV instead of}

S-A MV, the passage time and fuel consumption were 354.5 hours, 496.3

tons on the MIR and 401.9 hours, 603.6 tons on the GCR. Therefore, it

can be said that compared with EQ MV, the passage time was saved by 14.2

hours on the MIR and 13.7 hours on the GCR by the use of sails.

Fig.6 shows the minimum fuel route ( MER ) and the GCR of S-A MV.

The passage time was specified as 401.9 hours which is equal to that on

the GCR of EQ MV mentioned above. Thus it can be seen that compared

with the GCR of EQ MV, only about half the amount of fuel oil was

consumed on the MER of S-A MV.

6. CONCLUSIONS

The methods to perfOrm the advanced weather routing of sail-assisted

motor vessel.s were proposed, and their effectiveness was confirmed by the numerical simulations. The shipmaster/owner may easily evaluate the

reliability f calculated optimum route by the standard deviations of

passage time and fuel consumption. As a follow-up to this study, the

comprehensive simulations

Will

be executed in order to improve the

proposed methods.

ACKNOWLEDGMENTS

The author is indebted to the staff of the Hydronautics section of the Department of Maritime Technology, Delft University of Technology, particularly to Profi ir. J.A. Spaans for his kind advices on this study.

REFERENCES

/1/ Hagiwara, H and Spaans, J.A. ( 1987 ), Practical Weather Routin.g of

Sail-assisted Motor Vessels, Journal of RIÑ, Vol.40 No.1., pp.96-119

/2/ Hagiwara, H ( 1987 ), Weather Routing of Sail-assisted Motor Vessels

C in Japanese ),.NAVIGATION C JIN ), No.93

(8)

-7- 60-Ui 50-40 -j 30 20 o o DEPARTURE POINT ° 17 '5 9 ARRIVAL POINt AT t0+ (l1)t

Xi -.

o0f SAIL-ASSISTED (101CR VESSEL

PASS. TIME AV. SPEED FUEL CONS. (HOURS) (KNOTS) (TONS)

MINIMUM TIME ROuIE 340.3±7.2 ¡3.5 ±0.29 461.9±17.3 388.2±19.6 11.5±0.58 571.9±42.5

GREAT CIRCLE ROUTE

D&ARTURE O GMT NOV.10

itr'.

1980 PROPELLER REV. MIR : 75 RPM GCR : 75 RPM WIND SPEED o o LATERAL DEVIATION D11 IO 20 30 40 50 KNOTS

Fïg..5 Example of minimum time routing

SUBLANE 1(k)

- DESTINATION GREAT CIRCLE ROUTE BETWEEN X0ANDXf

ISOCNRONE (X1) AT t0+ lat

Fig.1 Construction of isochrone by modified isochrone methOd

'ROPELLëR REV. 75 R.P.M.

WINO SPEED 40 Kl

SEA ÑEIGHT S M

SEADIR. - WIND OIR.

SEAPERIOD

8

SEC

SAIL-ASSISTED MOTOR VESSEL

EQUIVALENT MOTOR VESSEL

SWELL HEIGHT 3 M

- SWELLDIR. FR011BOW 90°

-EQUIVALENT MOTOR VESSEL

SWEU. PERIOD 10 SEC

SAIL-ASSISTED MOTOR VESSEL - -

-t I-- t

t

-8- 60-w 50-e I- 40--j 30

20-MINIMUM ruEL ROUTE GREATCIRCLE ROUTE ÑESTBOUND VOYAGE

T OKT 8

140 120 IO IO IñO iño to -- IO

LONGITUDE WIND SPEED

Fig.2 Longitudinal forces X, lateral forces Y and yawing moments M

acting on the ship

dead weight 40,000

t

length between perp. 185.0 m design draught 11.4 m breadth moulded 32.0 m max. engine power 10,000 kW service speed 14 kt

total sail area 808 n2 ( two tri-plane wingsails )

Fig.4 Profile and main dimensions of the model ship

PASS. TIPlE AV. SPEED 402.0 HR 11.4 III 401.7 tIR 11.1 MT

%

i,

N

\\ ;, I /

ISOCHRONE OCR : 72.16 RPM FUEL CONS. 308.1 TN 524.8 TN DEPARTURE O GIlT NOV.10 1980 EAT T L E S FRANC O

\ ' \

PROPELLER REV. 11FR: 62.30RPM 180° 00 - 300 _60° _90° _120° _150°

TRUE WIND DIRECTION FROM BOW 8

Fig.3 Example of ship's speed and engine power

l.óo 10

LONGITUDE

140 160

10 20 30 40 50 KNOTS

(9)

APPENDIX SECTION 2 (j) Equation (2) R(cP) =a ( i - e ) ( i - e sin2c )_3'2 A-1) where a : radius of equator = 6378135 m _{( WGS-72 )}

e : eccentricity of meridian = 0.08181881 ( WGS-72 ) i + e. sjn. mP(q) = in{ tan( 71/4 +

_{4/2 )}

} - in i (A-2

In case V. cos( 0

. )

_'. N is close to zero, the middle latitude sailing is used instead of MercatOr's sailing.

I

çb. + {V. cos( e.+

.

) +

N. } t / R(.)

f ₌ _I

'

--

_(A-3)

+ .1 _V sin(

Q.+ ) + E

I it / R((q+411)/2)

where

R(q)

: radius of the parallel of latitude

R()

a cosçb ₍ i - e2 sin2

)1/2

(A-4)

(ii) Equation- (.3)

When is. close to is calculated by the middle latitude

sailing.

Rp((n+f)/2) (

A. X ) cosecO {[ V,. cos( 6n ) + N 2 + [ V sin( 0n ) + En ]2}_i/2 (A-5) SECTION 3 (i) Equation (6) Ci = ('S1 H51 1 _Hi D11 _Tì (A-6)

where _Swi : wind speed at time t0+ it

Dwi : wind direction

H5 significant sea height

D5 : predominant sea direction

average sea period

(10)

predominant swell direction

T1j : average swell period

(ii) Equation (il) and (12)'

and are assumed to be the diagonal matrices.,

= Ksw Kdw "hs O -lo-o

Kti exp( ._t/Tti - Ad/Dti )

exp(. -At/Ta - zd/D ) '

Ke ' = exp( _M/Te - ad/De

Ad is a distance sailed by a ship during the time interval t.

TswTdw1___TtlTnTe and

are correlation times

and correlation distances of prediction. errors respectively.

By investigating the predicted and actual _{( analyzed ) environment4l}

data fOr a lông period, We can determine: the correlation times and correlation distances. Kdl Kti (A-7)

R()

, (A-9) = R(4) LÀ (A-10) K O O K (A-8)

where Ksw = exp( -it/T _- _d/D5 )

Kdw exp( t/Tdw - d/Ddw )

(iii') Equation (15)

covariance matrix of ship's position

L4

(

(11)

x-y coordinate system

Í2

cov.X' E _I 2

L'

FR(4)2&2

R(c)R(q)&L4

LR()R()AX

R()22

From (A-12), we can calculate an errórèilipse of a ship's position

in local x-y coordinates.. ( The directions of eigenvectors of coV.X'

coindide with those of major/minor axes of an errOr ellipse. The square

roOts of eigenvalues of cov.X' are equal to the lengths of major/minor

axes of one-sigma ( 39 % ) errOr ellipse. )

On the Mercator's chart, the error ellipse is expanded by the

magnification factor M.

M,= a /

R(4)

(A-13)

SECTION 4.

(i) Equation (24),(25) and (26)

(1) Aerodynamic forces and moment due to sails

X 1/2

a A U Cxs(8a) (A-14)

= 1/2 'a A U _Cys(a) (A=l5)

n

1/2

a

EA5(i)

D5(i)

}

U

Cy(ß)

(A-16)

where

a : density of air

: total sail area

Ua : apparent wind' speed

apparent wind direction from bow n :nurnber of sails

, n

area of i-th sail A E A (i)

il

D5(i)

: distance from the center of gravity to i-th sail

-11-(A-12)

-& coOrdinate system :

cov.X = E L

(12)

where Af : transverse projected area of the above-water part

( excluding sails )

A1 : lateral projected area of the abOve-water part

(. excluding sails )

Loa :length overall

Cxa : fore and aft wind force coefficient

Cya : lateral wind force coefficient

Cma yawing moment coefficient (Fig.4-2 )

Hydrodynamic forces and moment due t hull

--1/2

S V{1

Yh=_1/2PwLdV2Cyh()

h 1/2 w

L dV Slh()

where

w : density of sea wäter

C resistance coefficient for zero drift angle

S : wetted surface of ship's hull

V ; ship's speed

d : draught _L : waterline length of ship

drift angle ( leeway )

Cxh added resistance coefficient caused by drift

yh hydrodynamic lateral force coefficient

Cmh : hydrodynamic yawing moment coefficient

Cxh132

Cyh = K1 + K2IIa

K1 -+ 1.4 Cb

Cmh=

K2=6.6 (1 =Cb )--O.O8

-12-(ct) }

(2) Aerodynamic forces and moment due to hull and superstructure

X = -1/2.

'a Af U Cxa(8a) (A-17)

= 1/2

a A1 U cya(a) (A-18)

Ma = 1/2

a A1 Loa U Cma(ßa (A-19)

C5 :

sail thrust coefficient

sail'lateral force coefficient _{( Fig.4-i}

(13)

where bloçk coefficient

breadth

Hydrodynamic forces and moment induced by rudder

Xr = - Fr sins (A-23)

=

- Fr cosâ (A-24)

Mr = Fr cosó.- (A-25)

where : rudder angle

Fr : rudder force _{( normal force )}

PwArV (l-w) (]+3.6S

)AR+2r2sin

where

'r

: rudder area

w : wake fraction

propeller slip ratio

ARr : aspect ratio of rdder

s = i

(i

wJ

V

p

np

where n .: number of propeller revolutions

p : propeller pitch

Added resistance dùe to waves

X -

(R

/H2)H2

_A26)

w wave w w

-where

_{( Rqj/H}

₎ : added resistance pér unit significant wave

height squared

significant wave height

For a given draught. and trim, _{( Rwave/H}

) is a funtiòn of the ship's

speed, wave direction from the bow and average wave period.. _{( Fig.4-3 )}

Propeller thrust

i -t) KpD4 n

where t :, thrust-deduction fractiOn

: thrust coeflicient

D : propeller diameter

n.: number of propeller revolutions

-1

(14)

The. thrust coefficient Kt is a moñótònically decreasing fûnction of the

advance ratio J which is defined by

nD

* In solving equations (24),(25) _{and (26), the influence of the drift}

angle OE Qn the apparent wind speed Ua and apparent wind direction

a

not taken into consideration,since it is estImated to be quite small.

(15)

-14-p C 80 20 9.88 -7.57 2.49 -7.57 5.86 0.87 -3.29 O.13 -7 57 1530.44 -1.64 1530.44

-3.4

3.16 188.18 5.06

(5,5)

P(6,6) P(8,8) 2.49 -1.64 O 78 -1.64 1.50 0.30 -0.74 0.03 variance of variance of variance of variance of variance of variance of variance of variance of --7.57 1530.44 -1.64-1530.44 -3.84 3.16 1B8. 1 5o06 wind speed _{( m/s} ₎

wind direction ( deg )

sea height C rn2 )

sea direction ( deg2 ) sea period C sec2 )

swell height ( rn )

swell direction ( deg )

swell period ( sec2 )

-15-5.86 -3.84 1.50 -3.84 3.74 0.53 -1.69 --0.01 0.87 3.16 0.30 3.16 0.53 0.41 1.51 0.23 -3.29 1I8.Ì8 -0.74 188 18 -1.69 935.49 5.73 -0.13 5.06 O 03 5!06 -0.01 0.23 5.75 3.94 (28) .F (60) G (60) H 0) M (56) N (60) 0 (60) P (51) Q (60) R (60) S (59) T (60). 1t0 i éO 1è0 léc 1(10 - 120 LONGI TUDE

Fig.3-1 Sub-areas used for investigating the mean values of covariance matrices, correlation times and correlation distances

( The number in parentheses denotes the number of

grid points included in each sub-area. )

Tab.3-1 Mean value of covariance matrices _{on the grid}

points in sub-area J.

( Investigation period May 20 - June 8, 1980 )

(16)

15.88 -31.55 4.83 = -31_55 9.30 3O7 -41.80 1.36

Covariance matrix for 48-hòur forecast

31.71 -34.73 541 -34.73 13.54 2.10 3.35 -0.09 -34.73 2922.76 -6.90 2922.76 -18.57 2.86 416.13 7.88 5.41 -6.90 1.67 -6.90 3.25 0.80 .31 0.23 -34.73 2922.76 -6.90 29227ô -18.57 2.86 416.13 7.88 13.54 -18.57 3.25 -18.57 8.69 1.25 0.05 0.17 2.10 2.86, 080 2.86 1.25 0.97 3.73 0.65 3.35 416.13 1.31 416.13 0.05 3.73 1357.71 3.66 -0.09 7.88 0.23 7.88 0.17 0.65 3.66 5.62

Covariance matrix for 72-hour forecast

20.28 -51.06 6.01 -51.06 11.93 3.25 -15.73 0.48 á51Ô6 3542.26 -13.47 3542.26 -31.25 5.36 763.15 7.69 6.01 -13.47 2.04 -13.47 3.53 1.21. -0h38 0.54 -51.06 3542.26 -13.47 3542.26 -31.28 5.36 783.15 7.69 11.93 -31.28 3.53 -31.28 7.36 1.86 -910 0.18 325 536 121 536 186 134 850 089 -15 73 763 15 -0 38 763 15 -9 10 8 50 1739 35 1962 0.48 7.69 0.54 7.69 0.18 0.89 19.62 6.51

Covariance matrixfor cl.imatological data

( The clirnatological datà denote the mean values of

actual data during the period between May 20 and June 8. ₎

-31.55 3795.00 -5.92 37Q5.ø -20 29 16.98 1109.65 .4.97 sub-area Ao.i0000E-09 0.10000E-09 0.39096E-05 0.28404Es.05 0.68593E 05 sub-area A..o.l0000E-09 0.10006E-31 0.10000E-31 0.48262E-07 O.35428E.Q6 4.83 -5.92 -5.92 2.83 1.20 -8.34 0.79 -31.55 3795.00 -5.92 3795.00 -20.29 16.98 1169.65 .4.97

Tab..3-2 Correlation times

of

_{the prediction error of sea height}

( mean value in each sub-area, unit : second )

0.37022E.05 o .43204E+05 o .30915E.05 O.42500E.05 O.61569E-05

-16-9.."

-20.29 2.83 -20.29 .5.64 1 77 -24.94 O 76 0.27011E.05, Ò.42113E,05 0.50262E-05 o .49198E.,05 0.54933E-05 0.26057E.07 0.10000E-31 0.100ÓOE+3i _0.10000E31 0.10000E-31 0.15264E-08 0.27556E.07 O.10886E.07 0o48o44E.06 0.58418E-06 3.07 16.98 1.20 16.98 1.77 1.70 8.45 1.66 -41.80 1109.65 -8.34 1109.65 -24.94 8.45 1705.40 23 12. 1.36 4.97 0.79 4.97 0.76 1..66 23.12 6.16 o .536210+05 0.530830+05 0.491690+05 0.46407E-05 0.55662E-05 -sub-area _T 0.871600+06 o 4721OE.06 0.489110+06 0.78928E-06 o.4822iE-o6sub-area T

Tab.3-3 Correlation distançes of the prediction error

of

sea height ( mean value in each sub-area, unit : meter )

(17)

V) (I .>( >-I-

I-w I-w

₀₀

u_ LU W

a a

L) -. L) . W V) L) a = LI. I--1 . LU V)

I-< -1

-1 -I

-2

)c

).-L)- "

1.0

-W -W L) '- _0.5 LI L. L. U. LU W

a a

L) L) W W L) L)

a a

U. CL.

-17-a -17-a

-0.5 I-U- < w a i-= .

-J-10-W I--- - I- - I - I - I-E -- 30° - - 600 - 900 120° 150° 180°

APPARENT WEND DIRECTION FROM BOW

Fig.4-2 Fore and aft wind force coefficient, lateral

wind fOrce coefficient and yawing moment coefficient

versus apparent wind direction from bow

-CMA - A CURVE

--- 0.05

0.00

-3

00 _30° 600 _90° 120° 150° 180° APPARENT WIND DIRECTION FROM BOW

8A

Fi.4-1 Sail thrust coefficient and sail lateral force

coefficient versus apparent wind direction

from bow

-CY

- 8A CURVE

-0.10

- -0.05

(18)

I-. 13 9 = LU vi , ' WAVE' W 20 LD C'J

- =

vi -w Q. W W . L =

¡5v,

vi I-.

- =

vi C.D W = LU W . 17 15 16 12 8 4 )

SHIP'S SPEED = 4 KNOTS

8 10 12 14 16 18 20 AVERAGE WAVE PERIOD ( SECONDS

Fig.4-3 Added resistance per unit significant wave height squared versus average wave period

-. PROPELLER REV. 75 R.P.M.

WIND SPEED 40 KT

SEA HEIGHT _{= 5} M

SEA DIR. WIND DIR. SEA PERIOD 8 SEC

-EQUIVALENT MOTOR VESSEL

-I I

----t

.---_--EQUIVALENT MOTOR VESSEL

SWELL HEIGHT = 3 M SWELL DIR. FROM BOW 90°

SWELL PERIOD = 10 SEC

i---00 3Q0 0 900 _120°

_150°180°

TRUE WIND ÓIRECTION FROM BOW

Fig.4-4 Ship's speed and engine.power versus true wind direction from bow

(19)

18-3° 2° w -j I-LL 00

1°

100 o 40_ V = 10 Kl V=1OKT -I

-V=14kT

SAIL-ASSISTED MOTOR VESSEL EQUIVALENT MOïOk 'ESSEL V : SHIP'S SPEED

TRUE WIND SPEED = 40 KNOTS

TRUE WIND DIRECTION FROM BOW

Fig.4-5 Drift angle versus true wind direction

from bow

V

-

O KT

V = 10 KT

TRUE WIND SPEED 40 KNOTS

-i - I-- - I --I

00 _3Ó° _6ó°

-19-j

900 1200

TRUE WIND DIRECTION FROM BOW

SAIL-ASSISTED MOTOR VSEL EQUI VALENT MOTOR VESSEL V : SHIP'S SPEED 150° s.. s. . '-s'

s.-Fig.4-6 Rudder angle versus true wind direction

from bow

1800

(20)

Li

50-<40

-J 30L 20-

60-SAILASSISTED MOTOR VESSEL

PASS. TIME AV. SPEED (HOURS) (KNOTS)

MINIMUM TIME ROUTE 340.3±7.2, 13.5±0.29 388.2±19.6 115±O.58

GREAT CIRCLE ROUTE

60 WESTBOUND VOYAGE T O T O WESTBOUND VOYAGE

t

DEPARTURE O GMT NOV.10 1980

Flg.5-1 Example of minimum time routIng ( sail-assisted motor vessel, westbOund voyage

EQUIVALENT MOTOR VESSEL

PASS. TIME AV. SPEED FUEL CONS. (HOURS) (KNOTS) (TONS)

ÑINIMUMTIME.ROUTE 354.5±6.9 12.9±0.25 496.3±15.8 GREAT CIRCLE ROUTE 401.9±15.3 11.1±0.42 603.6±33.1

:

- . ..= = = -TOKIO FRANC e t - _{PROPELLERREV.} ISOCHRONE MTR : 75.00 RPM

ONE-SIGMA ERROR ELLIPSES ) GCR : 75.00 RPM

10 iéo ièo io

io

LONGITUDE WIND SPEED 10 20 30 40 50 KNOTS DEPARTURE O GMT NOV.10 1980 PROPELLER REV. MTR 75.00 RPM GCR : 75.00 RPM 1O_ - 1O

Flg.5-2 Example of minimum time routing ( equivalent motor vessel, westbound voyage

-20-FUEL CONS. (TONS) 461 ..9 ± 1.7.3 571 .9 ± 42.5 EATTLE FRNt SEATTLE WIN) SPEED

iö iéo ièo

L@NGITUDE

.-

-10 20 30 40 50 KNOTS

30

(21)

20- 60-30 20- 60-30 20 SAiL-ASSISTED MOT PASS. TIME (HOURS) OR VESSEL AV. SPEEIJ (KNOTS) WESTBOUND 'VOYAGE ISOCHRONE

ONE-SIGMA ERROR ELLIPSES ) PROPELLER REV. = 75.00 RPM

DEPARTURE 0 GMT NOV.10 1980 WESTBOUND VOYAGE TOKYO -. .(: 8

-t

' . . ISOCHRONE

ONE-SIGMA ERROR ELLIPSES

DEPARTURE O GHT NOV.10 1980 COR. TIME 0 HR COR. DIST = O NM EATTLE FRANC -21-FUEL CONS. (TONS') EAT T LE

MINIMUM TIME ROUTE 340.3 ±7.2 13.5 ± 0.29 461.9 ± 17.3

GREAT CIRCLE ROUTE 368.2± 19.6 11.5 ±0.58 571.9 ±42.5

1O

10 t0

[0 120

LONGITUDE

Flg.5-3 All minimum time routes reaching each isochrone

PASS. TIME AV. SPEED FUEL CONS. (HOURS) (KNOTS) (IØNS)

MINIMUM TIME ROUTE GREAT CIRCLE ROUTE

340.3±7.0 13.5±0.28 461.9±16.6 308.2±17.5 11.5±0.52 571.9±37..9

140 ièo ièo 1èO 140.. 120

LONGITUDE

WIND SPEED - -..

-10 20 30 40 50 KNOTS

Flg.5-4 Minimum time routing with dumy correlation data correlation time = O hr, correlation distance = O nm

(22)

60- 30- 20- 60-30 WESTBOUND VOYAGE SÇ .

-i

_)

_W:

ISOCHRONE

ONE-SIGMA ERROR ELLIPSES f0Kyo . 2

t

-DEPARTURE O GMT NOV.10 1 980 S FRANC COR., TIME = 24 HR COR. DIST 500 NM EAT TLE WESTBOUND VOYAGE -22-DEPARTURE. O GMT NOV.10 1980 FRÑC SEATTLE

FASS. TIME AV. SPEED FUEL CONS. (HOURS) (KNOTS) (TONS) MINIMUM TIME ROUTE 340.3±9.0. 13.5±0.36 461.9±21.4 GREAT CIRCLE ROUTE 388.2±20.7 11.5±0.62 571.9±45.0

'O

'0

10

'léO

LONGÏ TUDE

WIND SPEED -

-10 20 30 40 50 KNOTS

FIg.5-5 Minimum time routing with dummy correlation data

correlation time 24 hr, correlation distance, = 500 nm

PASS. TIME AV. SPEED FUEL CONS. (HOURS) . (KNOTS) (TONS)

MINIMUM TIME ROUTE 340.3±10.5 13.5±0.42 461.9±25.2 GREAT CIRCLE ROUTE 388.2±23.9 11.5±0.71 571.9±52.0

20- _{COR. TIME = 48 HR}

COR. DIST.= 1000 NM

10

' 1è0 Ï0 10 1'O

LONGITUDE

WIND SPEED

--I-10 20 30 40 50 KNOTS

Fig.5-6 Minimum time routing 'with dummy correlation data

(23)

60-LiJ 50--4

-j

30 20- 60-30 20 s.- -FRANC EASTBOUND VOYAGE fOKYØ PROPELLER REV. MTR : 75.00 RPM 6CR :75.00 RPM WIND SPEED

Flg.5-7 Example of minimum time routing ( sail-assisted motor vessel, eastbound voyage

MINIMUM TIME ROUTE GREAT CIRCLE ROUTE

EASTBOUND VOYAGE TOKYO PROPELLER REV. MTR : 75.00 RPM 6CR : 75.00 RPM WIND SPEED

SAILASSISTED MOTOR VESSEL

PASS. TIME AV. SPEED (HOURS) (KNOTS) - r e

F

i. . r4

I?

ISOCHRONE

-20 20 30 EQUIVALENT MOTO PASS. TIME (HOURS) 323.6 ±2.5 325.3 ±3.5 MIR 6CR 4:.

40 50

R VESSEL

AV. SPEED FUEL CONS. (KNOTS) (TONS) 14.0 ±0l1 441.0 ±5.8 13.7±0.15 445.8±8.2 i ; _¡ ;

: :e

- . -:

I .:

J

* .- .r ? --..

-0.

10 20 30

23-DEPARTURE O GMT NOV.10 1980 DEPARTURE O GMT NOV.10 1980

j

ISOCHRONE FUEL CONS. (TONS) SEATTLE S FRANC -I-40 50 KNOTS SEATTLE KNOT S

MINIMUM TIME ROUTE 299.6±5.6 15.0±0.28 3797 ± 14.8

GREAT CIRCLE ROUTE 300.4 ±6.2 14.9 ± 0.31 383.8 ± 15.8

Fig.5-8 Example of minimum time routing ( equivalent motor vessel, eastboundvoyage )

-i410 LàO ièû iêo 1410 10

LONGITUDE

i410 ièo iéo

io

i0

(24)

60- 30- 20- 60-u.j

50-<4

30-

20-MINIMUM FUEL ROUTE GREAT CIRCLE ROUTE

WESTBOUND VOlAGE [OKT O ISOCHRONE ISOCHRONE

10

1O 10 IèO

1O

ièO LONGITUDE WIND SPEED -0.

-0.

0. 10 20 30 40 50 KNOTS

Flg.5-9 Example of minimum fuel routing ( sail-assisted motor

vessél, westbound voyage

EOUIVALENT MOTOR VESSEL PASS. TIME AV. SPEED

401.7 HR 11.5 MT 401.9 HR 11.1 MT ;i ₆

1 \":

/ /

f,

-24-iéo LONGITUDE DEPARTURE O GMT NOV.10 1980 t PROPELLER REV. MFR : 62.30 RPM GCR : 72.16 RPM DEPARTURE 0 GMT NOV.10 1960 S FRANC

10

1±0 SEATTLE FUEL CONS. 384.5 TN 603.6 TN FRANC PROPELLER REV. MFR : 66.12 RPM GCR : 75.00 RPM .10 1±0 EAT ILE WIND SPEED -0.

-0.

--0.

10 20 30 40 r 50 KNOTS

FIg.5-1O Examp'e of minimum fue' routing ( equlvaent motor

vessel, westbound voyage

SAiL-ASSiSTED MOTOR VESSEL

PASS. TIME AV. SPEED FUEL CONS.

MINIMUM FUEL ROUTE 402..O HR 11.4 MT 308.1 TN