Computation of optimum routes for ship weather routing

COMPUTATION OF OPTIMUM ROUTES FOR

SHIP WEATHER ROUTING

Prof .ir J.A. Spaans

r±nr. 769-P

International Symposium on

Wéàther-routing.

15

17 December 1987, Tokyo

Japan. Organized by:Departiflent of Transport

and Japan Foundation

for Shipbuilding

Advance-ment.

DPfI University of Technology Ship Hydromechanics Laboratory Mekeiweg

2----2628 CD Deift The Netherlands PhoneOl5-786862

COMPUTATION OF OPTIMUM ROUTES FORT SHIP WEATHER ROUTING

Prof. ir. J.A. Spaans Hideki Hagiwara Deift University of Technology Tokyo University of Section Hydronautics _{Mercantile Marine}

Abstract

After the problem definition and a historical review, the

môdif led isochrOne method is presented as a practical method to compute time fronts (1sochrozies) and the minimum time route.. With minor extensions. it is shown that the method is also

suitable,, to compute the constant number of propellor revolutions per minute to complete a voyage within a specified passage time. To meet the demands of the shipmaster to be informed about uncertainties in predicted arrival time and fuel consumption the standard deviations, of these quantities are computed,, taking into account the uncertainties in the predicted environmental conditions (current, wind, sea, swell). The expected duration of exposure to "shipping water" is additionally computed. The modified isochrone methoa is then extended to compute a route with minimum value of an object function taking j:,nto _account passage time, fuel consumption, standard deviations of these quantities and the expected duration of shipping . water. For practical use it is proposed to compute a number of advisAble routes each with assigned values of the mentioned data to leave the final route selection to the shipmaster according to his own weighting of the presented information. The advisories are adjusted regularly during the passage based on the new forecasts of environmental data. It is recommended to integrate the

route advice in a ship management system. 1.. Definition of the problem

Ship weather routing. is _{a procedure whereby an optimum route is}

developed based on the fOrecasts of weather and seas and the ship

charateristics for a particulai transit [1] For commercial operations the term optimum is used to mean:

minimum passage time

minimum fuel consumption within specified passage time minimum damage to ship and/or <deck.) cargo

maximum confort to passengers

a combination of the abOve criteria

-1-For most commercial purposes a combination of (i) and (iii) is used for initial route recommendations. For the last part of the passage a combination of (ii.) and (iii) is used.

Climato.logical routing is based on average values and frequency distributions of winds, sea state, ice limits: and ocean currents available in publications such, as

- Ocean Passages for the world Pilot charts

- Sailing djrec.t1ons - Climato'logical atlasses

In the "Ocean Passages" recommended '!seasonal" routes are given for sailing vessels,, low powered vessels and powered vessels.

Climatological routing is (was) usually carried out on board without computer aid.. The s.hipmaster assisted by his navigating, officer compares rhumbline and greatcircie. tracks, takes advantage of

currents, avoids areas of high storm freq.uency and _{areas with a high.} frequency of low visibility; the seasonal ice limits, and regulations of the loadline convention, are taken into account.

As contrasted with climatoioical routin _{strategic routing is based} on the. actual. forecasts of environniental data for several days. Ships

are advised by commercial routing organizations to follow a track where passage time, fuel consumption and. damage by the sea are

reduced. _{It is estimated that these services are used for more than}

15.00 oceanpassages per month [2]. Economical advantages of these services are published in several reports and articles [3], [4.], [5].

Tactical routing refers to the nianoeuvrers decided and undertaken on board to deal with the existing environmental conditions. Speed and (or) course are adjusted to redUce the.' probability of damage to ship

2.Historical review

Many optimization methods have been developed for strategic routing. Reference [6] gives a critical review of theories behind weather routing methods. From th.e mathematical point of view calculus of

variation methods are elegant 'but there are drawbacks in the numerical application., Convergence is sometimes difficult and the solution. is not always an absolute extreme.

Dynamic programming is a very general and powerful approach; convergence can always be achieved and one can be sure of the

existence of a minimum. The drawback is the large amount of computational effort and storage requirement.

Most minimum passage time programs provide isochrones: .S(t5 defined as

the outer botindary of the attainable region after t hours of passage

time. _{Isochrones have been used in ship navigation since the last}

centrury to indicate such a boundary. Figure 1 presents the average isochrones for sailing vessels, outward bound from the Lizzard, published in 1910 in "Segelhandbuch für den Atlantischen Ozear'1 by the

"Deutsche Seewarte".

figure 1. Isochrones outward bound from the Lizzard for sailing vessels (1910)

In 1957 R.W. James [7] proposed a manual graphic method to determine a

"least time track" based on sea state predictions and speedloss data of the vessel. In many routing offices this procedure is still practised. Figure 2 is an example of a result of this procedure. A sequence of isochrones with a time interval of 24 hours is developed whereupon the least time track is constructed form the destination backwards to the point of departure roughly perpendicular to the

isochrones.

-4-figure 2 Manually compiled isochrones and least time track; m.v. "Aalsum" in 1977. Royal Netherlands Meteorological Institute (KNMI)

In 1968 de Wit [8] formulated the least time routing into the class of optimal control problems and introduced a breakthrough by the

computerization. Using Pontryagin's maximum principle he constructed the least time track where the projection of the vessel's speed on the isochrone's normal was maximized.

Figure 3 Isochrones and least time track, De Wit 1968

I-...

Nantucket Shoals

Figure 4 Isochrones and least time track, Bijlsma 1975

-5-'o.w ,o-w '(N IN (N

./

- '>K/>

t#7WIiiIi,JI*i

Figure 3' gives an impression of the attained results in a computer simulation. Due to the small computer capacity at KNMI at that time this program was not implemented for practical routing,.

Bij.lsma L9]:' introduced in 1975 a program for the least time route

based on the so called control problem of Bolza.

in figure 4 a

computer output of this program is shown,. This program.has been used until now at the KNMI in the Netherlands to evaluate the advices after a passage1 to compare the route as advised based on the manual method with the computed route based on,hin4cast data. The overlap of the isochrones can clearly be seen after a . conjugate point. This phenomenon occurs when iscohrones are. bent backwards by an area of adverse weather. The conjugate point can be reached by a northrn and southern route in the same time.. For a mathematical treatment of this phenomenon, see [8] and [9].

All forementioned programs only compute the least time track. Although efforts were made to extend the programs for lea'st fuel routing ['9,

this has not been implemented. _{At the Massachusetts Institute of} Technology a routing program, was developed by Frankel and Chen [6]

based on Dynamic programming. This approach allows both minimum time. and, minimum cost programs. The program can handle easily system constraints such as admissable states and controls and can be extended to the stochastic case, although the latter has not been implemented

as

known by

the authors. Other studies on weather routing are

mentioned in [6J and [10.].

During the academic year 1985 - 1986 Hagiwara and Spaans conducted a

study at the Delft University of Technology on the practical application of weather routing [10]. Having reviewed several methods, they 'decided to implement the "modified isohrone method" as earlier'

proposed by one of the authors [11], a's the method combines many

advantages of other methods, is straightforward and very suitable for computerization. Above that, the method can easily be understood .by navigators as it is based on normal navigation routines, which makes acceptance easier. The method as. presented in [I0J was slightly amended later and has been .extended to cope with the 'stochastic nature of the problem to compute (sub) optimui routes for the various demands of shipmasters/owners. _{The research project is planned to continue} until mid 1989. The 'method will be implemented 'by the routing office which will continue the routing services of KNMI after reorganizations.

3. The modified isochrone method for least time

Let a ship depart from departure point X at time to and proceed to the destination Xf at the maximum (constant) number of propeller revolutions. The algorithm of the amended "mofified isochrone methodt' to compute the least time track is as follows.

The vessel is sailed for At hours from X following discretized headings C' ± iAC (i 0,1,2.. .m) where C is the initial course of. the great circle route from X to X and AC the increment of

0 f

heading.

In each heading the ship's speed through the water, engine power and driftangie by wind are computed based on the environmental forecasts, number of propeller revolutions and ship's: heading; ocean current speed is taken from the data base. The arrival points X1(i) I l,2,...2m+l are computed by rhumbline sailing. The set (X.1(i)) defines the isochrone at t+At.

Let X1(i) be the departure points at t+At. Navigate the ship for At hours from each X1(i) following discretized headings Ci+iAC _{around the arrival course C of the great circle route} from X to X,1(i). The computed arrival points at to + 2At are presented byX2 (.i,j) (i,j - 1,2,... 2m+l).

Now the sub-sector set (S2(k)) is. defined centered around the great circle route from Xto Xf where the pseudo meridians orignating in X0 have sub-sector angles AS2 defined by

cAd AS -2 sin(cd2)

It,

where c = 10800

d2 - expected travelled distance in n.m after 2At hours - 2At V (V - service speed in knots)

Ad = resolution of isochrone

The total sector angle and thus the number of sub-sectors is dictated by the admissible navigable area and takes into account constraints such as land mass, navigational hazards, icelimits

etc.

Within each sub-sector S2(k) the arrival point X2(k) is selected from {X2(i,j)) with maximum great circle (geodetic) distance from X. These arrival points define the' isochrone (X2} at time

+ 2At. 0

Then navigate At hours from each point .(X2(k)) by rhumbilne sailing in headings ck _{+ 1AC (i = 1,2. .m) where is the}

arrival course of the great circle from X0 to X2(k).. The new sub-sector set (S3(k)). is computed centered around the great circle, route from X to Xf where the sub-sector angle. AS3 is computed with (1) using a constant value of Ad and d3 being the expected travelled distance after 3At hours..

in each new sub-sector S3(;k) .the arrival point X3(k) is selected with maximum greatcircie. distance to X. The set (X3(k)) defines the third isochrone, an4 so on see figure 5.

This procedure is repeated unitil .the isochrone (X(k)} approaches the destination Xf sufficiently. Then from each point X(k). the passage time At(k) is computed between X(k) and X. The minimum passage time is given by:

Mm (nAt + At (k))

k n

?lorth

pole

grea.

circks d.eaj-tjq

ett&tor

figure 5 Construction of isochrone {X.+i) from isochrone (.X1)

-

(v) By tracing the isochrones memorized in the computer backwards, the ieas.t time track X

En

'X., X

_n-I

,. . .X can be obtained.

o'

The accuracy of this modified isochrone method can be increased by decreasing the local sub-sector width d and thus increasing the number of sub-sectors in a 4efi'ned total sector, angle.

Figure 6 gives the sector angle S1 'as a function of the number of days under way for M = 45 n.m. and a service speed op 14 kn.

sector angle V5= 14K T at :26 hours aD65n.m. 0 - 9' -0 4 6' 8 10 ' 12 16 16 I - raimber of days

figure 6 Sector angle S. for M 45 n.m. and sivice speed 14

kn.

in the practical application the least time 'track is recomputed with the actual vessel' position as initial point X _{after each} new update of the environmental forecasts. When the travel time from

X

₀ or X.(k) to X exceeds the forecast time of

' i

' f

environmental data, the wave 'distribution based on the zonal index [12] is proposed for the excess time.

in figure 7 simulation 'results are shown 'of a North Pacific crossing of the example vessel described in chapter 5. The voyage has been' simulated with and without sail assistance. For the environmental data the actual (observed 'and analysed) tqind,,

sea and swell data published on magnetic tape by the Fleet Numerical Oceanography Center of the US Navy are used, see [10].

e modified isochrone method for least fuel

In actual ocean crossing voyages it has been found by simulations that the control of ship's course is far more effective than the control of. propeller revolutions to minimize the total fuel consumption [13];. The authors propose therefore to compute the desired .constant number of propeller reolutions. per mm. in order to arri'e at the destination

in the specified .passage time T following a least time track.

A suitable number of propeller reyolutions. is: assumed first and the minimum time route and minimum passage time T . ar.e computed. Then

mm

the number o.f propeller revolutions, per mm is adapted in a iterative routine to make _I T -T

. 1 acceptable small. When the weather is

S mm

extremely seere and the

final isochrone bends backwards sharply (conjugate point) the algorithm should be applied in a second run on the o.ther side of the conjugate point, than, the first solution, to

check the possibility of a route with less fuel in th.e specified

travel, time.

The obtained, least time route with passage time T can be' considered as a sub-optimum for the least fuel case,. In figure 8 examples are given of simulation results with the example vessel described in

section 5.

Prediction of ship's speed, drift angle, rudder angle and engine power To pre.dict the ship's speed, drift angle, rudder angle and engine power of .a (sail assisted) motorvessel the method based on the

equilibrium between forces and moments on the ship has been developed

[.10]. For. a vessel proceeding in a s'eaway at constant 'speed, the

longitudinal forces X, the lateral forces Y and the yawing moment M should be balanced

X + X

+ X.

+ X + X

+ X 0 ₍₃₎ s 'a ti r w p

Y +y +Y +Y

=0

(4) s a h r 14 .+ 14 + 14. + M = 0 (5) a

fl

r 10

-where the subscripts mean: s : due to sails a :' aerodynamic. h hydrodynamic r : rudder w' : waves p : propeller thrust

When for equations: (3)', (4) and (5) the ship',s heading, number of propeller revoiutions n, draught, trim and environmental conditions are given, the ship's speed through the water v, the drift angle relative to the water a, and the rudder angle 6 are the unknowns to be

solved by an iteration routine. The engine power P is 'computed by

271Kq (V., ti, D) 5' 3 _/

'r

(6)

'where Kq (V.,n,,,D) torque coefficien, p density o'f sea water1

D 'propeller 'diameter, and

'

efficiency parameters'.

Th'e 'mathematical model ship used here was developed with the

assistance of hydromechanical 'experts of the Section Hydronautics o'f the Delft University of Technology. In, figure 9 characteristics of

this vessel are shown

6,. Estimation of standard deviation of passage. time and fuel. consumption It occurs not seldom that a _{econd best route - in least. time or least} fuel sense - _{only differs slightly from the bes't one. If in that a.se} the best route leads throught high wave, fields and the second best through calm seas (but makes a large detour) most shipma'sters would prefer the second best route. The expectation of arrival time/fuel

consumption may indeed be somewhat smaller on the least time /fuel ro,ute but the. uncertainty of arrival time/fuel consumption will probably be larger.. For reasors of good predictab i]1:ty Of' the arrival time i,t is indeed wiser, in such case toselec!t the second best,

route.

r

To meet these requirements of shipmasters and' shipope'r:ators a method is. developed to es:timat,e the 'standard deviations of passage time and fuel ' consumption to provide informations on the predictability of,

To derive this information we recall the rhuinbline formulae on which the computation of, the isochrones are based:

f

(Xi,, U, W, 9)

(7) where

Xi

- (.

= ( v

)t

(N E1)t

R()

-ship's heading at time

to +

it

= latitude longitude

V = ship's speed through the water - drift angle (leeway)

northerly component of ocean current

E1 easterly component of ocean current local radius of meridian, see [1];

mp()

meridonal parts, see [1]

The passage time between (X(k)) and

Xf

is computed by

sec 9

([V

cos

(9

+ a )

-F N

j2 +

n n n n n

- 12

-+ [V

sin

(9 ₊

) +

E:]2)½ (9)

where the heading is given by

tan

'((Af

-

A)

/

[mp (f) - mp ()j)

(10) f ). 1 . + (V + (mp

cos

+

+mp

+ N.)

t /R(.)

V sin (O

+ a,) +

_Ei (8) V. cos (e +

a)

+ N.

The passage time T between X and Xf is

nAt+t =T(X,U,W

n n n n)

].n' equation (7) the vector U may 'be regarded as a function of ship's

heading O,

number, of propeller revolutions per minute n and environmental conditions '(win4, se4

an

swell).. Using the vector C for representing the environmental condlti'ons', U1 can be written as

U ( C,

_0,

_(12,)

Since the fuel consumption C is a function

_'of

v1 and n it may be written as G(vi, n.). the accumulated fuel consumption Fji is given by

F. +

G(v,n)

₍₁₃₎

The equations. (7), (12) and (13) are expanded' in a first order Taylor series around the mean values of the random vectors C., W. and X.,

1 1 1 giving: bX. = f bit + f AU.. W. ' (14) i+l x i u 1 w

i

U 'C

(15) EF. + G V. (16) i+l 1 'v '1

The environmental prediction errOrs C1 and are regarded as Gauss-'Markov random sequences produced 'by the shaping filters,

*

AC'. + '

'

(17)

+

₍₁₈₎

where and are purely' random sequenses and and represent the degree' ofoYreiatiron.

-The cpmputation of the covariance matrix for the vector AW1 is now under development for this project 'at the Meteorological Office in

Bracknel], (U.K.). in 5 x 5' areas 'in the North Atlantic and North

Pacific the monthly mean components N and E and the (co)variances

NE' aE.E will be computed from a data base of five milion current

observations by 'ships,, gathered wor14 w1de since 1853. As, it is not possible to extract information on the correiatio,n of current-errors,. will tentatively be set to ero.,

From the ENOC data set of wind, sea and

for and the correlation matrix wil under development, where the computed

location, course and speed. In a 5' x 5 tabled for courses N,E,S,W' and

hrs.

The expressions (14) through (19) can be simply written as:

*

i+l A(i). + B AZ

t

*

*

*

where _AY.i A'

AC AL)

and' AZ

(AC1

The matrices A and B follow from' the equations (14)--(19).

The

covariance matrix for AY1 is then given by

P + B Bt

From the upper-left 2x2 matrix of

+l the position error standard ellipse

_can

be derived b means' of the eigenvaiues and eigenvec.tors

[14].

In figure 10 the standard ellipses (39,3 % confidence intervals) are

shown around the expected positions on the isochr.ones..

In order to estimate. the standaid deviations of passage. time and fuel consumption we consider the total passage ime expressed by formula (11) antheto.tal_fue1_co.ns.ump.ti.on expressed by

swell the covariance matrices 1 be derived. This work is now

corrrelation will depend on.

area the 'correlation will be. times.teps of 12 speeds 0,10,20 kn for

-H

F F + C (V , n , 1t )

f

fl

n n ii

Expanding the right hand sides of (IlL) and (22) in 'a first order Taylor series gives:

tTT

X +T

U +T MJ

x

n'

U fl W fl where U U C n C fl tF

+C

V +C tT

f n v n t

Using the correlation and these expressions can simply be written

as AY A LiY

+B.AZ*

f

nn

f where tY

(T tF

C AW

)t

,

-

(AX AF

AC AW

)t f f f f n

nn n

n and Z (AC

The covariance matrix of AYf can be computed from

P A P

At +BQBt

f

nnn

f

from where we find the standard deviations of passage time and total fuel consumption.

In figure 10 results of the stochastic modified isochrone. mehod are shown, where and are both set to zero. In figure 11 the increase

in standard deviations can be seen by the correlation

c in time and

distance. In this example a first order correlation was assumed in time and' distance. The eventual correlation model will be computed from real data for implementation in the final model.

7. Probabililty of shipping green water

In the cost function of the stochastic modified isochrone method the expected time Of exposure to "shipping green water" is included.

(22)

-The relative vertical displacement z(t of the bow relative to the local wave surface is assumed to be a Caussian random process with the local freeboard f as mean value and standard deviation a

z 12. (static and dynamic swell up neglected).

The amplitude

₂

of z(t) will then have a Rayleigh distribution [15], z

f(z)

exp (..

.4 )

(27)

where a2 =_z S_{zz (} ) d(w ) = in ;. S (w ) is the spectral density and

e e oz zz e

j 0

is the encounter frequency.

4'

shppn. woter

stII water

umve StirJtce.

f: free:bocwc(

fig. 12 _{Definitions of z, f and Za in"shipping water" model}

The probability that Za exceeds £ is given by

- f2

> f) exp '

2 (28)

in the cost function the sum of the er.iods where the probability of shipping green water exceeds a threshold (say 0.04) is included.

- 16

8. Object function for the stochastic modified isochrone method

To take into account all forementioned elements the following obj;ect cost) function is used

J=AlT+A2+A3Td+A4F+SaF+A6

(T-T)2 (29)

where :

T = passage time

T specified passage time

Td = time of exposure to shipping green water

F = fuel consumption

CT = standard deviation of passage time

CF = standard deviation of fuel consumption = weighting coefficients

With the stochastic modified isochrone method the final isochrone {X )

is computed.

_{For each route via X(k)}

_{to the value for J is} calculated. The route with minimum value for J is selected;

Deterministic or stochastic routing with or withouth shipping water for least time or least fuel can be selected by setting the appropriate weighting coefficients to zero

Research is carried out now to find practical values for Ai _l,2,--6. It is realized ,however, that these values depend on many factors such

a s:

- size and type of vessel

- presence of deck cargo - penalty on delay

- rIsk appreciation of shipmas'ter

For practical use it is therefore proposed to calculate for _{a number 'of} routes vta isochrone ('X) to X the values of T, Td, F, UT and _CF and leave the decision to the shipmaster.

9. Integration of route advice in Ship Management System .(SMS)

The selected route by the :(stochastc) modified isochrone method is an

advice by a shorebased routing bureau to the ship management team. The navigation team aboard should involve ths information in a ' "performance surveillance 'system" aboard where speed and fuel consumption is continuously monitored.

Within the framework of an energy saving project for ship operations sponsored by the Dutch government the peformance surveillance, system PERSUS is developped and now operational [161.

The sensor package of' the system consists o propeller pitch or r.p.m.

speed log (though water,)

torque meter at propeller shaft fuel meter at main, engine

Environmental conditions are used either from own observations or from forecast data.

The mathematical shipmod'el should agree with 'the model used in the routing office. Using monitored data aboard, model coefficients 'can be

adjusted (fouling) of which the routing office. should be informed. The PERSUS system presents averaged' values over 20 mm of

r.p.m. or pitch' waterspeed power

fuel consumption (m3/hr)

specific fuel 'consumption itt/kWh performance index (itr/n.m.)

The navigation- team aboard is now directly confronted by the s,stem with the (cost) performance of the vessel.

Figure 13 gives a few examples of informat.ion presented by the PERSUS system to assist the navigation team i1i decision making, for efficient operations.

10., Conclusions

in simulations the modified ,isochrone method has. proved to be a strong tool in route selection based on various: practical criteria.

in fIgure. 14, 15 an4 tables, 1, 2, 3 results. are given computed wIth' the de.términs.tic. method using environmental data; these results are earlier published in [10].

The

great circle route is used as meas ire of comparison.. It is.

realized: that the benefits of a ship which is nt being r.outed but IS nevertheless sensibly navigated are likely to be smaller than those achieved in simulation. in the "real world" benefits will also be smaller because. in the simulations" real weather" is used instead of forecast weather.

The increase in the number of routed ocean passages per month proves that shipowners and shipmasters are aware of the benefits of good route advice.

Good route advice is based. on three main elements: - accurate forecasts of environmental conditions - accurate predictions of ship" s speed

a practical algorithm to compute th best route.

The stochastic modifie.d isochrone method computes the necessary

information :to select. .a bes.t route.

Close co-operation between routing office and the navigating team aboard assisted by. a ship performance surveillance system will give best

results in the improvement of the economy o.f ship operations,.

-19-References

[1] American practical navigator Vol. 1

Defense mapping. agency Hydrographic Center Washington USA (1977).

[21

Máyes J. (1968)

Shipboard computers for navigation and, weather routing,. Society of Naval architects and 1arine Engineers.

.Korevaar, G.C. (1976)

Experiences and results of the Sh'iprouting.of the Royal Netherlands Meteorological institute. Scientific report 76-9 KNMI de But.

Report On the results of weather routing of KNMI Shell' International Marine Ltd MR/22 (1966).

Constantine W.G. (1981)

Weather routing for safety and economy

Ship Operation and Safety conference, Southampton.

Frankel E.G. and Chen H.T. (1978) Optimization of ship routing

National Maritime Research Center USA.

James R.W. (1970)

'The present state of. ship routing Interocean '70, Dusseldorf Germany.

[81 De Wit C. (1968)

Mathematical treatment of optimal ocean ship routing Dr. Thesis, Delft University of Technology.

[91 Bijlsma S.J. (1975)

On minimal time ship routing

Royal Netherlands Meteorological Institute (Dr. thesis)

[10] Hagiwara H., and Spaans J.A. '(1987)

Practical weather routing of sail assisted motorvesseis Journal_of_the_ROyal_Institute_of_Navigation Vol. 40, no

-[11], Hagiwara H!, K. Shojii and A.M. Sigisaki (1981>

A method _{of selecting the optimum route of sailing ships} Journal of the Japanese Institute of Navigation Vol. 64.

Suda K., T. Makishima , M. Horigone , S. Kuwashima , K. Ohtusu and

H. Hagiwara (1982>

Ship weather routing based on the mean atmospheric circulation international Congress of Institutes of Navigation, Paris.

Hagiwara H. (1983,, 1985)

A study on the niinimuin fuel:: consumption route I, II

Journal of the Japanese institute of Navigation Vol. 69, 72

Spaans J.A. (1987>

Reliability, accuracy and precision of navigation methods (in

Dutch)

Report 6:45-K Section Hydronautics, DeIft University

Ochi M.K. and E. Motter (1974)

Prediction of extreme ship responses in rough seas.

intern. syzp. on dynamics of marine vehicles London, paper 20.,

Journée J.M.J,, R.J. Rijke, Verleg G.J.H (1987)

Marine Performance Surveillance with a personel computer Automation days Helsinki Vol. I p. 117.

-6 0

30-

20-

60-NES I B:0U ND Vol AGE

NE ST 60 UINO V 0 IRGE

iL0

kJJ ND SPEED

+ 00 .+

>

- 0fG0

w;z::.:cc*+\

I'. /

0

f

t

t

TOKYO

1

1'

LU

50-D

- 4__'+ 00 \ + + 0

0.4%

_,

_I

.)P1;z::%oI

(1 / /

30 FOKTO +

.20-I'

DEPARTURE

0 GMT

NOV. 11

1980

subsector set

I I - I -

I-

--ILIO 160 180 160 1-110 120

LONGITUDE

I4I SPEED

-'--

. 10 20. 30 10 50 KNOTS

DEPARTURE

0 CMI

NOV.11

1980

subsector set

0 FR A N C EAT TLE SEATTLE ++ +

'.

-g S FRANC

'Fig.. 7 _{Examples of least time routing with modified isochrone- method}

SJRIL:ASSIST.ED M0JO

VESSEL

Pfl:SS. TIME AV. SPEED FUEL CONS.

MINIMUM TIME ROUTE 3:1102 HR 13.5 KT 1161.7 TN

GREAT CIRCLE ROUTE

377.7 HR

11.8

KT

5q5.3'

TN

0

leo

ib

LONCJtbEE

-

-0

0.

-10 20 310 110 50 KN011'S

EQ,UJ-VALENIT MOTOR VESSEL

PASS. TIME nV. SPEED FUEL CONS. MINIMUM TIME ROUTE 35111 HR 13.1 KT 1188. TN

60- 30- 20-60 30-

20-SAIL-ASSISTED M1OR VESSIEL

pAs:s. TIME: AV. SFEED

MINIMUM FUEL ROUTE _{402 0 HR 11 4 KT} GREAT CIRCLE ROUTE _{401.7 HR 11.1 tT}

IESTBOJUND VOYAGE

_D&ARTURE

_{0 GMT}

NOV.10

.1 980 SEAT IL E S FRANC QO .\

\

. PROPELLER REV. MFR : 62.30 RPM GCR : 72.16 RPM I I I I I - I 140 160 180 160 140 120

LONGITUDE

WI N.D SPEED 10 20 30 40 50 -INOTs

EaUIVALENT MOTOR VES:SESL

PASS. TI:ME AV. SPEED FUEL CONS. MINIMUM FUEL ROUTE 401.7 HR 'll.SKT 384.5 TN GREAT CIRCLE ROUTE 4O.1 .9 HR 11.1 KT 603.6 TN

WIND SPEED

10 20' 30 40 50 KNOTS

WESTBOUND VOYAGE

FUEL CONS. 308.! TN 524.8 TN ++ : t

4//

\

+4 0 _{# q}

-'eb1: \

%+9 Ii:

/

/ )

:

+ 0FP*

/ /IIf ((Ii

0 ISKTO a FRANC % \

\

\. \

PROPELLER REV. ISOCHRONE MFR : 66.12 RPM GCR : 75.00 RPM I I -I I - -140 1.6.0 180 160 140 120 LONG I TUD E GCR MFR

DEPARTURE

0 G:M.T

NOV.10

1. 980 SEATTLE

17 , IS 9

1!

S 20

KbG

e 1O 2' 0° -2' PROPtLLERREV. 7$ R.P.M. WIND SPEED 40CT SCAHEIGNT N

SEA DIR. WINO DIR. SEA PERIOD SEC

SAIL.ASSlSTEDMQT0RVCSSEI

EQUIVALENT NDIOR VESSEL

SWELL AUGHT 3 N SWILL DIR. rRONRODa

SWELL PERIOD 10 SEC - EQUIVALENT MOTOR VESSEL

- SAIL-ASSISTED MOTOR VESSEL -

-I I I I I

0 30° 60' 90° 120° IsO'

TRUE WIND DIRECTION FRON ROW 0

N' 50 1OKT , -V. SI IT SAIL-ASSISTED )O7TOR VESSEL EQIJI TALENT - - - - MOTOR VESSEL V SHIP!S SPEED

TRUE WINDS!ECD' 40 INOTS

0'

MIN OIP1IjI UfM WRUt RIIIP

SAW kAISHY II.SOIT MI. (11151 P51W... 11.104:5W tiIN(flh((5ftIt_ 151.111 101*1. IAILMIA 5AlI5

5111(11 SMJGST III IS I III tII.PIA.(NISSIAILI-) 1100010 MJ.510 35.011 11*01(1 15500 IS'IT

6 8 $0 12 14 IS ID 20

AVERAGE VAVEPERIOO (SECONDS SIIIP!SSPEED. II EMITS UI WAVCDIRECTIOII FRO4RDV =

0'

Fig. 9

characteristiCs of. example vessel

0.0 TS 0A cuRvE-o ;oo 90 110 I$0 01,041,5who ou,ocno,roesI , V 14 CT V IT_---:- IT

-TRUE WIIS0 SPEED 40 KNOTS

SAIL-ASSISTED - MOTOR VESSEL EQUIVALENT - - - - MOTOR VESSEL V s- SHIP,S SPEED 'I I- I I 0 30° 60° 90' i120° ISO'

TRUE WINDDIRECTIONFROM ROW S

0.10 0OS' 0O0 100° C U 30° 60° SO' 120° 150° 100°

TRUE WIIIDJDIRLCTIOV FROW BOW P

$80.

o' o' 60' 50' I20 iso

60- 20- 60- 30-20 S. FR AN C

WESTBOUND VOTAcE

OK TO

MINIMUM TIME ROUTE GREAT CIRCLE ROUTE

WESTBOUND VOTAGE

TOKTO

SAILASSISTED MOTOR VESSEL

PASS. TIME AV. SPEED

ISOCHRONE

( ONE-SIGMA ERROR ELLIPSES

SAILASSISTED M:OTOR VESSEL

PASS. TIME AV. SPEED:

(HOURS) (KNOTS) 340.3 ±7.0 13.5 ±0.28 388.2 ± 17.5 11.5 ±0.52 ,

-w

_I74

.

?-f!'

8 8

?*

ii

.t

t

-: ISOCHRONE

-( ONE-SIGMA ERROR ELLIPSES )

I U I I 140 160 160 160

Lt3NGITUDE

W IND SPEED

-

t

- S .10 20 30 FUEL CONS.. PEP AR TUR E

0 GMT

NOV.10

1 980 PROPELLER REV. 75.00 RPM SEATTLE FUEL CONS. (TONS) 461.9±16.6 571.9 ±37.9

DEPARTURE

0 GMT

NOV.10

1980

FRANC COR. TIME = 0 HR COR. DIST= 0 NM

10

SEATTLE S 40 SO KNOTS

Fig. 10 E*amplè of stO1iáic minimum time routing with modified isochrone method

(HOURS) (KNOTS) (TONS,)

MINIMUM TI:ME ROUTE

340.3±7.2

1:3.5±0.29 461.9 ± 17.3

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

ièo

l0

lee

L. 60-3O 20- 60-30

20-WESTBOUND VOIAGE

.-.

q

-B ISOCHRONE

C ONE-SIGMA ERROR ELLIPSES ) TOKYO

io

ièo

lea

leo

MINIMUM TIME ROUTE GREAT CIRCLE ROUTE

WESTBOUND VOYAGE

I OKIl

SAILASSISTED MOTOR VESS:E.L

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

DEPARTURE

0 GIlT

NOV.10

1980

FUEL CONS. (TONS) COR. TIME 24 HR COR. DIST = 500 NM SEATTLE FRANC I I. 140 120 - -. -g e

B-.

-, - -I SOCHRONE

( ONE-SIGMA ERROR ELLIPSES )

B

.

DEPARTURE

0 GMT

NOV.10

I 980 SEATTLE S FRANC COR. TIME = 48 HR COR. DIST 1000 NM

WIND SPEED

. 30 40 B. 50.

NOT5

Fig. ii influence of correlation in environmental data on standard

deviations computed with the stochastic modified isochrone method MINIMUM TIME ROUTE 340.3 ±9.0 13.5±0.36 461 .9 ±21.4

GREAT CIRCLE ROUTE 388.2 ±2.0.7 11.5 ±0.62 571.9 ± 45.0;

LONGITUDE

WIND SPEED

-

B.

F 0 20 30' 40 50 KNOTS

SAILASSISTED ,MOTOR V;ESS:EL

PAS:S. TIME AV. SPEED FUEL CONS.

(HOURS) (KNOTS) (TONS) 340.3 ±10.5 13.5 ±0.4.2 461.9 ±25.2. 38.8.2±23.9 11.5±0.71 571.9±52.0

I eo

ièo

iêo

.L@NGITUDE

2 a 015 210 ass 000

I"

I.' .9,

L

.1.00 .0 90 by 500 00.4 S SP000 IZ.00 ..000 0*I

...--

9 a draft

/.

I I Ba draft

--

I

7adraft

0.00 0 50 iblO I.) 1.00 I 10 0.00 Se .1 I... ENTER i

Fuel consumption based on speed.

OPTION CONTROL TAGS * OTHER VERT ICAI. SCALE

Fig. 13 PERSUS-infonnation of a tested example vessel

260 a35 230 rUEL CONS 225 (I 1..n.) 220 a's 210 205 35 30 ADDED 25 CONS 20 (1,n-, 15 10 2 5 0

Fuel consumption based on heading.

273 ENTER - OPTION CONTROL TAGS OTHER VERTICAL SCALE ENTER OPTION CONTROL TAGS OTHER 'iERT ICAI. SCALE '0 IOU so 90 90 60 a

-U a a a a

-U U

--.

11 Ip_ SIIIIU

SHIP1S SPEO . &2.51,n

-U -I U. a a. a U. U a U a. U. RU -u a

OUL _{NO CÔZFFIIENT HULL. IOC.0 . 6.57}

S. a U a 233 2'3 253 HEADING Cd.g) 263 1. _{S a .7 B 9 Ic,}

ii

SPEED Ikn) 12 13 16 a 8 9 10 11 SPEED (knI 12 13 16 as 16

Fuel consumption

Added fuel consumption due

to fouling.

based on displace-ment.

TONS

600

-0 H

500:

400

- SAIL-ASSISTED MOTOR VESSEL EQUIVALENT MOTOR VESSEL

I-WESTBOUND VOYAGES

O MINIMUM TIME ROUTE

GREAT CIRCLE ROUTE

-

I--

-I - -I DATE OP DEPARTURE NOV.1 11 21 OEC.1 11 HOURS

380

260 TONS

z

500-0 H

-

400-300 - -S.--

a:

-- = =

=-=.-=.

-

_-g

340

-

300-EASTBOUND VOYAGES o _{MINiMUM TIME ROUTE}

GREAT CIRCLE ROUTE

- SAIL-ASSISTED MOTOR VESSEL EQUIVALENT MOTOR VESSEL

I I - ;_-O.-, I I I--- I I NOV1 11 21 _{DELl 11} DATE OF DEPARTURE

Fig. 14 Passage times :and fuel consumptions fr each date _{Fig. 15 Passage times and fuel consumptions for each data} of departure (westbound voyage) _{Of .departure (eastbound voyage)}

Tab. 1 Mean values of 5 westbound voyages

Minimum Time Routinq (Propeller Rev. = 75 r.p.m.)

Mean Values of 5 Westbound Voyages

Tab. .2 'Mean, values of 5 eastbound voyages

Minimum Time Routinq (Propeller Rev. 75 r.p.m.) Mean Values of, 5 Eastbound Voyages

Sai"i.Assjsted M.V. _{'Equivalent M.V} M.T.R. 'G.C.R.., _{M.T.R. C.C.'R.} Distance 4571 fl1 4472' n!r 4595 nm 4470 mm Av. Speed 13.72 kt 12.59 kt ' l2.92 kt 11.7,21 kt Pass. Time 333.2 h 3561.8 h 355.,8 h 382.8 h Time Saving 49.6 h 26.0 h 27.0 h 0.0 h Time Saving 13.0 % , 6.8 % 7.1 % 0.0 % Fuel Cons'. 440.7 t 497.0 t 495.4 t '558.7 t

Fuel Saving ll8.'O t 61.7 t, 63.3 t 0.0 t Fuel Saving _{21.1 % 11.0 % 11.3' %} ' 0.0 % Sail-Assisted M.V. Equivalent ,M.V. M.T.R. G.C.R. M.T,.R. _{H G'.C.R.} Distance ' 4501 mm 4471 mm 4501 nm I 4471 mm Av. Speed _H 14.46 kt 14.21 kt r 13.91 kt 13.6.7 kt Pass. Time ' 311.2 'h 314.6 h 323.7 ii 1 327.2 h Time Saving I 16.0 h 12.6 h 3.,5 .h ' 0.0 h Time Saving' ' 4.9 1 3.9 % 1..l % 0.0 % Fuel Cons. 4.09.9 t 420.0 t . 441.0 t H 451.3 t Fuel Saving I 41 4 t i 31 3 t 10 3 t 0 0 t Fuel Saving 9.2 % 6.9 % . 2..3 % H 0.0%

Tab. 3

Summary of an example of minimum fuel routing

Minimum Fuel Routing

Departure: 00 GMT ii November 1980

Westbound Voyage

Specified Passage Time = 399. 8 h

Sail-Assisted M.V.

Sail-Assisted, ½ Sail Thrust

Equivalent M.V.

M.F..R.

G.C.R.

M.F..R. G.C.R..

NF.R.

G.C..R.

Pass. Time

400.0 h

400.4 h

399.6 h

399.8 h

399.3 h

399.8 h

Distance

4575 mm

4473 rim

4588

mm 4471 rim 4584 rim 4470 rim

Av. Speed

11.44kt

11.17 kt

11.48 kt

11.18 kt

.11..48kt

11.18 kt

R.P.M.

62.72

71.18

64.88

73.26

.66.70

75.00

Fuel Cons.

312.8 t

495.0 t

355.7 t

548.6 t

394..1 t

597.0 t

Fuel Saving

284.2t

102.0 t

241.3 t.

48.4 t

202.9 t

0.0 t