Operational Considerations and

Operational Considerations andConstraints in Ship-based Weather

Routeing ProceduresR. Motte and S. Calvert

(Institute of Marine Studies, Plymouth Polytechnic)

Weather-related ship loss statistics are assessed as a proportion of total losses to ascertain therequirement for route planning. A routeing assessment for suitability of on-board applicationis undertaken and a moveable grid is then proposed incorporating a time optimization pro-cedure for the on-board system.

i. I N T R O D U C T I O N . A ship may be damaged or delayed by the action of seawaves on her hull, structure or cargo. Paradoxically, the recent rapid transfer offreight to the through transport mode of containerization has highlighted this.The flimsy container (flimsy that is in comparison with the hull) often bears thebrunt of a breaking sea with disastrous consequences. The relatively poorer sea-keeping characteristics and higher potential speeds of these vessels, allied to therequirement to maintain a schedule as part of a multi-modal system, may causeship owners to take a harder look at the advantages a weather routeing systemhas to offer. Much of the recent effort to reduce ship damage and loss byapplications of technology has not been directed to loss due to environmentalcauses. Radar and navigational instrumentation are directed towards reducingcollisions and modern inertial gas systems reduce the risk of explosion and firein tankers. Little has been done in the application of new understandings and/ornew technologies towards minimizing the effects of stress and weather leadingto damage, foundering or abandonment.

Table i indicates that some 30 per cent of all ship losses are as a direct resultof press of weather and this relates to approximately half a million tonnes ofshipping each year. Consideration should be given in attempting to reduce thisalarming statistic. Not surprisingly the main areas of ship loss are in the middlelatitudes of the North Atlantic and North Pacific oceans. By far the greatestnumber of losses due to non-sustainable extremes of weather occur in these areas.Of course, these are the densest trade routes but that is not the complete answer.They are, coincidentally, the home of middle latitude, extra tropical depres-sions, which sweep across the baroclinic zone. They dominate the weather inthese regions covering great areas of ocean with uninterrupted wind fields of longduration which, in their turn, build up wide and fully developed sea states. Onsome routes as much as 30 per cent extra fuel is consumed, and an equivalentratio of time added to voyage lengths, because of their effects They also causedamage to vessel and cargo. One North Atlantic operator has calculated an annual

4 t 7 is-2

41 8 R. MOTTE AND S. CALVERT VOL. 41

TABLE I . RATIO OF WEATHER-RELATED LOSSES

Year

19781979

1980

1981198219831984198J1986

V/Ls

1 7 0

279

227249

2362 0 9

2 i j

189

i * 6

Totals

p-tonnes m.

•42-3

i -8

1 7

1-46

'IS1 3 0

1 2 9

1-2 I

Loss

Stress of weatherfounderings

and abandonment

V/Ls g-tonnes m.

— —96 o-61

88 042

74 0-496 2 0-40

72 0 2 9

86 —64 0'26

72 o-£7

Ratio

—0 3 4

0 3 9

C 3 0

0 2 7

0-2 2

0 4 0

0'20

047

The ratio of weather-related losses (i.e. stress of weather, foundering or abandonment) to alllosses varies from 02 to 047 but is generally above one third. It has been and continues to bea growing category, relatively, as a reason for ship loss. (Source: The Underwriters'Association.)

service cost of $800000, as directly attributable to these storms.1'2 Thedepressions travel in an approximately easterly direction at various speeds, whichover the open ocean may be meaned to some 30—40 kt. Vessels are most at risk onwestbound passages when they are closing these systems at a relative go or 60kt (for a 20 kt vessel). The consideration must be to minimize this system effectby judicious planning, a well defined criterion for routeing.

A discussion of some of the features of the baroclinic instability and thebaroclinic wave which give rise to middle latitude depressions has been presentedpreviously.3

2. ROUTEING APPLICATIONS AND SUITABILITY. Depression frequency

is of the order of one depression per week in the North Atlantic and the life cycleof a depression is also of this order.4 Coincidentally a modern vessel capable ofsome 20 kt is on a North Atlantic passage for one week. Thus on average theoperators of the vessel will need to consider the position of the vessel relativeto one and possibly two depressions per ocean transit.

On eastbound passages, a vessel will be travelling with the general movementof the depressions, the relative rate of approach of the vessel to the potentialstorm is decreased. Conversely, on a westbound passage the velocity of thebaroclinic wave is added to the wind velocity and the velocity of the vessel togive a higher rate of approach and, of course, a greater likelihood of adverse seasaffecting vessel performance. Indeed, claims of shore routeing agencies in savingtimes on recommended routes for eastbound passages are usually of the order ofone hour only for the total passage, whilst 10 hours is the order of time claimedfor westbound passages after several crossings have been averaged.

NO. 3 WEATHER ROUTEING PROCEDURES 419

Effective avoidance must lead to safer and smoother voyages and on occasions,as a bonus, to minimizing passage time. Better predictability of arrival time, forvessels with massive unit loads, indicates a further requirement. The generaltrend in the 1980s is for short holding time in port with faster, more specialistcarrier units. Expensive terminal facilities are provided with a timetabled usageby a consortium. The programming of such an operation has to be done with aminimum tolerance of voyage time fluctuation; thus each vessel's schedule isimportant to the whole scheme. There is little requirement to reduce passagetime; the demand is not to increase time on passage by, for instance, heaving toin a storm for a day. This tendency towards specialization and through transportsystems suggests a demand for strategic routeing. The long-term savings accruingby reducing heavy-weather damage both to ship and cargo on strategic routes arethe main reason, however, for adopting routeing procedures. The penalties of' off-hire' clauses relating to overdue vessels on time charters, the carriage ofsensitive cargoes and susceptibility of damage to vessels in ballast, are additionalarguments for a storm avoidance approach.

Thus on-board routeing should be conducted with the fundamental philosophyof storm or gale avoidance. A rigorous analysis of an individual vessel'sbehavioural characteristics and, therefore, performance related to relative windforce and direction should be undertaken to learn and catalogue the limitationsof environmental conditions to which that vessel should be exposed. It thenfollows that a good estimate should be made of:

(i) the short-term prevailing conditions that the vessel may immediatelyexperience on departure;

(ii) the medium-term or mid-ocean development of depressions;(iii) the long-term or far ocean features likely to occur before the vessel

completes her passage.It is of limited value to attempt to route vessels on the evidence of surface

information alone. It is always necessary to have an indication of storm movementand future development, particularly for the second half of the passage. Suchindication is only attainable with the assistance of upper air information toevaluate the growth and steering likelihood of depressions.

Optimization routines are generally based on a matching of ship performancedata with sea surface data, relating the seakeeping characteristics to an analysis andthe predicted sea wave fields. Unfortunately for the routeing analyst thesepredicted fields are only available for up to two or a maximum of three daysahead. Retrospective analysis using optimization techniques is, on the other hand,a highly accurate tool. As accurate or prevailing sea data are not normallyavailable and the ' optimization' is undertaken using raw and often inaccurateforecasted sea fields, after day one the term ' optimization' in such an applicationmay be perceived as a misnomer. It can lead to misinformation in that short-termindicators of measured or calculated sea states will not accurately relate to theposition and/or intensity of middle latitude transient storms during the laterperiods of a passage. Initial decisions on advised courses should relate to thepassage as a whole. Such subjective decision making, on board, can haveconsiderable advantages when backed up with an optimization programme, and a

420 R. MOTTE AND S. CALVERT VOL. 41

trans-ocean grid can be biased to the locality of the proposed route. For example,should the 500 mb flow indicate major storm activity to the south of aconventional route so that the prognosis advises a northerly passage, a grid canbe positioned so as to avoid unnecessary southerly coverage. This reduces theneed for high capacity machines for on-board operation and reduces the storageof unwanted environmental data.

In devising a working algorithm for an ocean wide grid which, of necessity,will use a set of sea states (Petri et al.5) for several time and space stages, itis necessary to be economical with data. For example, a basic ship-basedprogram with, say, 10 space states and 10 time slots at each stage will give 100variations at each stage and so there will be 10000 ways to travel. All routes mustbe examined in the dynamic programming; it follows that any pre-planningwhich reduces input data by causing a ship to proceed within a reduced grid sizeand strategic decision making which reduces comparisons in the optimizationprocedures, will assist the operation.

3. MODEL F O R M U L A T I O N . In designing an on-board system for optimalweather routeing several aspects were dependant upon the capabilities of thecomputer and its memory size. There is a need for a simple recursive algorithmand model using accurate predicted sea state data and ship data. Dynamicalprogramming (DP) was therefore accepted as the basis for the initial trials for anon board system, since:

(i) The model is a simple powerful tool for calculating the optimum routeacross an ocean.

(ii) The computer capabilities could be easily matched to the size of gridmesh required and the speed of computation. The Acorn CambridgeWorkstation which was used is quoted to be as fast as a lightly loadedmainframe system but is a stand alone machine.

(iii) The methodology can incorporate more than one objective function andmore importantly, for micro-based systems, the calculation constraintscan be levelled both linearly and directly.

(iv) Grid points can be labelled by latitude, longitude, objective policydecisions and environmental parameters.

The DP grid can be represented by a series of legs or zones, across an ocean,where each zone consists of several latitude points. It was found convenient forthe grid to be geared to the shortest distance across the ocean, that is the greatcircle route. Motte et al.,6 studied the grid mesh size for a rectangular gridsystem, and found that a four degree of longitude by a half degree of latitude meshwas adequate. In effect this grid stretches out the east—west dimension andtherefore, provides for a closer great circle fit.

Taking the great circle as the central line between departure and destination,the DP grid can be constructed by taking perpendiculars at, for instance, ^8intermediate points. Such a grid consists of 60 stages in the east—west directionand can be constructed in the north—south direction to a number of pointsdepending upon the distance taken along the perpendicular from the great circle.Mesh size is thus easily controllable and the discontinuous routes on a large gridcan be smoothed by reducing the north—south point spread.

NO. 3 WEATHER ROUTEING PROCEDURES 42 I

Since the requirement for micro-based systems is to reduce the calculationsthroughout the whole grid, the grid can be constrained or weighted (increased)depending upon the likelihood of storm movement. As has already been pointedout, by observing the £00 mb flow and predicted depressions, the grid can beweighted to avoid such an area and therefore omit unnecessary calculations. Chenet al.,1 Zoppoli8 and Motte et al.6 describe the constraints placed on the DPmethod, as applied to optimum ship routeing, under the headings of environmentand control, which cover the following.

Environmentally induced constraints. These may be seen to include naturalobstacles such as ocean basin geography, fog areas, ice areas and even extremesof winds and/or seas for accurate predicted or hindcast data. In the event of ' no-go ' areas at sea, small blocks can be omitted in much the same manner, but ona localized scale. These can be preset before calculation, however, sea state data,as previously noted, are only accurate for up to three days ahead and omission ofgrid points in the real time because of high sea states will have to be performedby other methods, for example using the £00 mb flow. The true optimum routeis never actually followed but, in terms of data storage capacity for the journey,smaller data files need only be held rather than the full environmental array(approximately 20000 bytes). At the present stage of the investigation the dataused are accurate observation and predicted hindcast data for early validation bycomparison with Oceanroutes (UK) Ltd advised passages. The grid can thereforeeasily be weighted without the need for 500 mb flow details.

Ship control constraints. These are concerned with aspects of power output,steering rates, maximum course deviation and maximum ship motions orresponses. These constraints tend to be more complex than those previouslydiscussed and are due to the reactions of the vessel in the seaway. Vesselperformance is difficult to quantify and for use in the micro-computer where theresponse needs calculation many thousands of times, a simple speed-weatherfunction is required. Speed reduction curves were therefore used, based upon seaheight, sea direction, wind speed and so on. Three such approaches wereinvestigated, namely those of James,9 Townsin10 and Babbedge,11 and the lastwas found to be most applicable. In program execution, the vessel transits theocean along the great circle route (GCR) from departure point at a set time tothe destination point and this results in an estimated transit time along that route.Bellmans principles'2 then state that the DP grid should be transitted backwardssince decisions taken in the future have no bearing upon decisions made in thepast. The optimum route transit time is then that of the GCR or less. However,the initial aim of the program for validation purposes is to match as closely aspossible the departure point time which can result in further time iterations.Obviously this increases calculation time but results in a more realisticroute.

If large wave heights are encountered on any route, a low speed may be derivedfrom the ship response algorithms. A speed flag is set to mark such an occasionand recalculation is commenced. In effect the vessel 'heaves to ' for some timeuntil an acceptable speed is accomplished. The speed reduction curves are thusregarded as being operative for wave heights up to a set value (that is for power

4 2 2 R. MOTTE AND S. CALVERT VOL. 41

limited states). Beyond that value, voluntary speed loss is not included in thealgorithms although the vessel is required to 'heave-to'. If the weather ispersistent and time is removed for heave-to then the time available for theremainder of the voyage may become zero. If such a situation occurs, typicallyduring the winter months, then an omission flag can be triggered withdrawingcalculations from that point. This restriction has to be waived near the start pointof a voyage as it may prevent the route reaching its goal during furtheriterations.

In transiting a zone from an ' end' point, several ' next' points are looked to.(See Fig. i.)

Course deviation is restricted in the program to a number of points either sideof the central or 'end' point, depending upon the grid mesh size. Powerlimitations are governed by the set service speed and correspond with the speedreduction limitations. The full program flow is shown in the Appendix.

4. DYNAMICAL PROGRAMMING WITHIN THE COMPUTER MODEL.

Dynamical programming was favoured over other possible models for itssimplicity and power. The methodology was first proposed in 1957 and the formof the deterministic ship optimization equations are as follows:

terminal cost function J(Xn) = A(*destlnatlon) (1)

intermediary points /(*.) = m i n ^ , Xi+l)+J(Xi+l)} (2)

origin point J(XQ) = min{f(XQ,X{) + / ( * , ) } + g(XQ) (3)

origin cost function S(^o) (4)

The state X, defines the vector of latitude and longitude, the optimizationparameter and the environmental conditions at that point for the purposes of thismodel. The process is then to find the minimum to that point by reference to theforegoing (backward recursion). The function between the points is one ofenvironmental conditions on that route and the response of the vessel to thoseconditions.

In the model, the defined states at the DP grid points are determined bymaximizing the speed of the vessel, that is maintaining a constant vessel power,and obtaining time functions from the vessel speed and weather parameters. Thestates at the point are defined by geographical coordinates and time, however ina more realistic situation it might be prudent to slow the vessel down in theearlier stages of a shorter distance route rather than maximizing vessel speed.Thus there is a necessity in this respect for forward looking storm observationsand an expanded time state. The state is found by speed variation and theoptimization objective function becomes more complicated. The amount ofcalculation is raised by a large factor and it is felt best at this stage to limit themicro-computer advisory system, to the simple time state.


Latitude steps

Fig.

The environmental inputs. The data used for the time optimization programswere initially entered by manual /computer overlay block means to produce anarray data file for each day of weather. For ease therefore, a one degree gridsystem was adopted and DP grid point weather data found by close matching ofthe two grids. The data were taken from wave charts and consist of significantwave heights and directions. The data are produced for each one degree gridpoint in the ocean and since the optimal grid can be of the order of 2000 points,each holding several parameters, the process becomes tedious. For analysispurposes output from the UK Meteorological Office's wave model is used andis more accurate and efficient. The number of data points is not increased butrather the number of data parameters (see Fig. 2). There is a need to investigatethe computer calculation time for such a large data box, either to reduce the datavolume or expand the grid spacing. The data arrays can be represented by a three-dimensional grid, as shown. Each layer of the grid box represents one dataparameter, where that parameter is defined by latitude and longitude. At thepresent stage the data box is only two layers deep, representing wave heights anddirections. However, a simple empirical formula for wind speed and an assumedwind direction are used to provide the inputs to ship response formulae. Waveand wind data from the Meteorological Office model provides many moreaccurate inputs, taking the grid to nine layers deep (see Fig. 2).

As stated by Chen et ah, the data field can be represented by a data plane,where: <P = latitude; A = longitude; subscript 1,2,3 = points one, two andthree; and z = data parameter in use.

R. MOTTE AND S. CALVERT VOL. 41

i = . . . 11 ri = 6

i = 5

i = 4-

/ = 3

60i = 2

30

Grid points

i = 1

80 W-«— Longitude

0 W

Fig. 2. Grid data box. i, significant wave height; 2, swell wave direction; 3,significant wave period; 4, swell wave period; j , wind speed; 6, wind direction; 7,swell wave height; 8, wind wave height; 9, wind wave period; 10, current speed; 11,current direction

The equation of the plane passing through the three points,

is:

A2-A,

A2-At

A, —A,

(A-A,)

(5)

The formulation of intermediary data values requires three points and these aretaken to be the two points involved in the transit plus one other next to thedestination point. Three intermediary points are used between transit points andtheir latitudes and longitudes 0, A are found by thirding the distance betweentransit points and inversing Mercator's formula. This then occurs for each dataparameter to give a closer representative value than a simple mean for the transit.

NO. 3 WEATHER ROUTEING PROCEDURES

The data plane formula (equation ($)) is used 31' times, where i is the number ofdata parameters listed in Fig. 2. The inclusion of the added data will go hand inhand with improved ship response algorithms. The ship response formula thenprovides an optimal parameter for the intermediate zone transits.

The ship response. The response of the vessel in a seaway is of prime importanceto the weather optimal routeing programs. The development of the programs hasinvolved the speed loss curves proposed by James,9 however, the furtherimprovement of these formulae by Babbedge'' has also been included and it ishoped that the next stage of development will be a simplified ship model todescribe all motions applied to the sea spectra by superposition techniques. Therewill then be a balancing of power and resistance from which fuel and/or costobjective functions can be found.

The James speed-loss curves describe the speed loss of a vessel under theinfluence of wave height and direction. Typically there are three curves,representing three sea regimes — head, beam and following — however, no testswere made with this model as further advances were made to use theBabbedge1' formula, which is described later. The advantages and disadvantagesof the James speed loss curves are :

(i) They can easily be described by third degree polynomials fromexperimentally derived data. The information from curves supplied in theBales13 paper was tried out using the curve fitting routines.

(ii) The equations are simple and therefore are ideal for repetitive use in therouteing programs since many calculations are made through the grid. It isquestionable if the size of the DP grid can still be used when the response sectionis expanded to incorporate a ship model.

(iii) The curves can only be found by extensive experiments at sea, thus theyare individual and require much time and effort.

(iv) The curves only describe a wave encounter angle of 1 20 degrees for eachsea regime. Thus differing combinations of wave heights and directions will effectthe same speed reduction whereas in reality this is not so.

(v) The curves only utilize a small amount of data and, in fact, only use wavedirection as a pointer to which equation to use.

The form of the equations is as follows:

speed = ai + biHx + q Hi + </j W| (6)

Where Hi_ = significant wave height; i = (1) head sea, (2) beam sea, and (3)following sea; a, b, c, d are coefficients of the polynomial.

The equations have been modified by Babbedge'' but still are individual to theship. Observations carried out aboard four ships were analysed statistically inorder to establish the main causes for ship speed loss and to incorporate them ina speed reduction equation. The equation thus does away with the sea regime andactively uses the wave direction as a parameter in the equations. The equationsalso incorporate power, maximum speed in calm conditions, wind speed, winddirection, wave height, wave direction, sea temperature and ship displacement,but still fall short of fully describing the ship response since the seaway is onlydescribed by significant wave height and primary direction. It is well known that


sea spectra for many differing seas can have the same significant wave heights anddirections, thus the response of the vessel will be predicted to be the same incases where it can be grossly dissimilar. The Babbedge formulae still have thesame advantages of the previous approach, however, they improve the routeingalgorithms at this stage.

The form of the Babbedge equations are:

'est = i9"93 + 6-44(lnP-ln 20000)

- 1 0 - 2

r i+ 0-04 (0— 12) — 0000 1 2 (A — 37ooo) + o-27 (7)

(for the Dart Atlantic, a 42000 d.w.t. container ship).Where :P = power; V = calm speed setting; VR = wind speed; Hw = significant waveheight; /i = wave direction; /? = wind direction; 0 = sea temperature; andA = ship displacement.

Scott's empirical wind/wave formula used:

Ww = °°7S VI (8)

where Hw = significant wave height; and Kw = wind speed.The formula can be used for a specific speed in calm conditions with due

respect to the maximum power available for the ship. Under the present programfor time optimization, power is constant and speed is maximized with respect tothe particular meteorological conditions.

Equation (7) formed the initial basis for trials as mentioned but it was felt thatthe amount of calculation required might be unduly increased by variations forsea temperature and/or ship displacement. A series of trials were then simulatedusing varying significant wave heights, displacements and temperatures toestablish the effect these parameters have on the speed calculated. The windspeed was formulated on the Scott formula, equation (8), as used by Babbedge.However, this formula is not strictly accurate and the formula adopted by the UKMeteorological Office incorporated a simple constant for wave height in thepresence of no wind. The standard curve for comparison was that without thisparameter (see Figs 3—6). The Babbedge equations can be rearranged to optimizefor power given a speed to be maintained across the ocean. This demonstrates theversatility of such equations and their importance in micro based systems.

Equation (7) can be represented by:

: 644 In P - ^ F{alm (wave) - K{alm (wind) j (9)

giving,

^ = 6-44 l n P — (10)' " wave-Kc a l m wind] ++ P K }


2000

17-14-

_ 14-29

x 11-43

2 8-57

5 71

206

0

•x—«

«<J 72-65 76 87 2708Sig wave ht (M)

1500

12-86

j 70-77o

£ fl-57

g. *•«

4-29

2-74

04-22 <J<J 72-65 76S7 27-06

Sig wave ht (M)

Fig- 3 F'g- 4

Fig. 3. Wave height versus speed for constant power with variations. Dart Atlantic:maximum speed, 20 kt; d.w.t., 41 000: A, following sea; • , beam sea; + , head sea.Wave factor: x , following sea; D, beam sea; • , head sea

Fig. 4. Wave height versus speed for constant power with variations. Dan Atlantic:maximum speed, i j k t ; d.w.t., 41000. Temperature factor: x , following sea; n,beam sea; • , head sea. For key to other symbols see Fig. 3

15 00

12-86

10-71

' 8-57

613

4 29

2 14-

00 4-22 8-43 12-65 16-87 2108

Sig wave htlM)

1500

12-86

70-77

8-57

6-43

4-29

2 14

04-22 8-4-3 12-65 16-87 21-08

Sig wave ht (M)

F'g- S Fig. 6

Fig. j . Wave height versus speed for constant power with variations. Dart Atlantic:maximum speed, i j k t ; d.w.t., 41000. Displacement factor: x , following sea; n,beam sea; • , head sea. For key to other symbols see Fig. 3

Fig. 6. Wave height versus speed for constant power with variations. Dart Atlantic:maximum speed, 1 c kt; d.w.t., 41 000. Wind factor: x , following sea; n, beam sea;• , head sea. For key to other symbols see Fig. 3


19-66 r

1667

H-06

O6-43

5-52

A T

I J Max power

0 1660-8 3721-6 55624. 74-43-2 9304-0

Power (HP)Fig. 7. Wave height versus power for constant speeds. Dart Atlantic: d.w.t., 41 000.

A, j kt; T, 10 kt; +, i j k t , encounter angle, 00

0)

1

19 68 r

1687

14-06

11-24

8-43

5-62

2-81

Max powerj

" 0 18608 3721-6 5582-4 74-432 9304 0Power (HP)

Fig. 8. Wave height versus power for constant speeds. Dart Atlantic: d .w. t . , 41 000.

A, j k t ; T, 10 kt, + , i j k t ; encounter angle 1800


Certain graphs have been produced to show the variation of power setting againstwave heights, to maintain a required speed (see Figs 7 and 8).

c. ROUTEING COMPARISON. Several runs were made for the NorthAtlantic based on the Dart Atlantic formulae as described by Babbedge.'' Theseruns were then compared with the routes advised by Oceanroutes (UK) Ltd, forthe same period of weather which was chosen to be during the winter months(Nov. 86—Dec. 86). Obviously the ships routed are not identical and so largediscrepancies can occur. However, with this in mind the Dart Atlantic was set atdifferent service speeds and different loading conditions in order to give adifferent actual vessel speed during transit. The deadweight tonnage (d.w.t.)only provides one input to the speed estimate so different combinations of d.w.t.and set service speed may provide the same speed estimate.

The information provided by Oceanroutes was the actual advised route sailed(only open ocean), the type of vessel involved, the d.w.t. of the vessel and thedeparture and destination times. It was hoped that the vessel matching could bemuch closer, but the only possible matching was that of d.w.t. and notservice speed. The initial routes were run on a DP grid derived by taking pointsat increments of 60 nautical miles from the great circle route. The routes advisedshow some degree of discontinuity but changing the grid mesh size orincorporating a smoothing algorithm through the rough route removes thejaggedness.

A routeing case is shown in Fig. 9, west-bound from Cork (S. Ireland), to NewYork (N. America). Several runs were performed with differing loadingcharacteristics and set service speed. The program runs therefore illustratetheoretical vessels for the period in question. Fig. 9(6) illustrates a run for42000 d.w.t. and a set service speed of i$kt , Fig. 9(c), however, illustratesthe same run for a 48 000 d.w.t. vessel at a service speed of 18 kt. The latter runis intended to represent the Oceanroutes advised course as given to a 48 000d.w.t. bulker. The routes are performed on the larger DP grid system andtherefore show a degree of discontinuity. However, Figs 10(a) and (b) showthe same runs on a finer grid, at 14 and 15 kt and it may be noted that smoothingof the optimum route removes extreme values of course change.

6. CONCLUSION. The intention of this work at Plymouth Polytechnic is toproduce an on-board advisory weather routeing package. In designing such asystem it is necessary to take into account the capabilities of the machine and sothis paper has tried to outline both the limitations and methods for utilizing thatcapability.

It is suggested that advantages can be gained by using a simple optimalalgorithm and ship response algorithm for the calculation of optimum timeroutes. However, there is a trade-off in this approach when further optimalparameters are required. The moveable grid system is shown to reduce bothcalculation time and required memory space and is considered an ideal methodfor including constraints in the optimal calculations. There is a need forobserving the 500 mb flow details and biasing the grid depending upon the resultssince accurate forecasts do not exist for a complete North Atlantic transit.Optimal routeing for the whole voyage would require complete and accurate data

I I I I 30

80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

(a)60

55

80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

(b)

SO 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0(c)

Fig. 9. North Atlantic crossing, (a) d.w.t., 39000; speed, I J kt: (b) d.w.t., 42000;speed, I J kt: (c) d.w.t., 48400; speed, 18 kt. A, advised route; O, optimum route;G, great circle


Optimal path — Mercator projection Key

N-S

55

50

iS

40

35

30

Optimal 1Great Circle 2Advised route 3

Review

DART ATLANTIC 46 000 d.w.t.QCR dist: 2363-4 OCR dist: 2704-8OCR time: 319-76OCR time: 26231T saving: 37-47

Departure time20-2

Departure Arrival

4900 700 40-40 62-40

SO 70 60 50 40 30 20 10 W-ECurrent ship status

Position4900 700

Remaining

Heading212-0

BunkersTotal used

ETA16-306-11

Estimated total

(a)

Optimal path— Mercator projection Key

N-S

55

50

40

35

30

Optimal 1Great Circle 2Advised route 3

Review

DART ATLANTIC 46 000 dw.t.OCR dist: 2363 4 OCR dist: 2751-9GCR time: 294-81OCR time: 256 34T saving: 36-47

Departure time20-2

Departure Arrival

1900 700 40-40 62-40

60 70 60 50 40 30 20 10 W-ECurrent ship status

Position4900 700

Remaining

Heading209-9

Bunkers

Total used

ETA16-337-10

Estimated total

(b)

Fig. 10. (a) Smoothed d.w.t., 48000; speed, 14IU: (fc) smoothed d.w.t., 48000,speed 1j kt


for the transit, however this is not available and it is believed that observing asteering level and and long range forecasts will provide better results than relyingupon climatological 'fill-in' data.

The authors believe that it is essential to concentrate on the physics of theoperation rather than to have the mathematics 'take control'. For example, theproblem of relating vessel response to the sea state demands in the optimizationroutine a good estimate of sea conditions for the complete passage. How is thisto be best achieved? Assumptions have to be made that the prediction for theforecasted period remains good when the next set of data takes over. Is this arealistic proposition, or can the two sets of data be examined and a linear time-varying sea state obtained for the period in question?

REFERENCES

1 Heijboer, D. (1974). Weather routeing — a modern aid to navigation. Fairplay International.8 March.

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APPENDIX. PROGRAM RESTRICTIONS

| Split distance into thirds |

| Calculate intermediate points |

VCalculate data parameters

for intermediate points basedon data plane

Calculate intermediate speedand time

| Calculate total zone transit time |

Perform policy decision choicerecord optima) route path

Compare start times j

T Within limitsEND

Operational Considerations and

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