PRACTICAL WEATHER ROUTING OF SAIL-ASSISTED MOTOR VESSELS
by
H. Hagiwara and J.A. Spaans Reportnr. 718-P
Publication in "The Journal of Navigation", Vol.40 No.1, 1987
852088 202.01 .27
The JOURNAL of
NAVIGATION
VOL. 40 NO. I JANUARY 1987
Early Navigation: The Human Factor (Duke of Edinburgh Lecture)
TIM SEVERIN
Navigation of Spacecraft on Deep Space Missions 19
JAMES F. JORDAN
.
The Distribution of Navigational ErrorsCAPTAIN PETAR UMBELI
ATS and VTSSome Observations Towards a Synthesis
R. BOOTSMA AND K. POLDERMAN
The Calculation of Crossing Collision Risk at Sea W. G. P. LAMB
Search Area Determination and Search Unit Deployment 63 JOHN ASTBURY
Sea Trials of a Navigation System Based on Computer Processing of
Marine Radar Images 73
L. AUSTIN, A. BELLON AND E. BALLANTYNE
Coordinate Conversion Techniques in Microprocessor-based Receivers for
Hyperbolic Radio-navigation Systems 81
DAVID LAST AND CHRISTOPHER SCHOLEFIELD
Practical Weather Routing of Sail-assisted Motor Vessels 96
HAGIWARA AND J. A. SPAANS
Flight Inspection Procedures and Position Fixing Techniques I 2o
D. R. REIFFER
Military Flight Checking of Navigation and Landing Aids 132
WING-COMMANDER M. A. RADFORTH, RAF
Forum: Proposal on the Modification of Sailing Calculations 138 T. HIRA1WA
THE ROYAL INSTITUTE OF NAVIGATION
OXFORD UNIVERSITY PRESS
30
Practical Weather Routing of
Sail-assisted Motor Vessels
H. Hagiwara and J. A. Spaans
This paper reports on a study conducted during the academic year 198 -6 by Assistant Professor H. Hagiwara of the University of Mercantile Marine in Tokyo and Professor J. A. Spaans of Delft University of Technology.
i. INTRODUCTION. In recent years, many sail-assisted motor vessels have been operated showing remarkable advantages in:
saving passage time; saving fuel oil;
damping ship's motions"2
In order to operate those vessels more effectively in ocean-crossing voyages, the following requirements should be fulfilled:
accurate forecasts of environmental conditions (wind, sea, swell and ocean
currents) for a sufficient prediction period;
good predictions of ship's speed, engine power and drift angle (leeway)
for the particular vessel for various conditions of draught, trim and environment;
a practical algorithm for the computation of a (sub) optimum route. Until now, the above-mentioned requirements have not been satisfied simul-taneously and the practical weather routing of sail-assisted motor vessels has
not yet been established.
In this paper, the authors propose methods which meet requirements (ii) and
(iii). Requirement (i) is not fully met in practice, although the accuracy of
forecasts has been steadily improved. For this study the actual (observed and analysed) wind, sea and swell data published on magnetic tape by the Fleet
Numerical Oceanography Center of the U.S. Navy are used.
A practical way of computing 'minimum time route' and 'minimum fuel route for a specified passage time' for a sail-assisted motor vessel - which is called the
modified isochrone method by the authors - is described in Section 2.
In Section , sophisticated methods are described to predict the ship's speed,
engine power and drift angle in a seaway based on the equilibrium between resistances and thrusts, using a 40000 d.w.t. product tanker with 8o8 m2 sail
area as a mathematical model ship.
Examples of actual environmental data in the North Pacific Ocean are shown in Section 4.
852088 202.01 .27
NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS 97 In Section ç, computer simulations are performed using the modified isochrone method with a sail-assisted motor vessel and an equivalent motor vessel in actual
environmental conditions. By comparing passage time, average speed and fuel
consumption of the sail-assisted motor vessel with those of the equivalent motor vessel, the advantages of sail-assisted operation are investigated. The benefits of
weather routing are also investigated by comparing the results of the minimum time/fuel route with those of the great-circle route.
2. MINIMUM TIME/FUEL. ROUTING. Manyoptimizationmethodshavebeen reported for selecting the optimum route of a ship in an ocean-crossing voyage. Those methods can be classified into three categories:
calculus of variations ;3 4, 5, 6 dynamic programming ;7 B isochrone method.9
Although the calculus of variations seems elegant in mathematical treatments, its solution only fulfils the necessary optimum route conditions and difficulties arise
in the application in converging on a route to the destination. Other difficulties are inherent in the calculus of variations which make it an impractical method
for ship weather routing.6
In spite of the fact that dynamic programming is a very powerful optimization technique, it needs many grid points for the search routine to obtain an accurate solution and uses a lot of calculation time and memory space.
The isochrone method, since it was proposed by R. W. James,9 has been used
in many weather routing facilities as a practical (hand) method to obtain the minimum time route. The method proposed by James, however, does not give
the correct isochrones in a strict sense, and it is less suitable for computerization. In this section, the algorithm of the modified isochrone method previously proposed by one of the authors'° is described. Calculation of the correct isochrones with this method is straightforward and very suitable for computerization.
Minimum time routing. Let a ship depart from departure point X0 at time t0 and sail to the destination X at the maximum (constant) number of propeller
revolutions. The algorithm of the modified isochrone method to calculate the
minimum time route is as follows.
Simulate the navigation of a ship for At hours from departure point X0,
following headings C0±iAC (i = o, i, . .. , m), where C0 is the initial course of the great-circle route from X0 to X1 and AC is the increment of heading. In
each heading, ship's speed through the water, engine power, drift by wind (leeway) and drift by ocean current are calculated as a function of forecast
environmntal data, ship's heading and number of propeller revolutions. The calculated arrival points at time t0+At are represented by X,(i) (i = I, 2, . . .
2m+1). The set {X1(i)} defines the isochrone at t0+At.
Let X1 (i) be the departure points at t0+At. Navigate the ship for At hours
from each X1(i), following headings C ±jiC (j = o, I, . . ., m), where C, is
the initial course of the great circle from each X1(i) to X1. The calculated arrival
98 H. HAGIWARA AND J. A. SPAANS VOL. 40 points at t0+ 24t are represented by X2(i, j) (i, J = I, 2, . . ., 2m+ i). Then
calculate the lateral (cross-directional) deviations D2 (i, J) of X2(i, j) from the great-circle route connecting X0 and Xf, where D2 (i, j) is negative on one side of the great circle, and the remaining great-circle distances R2(i, j) from X2(i, j) to the destination X1.
Now define a lane of width D on each side of the great circle from X0 to X1
and divide each lane into p sub-lanes of width AD; the sub-lanes are identified
by L(k), where k
= p, p+ 1,
. . .,- i, + r,
. .., p
i, p. The lateraldeviation D2(i, j) identifies the sub-lane L (k) to be assigned to each X2(i, j).
From all X2(i, j) included in each sub-lane L(k), the X2(k) is selected with minimum R2(i, j). The set {X2(k)} (k = - p, - p + i, . . .,
i, + i,
. . . , p)defines the isochrone at t0+ 2zIt.
Changing the argument from k to i, let X2(i) be the departure points at t0+2 At.
Navigate the ship for At hours from each X2(i), following headings C1±JAC (j = o, r, . . ., m), where C1 is the initial course of the great circle from each
X2(i) to Xf. The calculated arrival points at t0+ 3At are represented by
X3(i,j)
(I =p,
.. ., i, +z,
. .., p;j = i, 2,
. . ., 2m+I).In the same way as stated in (ii), calculate D3(i, j) and R3(i, j) for all X3(i, j). Comparing R3(i, j) of all X3(i, j) included in each sub-lane L(k), find X3(i, j) having minimum R3(i, j) and represent it by X3(k).
The set {X3(k)} (k
= p, .
. ., - i, + i,
. . . , p) defines the isochrone att0+3At. (Fig. i.)
Repeating the procedures in (iii), calculate the isochrones {X4(k)},
{X5(k)}, . . . at time t0+4At, t0+ At...
When the isochrone {X(k)} at time t0+nAt approaches the destination
X1 sufficiently, navigate the ship along rhumb lines from X(k) to Xf and calculate
the passage times At(k) between X(k) and Xf.
to + t X7(,).-Isochrone -o0 t0 +3 t 4 X(' I I Sublor,e L(k)
Fig. i. Modified isochrone method
L (1)
L (-1)
o Great circle route betweeoX0or,d Xf
L.
852088 202.01.27
NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS 99 The minimum passage time is given by
Mm {nAt + At(k)}.
Ic
Represent X(k) giving that minimum passage time by X.
(vi) By tracing the isochrones memorized in the computer backwards, the
minimum time route Xf, X, X_1, . . ., Xi', X0 can be obtained.
The accuracy of this modified isochrone method can be increased by decreasing
the width of sub-lane 4D. Since the number of arrival points constructing an
isochrone after each interval does not exceed p = 2D/4D, the amount of calculation is always kept within a certain feasible limit. In addition, this method can easily take into account the limits of the navigable area and voluntary speed reduction to avoid excessive ship's motions.
In the actual minimum time routing, since the forecast data of wind, sea and
swell are updated every i 2 or 24. hours, it is necessary to recalculate the minimum time route by using the updated forecast data and ship's position at each updating
time as a new departure point.
Minimum fuel routing. Consider a ship leaving departure point X0 at time t0 and arriving at destination X at time t, and let us minimize the total fuel consumption during the voyage. In this problem, the arrival time t is specified and the passage time T = t.t0 is fixed.
From the mathematical point of view, as ship's heading and number of propeller revolutions (or engine power) have to be controlled simultaneously in minimum
fuel routing, the problem becomes more complicated than in minimum time
routing. In actual ocean-crossing voyages, however, it has been found by simulations that the control of ship's course is far more effective than the control
of engine power to minimize the total fuel consumption.6 Therefore, from a practical standpoint, the authors propose the following algorithm to perform
minimum fuel routing.
Setting a suitable number of propeller revolutions, calculate the minimum time route and minimum passage time Tmjn by using the modified isochrone method. In this case, Tmjn is a function of the number of propeller revolutions.
Correct the number of propeller revolutions so as to get Tmjn close to
the specified passage time T = tt. Using the corrected number of
propeller revolutions, recalculate the minimum time route and minimum passage time Tmin.
If 1T Tminl becomes small enough, stop the calculation. Otherwise,
repeat the procedures in (ii).
The calculated minimum time route can be regarded as the minimum fuel route for a specified passage time. Newton's method or regula-falsi method can be used
for the correction of the number of propeller revolutions.
The minimum fuel route calculated by the above algorithm is not an optimum
from the mathematical viewpoint, but it may be acceptable from the practical 4-2
100 H. HAGIWARA AND J. A. SPAANS
viewpoint. In the actual minimum fuel routing it is necessary to recalculate the
minimum fuel route whenever the forecast data of wind, sea and swell are updated.
3. PREDICTION OF SPEED, POWER AND DRIFT ANGLE OF A SAIL-ASSISTED MOTOR VESSEL IN A SEAWAY. The methodsused to calculate the speed, engine power and drift angle (leeway) of a sail-assisted motor vessel in a seaway are described here, using a o 000 d.w.t. product tanker with 8o8 m2 sail area as a mathematical model ship. These methods are mainly based on the studies
of the Hydronautics section of the Department of Maritime Technology, Delft
University of Technology. A profile and main dimensions of the model ship are
shown in Fig. 2. Hereafter, the model ship is assumed to be in full loaded condition, i.e. draught = II 4 m, and even keel.
Fig. 2. Profile and main dimensions of the model ship. Dead weight = 40000 t; maximum engine power = 10000 kW; length between perp. = i8ço m; total sail area (two triplane wingsails) = 8o8 m2; design draught = 114 m; breadth moulded = 320 m; service speed = 14 kt.
Prediction of ship's speed. The longitudinal resistance of a sail-assisted motor vessel proceeding in a seaway mainly consists of:
still water resistance;
wind resistance;
added resistance due to waves.
On the other hand, the longitudinal thrust consists of: propeller thrust;
sail thrust.
The speed of a sail-assisted motor vessel can be calculated so as to achieve equilibrium between the above resistances and thrusts. First, the methods to calculate the above resistances and thrusts are noted below (p. it).
(i) Still water resistance. The still water resistance R5 is calculated by
p 1
r
stw
-where Pw = density of sea water, C = resistance coefficient, S = wetted surface
of ship's hull, V = ship's speed.
VOL. 40
10 IL-(-) 05 o -05 0 . 00
10
852088 202.0127 CwFfiA Curve CWL/3A Curve I I I I I 0' 300 60' 90' 120° 150' 160'Apparent wind direction from bow I'3A
Fig. . Fore and aft wind force coefficient and lateral wind force coefficient versus apparent
wind direction from bow
(iii) Added resistance due to waves. The added resistance due to waves 'wavewhile
a ship proceeds in irregular waves with a cosine squared directional spreading
can be calculated by
Rwave = (Rwave/Hr)JAWf42
where (Rwave/H) = added resistance per unit significant wave height squared,
H = significant wave height. For a given draught and trim
(Rve/Hj) is a
function of the ship's speed, wave direction from the bow and average wave
period.
In the model ship (Rwave/H) were calculated as a combination of linear
expressions of average wave period for the ship's speed of 2, , 8, . . ., 2okt,
and wave direction from the bow of o0, 200, 4.0°, . . ., i 8o°. (Rwave/Hv) for
(3) NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS 101
C consists of the coefficients representing the frictional resistance, residuary resistance, etc., and is a function of ship's speed, draught and trim. S is a function of draught and trim. R51 of the model ship is 84, 38 and 1069 kN for ship's
speeds of , ii and 17 kt, respectively.
(ii) Wind resistance. The wind resistance RWjfld is given by
i
_I
r
Awind PA'--WF''FA 2
where PA = density of air, CWF = fore and aft wind force coefficient, AF = transverse projected area of the above-water part (excluding sails),
UA = apparent wind speed.
CWF is a function of the apparent wind direction from the bow flA. For the
model ship, CWF was calculated based on the Isherwood method.12 TheCWF versus
flA curve of the model ship is shown in Fig. 3. A is a function of draught and trim, and is 56o m2 in the model ship. When the model ship meets a wind of
the ship's speed of ii kt are shown in Fig. . For an arbitrary ship's speed and
wave direction, (Rwave/JJ2w) is calculated by using quadratic interpolation. When the model ship proceeding at 14 kt meets the waves (H = 7 m, average
period = 10 s) coming 0°, 6o°, 120° and i8o° from the bow, Rwave becomes
751, 434, i 8 and 2 13 kN respectively.
(PwoveIH)
20
I I
Ships speed=l4kt ,u: Wove direction from bow
102 H. HAGIWARA AND J. A. SPAANS VOL 40
4 6 8 10 12 14 16 18 20 Averoge wove period (seconds)
Fig. 4. Added resistance per unit significant wave height squared versus average wave period
In general, since the ocean waves consist of sea (wind wave) and swell, Rwave can be calculated as the sum of the added resistance due to sea Rsea and the added resistance due to swell Rsweii. Thus,
wave = sea+ swell (4) Besides the above-mentioned three principal resistances, there exist the added
resistances caused by rudder and by drift. These resistances, however, can be regarded as sufficiently small compared with the three principal resistances,
therefore we neglect these secondary resistances in the calculation of ship's speed.
Furthermore, in a sail-assisted motor vessel the added resistance due to waves may be reduced to some extent as a result of the damping of ship's motions by using the sails. The method used to calculate the amount of such a reduction,
however, has not yet been established, so that we neglect that phenomenon too. The effects of neglecting the added resistances caused by rudder and by drift will however cancel the effect of neglecting the reduction of added resistance due to waves by the damping of ship's motions to some degree.
(iv) Propeller thrust. The propeller thrust 1rop is calculated by
1rop = (It)KTPWD4N2 (5)
where t = thrust-deduction fraction, KT = thrust coefficient, Pw = density of
sea water, D = propeller diameter, N = number of prcpeller revolutions per second.
852088 202.01 .27 () Cy/3A Curve Curve I I I (6) 0' 30' 60° 90° 1200 150° 160°
Apparent wind direction from bow
Fig. ç. Sail thrust coefficient arid sail lateral force coefficient versus apparent wind direction from bow
NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS 103 WhenNis kept constant, the thrust-deduction fraction t increases as the ship's speed increases (i.e. as the loading of the propeller decreases); t changes also with draught and trim.
The thrust coefficient KT is a monotonically decreasing function of the advance ratio J which is defined by
V(iw)
NDwhere V is the ship's speed and w is the wake fraction; w changes with draught and trim. When the model ship proceeds at , ii and i kt with N = r.p.s.,
1rop becomes 1218, 847 and 429 kN respectively (v) Sail thrust. The sail thrust 1a11 is given by
T
sail2PA X
r
A /S A
where PA = density of air, C = sail thrust coefficient, A5 = sail area, UA = apparent wind speed.
As shown in Fig. 2, triplane wingsails are installed on the forecastle and the bridge of the model ship. This triplane wingsail possesses a lift coefficient of and drag coefficient o8.
C,< is a function of the apparent wind direction from the bow flA. The C, versus
curve of the model ship is shown in Fig. ç. In this C, versus /1A curve, the
interaction between sails and hull as well as the interaction between fore wingsail and aft wingsail are taken into account. In stormy weather it is necessary to protect
An example of the speed of the model ship calculated by the above-mentioned method is shown in Fig. 6, where the speeds of the model ship (sail-assisted
motor vessel) and the same ship without sails (equivalent motor vessel) are shown
by solid lines. Figure 6 shows that, for true wind direction between 70° and
(
0
, LjV
8).
Equivalent motor vessel
=
j
-..-__T- --.--
-I I
17 Propeller rev. = 75 rpm. Sailossisted motor vessel
Wind speed 40 kt Sea height = 5 m
Sea direction = wind direction 15 - Seo period = 8 sec
13
Equivalent motor vessel Swell height =3m
11
Swell direction from bow =900 Swell period = 10 sec
104 H. HAGIWARA AND J. A. SPAANS VOL. 40
the sails against an excessive aerodynamic force by reducing the attack angle of
sail to the wind. In formula (i), when UA exceeds 20 m/sec and the sign of C,
is positive, 1a11 is assumed to be equal to the sail thrust for UA = 20 rn/sec. When the model ship receives a wind of UA = kt and flA = o°, 6o°, 120° and i8o°,
1ai1 becomes - 14, 403, 6o6 and 256 kN respectively.
For a sail-assisted motor vessel proceeding in a seaway at constant speed, the sum of resistances (i), (ii) and (iii) has to be equal to the sum of thrusts (iv) and (v).
R5 + + Rsea + 'sweI1 = 1rop + 1aj1 (8)
If the ship's heading, number of propeller revolutions and wind, sea and swell are given, each resistance and thrust in equation (8) becomes a function of the
ship's speed. Hence the ship's speed through the water can be calculated as follows.
(i) Assuming a suitable ship's speed, calculate both sides of equation (8).
(2) Correct the ship's speed so that the difference between both sides may become smaller. Using corrected ship's speed, recalculate both sides of equation (8). () Repeating the procedures in (2), find the ship's speed which satisfies equation
Soilassisted motor vessel
0' 30° 60° 90° 120° 150° 180°
True wind direction from bow /3
Fig. 6. Ship's speed and engine power versus true wind direction from bow
852088 2020127
NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS ioç 1300, a sail-assisted motor vessel can sail 2ç-35 kt faster than an equivalent motor vessel. Since the sails do not generate thrust for true wind directions between 00 and and they increase the wind resistance, the speed of a sail-assisted motor vessel becomes slightly less than that of an equivalent motor vessel.
Prediction of engine power. When the number of propeller revolutions and ship's speed are given, the engine power P can be calculated as follows,
P = 21r KQpW D N3/(i/ri/m) (9)
where KQ = torque coefficient, Pw density of sea water, D = propeller diameter, N = number of propeller revolutions per second, i/r = relative rotative efficiency, 1/rn = mechanical efficiency of shaft bearings. Torque coefficient KQ is a monotonically decreasing function of advance ratio J. v and i/rn of the model ship are i oi 7 and 099 respectively.
When the model ship proceeds at , ii and 17 kt with N = i2ç r.p.s., P
becomes and ço28 kW respectively. In Fig. 6 the engine powers of
the model ship (sail-assisted motor vessel) and the same ship without sails
(equivalent motor vessel) are shown by dashed lines. For true wind directions
larger than 0 a sail-assisted motor vessel can sail faster with smaller engine
power than an equivalent motor vessel.
Prediction of DrJi Angle. The drift angle (leeway) of a sail-assisted motor vessel will usually not exceed a few degrees. Nevertheless, since even a small drift angle gives a large cross-track deviation for long sailing distances, the prediction of the drift angle is important from the navigational point of view.
The drift angle can be calculated using the equilibrium between aerodynamic
lateral forces and hydrodynamic lateral force. The aerodynamic lateral force
acting on a sail-assisted motor vessel consists of the sail lateral force and the lateral wind force due to hull and superstructure. The ship's hull underwater part
receives a hydrodynamic lateral force caused by drift. The methods used to calculate the lateral forces are described below.
(i) Sail lateral force. The sail lateral force 1ai1 is given by
(io) where PA = density of air, C = sail lateral force coefficient, A = sail area, UA = apparent wind speed.
C is a function of the apparent wind direction from the bow f1A The C. versus
flA curve of the model ship is shown in Fig. ç. Because the wingsail installed on
the model ship maintains an approximately constant attack angle to the wind
( ic0) for /3A between Iç° and i6o°, the sign of C becomes negative for /1A
greater than i o°. For flA i 8o°, since the wingsail takes the attack angle of
90°, C.,, becomes zero.
In equation (io), as stated in the calculation of sail thrust, ',aj1 is assumed
to be equal to the sail lateral force for UA = 20 rn/sec when UA exceeds 20 rn/sec. When the model ship meets a wind of UA = kt and e8A = 30°, 900 and Iço°, 1sail becomes i6o and -391 kN respectively.
io6 H. HAGIWARA ANt) J. A. SPAANS VOL. 40
Lateral wind force due to hull and superstructure. The lateral wind force due to hull and superstructure FWIfld is calculated by
j
_I
( A I1win(I_2PAWLfIL(JA I1
where PA = density of air, C1 = lateral wind force coefficient, AL lateral
projected area of the above-water part (excluding sails), UA = apparent wind
speed.
CWL is a function of the apparent wind direction from the bow flA. For the
mo(lel ship, CwL was calculated based on the Isherwood method.12The C1 versus
flA curve of the model ship is shown in Fig. . A1 changes with draught and trim, and is 1400 m2 in the model ship. When the model ship meets a wind of
UA kt and flA = 30°, 90° and Iço°, Fwjfld becomes 83, 183 and i 14 kN
respectively.
Hydrodynarnic lateral force caused by drfi. The hydrodynamic lateral force caused by drift F.ater is given by
Fwater = pC11 Ld V2 (12)
where p = density of sea water, CH = hydrodynamic lateral force coefficient, L = waterline length of ship, d = draught of ship, V = ship's speed.
CH is a function of the drift angle (leeway) A, and can be approximated by
CH = K1A+K2IAIA ('3)
where coefficients K1, K2 are functions of l)lock coefficient, draught, waterline length and breadth.'3 When the model ship proceeds at i kt with A = 1°, 2°
and °, Fwater becomes 8ç, 784 and 1196 kN respectively.
For a sail-assisted motor vessel proceeding with constant drift angle, the sum
of aerodynamic lateral forces (i) and (ii) should be equal to the hydrodynamic
lateral force (iii).
'aiI + Fwind = 'vater (14)
If the ship's speed has been obtained by equation (8), 'ai1 and 'vind can be
calculated by using wind speed and wind direction. 'vater becomes a quadratic
expression of the unknown variable A. Therefore, by solving the quadratic equation for A, we can calculate the drift angle A.
Figure 7 gives an example of the drift angle of the model ship calculated by the above-mentioned method. In Fig. the drift angles of the model ship (sail-assisted motor vessel) and the same ship without sails (equivalent motor vessel) are shown for various true wind directions from the bow fi. It can be seen that the A versus curve of the sail-assisted motor vessel becomes flat for fibetween 30° and 6o°. This is because when the apparent wind speed U exceeds 20 m/sec, the sail lateral force is kept equal to that for UA = 20 m/sec l)y reducing the attack angle of sails to the wind.
4. ENVIRONMENTAL DATA USED IN SIMULATIONS. In practical ship
weather routing, actual (observed and analysed) and predicted environmental data are used, and the effectiveness of weather routing largely depends on the accuracy of forecast data. For the simulations performed in this paper, however, only actual environmental data are used to evaluate the maximum benefits of weather routing.
NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS 20-852088 202.0127 40 30 2° 0° 1° Q0 300 60° 90° 120°
True wind direction from bow ,i3
Fig. i. Drift angle versus true wind direction from bow
The wind, sea and swell data were prepared from the global-band data set
published on magnetic tape by the Fleet Numerical Oceanography Center of the US Navy. The actual data for the North Pacific Ocean at 0000 hours and 1200 hours GMT for November and December in 4980 were selected from that
data set for the simulations. The intervals between grid points of the data are I9° (on average) for latitudinal direction and ç° for longitudinal direction.
These data were memorized in a random-access file to be used in the simulations. Examples of the actual wind, sea and swell data are shown in Fig. 8 (0000 hours
True wind speed = 40 kt
I I Wind speed 150° 180° 107 0000 hours GMT 2 Nov. 1980
\ / ,\
/\
\ \
/ 7
N I/
I \ I I/
\N
I--/N 1/ /
I I I +I \// I
I \-I
I/ l----'///
/ V V /
/
-140 160 180 160 140 120 Longitude>
10 20 30 40 50 ktio8 (b) 6050 -0 -J 3020 -Sea chart
xx
\ \
-c -v -c-/
N '
j
/I--, \
\N
/
I/
\
/
/ r/ /
1/0 160l0
10 Longitude -*4 -4>6-6
--9----
/---Sea height -c--2 Sea period 3 140 160 Swell height --2 Swell period - 3F!. HAGIWARA AND J. A. SPAANS
0000 hours GMT 2 Nov. 1980
/ -_c_7
12 180 10 Longitude -*4 -{>6 [>e F-9 I-12 140 10 rn l-15 secFig.8.(a) (On previous page) Example of actual wind data; (b) example of actual sea data; (c) example of actual swell data
VOL. 40
71Q 120
-c> 10 m
F
15 sec(c)
Swell chart 0000 hours GMT 2 Nov. 1980
60-
1J/
xxx
\JJ/x /\
(X X 50 -40----\
-c/-F--30/ / / \
20- I/ / \
I
/
60- 30-852088 202.01.27 Surface current I
/\\//
/ /
I - -c - '-c 1)sl - -__ . - -Na vemberf
140 760 780 160 74.0 Longitude Current speed.02
t.Q4 c'-Q'6 -f>Q8 (>70 ktFig. 9. Climatological ocean current data
ç. SIMULATIONS ON WEATHER ROUTING OF A SAIL-ASSISTED MOTOR VESSEL. Using the modified isochrone method, the methods of calculating ship's
speed, engine power and drift angle, and the actual environmental data, the
numerical simulations of weather routing are performed.
The sail-assisted motor vessel (40000 d.w.t. product tanker with 8o8 m2
sail area, full loaded condition) and the equivalent motor vessel (the same vessel
without sails) described in section 3 are sailed in the simulations. The specific fuel consumption of these vessels is assumed to be o2 I kg/kW per hour.
Generally, in weather routing simulations, the voluntary speed reduction should be taken into consideration to avoid shipping green water, slamming, excessive vertical acceleration, etc. in high head waves. However, since the
engines installed in the above mentioned vessels are not so powerful, it is expected that the ship's speed decreases naturally to a safe level in such waves.
Therefore the voluntary speed reduction is not taken into account here. (When
necessary, it can be easily treated in the routing algorithm.) In the simulations, NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS 109 GMT 2 November 1980), where the typical fields of wind, sea and swell formed by the depressions can be observed. For the ocean current data, the climatological
values of November taken from the Pilot Chart of the North Pacific Ocean by the US Defense Mapping Agency are used. The interval between grid points
of those data is ° for latitudinal and longitudinal directions. Ocean current data are shown in Fig. 9. The environmental data for intermediate points are determined by linear interpolations.
20 -
- - - -
- - -
- - - z_ /-
- - --
50-0
40-60
50-0
-
40-Westbound voyage Departure
0000 hours GMT 11 Nov. 1980 0 Seattle San-Fran cisco 140 1GQ 180 160 140 120 Longitude Wind speed -10
p20
ø30
40 -ø50 ktFig. io. Minimum-time route and great circle route of the sail-assisted motor vessel (westbound voyage)
110 H. HAGIWARA AND J. A. SPAANS VOL. 40
each isochrone is calculated with a time interval of 24 hours, whereas the ship's
speed, engine power and drift angle are calculated every i 2 hours. From each point for constructing the isochrone, the ship is sailed following headings C1 ±j x 100 (j = 0, 1, 2,. . . 6), where C1 is the initial course of the great
circle route from each point to the destination.
By performing simulations of minimum time routing and minimum fuel routing for voyages between Tokyo and San Francisco, the effectiveness of weather routing and the advantages of sail-assisted operation are investigated. Hereafter, we use the following abbreviations: Minimum time route, MTR; Minimum fuel route, MFR; Great circle route, GCR; Sail-assisted motor vessel, S-A MV; Equivalent motor vessel, EQ MV.
Simulations of minimum time routing. Using the algorithm stated in section 2, simulations of minimum time routing were carried out. The S-A MV and EQ MV were sailed between Tokyo and San Francisco with a constant number of propeller revolutions (i r.p.m.) departing from both points at 0000 hours GMT on i, ii and 2 i November and i and is December in 1980.
The tracks of MTR and GCR in the westbound voyage (San Francisco -* Tokyo) departing at 0000 hours GMT on ii November 1980 are shown in Fig.
(S-A MV) and Fig. ii (EQ MV). In Figs io and ii, the solid lines and dotted
lines denote the MTR and GCR.
Soil-assisted motor vessel
Passage time Average speed Fuel consumption Minimum time route 3402 hours 135 kt 4611 tons Great circle route 3777 hours 118 kt 5453 tons
30
20-NO. I 60 - 50-0 -1 852088 202.01 .27 40
-WEATHER ROUTING OF SAIL-ASSISTED VESSELS III
Minimum time route Great circle route
Westbound voyage
Equivalent motor vessel
Passoge time Average speed Fuel consumption 3497hours 131 kt 4849 tons 3998 hours 112kt 5970 tons
\\
Departure 0000 hours GMT llNav. 1980 San Francisco 140 160 180 160 140 120 LongitudeWind speed -10 a20
*30
40 --50 ktFig. it. Minimum-time route and great circle route of the equivalent motor vessel (westbound voyage)
The tips, directions and lengths of the arrows attached to both routes represent the ship's positions, wind directions and wind speeds for every 24 hours,
respectively. The isochrones at 1, 3, . . . days and 2, 4., 6. . . days after the departure time are shown by circle marks and cross marks respectively. From Figs io and I i, it can be seen that the MTR of S-A MV hardly differs from the
MTR of EQ MV in this westbound voyage.
The isochrones bend backwards sharply at the south of GCR west of 1700 W.
This is because a westerly gale prevailed in that area and the westbound ship
received strong head winds and high head waves. To investigate these sharp bends of the isochrones in detail, all minimum time routes reaching each isochrone are depicted in Fig. i 2; the thick line indicates MTR from San Francisco to Tokyo. From Fig. i 2 it is found that two minimum time routes exist from San Francisco to the sharp bending points of the isochrones. These bending points are usually
called 'conjugate points' to the departure point. In a case where the destination
corresponds to a conjugate point, two minimum time routes from the departure point to the destination exist. In such a case no matter which minimum time route is chosen, a ship should deviate considerably from the great circle route.
In this westbound voyage, compared with the GCR of EQ MV, the savings of passage time and fuel oil were so i hour, 112-1 ton on the MTR of EQ MV,
22! hour, ç7 ton on the GCR of S-A MV, and 596 hour, 13ç9 ton on the
MTR of S-A MV. These savings are regarded, respectively, as the benefits of
6 7$9O I
30
2060 -50 30 20 - 60- 50-0 a 40- 30-
20-Minimum time route Great circle route
140 160 180 160
Longitude
Departure
0000 hours GM llNov. 1980
Sail-assisted motor vessel
Passage time Average speed Fuel consumption 307 6 hours /4,7 kf 4006 tons 3098 hours 144 kt 4082 tons
Departure
0000 hours GM 11 Nov. 1980
140 120
112 H. HAGIWARA AND J. A. SPAANS VOL. 40
Sail-assisted motor vessel
Passage time Average speed Fuel consumption Minimum time route 3402 hours 135 kt 4611 tons Great circle route 3777 hours 118 kt 545'3 tons
140 160 180 160 140 10
Longitude
Fig. 2. All minimum-time routes reaching each isochrone
Wind speed -10
20 '30
60 50 ktFig. 13. Minimum-time route and great circle route of the sail-assisted motor vessel (eastbound voyage)
NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS 113 weather routing for the MTR of EQ MV, benefits of sail-assisted operation for the GCR of S-A MV, and benefits of weather routing plus sail-assisted operation for the MTR of S-A MV. Hence, in this voyage, it can be said that the benefits of weather routing were greater than those of the sail-assisted operation.
Next, the tracks of MTR and GCR in an eastbound voyage (Tokyo -± San Francisco) departing at 0000 hours GMT on II November 1980 are shown in
Fig. 13 (S-A MV) and Fig. i (EQ MV). From Figs 13 and i it is found that
since the sharp backward bends of the isochrones are not observed, the area of strong head wind and high head waves did not exist in this eastbound voyage.
Compared with the GCR of EQ MV, the savings of passage time and fuel oil were
ii hour, 42 ton on the MTR of EQ MV, 128 hour, 32o ton on the GCR
of S-A MV, and I ç0 hour, 396 ton on the MTR of S-A MV. Therefore, it can
be said that the sail-assisted operation was more effective than weather routing for saving passage time and fuel oil in this eastbound voyage.
Passage times and fuel consumptions on MTR and GCR of S-A MV and EQ MV for the voyages departing on i, i i and 2 I November and i and I I
December are shown in Fig. i (westbound voyages) and Fig. i6 (eastbound
voyages). These figures show that both value and variation of passage time and
fuel consumption in westbound voyages are far larger than those in eastbound
voyages. The mean values of sailed distances, average speeds, passage times and fuel consumptions in five voyages departing every i 0 days are shown in Table i (westbound voyages) and Table 2 (eastbound voyages). In these Tables the time
6050 -0 40- 3020 -852088 202.01 .27
Minimum time route Great circle route
Equivalent motor vessel
Passage time Average speed Fuel consumption 3275 hours 14Okt 436Otons 3226 hours 139 kt 4402 tons Departure 0000 hours GMT 11 Nov. 1980 140 160 180 160 140 120 Longitude Wind speed --10 0.20
0-30
40 ,50 ktFig. 14. Minimum-time route and great circle route of the equivalent motor vessel (eastbound voyage)
Dote of deporture
Fig. . Passage times and fuel consumptions for each date of departure (westbound
voyage). 0 = Minimum-time route; = great circle route; = sail-assisted - = equivalent motor vessel
motor vessel;
-Nov.1 11 21 Dec.1 11
Dote of departure
Fig. i6. Passage times and fuel consumptions for each date of departure (eastbound voyage). 0 = Minimum-time route; S = great circle route; - sail-assisted motor vessel; - - - - = equivalent motor vessel
savings and fuel savings are related to the passage time and fuel consumption of the EQ MV on the GCR. From the tables, it can be seen that, as a general rule, the MTR of S-A MV yielded the largest time and fuel savings. Since in westbound voyages, the savings on the MTR of EQ MV are nearly equal to those on the GCR of S-A MV, it can be said that the benefits of weather routing are on the average equal to those of sail-assisted operation. On the other hand, in eastbound voyages, as the time saving and fuel saving on the GCR of S-A MV are 3 and times
Hours 380 340 I I -- _o--__ ..
-- --==.=_
_. 0 300 0 0. 260 I I I I Tons 500 0. E-
----o_.-. (I, 400 o U. 300 I I I I I 14 H. HAGIWARA HoursAND J. A. SPAANS VOL. 40
430 S... 390 0 0 350 0 0 0. 0 310 1 1 I Tons S_S 600 0. :3 C', 500 0.. 5._So __o.._::--...---.5'. _o__ S U' o :3 400 Nov.1 11 21 Dec.1 11
852088 2020127
TABLE 2. MEAN VALUES OF FIVE EASTBOUND VOYAGES Minimum time routing (propeller rev. = 7 r.p.m.)
larger than those on the MTR of EQ MV, respectively, it is found that sail-assisted operation was more effective than weather routing on the average.
Simulations of minimum fuel routing. Using the algorithm mentioned in section 2, a simulation of minimum fuel routing was executed for the voyage from San
Francisco to Tokyo departing at 0000 hours GMT on II November 1980. The
passage time was specified as 3998 hours, which was equal to that on the GCR
of EQ MV with the number of propeller revolutions being c r.p.m.
A suitable number of propeller revolutions was adopted and then corrected so as to get the passage time as close as possible to 3998 hours. When the passage
time converged to the range of 3998 ± Io hours, the calculation was stopped.
The tracks of the MFR and the GCR are shown in Fig. t (S-A MV) and Fig.
I 8 (EQ MV). It is found that the tracks of MFR In Figs i and i8 hardly differ from those of the MTR in Figs 10 and II. In addition, the shapes of the isochrones of the MFR in Figs 17 and 8 closely resemble those of the MTR in Figs 10 and
II. Hence it can be said that provided the specified passage time on the MFR does not differ largely from the passage time on the MTR, the track of MFR almost
)6i8)O12 Sail-assisted MV Equivalent MV MTR GCR MTR GCR Distance (nm) 4ç7 i 4472 4595 4470 Average speed (kt) i 372 I 259 I 292 1172 Passage time (h) 3332 3568 3558 3828
Time saving (h) 496 26o 270 00
Time saving (%) i 30 68 71 00
Fuel consumption (t) 4407 4970 495.4 çç8
Fuel saving (t) i i8o 617 633 00
Fuel saving (%) 211 1I0 I 13 00
Sail-assisted MV Equivalent MV
MTR GCR MTR GCR
Distance (nm) 4501 447' 4501 4471
Average speed (kt) 1446 142 I I 39 I I 367
Passage time (h) 3112 3146 3237 3272
Time saving (h) i6o 126 3.5 00
Time saving (%) 49 3.9 11 00
Fuel consumption (t) 4099 4200 441 0 4513
Fuel saving (t) 414 3 13 103 00
Fuel saving (%) 92 69 23 00
NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS IIç
TABLE 1. MEAN VALUES OF FIVE WESTBOUND VOYAGES Minimum-time routing (propeller rev. = 7c r.p.m.)
i i6 H HAGIWARA AND J. A. SPAANS 60- 50--a
"-<\
-'++ç.
. a ++ *-r)fr'
I
0 Tokyo 201
140 160 180 160 140 120 Longitude Wind speed -'10'90
--'30
40 '50 ktFig. 17. Minimum-fuel route and great circle route of the sail-assisted motor vessel
60-40
30-
20-Minimum fuel route Great circle route
Westbound voyage
Tokyo
Minimum fuel route Great circle route
Westbound voyage
+t+
Soil assisted motor vessel Passage time Average speed
4000 hours 114 kt
4004 hours 112 kt
Equivalent motor vessel
Passage time Average speed Fuel consumption 3993 hours 115 kt 3941 tons 3998 hours 112 kt 597-0 tons t Departure 0000 hours GMT 11 Nov. 1980 Departure 0000 hours GMT llNov. 1980 Fuel consumption 3128 tons 495-0 tons VOL. 40 Seattle San Francisco 14-0 160 180 160 140 120 Longitude Wind speed *10 '20 *30 '40 50 kt
852088
We also find from Table that the amount of fuel saving by the above half-sail-thrust vessel on the MFR and GCR lies approximately halfway between those by SA MV and EQ MV. Therefore, it can be said that provided the passage time is specified, the fuel saving on a certain route is almost directly proportional
to the sail thrust.
6. cONCLUsIONS. The modified isochrone method to perform minimum time routing and minimum fuel routing was proposed first. Next, the methods
to predict the ship's speed, engine power and drift angle of a sail-assisted motor
vessel in a seaway were described, using a o 000 d.w.t. product tanker with
8o8 m2 sail area as a mathematical model ship. Using those methods, the model ship, and the actual wind, sea, swell and ocean current data of the North Pacific Ocean, computer simulations were carried out to evaluate the maximum benefits of weather routing and sail-assisted operation.
7 78)0 1 2 34567 )OL. MFR GCR MFR GCR MFR GCR Passage time (h) 4000 4004 3996 3998 3993 3998 Distance (nm) 4575 4473 4ç88 4471 4484 4470 Average speed (kt) 1144 1117 1148 1118 1148 1118 R.p.m. 6272 7118 6488 7326 6670 7500 Fuel consumption (t) 3128 4950 3ç57 5486 3941 5970 Fuel saving (t) 2842 1020 2413 484 2029 00 Fuel saving (%) 476
iji
4o4 81 340 00 NO. I WEATHER ROUTING OF SAIL-ASSISTED VESSELS 117 coincides with that of MTR. In other words, a ship following the track of MTR with reduced engine power will have maximum fuel savings. This fact has been verified in other simulations by one of the authors.6' SThe passage times, sailed distances, average speeds, numbers of propeller
revolutions and fuel consumptions on the MFR and GCR of S-A MV and EQ MV are shown in Table . It can be seen that only approximately half the amount
of fuel oil consumed on the GCR of EQ MV was necessary on the MFR of
S-A MV in that particular period.
As shown in Fig. 10, since the passage time and fuel consumption were 34o'2 hours and 46II tons on the MTR of S-A MV, it is found that 148'3 tons fuel oil was saved by the S98 hours extension of the passage time in the MFR
of S-A MV.
In Table , the calculation results for the MFR and GCR of a vessel which
has half the sail thrust and half the sail lateral force of the former S-A MV are
also shown. (The shape of the MFR of that vessel was similar to that of the MFR of S-A MV and EQ MV.)
TABLE 3. SUMMARY OF AN EXAMPLE OF MINIMUM FUEL ROUTING
Departure: 0000 GMT ii November i 980; westbound voyage, specified passage time 3998 hours
Sail-assisted
9012 1 23456 7890123456
i i8 H. HAGIWARA AND J. A. SPAANS VOL. 40
The principal results of the simulations are as follows.
Using minimum time routing rather than the great circle route of an equivalent motor vessel, the passage time of a sail-assisted motor vessel could on average be reduced by 130 per cent (westbound voyage) and per cent (eastbound voyage). At the same time, 21-i per cent (westbound voyage) and 92 per cent (eastbound voyage) fuel saving could be achieved on average.
Using minimum-fuel routing the fuel oil consumption could be reduced
by 47-6 per cent on the minimum fuel route of a sail-assisted motor vessel compared with the great circle route of an equivalent motor vessel.
Provided the specified passage time on a minimum fuel route does not differ largely from the passage time on a minimum time route, the routes are
almost the same.
On a sail-assisted motor vessel, when the passage time is specified, the fuel saving on a certain route is almost directly proportional to the sail thrust.
From these simulations, the effectiveness of weather routing by the modified
isochrone method and the advantage of sail-assisted operation could be verified. Using an IBM 3o83JXI mainframe computer, the calculation time for a
minimum time route on the North Pacific was around o sec, which meets the
requirement for practical weather routing. These simulations are a powerful tool to determine sail performance and sail area to be provided for a particular sail-assisted motor vessel for a particular trade.
As already mentioned, although the added resistance due to waves is reduced
to some degree by the use of sails, this phenomenon was neglected because of
insufficient knowledge. It will be necessary to develop a calculation method for this interesting phenomenon.
For the simulations of this study, the actual environmental data were used to
evaluate the maximum profits of weather routing. In a case where the forecast data are used as a matter of course, those profits decrease to some extent.
A follow-up to this study will investigate the effects on weather routing of the accuracy of the forecasts. At that stage, stochastic processing will be introduced
to the routing algorithm to take into account the uncertainties of the forecasts.
The aim of this follow-up will be to determine a set of routes each with a specified probability of time, fuel and damage saving in order that the shipmaster/owner may make his own choice.
7. ACKNOWLEDGMENTS. The authors are indebted to the staff of
the Hydronautics section of the Department of Maritime Technology, Delft University of Technology, particularly to Professor ir. J. Gerritsma and
ir. J. M. J. Journe for their guidance and discussions on ship's performance
problems. We are also indebted to H. J. de Koning Gans, a student of the above department, for his assistance in making a program to predict ship's speed and engine power in a seaway. In addition, our thanks are clue to Walker Wingsail Systems Ltd in England and especially to ir. 0. Steinert, a member of that company. The performance of the wingsail described in Section 3 was derived from the information offered us by that company.
NO. I
obzUbb LU..Ol.LJ
REFERENCES
RINA. (1980). Symposium on Wind Propulsion of Commercial Ships, 1980, London, Royal Institution of Naval Architects.
2 University of Southampton (1985). International Symposium on Windship Technology.
Southampton. Department of Ship Science.
Faulkner, F. D. (1964). Numerical methods for determining optimum ship routes,]. U.S.
Inst. Navig. 10, No 4.
Dc Wit, C. (1974). Progress and developments of ocean weather routing, Report No. 20! S.
Netherlands Ship Research Center TNO.
Bijisma, S. J. (ijç). On minimal-time ship routing, Report No. 4, Royal Netherlands Meteorological Institute.
6 1-lagiwara, H. (1983; 1985). A study on the minimum fuel consumption route I, II (in
Japanese).]. Japan Inst. Navig. 69; 72.
Frankel, F. G. and Chen, H. T. (1980). Optimization of ship routing, Report NMRC-KP-,89, U.S. National Maritime Research Center.
8 Hagiwara, H. and Makishima, T. (1980). A study on the optimum ship routes (in Japanese),
]. Japan Inst. Navig. 62.
James, R. W. ('95:1). Application of Wave Forecasts to Marine Navigation, U.S. Naval Oceanographic Office, SP-i.
1 Hagiwara, H., Shoji, K. and Sugisaki, A. M. (1981). On the operation of hybrid power (sails and engines) driven ship I - A method of selecting the optimum route of sailing ship (in Japanese),]. Japan Inst. Navig. 64.
Journe, J. M. J. (1984). Report on the development of an on-board energy saving device (in Dutch), Report No. 6o6, Dclft Shiphydromechanics Laboratory, Delft University of Technology.
12 Ishersvood, R. M. (1973). Wind resistance of merchant ships. Trans. R.I.N.A. iii.
Skogman, A. (1985). The practical meaning of lateral balance for a sail-assisted research
vessel, International Symposium of Windship Technology.
NOTE. A further contribution by Professor Spaans relating to Section 2 of this paper will be
printed in the Forum section of the next Journal. Ed.
WEATHER ROUTING OF SAIL-ASSISTED VESSELS 119
1234367890123496 79O 12
S
PRACTICAL WEATIIER ROUTING OF
SAIL-ASSISTED MOTOR VESSELS
by
H. Hagiwara and J.A. Spaans
Reportnr. 718
S
Practical Weather Routing of Sail-Assisted Motor Vessels
H. Hagiwara
(Tokyo University of Mercantile Marine)
J.A. Spaans
(Delft University of Technology)
1. INTRODUCTION
In recent years, many sail-assisted motor vessels have been operated showing remarkable advantages in:
- saving passage time
- saving fuel oil
- damping ship's motions (l),(2)
In order to operate those vessels more effectively in
ocean-crossing voyages, the following requirements should be fulfilled:
accurate forecasts of environmental conditions
(wind, sea, swell and ocean currents) for a sufficient
prediction period
good predictions of ship's speed, engine power and drift
angle (leeway) for the particular vessel for various
con-ditions of draught, trim and environment
a practical algorithm for the computation of a (sub)optimum
route
Up to now, the above mentioned requirements have not been satisfied
simultaneously and the practical weather routing of sail-assisted
motor vessels has not been established yet.
In this paper, the authors propose the methods which meet the
requirements (ii) and (iii). Requirement (i) is not fully met in
steadily. For this study, the actual (observed and
analyzed)
wind, sea and swell data published on magnetic tape by the Fleet
Numerical Oceanography Center of the U.S. Navy are used.
The practical way of computing 'minimum time route' and 'minimum fuel route for a specified passage time' for a sail-assisted motor vessel - which is called "modified isochrone
method" by the authors - is stated in chapter 2.
In chapter 3, the sophisticated methods are described to predict
the ship's speed, engine power and drift angle in
a seaway based
on the equilibrium between resistances and thrusts,
using a 40,000 DWT product tanker with 808 m2 sail
area as a mathematical model ship.
Examples of actual environmental data in the North Pacific Ocean
are shown in chapter 4.
In chapter 5, the computer simulations are performed using the
modified isochrone method with a sail-assisted motor vessel and
an equivalent motor vessel in actual environmental conditions.
By comparing the passage time, average speed and
fuel consumption
of the sail-assisted motor vessel with those of the equivalent
motor vessel, the advantages of sail-assisted operation are
in-vestigated. The benefits of weather routing are also investigated
by comparing the results of minimum time/fuel
route with those
of the great circle route.
2. MINIMUM TIME/FUEL ROUTING
Many optimization methods have been reported to select the
optimum route of a ship in an ocean-crossing
voyage. Those
methods can be classified into three categories:
- calculus of variations (3),(4),(5),(6) - dynamic programming (7),(8)
to converge a route to the destination. Above this, other
diffi-pculties are
inherent in the calculus of variations, so that it can not be a practical method for ship weather routing (6).In spite of the fact that dynamic programming is a very powerful optimization technique, it needs many grid points for the search routine to obtain the accurate solution and it takes a lot of
calculation time and memory space.
The isochrone method, since it was proposed by R.W. James (9), has been used in many weather routing facilities as a practical (hand)method to obtain the minimum time route. The method proposed by James, however, does not give us the correct isochrones in
a strict sence, and it is less suitable for computerization. In this chapter, the algorithm of the modified isochrone method
is described, as earlier proposed by one of the authors (10).
Calculation of the correct isochrones with this method is
straight-forward and very suitable for computerization.
2.1. Minimum Time Routing
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. The algorithm of the modified isochrone method to calculate the minimum time route is as follows.
(i) Simulate the navigation of a ship for At hours from departure
point X0, following headings C0 iAC (i =
where C0 is the initial course of the great circle route
from X to Xf and AC is the increment of heading. In each
heading, ship's speed through the water, engine power,
drift by wind (leeway) and drift by ocean current are cal-culated as a function of forecasted environmental data,
ship's heading and number of propeller revolutions.
The calculated arrival points at time to + At are represented
by X1(i) ( i = 1,2,---, 2m + 1).
The set { X1(i) } defines the isochrone at to + At.
Let X1(i) be the departing points at to + At.
Navigate the ship for At hours from each X1(I),
following
headings C1 ± jAC (j = O,l,---,m), where
C1 is the initial
course of the great circle from each X1(i) to Xf.
The calculated arrival points at to + 2At
are represented
by X2(i,j)
(i,j = 1,2,---, 2m + 1).
Then calculate the lateral (cross-directional)
deviations
D2(i,j) of X2(i,j) fromthe great circle
route connecting
X0 and Xfwhere D2(i,j) is negative
on one side of the great
circle, and the remaining great circle distances R2(i,j)
from X2(i,j) to the destination Xf.
Now, define a lane of width D on each side
of the great
circle from X0 to Xf and divide each lane in
P sublanes of
width AD; the sublanes are numbered by L(k),
where
k = -P, -P+1,----,-1,+1,---,P-1,P. The lateral
deviation
D2(i,j) identifies the sublane L(k)
to be assigned to each
X2(i,j).
From all X2(i,j) included in each sublane L(k),
the X2(k) is
selected with minimum R2(i,j).
The set
{X2(k)
}(k = -P,-P+l,---,-1,+1,----,P) defines the
isochrone at to + 2At.
Changing argument from k to 1, let X2(i) be the
departing
points at to + 2At.
Navigate the ship for At hours from each X2(i),
following
headings C
± jAC
(j = O,l,---,m), where C
is the initial
course of the great circle from each X2(i) to Xf. The
calcu-lated arrival points at to + 3At
are represented by X3(i,j)
(i
-P,---,-1,+1,---,P;
j =l,2,---72m+l).
Same as stated in (ii), calculate D3(i,j) and R3(i,j)
for
all X3(i,j). Gmparing R3(i,j) of all X3(i,j)
included
in each sublane L(k), find X3(i,j) having
minimum R3(i,j)
and represent it by X3(k).
The set {X3(k) }
(k = -P,---,-1,+1,---,P) defines the
-5
Cv) When the isochrone{Xn(k)}at time to + nAt approaches the destination Xf sufficiently, navigate the ship along
rhumb-lines from Xn(k) to Xf and calculate the passage times
Atn(k) between Xn(k) and Xf.
The minimum passage time is given by Mm { nAt + At(k) }.
Represent Xn(k) giving that minimum passage time by
Xn
(vi) By tracing the isochrones memorized inthe computer back-*
* *
ward ,the minimum time route Xf X, X1, X0 can
be obtained.
The accuracy of this modified isochrone method can be increased by
decreasing the width of sublane AD. Since the number of arrival
points constructing an isochrone after each interval does not
exceed 2P = 2D/AD, the amount of calculation is always kept within a certain feasible limit.
In addition, this method can easily take into account the limits
of the navigable area and voluntary speed reduction to avoid
excessive ship's motions.
In the actual minimum time routing, since the forecast data of
wind, sea and swell are updated every 12 or 24 hours, it is
ne-cessary to recalculate the minimum time route by using the
up-dated forecast data and ship's position at updating time as a
new departure point.
2.2. Minimum Fuel Routing
Consider a ship departing from departure point X0 at time to and
arriving at the destination Xf at time tf and let us minimize
the total fuel consumption during the voyage. In this problem,
the arrival time tf is specified and the passage time
T = tf - to 5 fixed.
From the mathematical point of view, as ship's heading and number
of propeller revolutions (or engine power) have to be controlled
simultaneously in minimum fuel routing, the problem becomes more
complicated than in minimum time routing. In actual ocean-crossing voyages, however, it has been found by simulations that the control
power to minimize the total fuel consumption (6).
)
Therefore, from the practical standpoint, the authors proposethe following algorithm to perform the minimum fuel routing.
Ci) Setting a suitable number of propeller revolutions, calculate
the minimum time route and minimum passage time Tmin by
using the modified isochrone method. In this case, Tmin is
a function of the number of propeller revolutions.
Correct the number of propeller revolutions so as to get
Tmin close to the specified passage time T = tf - to.
Using the corrected number of propeller revolutions,
re-calculate the minimum time route and minimum passage time
Tmin.
If T - Tmin
f becomes small enough , stop the calculation.
Otherwise, repeat the procedures in (ii).
The calculated minimum time route can be regarded as the minimum fuel route for a specified passage time. Newtonts method or
regula-falsi method can be used for the correction of the number of
propeller revolutions.
The minimum fuel route calculated by the above algorithm is not
an optimum from the mathematical viewpoint, however, it may be
sufficiently optimal from the practical viewpoint. In the
actual minimum fuel routing, as stated in 2.1, it is necessary
to recalculate the minimum fuel route whenever the forecast data
of wind, sea and swell are updated.
3. PREDICTION OF SPEED, POWER AND DRIFT ANGLE OF A SAIL-ASSISTED MOTOR VESSEL IN A SEAWAY
The methods to calculate the speed, engine power and drift angle (leeway) of a sail-assisted motor vessel in a seaway are stated
A profile and main dimensions of the model ship are shown in Fig. 2
Hereafter, the model ship is assumed to be in full loaded condi-tion, i.e. draught = ll.4m,and even keel.
3.1. Prediction of Ships's Speed
The longitudinal resistance of a sail-assisted motor vessel pro-ceeding in a seaway mainly consists of:
still water resistance
wind resistance
added resistance due to waves
On the other hand, the longitudinal thrust consists of: propeller thrust
sail thrust
The speed of a sail-assisted motor vessel can be calculated so as to perform the equilibrium between above resistances and thrusts. First, the methods to calculate above resistances and thrusts
are mentioned below (11). (i) Still water resistance
The still water resistance Rstw is calculated by
Rstw = ½ S V2 (1)
where : density of sea water
CV : resistance coefficient
S : wetted surface of ship's hull
V : ship's speed
C consists of the coefficients representing the frictional
resistance, residuary resistance, etc., and is a function of ship's speed, draught and trim. S is a function of
draught and trim.
Rstw of the model ship is 84, 385, 1069 kN for the ship's
where density of air
CWF: fore and aft wind force coefficient
AF : transverse projected area of the above
water part (excluding sails) UA : apparent wind speed
CWF is a function of the apparent wind direction from the
bow For the model ship, CWF was calculated based on
the method by R.M. Isherwood (12). The CWF versus
A curve of the model ship is shown in Fig. 3.
AF is a function of draught and trim, and is 560 m2 in the
model ship.
When the model ship meets a wind of UA 25 and 50 knots
from right ahead, Rwifld becomes 59 and 237 kN respectively. (iii) Added resistance due to waves
The added resistance due to waves Rwave while a ship proceeds in irregular waves with a cosine squared directional spreading can be calculated by
Rwave = ( Rwave/H H
where ( Rwave/H2 added resistance per unit significant
wave height squared HW: significant wave height
For a given draught and trim, ) is a function of
the ship's speed,wave direction from bow and average wave
period.
In the model ship,( Rwave/Hj ) were calculated as a
combi-nation of linear expressions of average wave period for the ship's speed of 2,5,8,---,20 knots, and wave direction from
(ii) Wind resistance
)
The wind resistance Rwind is given byWhen the model ship proceeding at 14 knots meets the waves
0 0 0
(Hw = 7 m , average period = 10 sec) coming 0
, 60 , 120
1800
from bow, Rwave becomes 751, 434, 158, 213 kN
respec-tively.
In general, since the ocean waves consist of sea (wind wave)
and swell, Rwave can be calculated as the sum of the added
resistance due to sea Rsea and the added resistance due to
swell Rswell.
Rwave = Rsea + Rswell
Besides above mentioned three principal resistances, there
exist the added resistance caused by rudder and the added
resistance caused by drift. These resistances, however, can
be regarded as sufficiently small compared with the three
principal resistances, therefore we neglect these secondary
resistances in the calculation of ship's speed.
Furthermore, in a sail-assisted motor vessel, the added
resistance due to waves may be reduced to some extent as
a result of the damping of ship's motions by using the sails.
The method to calculate the amount of such a reduction,
how-ever, has not yet been established, so that we neglect that
phenomenon too.
The effects of neglecting the added resistances caused by
rudder and by drift will however cancel the effect of
neg-lecting the reduction of added resistance due to waves by
the damping of ship's motions to some degree.
(iv) Propeller thrust
The propeller thrust Tprop is calculated by Tprop = (1-t) KT
D N2(5)
where t : thrust-deduction fraction
KT : thrust coefficient
density of sea water
D : propeller diameter
N : number of propeller revolutions per second
In case N is kept constant, thrust-deduction fraction t
increases as the ship's speed increases (i.e. as the loading
of the propeller decreases)
; t changes also with draught and
x A S
10
-Thrust coefficient KT is the monotonically decreasing function of advance ratio J which is defined by
V(l-w)
ND
where, V is the ships speed and W is the wake fraction;
w changes with draught and trim.
When the model ship proceeds at 5, 11, 17 knots with N =
1.25 r.p.s., Tprop becomes 1218, 847, 429 kN respectively.
(v) Sail thrust
The sail thrust Tsail is given by
-1
sail
-where density of air
C< : sail thrust coefficient
A : sail area
UA : apparent wind speed
As shown in Fig. 2, tn-plane wingsails are installed on
the forecastle and the bridge of the model ship. This
tri-plane wingsail possesses a lift coefficient 3.3 and drag
coefficient 0.8.
C is a function of the apparent wind direction from the
bow 3A . The C versus 13A curve of the model ship is shown
in Fig. 5. In this C.versus
13A curve, the interaction
between sails and hullas well as the interaction between
force wingsail and aft wingsail are taken into account.
In stormy weather, it is necessary to protect the sails
against an excessive aerodynamic force by reducting the
attach angle of sail to the wind. In formula (7) when UA
exceeds 20 rn/s and the sign of C is positive, Tsail is
assumed to be equal to the sail thrust for UA = 20 rn/s.
For a sail-assisted motor vessel proceeding in a seaway
at constant speed, the sum of resistances (i), (ii), (iii) has to be equal to the sum of thrusts (iv), (v).
Rstw + Rwjfld + Rsea + Rswell = Tprop + Tsail ---(8)
If the ship's heading, number of propeller revolutions and
wind, sea, swell are given, each resistance and thrust in
equation (8) becomes a function of the ship's speed.
Hence, the ship's speed through the water can be calculated
as follows.
Li) Assuming a suitable ship's speed, calculate both sides
of the equation (8).
2) Correct the ship's speed so that the difference between
both sides may become smaller. Using corrected ship's
speed, recalculate both sides of (8).
13) Repeating the procedures in (2) , find the ship's speed
which satisfies the equation (8).
An example of the speed of the model ship calculated by the above mentioned method is shown in Fig. 6. In Fig. 6, the speeds of the model ship (sail-assisted motor vessel) and the same ship without sails (equivalent motor vessel) are
shown by solid lines.
It can be seen from Fig. 6 that, for the true wind direction
between 7Q0 and 1300, a sail-assisted motor vessel can sail
2.5 - 3.5 knots faster than an equivalent motor vessel.
Since the sails do not generate thrust for true wind
direc-tions between 0 and 150 and they increase the wind
resis-tance, the speed of a sail-assisted motor vessel becomes slightly smaller than that of an equivalent motor vessel.
3.2. Prediction of Engine Power
When the number of propeller revolutions and ship's speed are given,
