IR.I. ¡EF
THE SOCIETY OF NAVAL ARCHItECTS AND MARINE ENGINEERS
74 Trinity Place, New York, NY. 10006
Paper to be presented at its Diamond Jubilee International Meeting, New York, N.Y., June 18-21, 1968
The Braking of Large Vessels
By H. E. Jaeger,' Visitor, and M. Jourdain,2 Visitor
The braking and stopping of large vessels have become more and more difficult because of the ever-increasing size of modern bulk carriers and tankers. The authors have studied
this problem for more than five years, and the results of their collaboration are given ¡n this paper. They show the possibilities of braking large ships by means of the screw-propeller, the rudder, or special braking devices like braking flaps installed at the fore-side of a ship. Many model tests were made to check "crash-stop" trials at sea. These tests are reviewed. Also, attempts to explain the mechanism of stopping are made and
the correlation between real ship stopping and model tests is: investigated.
Infroducfion
THE SHIPOWNER, when taking overanew ship from the
yard, requires that mäny tests shall be made to show
that the ship fulfills the conditions which he wants her to meet. One of these is the "crash-stop" test, which has become möre and more important as ships grow in size. It has been recognized generally that the headreach or stopways of large tankers have become quite imprac-ticably long; distances of more than three miles have been measured while trying to stop tankers of more
than 100,000 tons deadweight on a straight course. The Institut de Recherches de la Construction Navale in Paris therefore took in hand a series of stopping and maneuvering tests during the sea trials of large tankers with the intention of studying stopping conditions it detail and of analyzing the results.
At the same time (1961) the Netherlands Ship
Re-search Centre followed up a suggestion of the first author that model tests of a new hydrodynamic brake system should be. made with à view to achieving an efficient means of braking these large vessels. As a result, both
the French and the Dutch research
institutes have worked together for many frars to solve this problem and have exchanged their results in close collaboratiön. The most important of these were published by théATMA' between 1962 and 1967, during which time tank-ers became even larger.
'Professor of Naval Architecture, Technological 1Jni'ersity of
Delft, Delft, The Netherlanth. - i?
'Director of the French Shipbuilding Research Institute, Pans, France.
3Association Technique Maritime et Aéronâutiqtie, Paris.
-Las y.
Sckeepsbouwkunde.
Technische
Hogeschool
DeiIt
no.11
One of the goals of these studies was to envisage the braking qualities which future tankers should possess, taking into account their working conditions.
The first step was to try, to determine the correlatiön between the results of model tests and of real sea trials; consequently extensive model tests were carried out in the Netherlands Ship Model Basin at Wageningen and, in the
Model Basin of the University of Delf t on a French tanker, which was the subject of extensive braking and stopping trials at sea. Furthermore, the 'influence of
lim-ited depth of water under the keel was investigated. These large ships will in fàct largely operate in harbour entranceswith shällow water while they are maneuvering to enter port, and here the necessity for emergency crash-stopping may easily arise. This problem was studied at sea and in the model basin..
The ATMA papers are summarized herein, and some more recent införmation is given.
The Setting of the Problem
To stop a ship, obviously it is necessary to eliminate its kinetic energy (1/2rn V2) when under way, which means that the mass and the initial speed of the vessel are pre-dominant. The mass is proportional to the displacement, and in ballast condition that displacemeñt may be reduced to about half its value in loaded condition. For all big tankers the service speed is about the same, about 16 knots. Especially when entering port and during maneuL vering, the 'advance speed may fall to a low value, - the initial speed of the "crash-stop" manèuver.
n
z
E
G
2
publications on the subject have come forward, especially in the United States [1, 2].
Elimination of the aforementioned kinetic energy is accomplished by means of thé hydrodynamic hull resist-ance and propeller thrust under backing conditions, inso-far as wind and sea effect and exterior forces acting on
the ship are ignored. The hydrbdynamic phénomena also depend On the depth of water, where this has it's rátio to the ship's draft dosé to unity. if thé efficiency scattering while gOing astern is neglected, it may be'adrnitted that
the propeller thrust under baci ing conditions is propor-tional to the available backing power delivered by the screw propeller. This backing power depends of course on the engine power installed and on the type of machinery. But in going astern another element must be taken into account: the time in which the available backing powr becomes effective. This time depénds both on the type of machinery and on the way in which it is maneuvéred.
If this simple scheme iS accepted as an approìimation, an elementary calculation shows that, on the basis of a given initial, speed,. the stopping, time and te stopway are proportional to the length, for ships of the same type An experimental study might enable us to estimate the degree of validity of this approximation if the ship's proportions and the shipform vary within the usual limits This study also provides evidence of the influence of the process of maneuvering the engine. On the other hand, the factors whose influence is difficult, to estimate theoretically-that is tQ say, the displacement in ballast, the initial 4Numbers in-. bra'ckets designate Rferençes at end of paper.
Fig. i "Natural" slowing-down trial of tanker A
11-2 The Brakiñg of Largé Vessels
100 C 50 E s £ 41 E
speed, and the depth of the watermust also be
investi-gated.
Finally, special braking installations were also studied in the model basin, and an attempt made to temporarily increase the ship's resistance by means of hydrodynamic braking-flaps. The use of the rudder as a braking facility was also studied at. sea.
Sea TriaÍs '
The sea trials were carried out under favorable -condi tions so that different aspects of the stopping character-istics could be studied. All the ships tried were single-screw turbine tankers, varying in déadweight from 50,000 to 100,000 tons (toné of 1000 kg). Most trials were made in the loadéd condition.' Three of the ships were sub-mitted to more extensive triáIs.
Tanker A (length 217m) was tried at three displace-ments (66,000, 49,000 and 38,000 tons of 1000 kg). The initial speed and ihe type of maneuvers were varied. One trial, theso-called "natural" trial, was executed by stop-ping the- screw propeller in order tó isolate the. influence of- the hydrod3,namic' resistance.'
Tanker D (length 220 m) was tried at a constant dis placement of 67,000 toils of 1000 kg in a series of special trials in ordér to study the influence of rudder maneu
vering.
' -'
Tanker E (length 238 m) was tried at a constant dis-placement of 89,000 tons if 1000 kg in. a series of trials designed to -stUdy the influence of the initial speed.
A few otheì tankers were tried, normal crash-stop tests only being executed.
maneuvering without excessive hurry. The thrust
indica-tions, not measured at these trials, are deduced from
analogous trials conducted with other ships.
Compared with the "natural" trial, the essential differ-ence is that the direction of rotation of the propeller shaft is changed in about one minute, the torque becoming rapidly negative at about one third of the initial posithre value. Notwithstanding this, the maximum initial decel-eration remains of the same order as with the "natural" trial, Fig. 2 representing a good mean value.
After its first maximum, the decelerationdecreases_very rapidly during the first five thinutes, though the number of revolutions and the applied torque are very important. As during thisperiod the evolution of the speed is quite in
conformity with that of the" "natural" trial, the con-clusion must be that the developed torque to the pro-peller has hardly any effect as regards the braking of the
vessel.
There are great fluctuations in this torque, and the same applies to the thrust. Thèse fluctuations are less marked if the number of revolutions remains constant, and they increase in importance when an attemptis made to modify the number of revolutions. The irregular func-tioning of the propeller in this respect has been studied in [8]. Though this irregular functioning induces intoler-able vibrations, it may be asked whether, if they are kept within bearable limits, there is not an advantage in brak-ing more quickly. The answer to this suggestion is given in Fig. 3.
This figure relates to a trial with tanker D in load; the number of revolutions decreases constantly, without variations, the evolution of the speed being of the same typè às in Fig. 2, and the initial deceleration decreases for 8 mm, while the revolutions then increase to a con-stant rate. The moment the number of reverse revolutions has reached a maximum, the torque, the thrust, and the deceleration decrease. After five minuïtes, Fig. 2, or about eight minutes, Fig. 3, the number of revolutions remaining
constant, the disturbance dies off - the fluctuations disappear, the torque and the thrust increase till they reach the normal level, the slowing-down increases pro-gressively, and the speed is reduced towards 'zero. .These latter phenomena well illustrate the final period of stop-ping. During this period only, the breaking of te vessel depends' directly on 'the applied astern power of the
propeller.
'.:
'-The authorshave tried tó arrive at a simple theoretical approach to describe- these trials. They -have considered the vessel, not taking into account the entrained mass of water. Therefore -the mass M is constant and sharply defined. Thé measùrement of the sp'éed V à 'a fundion of the time make it' possible to express the slowing down as
dV/dt,'andthé braking force K is given 'by - '
-.
. K
MdV dt
(Note.: This definitioh is.,not the same as the one 'given in the chapter concerning' the analysis of the mòdel' tests
The Braking of Large 'fesselÑ .11-3
With ships A, D, and E, the headreach was measured by simultaneously measuring the headings indicated by the gyrocompass and the distance covered at sea, the latter by means of a Pitot log during that time and as a function of it. Certain ships had their stopping way measured by radar or by Decca Navigator.
In ships A, D and C, the latter being a tanker of
246.5-m length and 95,000 toñs of 1000-kg displacement, strain-gages were installed to record the torque and the thrust. The number of revolutions of the screw-propeller and the characteristic moments of changing the maneu-vering of the machinery and the steam pressure were recorded also. All the detailed results of, these trials and experiments have been published in ATMA publications
13-61.
"Natural" Trial of Tanker A
As the command "going astern" cannot be followed up immediately, there is always an initiài phase, more or less long, during which the slackening of the speed is caused only by the hull resistance. This way of slackening will be called "natural." Therefore, as a basis of comparison, the natural slowing down of the ship, with cutoff steam and propeller turning slack, was measured in the afore-mentioned "natural" trials.
Figure 1 gives the results of these trials carried out with tanker A in ballast. It is clear from this figure that during the first half-minute the number of revolutions and the torque decrease very rapidly; but, while the number of revolutions decreases more slowly after it has reached about half its initial value, the torque remains thereafter practically constant and practically zero. Furthermore, other trials were carried out from which it appeared that the evolution of the thrust is analogous to that of the
torque, except that the final values are slightly negative. Gradually, the number of revolutions decreases very slowly and uniformly and the torque and the thrust re-main constant. During these "natural" trials, the speed decreases sharply during the first minute, the deceleration reaching a maximum of 0.018 rn/sec2 at the end of that period. At the end of the trial the deceleration was low and the slow evolution of the speed was analogous to that
of the number of revolutions. On the other hand, the transitional period for the speed was much longer and
I
more progressive than for the number of revolutions. There are all kinds of fluctuations in the deceleration of the vessels, caused probably by the wave system generated
by the ship itself [7]. It will be seen from Fig. i that
the speed decreases during the first minute by 10 percent. In two minutes it is reduced by 20 percent, iñ three by 30 percent, in five by 40 percent, and in ten by .abput 60 percent. A further deduction from the test, results is that merely through hydrodynamic rçsiance,, the vessels lose about one fifth of their kinetic enegy in one minütè, about one third in two minutes, nd. about half i three
minutes. '
Convenfionät Trials
In Figure 2 the results. of a' measured conventional trial with tanker C are' given. This trial, was" carried out b3'
u
m
E
>
for the study of the correlation between model and ship by means of the quasi-stationary method.)
This braking force is the resultant force parallel to the axis of the ship and consists of: the total of all forces of whatever kind exerdsed by the water on the propeller and the underwater hull. This force K is arbitrarily
broken down as follows:
K=T+R+W
where:
T = resultant fòrces taken up by propeller ñorninal resistance of underwater hull
W complementary resistance of underwater hull These symbols are defined as follows: T is at every moment equal to the thrust transmitted through the thrust block to the ship this thrust cañ be measured and
there-fore is well defined. R is defied at every determined speed as the force. neessary to maintain the vessel at
02
OEa'
PRESSURE (Pr)
PHESSURE ADMISSION OF STEAI4PRESSURE TO THE TURBINE TURNING ASTERN
Fig. 2 Conventional "crash stop" trial of tanker C
TIME(mm) 30_ 20_ 10_ 200 150 100 50 E
at
.0 -100that speed. It is the normal hydrodynamic resistance aug-mented by the thrust deduction forces. By measuring the thrust at different stationary speeds, it would be possible to determine this nominal resistance. As this was not done in these trials, it is assumed that the thrust is proportional to P. The value measured at the initial speed is chsen
as a basis. W = K - T - R and represents globally
the forces of every kind working on the underwater hull subject to the fluctuating character of the flow.
Fig. 4 is deduced from Fig. 3. It represents the
break-down of this normal trial
into braking force K =
M (dv/dt), thrust T, nominal resistance R, and the
süth of T + R,.. The difference between K and T + R gives an estimation of the complementary resistance W. Fig. 4 makes it possible to subdivide schematically the stopping maneuver into three parts, indicated in that
figure,. giving three successive comparable periods:
100 75 50 25 e C -25 -50 200
During the first_period Fig. 4, the thrust T is reversed and then attains progressively a value of the order of importance of the decreasing nominal resistance R. The
complementary resistance (K T R4 = W is great.
During the secoid eideriod when T has become as great as
R, both forces decrease more or less together, as if some interaction between them makes them follow the same law. The complementary resistance W is small and
nega-tive. During the third period, the nominal resistance having become snTál1ë and smaller, the thrust becomes bigger than this resistance and grows till it reaches the normal thrust for the number of revolutions astern. The period ends when L + T T or R,. = O. During this end period the complementary resistance is uncertain and
feeble.
During the first period, the speed decreases by one third over a distance of about 40 percent of the head reach. At the end of the second period, about 80 percent of the stopway has been covered and the speed is reduced to about one half.
At all normal trials it was found that these values differed little, while the parallelism between thrust and resistance during the second period was always present. This remarkable particularity is probably related to the effect of the suction of atmospheric air in the propeller (ventilation) as explained by Bindel and Garguet [8].
Thus the slight influeúce of the astern power installed ma ship may be explained. In fact, this power cannot be important during the first period, when it grows slowly
Fig. 3 Conventionál "crash stop" trial of tanker D
The Braking o o o 100 80 . 60 Q ¿0 C 20 120 0 ' ciç.ii OtW\ 10 B 6 0.06 11.
and progressively, nor during the second period, when the growing of the thrUst is braked off. It can only become fully effective in the third period, but this period only consists of 20 percent of the stopway and every gain
will be only a small part of the whole way. Therefore, one
can say that the hydrodynamic stopway of a ship depends
,-(,
on the design of the submerged part of the hull and not on the power installed in the machinery.9j1.I
JV.t (.
of Large Vesselsj
- f i l'-5 , 'J!!1!.I
80 0_
¿0U
!-_ TIME
;
2L'
IO H'
/
-80osai°
-120 MI4BER OF RE ÌONS(ñ) I\'
K BRAKING FORCE R_ NOMINAL RESISTANCE I\.
/\
'.1 I, i Ql j\
'
I ilit'-
I A jj
ii IÎ.-_' U
i '7 ¡ :-'.
''
\t-1' ROD 2' RIOD D 2 e S-E > o 0.01. B 10 12 0 2 4 6 TIME (mm)16
12
11-6
Two small observations mús'be made: First of all, it is essential, when stopping a ship with its machinery, not
to lose time between the .ordèr "full astern" and the execution of that order. Otherwise one prolongs the first period unnecessarily This supplementary "dead time" is an explanation of the great dispersion observed in "crash-.stop" trials at 'sea. Secondly, as mentioned in the foré-going, ,at the beginning of the third period the speed is about half the initial speed. Now, if' this initial speed is only about half full spèed (vessel in harbor, in fog, and so on), the first and second periods are, appreciably re-duced and the thrust availáble may be used more efficient-ly and more quickefficient-ly. As seen in Fig. .5 and as discussed in [6], the stopway curves, wheñ starting from diffèrent initial speeds, cannot be superimposed. On the other hand, the influeñce of the 'initial speéd on the stopping time and the stopway is considerable, Fig. 6.
Itmay be deduced from this last figire that, with initial speeds of the order of magnitude of the full service speed, the stopway is approximately proportional to that initial
o
o
'The Braking of Large Vessels
Tank-er (tons) L,,, (in) V, (kn) t (sec) D (m) A ' 3805Ó 217 153 585 2155 A 6637Ó 217 ' i73, 735 2930 A' 62500 217 16.8 660 .2575 A" 35000 217 ' 18 490 2310 C. 954òò 246.5 17 645 3200 C' 95400 246.5 15.5 770 3070 D 67250 222 17.25 810 3590 'E' 88835 238 '16.5 815 ' 330 F 62560 215 16.5 465 2150 G 103780' 258.5 16.6 '960 3300 £000 3000 15 2000 10 C C u. u, E s C e E 1000 D,6 (in)
a
(mf se&) D,6/L Track Observa-tiòns 2250 0.013 10 Quarter of a circle 2710 0012 ' 12.5 Half-circle 2400 0.013 11 Half-circle 2050 Ô.O1 ' 9.5 Quarter of -'adrcle Windf orce 7, - 'Rough sea 3000 0.013 12 Quarter of a circle 3170 0.010 13 Slight curvature Windforce 5, Rough sea 3330-' 0.011 15 Slight S-curve Windforce4, - Rough sea 3200 0.010 13.5 Half-circle -2080 0.018 9.5 Half-circle 3180 0.009 12.5 Half-circle Windiorce 4, Rough seaTäble 1 Summary of Conventional Trials
= displacement D stopway A' and Ä' are sister-ships
(tons of 1000 kg) D, stopway 'corrected of'A
V., = initial speed for a basic speed C' is a sister-ship of' C t = stopping time of 16 knot
0 5 10 il 20
V0 (knots)
Fig. 6 Tanker D. Influence of initial speed on stopping-time and stopway
speed. If this is so, then the normal triáIs executed at different speeds may be brought back to a basic speed, as is done in Table 1, where this basic speed is taken as 16 knots. In this table the stopping times and stopways are indicated, not taking into account the aforementioned "dead time." The stopway Dis measured along the track covered by the vessel. The stopway D11, is the length of the path ':as corrected for' an initial speed of 16 'knots. 'The modalities of, the maneuvering of the engine are not taken into account, as it is already proved that the astern-power used has not much 'influence. The mean deceleration
of the,, ship (dV/dt) and the ratio D11/LPP are
indi-cated.:
With regard to the' track of the vessel while stopping,'
2 1. 6 10 12 14
TIME ;c nun)
it is well known that, while working with an astern-turning propeller, the ship cannot be steered by the rudder. There-fore the rudder was always blocked in the middle position
at all the trials. The tracks observed, which are com-pletely erratic, are indicated in Fig. 7. This figure gives observed tracks for tankers analogous to tanker A. The turning circles for this latter ship are also indicated. Furthermore, the geometrical endpoints of the path cov-ered by the vessel after 12-min of maneuvering are indi-cated, and the limit line of these endpoints gives an idea of the area into which the ship may run while stop-maneuvering.
It can be seen from Table i that, for the loaded vessels (F and A'), the shortest stopways have semicirculär paths, the longest stopway (D, = 15 ships' lengths) following nearly a straight course. This seems to be so in most of the cases. Many stopways were measured and found to be be-tween 12 and 13 ships' lengths for loaded tankers and about 10 ships' lengths for tankers in ballast. Another
re-markable point is the constancy of the mean slowing down, which remains of the order of 0.01 m/se'c2. The published figures fOr the Idemitsu Maru [9] are of the same order: stopway 15 ships' lengths, deceleration 0.07 rn/sec2 for a,
vessel twice as large as the biggest ship tried.
The conclusion tO be drawn from these triàls is that a captain of a large tanker who gives the order, "füll-astern" to brake the ship takes a considerable risk. För nearly a quarter of an hour he will be incapable of either steering his ship or regulating his speed. He is at the mercy of any fixed or floating obstacle within the area indicated in Fig. 7. The tankers tried were only of 60,000 to 110,000 tons dwt. But the risks will grow with the dimensions of the vessel. It has already been stated and proved that the ad-vantages to be expected from more elaborate maheuvering or greater astern power from the engine are insignificant. TherefOre, two series of special trials were carried out in the hope of solving this problem.
Use of Rudder for Stopping Purposes
Fig. 7 suggests that if, before reversing the propeller, the rudder is turned, the ship in its gyration would have a more definite course. Furthermoré, such a maneuver With a large rudder angle would be of considérable use in
brak-ing the vessel. The special trials executed with tanker D and described in [5] confirm this. The half circles of the course go over into the tangent at this circle, opposite to the initial heading. The stopway in the initial direction' becomes about three ships' lengths; the lateral transfer about five. The total length of the track is about 10 ships' lengths.
The -aforementioned extra brake effect increases the deceleration to 0.018 rn/sec2 and decreases the stopping time to about 7 min fOr initial speeds superior to 17 knots.
Use of,Reduced Initial Speed ' '
Another obvious solutiOn consists in reducing the speed and thus beginning the maneuver with a' lower ihitial speed. The question is how to know the quantitative
in-2 7 6, 300Dm '--S--min 200Dm min
Fig., 7 topping tracks
fluence o,f reduced speeds, as these are used in practice during the fog.
Special trials of this sort have been carried out with tanker E and are described in [6]. The results are 'also given in Fig. 6. With an initial speed of between 10 and 16 knots, the stopping remains practically proportional to that speed. With véry low speeds, the variation is para-bolic. At 10 knots initial speed, the' stopway is still eight ships' lengths, at 5 knots initial speed it is hardly more than two ships' lengths.
Influence of Depth of Wafer
Another special trial, which has not yet been carried out, will try to establish the influence of the depth of water under the keel. These large vessels will always be on re-stricted depths when coming into harbor, alongside
quays, and so on. It should be noted that this sort of trial
is only f interest at 'very low speeds. As it is' more a
ques-tion of maneuvering than of braking of large vessels, it, must be looked into more carefully and in more detail
elsewhere.
Braking of Large Vessels by Propeller: FirSt
COn-clusiOns " '
In view of what hâs been said in the foregoing, a general solution 'of the braking problem seems at first sight some-what uncertain, Still, some preliminary conclusions can
be drawn. '
The course of a large ship during stopping by means óf the propeller put into reverse is absolutely àrbitrary and cannot be changed 'by the rUdder from the moment the engine turns astern. Only when a definite turning
move-ment is 'given to the wholé ship before the propeller 'is put into reverse will the vessel follow the direction of the rudder. The ship will then follow a predetermined track,
-S S-'S
S-'
\ S S -S---''
-SS S S,i'i'
7Fig. 8 Perspective drawing of model ship in the shallow-water laboratory of the Netherlands Ship Model Basin
which looks like a change for the better but which track can only be used when the turning side is "free." As stated earlier, the stopway is very little influenced by the engine's maneuvering and developed power while going astern. This is less true when the speed is reduced.
In all cases, the main effect of an increase of backing power is to decrease the duration of the final phase or third period. But, owing to the small values of the speed during this period, the influence on the stopway remains very moderate.
If the tactic of beginning to turn with the ship just be-fore braking is considered impractical, then the fact re-mains that for large vessels with an initial speed of 16 knots a stopway of about 13 ships' lengths must be reckoned with. Moreover one has to count on the erratic course of the ship.
The foregoing figures are reduced to about ten ships' lengths in ballast condition with full initial speed, and eight ships' lengths on full load at 10 knots initial speed. But only with a very slow initial speed may a real shorten-¡ng of the stopping way be expected.
The influence of shallow water is probably important, but no quantitative nor qualitative data are available for the moment.
Model Trials
Purpose of Model Trials
The aforementioned rather definite first conclusions have induced the authors to try to obtain more informa-tian by executing trials on models. Even before the results
of the systematic sea trials were analyzed, trials with
models were made. Some of these complete the study of the influences detected at sea trials; others make it pos-sible to study solutions which do not occur on any real ship; finally, several such tests were carried out to try to find a correlation between the model and the real ship, so as to arrive at comparative predictions on the behavior of future vessels.
During the six years that model tests were carried out
11-8 The Braking of Large Vessels
QUAY
Fig. 9 horizontal section of the shallow-water laboratory
of the Netherlands Ship Model Basin
at the towing tanks at Wageningen and Deift, three types of programs were investigated:
Program i is a replica of the sea trials of tanker E, con-stituting a repetition and a systematic development of these sea trials with the object of analyzing the different influences for this particular ship.
Program 2 is a study to investigate the performances of an original system of hydrodynainic braking flaps. In
PASSAGE RAIL
AU!
r MEASUREMENT PLATFORM CARROE I-hpractice this program was partially executed along the lines of program 1.
Program 3 is a kind of appendix to program i and con-sists of special model trials with the object of being able to apply certain methods of correlation. A special chapter is devoted to this correlation at the end of thispaper. Program 1- Braking by Propeller
The model trials for this program were carried .out in, the "shallow water" laboratory of the Netherlands Ship Model Basin at Wageningen, described in [101. A
per-spective drawing of the basin is given in Fig 8 and a hor izontal section of it in Fig. 9. The great breadth of this basin permits the free maneuvering of a model of 3-m length, telecommanded by electronic devices without in
terference of the basin walls.
Table, 2 gives the principal dimensiOns of tanker E and its model as well as those of the propellers añd the brákiñg flaps used during the éxecution of program 2. The model on a scale of i : 80 navigated absolutely freely. It as equipped with unfolding braking flaps (see program 2), propulsive machinery, and electrical steering gear: All these devices were telecommanded from the carriage
fol-lowing a predetermined program.
-The scheme. of each trial was as follows:
The propeller was maintained at a certain prede-termined constant number of revolutions depending on the initial speed for the stopping trial.
The model was maintained on a straight cOurse. When the model reached a constant service speed,
3 3A IB 3C 3F 3G 2B 2Ç 2D 2E 6 8 10 12 TIME (minI SEA TRIAL -125 100 75 50 25 C E . o C -2 -50-i 2A 20 2C 2D 2E 3 3A 3B IC 3F 3G 2838 3C .75
Fig. lo Number of revolUtions prOgrams (1, 2 and 3) fOr full-speed ahead (140 and 105 rpm)
Table 2 Principal Dimensions for Model, Ship and Their Propellers - Tanker
of 65,000 tons dwt of 1000 kg; scale 1:80
Loaded Condition Ballast Condition
Ship Model Ship Model
Model No. 3093 (Wageningen)
Length between perpendiculars, m 237.74 2.9718 237.74 2.9718.
Length on waterline, m 244.64 3.0580 232.60 2.9075 Molded breadth, in 34.80 0.4350 34.80 0.4350 Draft forward, in 12.99 0.1624 7.35 0.09 19 Draft aft, m 12.99 0.1624 9.30 0.1163 Mean draft, in ... 12.99 0.1624 - 8.325 0.1041 tisp1acement 86743 rn3 169.42 din3
Wetted surface without
appendices, sq m 12134 1.8960 9771 1.5267
Wetted surface rudder included, sq m Ï2366 1.9322 9873 1.542 7
Block coefficient (between PP.),C5 0.808 0.808 Coefficient of midship section, CM - 0.991 0.991
Prismatic coefficient (between
P.P.), Ç, 0.815 0.815
Center of buoyancy after
forward perpendicular, m 115.19 1.440
Propeller No. 1492; Type: Series B
(Wageningen)
Number of blades ... 4 4
4-
4..'
Diameter (D), mm 7200 90.00 7200 90.00
Pitch (right-handed) (H), mm 5000 62.50 5000 62.50
Pitch ratio (HID) .. 0.694 0.694 0.694 0.694
Boss diameter ratio (dID) 0.187 0.187 0.187 0i87 Fraction of developed súrface (A,/A) 0.539 0.539 0.539 0.539
Braking Flaps
Total surfàce of one flap: 76.6 sq cm
Immerged surface for two flaps, sq cm 138.8 92.6
SEA - TRIAL
Fig. 11 Number of revolutions. programs (4) for half-Speed ahead (70 rpm) E C 2 I. TIME(mm) SEA TRIAL
Fig. 12 Number of revolutions programs (7, 10 and 11) forslowspeed aheäd. (50 and 30 rpm)
the braking of the vessel by means Of the propeller began, as predetermined by the program for the number of revo-lutions (in accordancewith the, program for the sea triáis), from the initiaj number of revolutions. ahead to the final number astern.
This final number of revolutions was maintained until the model stopped completely.
Duringphases (c) and (d),the model was free and the rudder was maneuvered as preetermined by the pro-gram.
As stated under (c), the stopping trials were set up in accordance with the "crash-stop" sea trials for tanker E. To repeat these sea. trials as exactly as possible, a model program no. i was drawn up as indicated in Fig. 10. The
11.10 The Braking of Large Vessels
5121. (2D). ..A'5057 1
51h0(3F ) ...' ..-513S (3B)
5109(2B)-+5097(1.)
THE FIRST HARK. IS THE NÚMBER OF THE TRIAL. THE SECOND MARK () IS THE NUMBER OF THE PROGRAM OF NUMBER OF REVOLUTIONS.
THE FIRST MARK TRIAL.THE SECOND NUMBER OF THE OF REVOLUTIONS. IS THE NUMBER MARK () PROGRAM OF THE IS THE OF NUMBER
/
/
(ID) 5116 LA) (L) 0.40 0.50 0.60 0.70 0.90 V (m/ec)Fig. 13 Inflüence of maneuvering of the engine for tanker E in loaded condition
O 5 10 15 20
V (knots)
Fig. 14 Correlation model ship
rudder angle was maintained at zero dèg during the whole of these trials. As similarity in the number of revolutions for sea and model trials was sought, similarity of speeds could not be pursued (see B, second seriés of tests). This question is debated when the correlation tests are discussed at the end of the paper.
-Four series of programs were executed, whith include the following trials:
A. First Series.,To study thé influence of the maneuver-ing of thé engine, followmaneuver-ing the number of revólutions (program i). This series is illustrated in Fig. 10. First
there was the class 2 program (No. 2A to 2 E), identica.1 to program I up to the speed of 10 rpm astern, followed thereafter by different types of increasing rates of revolu-tions until the full stop of the vessel. Next, class 3
pro-30 20 E. ! 10 e o 4000 3000 E 2000 C w D. e w 1000
30
gram (No. 3A to 3G) was carried out. It was based on program 3, simulating the maneuvering of a Diesel engine between the same limits of numbers of revolutions (105 forward up to 50 backwards) as program 1, Fig. 10.
Second Series. Repetition of the sea trials for study of the influence of the initial speed [6]. This series also was based on program 1. A special program ID was exe-cuted, extrapolating the forward number of revolutions at
sea up to 140 per minute to give the model an initial speed comparable with the initial speed of the vessel at sea. Furthermore, programs 4 (Fig. 11) and 11 (Fig. 12) were carried out, thereby simulating special trials of tanker E. Programs 4A (Fig. 11), 7 and 10 (Fig. 12)
closed this series.
Third Series. Executed to investigate the influence of displacement. The model was ballasted as indicated in Table 2 and trials were made in the conditions described as programs 1, 2E, 3, 3G, 4A, 7 and 10.
Fourth Series. To investigate the shallow-water ef-fect. All the trials were executed in accordance with pro-gram I for the number of revolutions, the ship being tried
fully loaded and in ballast. The "real" depth of water
tried with the model corresponded to 73, 30, 25, 20 and 15 meters.
The results of all these model tests represent a consider-able volume of data. As these concern only tanker E, the results given in a number of tables in [6] are not repeated here. It is only of importance to consider what these trials confirmed or added to the knowledge about the actual ship. The following figures . indicate, therefore only the most important results:
Fig. 13 shows thé influènce of the maneuvering of the engine (A). Though the model probably overestimates that influence, its effect seems small at normal speed. Only in program 2E some gain is shown, but this fast maneuver-ing does not seem practicable. At low speed the difference between maneuvers 4 and 4A shows that the maneuvering of the engine has more effect at such a low speed. The model test confirms here the theoreticàl analyses.
The results of the repetition of the sea trials (B) are
TYPE t TYPE U
.o FRAMUS4 L_umi» AFTERFRI
J60 UMULATOR OF 3ATM SCALE o r n.. TYPE IS FRAME
Fig. 16 Braking flaps of model and situation of flaps in ship
shown in Fig. 14. The curve for the model tests and that for the sea trials are similar, and the conclusion is that, withiñ a limited zone, the model results are transposable to the ship, for comparative purposes only.
This observation lends credit to Fig. 15, which indicates the influence of the displacement (C). It seems that this influence is relatively small: the .stopway is reduced by one fourth for half the displacement.
The results of the tests on the influencé of the water depth (D) do not lead to clear indications. The models were following very irregular courses and no deductions could be made from these tests. It seems that other model techniques must be invented with a view to achieving cor-relation between model and ship in this réspect.
The trials concerning the special maneuvering of the rudder have qualitatively confirmed the observations made during the sea trials. In this case also, correlation between model and ship is next to impossible to obtain.
Program 2 - Braking by Special Devices
Having become aware of the fact that, when the propel-lers are put into reverse, thé stopway of a large vessel al-ways remains excessively long, the first author tried to find a better and more effective solution to this problem. Therefore braking flaps were installed on a model. These flaps were real hydrodynamic brakes like the aerodynamic flaps on several jet airplanes. The flaps can be folded out of the underwater body of the ship, and norinlly stay in-side and form a part of the shipform. When folded out, they remain within the sectional projection of the
mid-The Braking of Large Vessels 11-11
II ISI
llf
111 ..r %lf1t
j
111 «I J t.QI% A Mil_u
111il_I
______ i_______III
____»iiiiJi_____ 1'IiAPIi1flWì/
_Ii;TJI_I_
i
,EXTREME BREA. . EXTREME BREA.1 . EXTREME BREA.T
/
THE FIRST MARK S THE NUMBER OF THE TRIAL.THE SECOND MARK () IS THE NUMBER OF THE PROGRAM OF NUMBER OF REVOLUTIONS. 20 E C .2 io o 020 00 060 0.80 V0 (m/sec)
RING 5URFACE SKETCH E PRESSURES
P. CENTRE OF GRAVITY F THE
OUTER PART OF
INIFLAP
ARTICULATIONS
20
EXTREME BREADTHJ
Fig. 17 Installation scheme of one flap
TANK
OIL - TANK
I4YDRAUL RAM OF BO ATM
HYDRAULIC LCWPRESSURE PIJ4PS
2 HYDRAULIC HRN -(:S' PRESSURE PUMPS AUMuLATORS OF 60 ATM. DECK
SPINDLE -OF THE FAP
NICHE
.-AcCUMULATGRS OF ATM.
MAIN - COCK OF THE
S'ISTEM FGR MOVING THE VALVE DOUBLE RETURN -VALVE HYDRAULIC REGULA -TINO VALVE
DOUBLE - RETURN - VALVE
Fig. 18 Scheme of double hydraulic system -for manipu-lation of the braking flaps
ship section. The disposition of the flaps is shown in Fig. 16. Fig. 17 gives a schematic view of the installation on board ship, and Fig. 18 fndicates the hydraulic manipula-tion of the flaps from the navigating bridge.
Program 2 gives indications as to thereal efficiency of such an installation. In this program also several series of tests were executed:
A. First Series. Executed before program i with a model of the Todd 60 series with a block-coefficient of 0.80
(scale .1 .: 54). This model was equipped with built-on
braking -flap's, the characteristics of which are given in Table 3. The flaps are installed in the fore -part of the
il-12
- The Braking of Large Vessels2 E L 9 10 12 TE 15
V C knot,)
Fig. 19 Specific ship resistance extrapolated according to the 1957 International Towing Tank Conference
Table 3 ModeÏ No. 42 - (Deift) Todd Scale = 1:54 Séries 60 DTMB CB 0.80 No. 4214W-B4 Ship Mädel Length on waterline (LWL), m 123.962 2.2956
Length, between perpendiculars
(L), m
_..._... 121.918 2.2577Breadth (B), m
_.
- 18.75-7 0.3474Draught (T), m 7.495 0.1388
Displacement () _..._..._... 13737m3 87.091dm2
Waterline coefficient (C) ... 0.871 0.871
Midship section coefficient (CM) 0.994 0.994
Block coefficient (Ç5) ..-...
-- 0.800 0.800
Prismatic coefficient (Ce) . 0.805 0.805
Area of midship sectión (AM) ..._ 139200m3 4.79dm2
Center of gravity after forward
perpendicular (FG), m 57.911 1.07245
Wetted surface (S)-, sq. m - 3455.8, 1.1851
ship. This has, among others, the advantage that the brak-ing force acts on the hull as -a compression- force and not as a tensile force. Apart' from the trials without flaps,
three types of flaps were mounted. 'Fig. 16 gives the di-mensions of these types (meäsures for a real ship).
Type L Total braking surface (2 flaps) 25.672 sq m or 18.45 percent of the midship section under water.
Type II: Same form but perforated with 45 holes per
flap of 324-mm dia. The remainder of the sUrface
amounted to 18.256 sq m or 13.1 percent of the midship section under water.
Type III: Bràking surface (2 flaps-) reduced to 12.840 sq m or 8.96- percent of the midship section under water.
The thickness of .the 'actual flaps was supposed to -be 760 mm so that they could be introduced- into the- ship's structure within one frame space.
For 'each of the four' situations so created (withoùt flaps, Type I flaps, Type II flaps, and Type III flaps), two trials were made:
-(a) One conventional towing triai to determine the: hy-drodynamic resistance in the forward direction.
L-SHIP WITH BRAKING- -
L
FLAPS OF TYPE X-!'jSHIP WITH BRAKING - I
FLAPS Oc TYPE S
4"
//
RAP WITH
-BRAKYG
--
- FLAPS OF TYPE,
SI WITHOUT BRAKING
--r
- FLAPSz
_SPECIFIC FRICTIONRE5ISTATE ACCONGING TO THE I.T,IC, 0.00 0DB 0.12 GIB - - 020 020 020 032
I
-RAM ..._RAM
(PORT) C S TAR BOAm
le 20 20 te t2 IM R
24 22 20 1Í 16 14 12 o
Fig. 21 Sketch of modeLusing braking flaps
00 50 0
t
z. o o w 4 o zThe Braking of Large Vessels 11-13
4
4
-/
/-I.
/
- SHIP WIT BRAKING - FLAPS s
SMP WITH BRAKING
J,,,
- FLAPE OF TYPE
JI.-SHIP WITH BRAKING - FLAPS
/
OF TYPE I,_f-
-.---/
f'/4
SHIP Wif H BRAIC NG - FLAPS OF TYPE'I'
BRAKPG WITHOUT BRAKING-FLAPS - FLAPS/
-- WITH
/
¡ eL.. e -.'I
I//Il
WI
H,::
0 20 40 60 TIME (s.s IFig. 22 CourSe-keeping stability of models with propeller
turning astern
-flaps. All was recorded automatically and a full descrip-tion of these trials is given in [4]. Fig. 21 shows a sketch
f the model with type II flaps out at the beginning of
the braking period.
As the Deift basin has not much breadth, the course stability was detérmined by letting the ship go on an
initiai straight course, rùdder angle at -zerO, autopropul-sion at 0.5 :m/sec, equivalent to a 7-knot speed for the real ship. When, during braking with the flaps, the course remained straight, it was considered that the course sta-bility was all right; otherwise, each tendency to turn was considered as an index of nonstability. When, in a straight course, the speed of 0.5 rn/sec was reached, the following telecommunications were given to the model:
Stop propeller.
Simultaneously stop propeller and open flaps. Put propeller in reverse.
Put propeller in reverse and open flaps.
The results of these trials were very convincing. In cases (a) and (b) no deviation from the course was ob-served, even when the port and starboard flaps did not
0 2 4 0 12 1.4 10
V knot3)
Fig. 20 Stopways in number of ship lengths to come to a final speed of 2 knots
(b) One stopping trial beginning with a fixed initiál
speed. The natural slowing down was measured as a function oí the tirpe until the speed was reduced to 2 knots.
Measurements at lower speeds became erratic, bUt they had no significance as in practice the propeller braking iñterferes long before the speed has come down to 2 knots. The results of the towing-tests (a) are given in Fig. 19, which shows the specific resistance in terms of the wetted surface and extrapolated following the ITTC law, 1957.
Flaps I and II are practically equivalent; flap III is less efficient, but this is due to the much smaller braking surface. The braking power of the flaps is shown to be considerable. Fig. 20 gives the results as headreach mêas-ured in ship's lengths. If one considers that the stopway with initial speeds of 8 up to 16 knots is the most repre sentative for the use of these flaps, this figure indicates that the best flaps, of type II, reduce the stopway by about 60 percent. Therefore, as these flaps are construc-tionally feasible [3], the conclusion is that they must be extremely useful .in solving the problem of the braking of
large vessels.
L Second Series. To study the influence of these flaps on the route stability of the ship, an autopropulsive model with electrically controlled movable flaps and an elec-trically controlled maneuverable rudder was made at the towing tank at Delft at a scale of I : 50 (instead of
I : 54). Télecommands by radio governed the number of
revolutions of the propeller, the rudder angle, and the
;4o e )0 z o w n 20 o w z 10
3003
Fig. 23 Model with braking flaps brought out
move simultaneously. Moreover, when the rudder angle was maintained at zero, maneuvering the ship with the flaps was. possible. In conformity with the tests of the first seriés (A), the headreach was much shorter with the flaps out, case (b). As dûring the sea trials, the model became impossible to steer in cases (c) and (d), the lat-ter giving slightly betlat-ter. results than the former, probably due to the small stabilizing effect of the flaps, Fig. 22.
The conclusion is that, although the flaps do not have great stabilizing influence when the propeller is turning astern, they control the beginning 'f the track by reducing the speed more rapidly, so that the braking effect of the propeller comes into action earlier.
C. Third Series. Executed as a subtriàl of Program 1. During these trials the flaps were manipúlated under the same circumstances as in the principal trials Of that program. All these priñcipal trials were also carried out. with the braking-flaps "out" and "in." The influençe of the flaps "out" is given in [6].. Fig. 23 shows the fore-part of the model with flaps "out." Fig. 24. gives the principal results during the normal maneuvers, both flaps being moved simultaneously while the rudder anglé re-mains at zero. On this figure are indicated in dotted lines
the linearized curves of Fig. is concerning the model without flaps for both conditions, loaded and in ballast (program types I and 4A for a determined number of revolutions) The drawn lines indicate the representative results for the models with flaps "out," using the same program for the number of revolutions.
Fig. 24 underlines two remarkable facts: The straight (dotted) lines, representative of the trials withOut flaps, are clearly convergent, while the (drawn) lines, relating
to. the trials with flaps, are practically parallel. The dotted lines (without flaps) have an impoftant
inclina-tion while the drawn lines (with flaps) are nearly hori-zontal. This tendency is easily explained The flaps give muth more hydrodynamic resistance, the more so when the speed is higher. This, in Fig. 24, teduces the
in-11-14 . The Brakiñg'of Large:Vessels
clination. As this inclination is small (nearly horizontal), the convergence is completely hidden. Furthermore, the effect, of the flaps is reduced when the immersed surface is smaller ; hence the smaller èfficiency of the flaps when navigating in ballast.
It is no exaggeration to say that the action of the flaps tends to render the stopway constant, independent of displacement and initial speed. The stopway in loaded conditiön, using flaps at an initial speed of 14 knots, is about the same as without flaps at 7½ .knots initial speed loaded or 8 knots in ballast. Extrapolating the straight lines using flaps to 17 knots initial speed, the initial speeds giving the same stopways for ships without flaps come respectively to 8 knots loaded and 8½ knots in ballast.
If one transposes these values to the real vessel, the ship with flaps at the normal service speeds of 16 knots will have the same stopping conditions as the conven-tional ship without flaps at 8 knots. This means (see
Fig. 6) a stopway of 1400 m, which is considerably (more than 50 percent) below that of the conventional vessel.
These model trials confirm all the conclusions about flaps given in [3] and [4]. Therefore the installation of braking flaps is an important step in solving the prob-lem braking large vessels.
lrogram 3 - Correlation Model Ship
When program 1 . of the model tests was establihed, the initial object was to obtain from the results a com parison between ship and model. This comparison was
to be a global one, without entering into details of how the. parallel between these tests woüld be constituted. [f
this global comparison were. satisfactory, an extension of
program ito cover a critical evaluation of the
differ-ent influénces would be necessary. The global comparison has been covered in the description of program 1, but the transposition from the model to the ship which was then used was not accurate. If one is to use a free model
THE FIRST MAR11 TRIAL.THE SECOND NUMBER OF THE OF REVOLUTIONS IS THE NUMBER MARK ((IS PROGRAM OF THE THE OF NUMBER .-o 5125('E(+ 5105(3) 5152 (3) +RILI(3G( ,..iPS 5120)2E) SI 3G -5OiTLOADE - . _ cOHOITIOM (WTh 510R)3(G FI.APS( ON (WITH F 5153 3 \5151(2E( u7(T( SITUA ON F LOADED CONDITION BEL LA S Î CONDITION 01.0 050 060 070 0.90 0.90 V (rn/sic)
Fig. 24 Influeñce of use of braking flaps on the stopway
¿0 30 E à 20 II Q. o 10 o
I-4
-F
i UGHT SOURCE 2 PHOTO-ELECTRIC CELL
3 GUIDING PINS CONNECTED TO THE CARRIAGE ¿ SLOTTED WHEEL
5 GEAR WHEEL WITH THOUSAND TEETH CONNECTED TO WHEEL h
Fig. 25 TriaIs of model on a straight course (trial No. 2)
in order to reproduce sea conditions, the initial condi-tion has to be one of autopropulsion for the model; that is to say, one has to choose between the similarity of the number of revolutions or the similarity of the speeds, the two being impossible of realization at the same time.
In program I the choice of the similarity of the number of revolutions was adopted for practical reasons. Never-theless, the extrapolation of the results from model to ship was actually made on a speed basis, because the speed was the essential parameter for the ship. But similarity as regards the ship's resistance, also essential, could not then be achieved because of the scale effect of the friction coefficient. To escape from this dilemma, the Model Basin in Wageningen propised to forego a direct and global comparison and to use a fictitious model trial in complete similarity with the ship, in the same way as is done in determining a ship's resistance by applying a friction correction to the friction of the model. On the hypothesis that, at any moment, the variables used were interdependent of each other, as if the whole procedure were stationary, the relations of stationary trials could be determined and thereafter one could reconstruct the whole trial as a continuous sequence of these stationary states. This so called "quasistationary" method was proposed by van Manen, and is explained by him [11] on the basis of the work done in the U. S. by Thau [12].
Program 3 consisted of three series of model-tests: A first series of trials analogous to the autopro-pulsive trials at constant speed and variable decreasing number of revolutions. At each trial, the force, which exists between the model and the carriage, here called braking force K, was measured and thus K = f(V.N),
the force of themodel in a stationary state, was obtained. A second series of trials consisted of model stopping tests on a straight course. The program for the number
of revolutions either belonged to program 1 or this
number of astern revolutions was held constant and was fixed from the beginning of the trial. The second series was executed in the shallow-water towing tank at Wa-geningen. The following experimental set up was used
-500 -250 0 250 500 750 1000
ASTERN n (revS/mul) AHEAD
Fig. 26 Braking force of model on a straight course
measured as a function of the number of revolutions of the propeller (trial No. 1)
The Braking of Large Vessels
il-15
vn 0h6 VmSPE D O 1H _________________ MODEL
I
n - THE FOR NUMBER THE PROPELLER 0F REVOLUTIONS OF THE ¡min MODEL\nn
n-.
n----n--. n-.. 0 50 100 150 200 250TIME IN SECONDS FOR THE MODEL
Fig. 27 Stopping trials for model on a straight course (trial No. 2)
(see Fig. 25): The model was attached in its midship
section to a cord, which was rolled around a wheel 1. On this wheel were mounted an electric light I and a photo-electric cell 2. In this way the relative movement of the model to that of the carriage was transformed into an oscillating rotation of the wheel 1. Wheel 5, with a thou-sand circumferential teeth, was fixedly connected to the slotted wheel 4, which. rollèd along the rails of the car-nage. This wheel 4 had one-meter circumference. The circumferential speed of the slotted wheel equals the linear speed of the carriage and the speed of the model was given by superimposing the speed of wheel i in re-lation with that of wheel 5.
The third series of tests consisted of the normal stopping tests for the free model in accordance with the programs for the number of revolutions of program i (numbers 1, 4A, 7 and 10; see Figs. 11 and 12). For all these three series, the model was the same as the one for program 1. The results of the first series A are indi-cated in Fig. 26; they include five different speeds. The
0.75 5O w c-I 025 o il. (D z 4 -025 loo
I
w o aso w z e o 025 w w Lu' oresults of the second series B are indicated in Fig. 27; they include only the trials with a constant, number of revolutions. The results of the third series C and those of the second series B concerning the trials with a proa gram of numbér of revolutions in accordance with the sea trials of tanker E are given in Fig. 28.
Principle of Quasistafionary Method
As explained by van Manen: [11], it is possible to study the stopping of a vessel by means of the funda-mental dynamic law. Force equals mass. by accelera-tion or, in this case
K
d[(M±m)V]
(1)dt
where K equals braking force, not only deriving from the mass M of the vessel at speed V but also from the mass rn of the water carried along with and surrounding the ship, which is supposed to advance also with the mean
speed V.
The global effect of this surroÙnding water is included
in equation (1) Hence the fictive mass (M + m) of
the vessel is only considered when solving this equation. In a first approximation, van Manen [11] has admitted that m = constant and a certain percentage of M. Hé takes therefore M + m = 1.05 M. If V0 represents the initial speed at the moment t. and V represents the speed at an arbitrarily chosen moment, the integration of (1) immediately gives the time difference (t - t0) necessary to reduce the speed V0 to V.
T,
tto
= - (M
+ m) f.dV
(2)vo
In the Same way the distance covered (S -- S0) is found,
while keeping in mind that dV/dt = (dV/dS) (ds/dt) =V(dV/dS), by the integration
5_So=(4+rn)f
.dV
(3)If the integrals are continued until V = 0, formulas (2) and (3) give respectivély the stopping time and the
stop-way until the "full stop" of thé ship from an initial
speed V0. Both formulas can be used both for the vessel and for its model. As M + rn is supposed to be a known constant in this approximation, it is only necessary to apply (2) and (3) to know the relatiOnship between K and V. Here the quasistationary hypothesis makes its appearance.
The trials 1 have made it possible to determine for a model in a stationary state the relation K = f (V,N), represented graphically by Fig. 26
In this case it is admitted that the variation of V and N (number of revòÍutions) is slow enough during a stopping test to remain valid within that interval for this
5See note after equation in earlier sectiOn, "Conventional Trials."
E
E
> to
11-16 The Braking of Large Vessels
NUMBER 0F REVOLUTIONS / MINUTE
i (FIG.iO)
ACCORDING
4 10 PROGRAM NR
MODEL FREE
&EM
PROGR IDEM PROGRAI4
O(FlG%Ç7IG.i2)
o 25 50 75 100
TIME IN SECONDS FOR THE MODEL
Fig. 28 Stopping trials for free model (trial No. 3) and for model on a straight course (trial No. 2)
relationship. Especially when N = constant during the stopping maneuver, the relation K = g(V) may be im-mediately obtained, by reading the values of the ordinates
from Fig. 26 in relation to the abscissas N. If N is
variable as a function of the time, one has to proceed by successive approximations by 'choosing arbitrarily a function V = h (t ) as a first approximation, which will give a second approximation of the same function,so that at the end the convergence by an iteration process is given. In principle, this process makes it possible to cal-culate, starting frOm Fig. 26, representing the trials 1, the results of a stopping test from the same model exe-- cuted at a given program of number of revolutions.
Now, what one wants are not the results from th model, but from the ship. Therefore, it is necessary to deduce the braking force K, of the ship from the braking
force K of the model. To achieve this, the following
reasoning is followed: The braking-force K, may be con-sidered as the sum of the propeller thrust and the hydro-dynamic resistance of the underwater body of the ship, the interaction between these two terms being neglected because the relationship between them is unknown. By the same hypothesis it is admitted that the ,propeller thrust only depends on V and N. If K is the braking
force of the model deduced from trial I for a, torque given 'by V and N, the part of K due to the propeller thrust is the same for the vessel, while the hydrodynamic resistance
of the underwater body is diminished by the friction
correction R0, which is a function of the speed only, and which if convenient may be augmented by different
cor-rections, R, due to rugosity, meteorological influence, and so forth.
In the case that a ship trial should actually have been performed, it shOuld be possible to evaluate these cor-rections with a certain amount of precision through this ship's propulsion triâl. On the Other hand, if oné wants to predict results from sea trials, one must take care not to be too optinthtic. However, it seems sufficient to appraise the rugosity by means of previous examples and to neglect further corrections.
The proposéd method is simple and complete, but it includes the hypothesis of the constancy of (M ± in), a value arbitrarily chosen, which leads tO a fairly rough ap-proximation. Consequently, the Wageningen Model Basin considered the possibility of determiñing experimentally the value of (M + m). This was the goal of trials No. 2. indeed each of these trials gives the relationship V = h(t) achieved with a program N = 3(t), chosen expressly, Fig. 27, and consequently determines the relationship between V and N, which makes it possible by means of the hypoth-esis of quasistationarity to define the braking force K at each moment, as a function of V. This is done with the help of the results of the trials No. 1, Fig. 26.
Returning to the integration of formula (1), considering that (M + m) is variable, one finds
.n.;20
n,.105 n0.-50
o . 0.25
V Cm/lic)
Fig. 29 Model of tanker of 65,000 dwt (M + in) as func-tion of the speed
-stant number of revolutions of - 20 per minute, is clearly
different from the liñe óf - 50 rpm although with a
similar outline.
Furthermore, M for the model is 17.28 kgf/m sec-2 and thus 1.05 M = 18.14. kgf/m sec:2 Fig. 29 shows that M + m deduced from trials 1' and 2 varies approximately between 6.5 and 22 and depends clearly both on the speed and on the number of revolutiOns. This proves that, if the validity of this procedure to determine (M + m) is aç-cepted, the approximation of (M ± m) = 1.05 M is too rough and hardly susceptible of ameliorati6n by taking iñto account any other factor than 1.05. The Model Basin. in Wageningen tried a better approximation by adopting,
as the relationship between (M + m) and V, a mean
curve deduced from Fig. 29 and neglecting the influence of N on (M + m). Alas, if one adopts this second ap-proximation, a new difficulty turns up when evaluating the extrapolation to the ship. A supplementary hypothesis is required for the extrapolation of M + in; viz, that m/M depends only on the Froude number.
If this second hypothesis js accepted, the calculation can be continued as for the first approximatiom The. inte-gration of formula (1) gives 'instead of formulas (2) and (3) the following:
M+in
dV (7) dm dtt - to =
s - s0 = -
V.dV (8).The Braking of Large Vessels
li-17
fK . dt = -
[(M + ni) V] + [(M + m) V0 (4)r0
If the limit of the integration is te where V = 0, one ar-rives at
¡e
K.dt
[(M+rn) V]0 (5)because at that moment
[(M +in.)V]te 0
Combining (4) and (5). it is clear that
fKd = -[(M,+ th) V]
+ K . dt or [(M + m) V} K . and [(M+m)V] =f
Kdt
. (6) teTbe result of this calculation is given in Fig. 29 for all No. .2 trials worked out' for a final number of revolutions of 50 rpm astern (continuous line). This figure shows that the accuracy and the reproducibility of the trials are excellent since all curves coincide at the speeds where the .rate of - 50 rpm is stabilized. But in the beginning of
the trial, where the number of revolutions is variàble and rapidly varying, the curves are frankly diverging. Also the dtted line of Fig. 29, representing the trial at a
con-25 20 15 e E
- Io
E +I
sK+ V
M+m
The K values necessary for the extrapolation from K to the ship's braking force are estimated as for the first approximation, but it is difficult to allow a value for dm/dt, which is not absolutely arbitrary. Theoretically this difficulty can be overcome, if one starts by' träns-forming forniula (1) to
K
d[(M+m)V1.
dV-.
dV dtand integrating this formúla to
and
t to =
s s0 =
-Vdm M + m) + dV dV (10) K T1,l, (9) y (M + m) +r
dV V.dV (11)J
K voso that the differential quotient dm/dt is replaced by dm/dV. This last is known because the hypothesis was that (M + m) is a function of V.
Now, Fig. 29 shows that dm/dV depends to a large ex-tent on the program of the number of revolutions, so that a value deduced from the mean curve of Fig. 29 does not represent an admissible approximation. It seems extremely inconvenient to find a suitable experimental procedure to overcome this difficulty; therefor, it is to be feared that notwithstanding its gréater complications the second ap-proximation does. not serve ou,r purpose any better than the first one.
So a more direct way of calculation is necessary. One must try to avoid the calculation of (M + m). Coming back to the hypothesis that (M + m) only depends on
the Froude number, one admits that this may correspond to a fixed program of the number of revolutions. Both formulas (10) and (11) can be written as
Y=f'2dV
(12)y representing here one or the other of
the terms t -
t0or S - S0, and f(V) representing here one or the other of
the terms [(M + m) + Vdm/dV] or
[(M + m) + (Vdm/dV)] V..
'This third approximation to determine y is best handled in the following way: One begins with a model test of a certain program of number of revolutions corresponding to the program of a real ship on which stop tests have been
11-18 The Braking of Large Vessels
carried out. Startiiig with the same initial speed, taking into account Froúde's law, the functions y are experi-mentally 'determined, starting from a speed V. This test is executed by applying to the model, until the moment that it becomes. free of the carriage, a tensile force equal to the friction correction as set by the ITTC. Thus the
braking force K of the modél may be determined as given in Fig. 26.
If a fictitious trial is now imagined, where this tensile force is not only applied before the stopping maneuver but also during that whole maneuver itself, it must be possible to achieve the corresponding braking force K1 of the vessel.
This K, may be calculated by formulas (2) and (3).
Then the functions y, for the vessels are given by the same formula (12), replacing K by K,. Hence
dy1
-. dy
KdVdV
K1In the right-hand part of the equation, all the valúes are known, dy and K by the trial, K, by the calculation.
It is now sufficiént to calculate the integrals f' to
obtain y, as regards the fictitious model trial ¡n total
similarity to the sea trial. This procedure gives a possible extension to the solution of the problem. Submittiñg the model permanently to a variable traction, which equals the friction correction for the given speed by means of a convenient dependable contraption, it will be possible to realize a fictitious trial; and an extrapolation of the re-suits to the ship is true if it is admitted that there is no scale effect other than that of the friction. This procedure
requires another set of experiments, but on the other hand the trials No. i may be omitted. The extrapolation does not use any stationary trial nor the basic hypothesis of the quasistationary method.
Results Obtained
To the tanker E of 65,000 tons dwt of 1000 kg, the
different methods have been applied. The friction correc-tion has been calculated following the ITTC formula of, 1957 with a roughness allowance Cf = 0.0002. This co-efficient was deduced from the propulsive sea trials of the same day. As the weather was fine (Beaufort scaleNo. 1), no other correction was applied. With these figures, the relationship between the braking forces of the ship and its model at corresponding speeds remained in the neighbourhood of 2/3 (taking account of the scale), from full speed to half speed. Consequently, whatever the ex-trapolation procedure may be, the predictions for the ship are expected to be about 50 percent higher than the un-corrected results obtained with the model.
No model trial was directly comparable with the sea trials, but it is evident, as a comparison with Figs. 27 and 28 confirms, that the trial starting with 16 knots initial speed and propeller in reverse with a constant number of revolutions of - 50 is optimistic in relation to the trial (13)
