1 INSTITUTTET FOR SKIBS - Oc7 HIA Department of Ocean Engineering Factors Affecting the STOPPING ABILITY OF SHIPS by Sv. Aa. Harvald June 1975 DANMARKS TEKNISKE HØJSKOLE The Technical Untversity of Denmark LYNGBY Danmark CONTENTS, Page O Summary 3 i Introduction 3 2 Sthbols and Units 5 3 Definitions 7 4 Manoeuvre Nomogram 10 5 Stopping Procedure 11 6 Mathatical and Physical Models 13 7 Parameters significant for Stopping Manoeuvres 13 8 Calculated Track Reach and Stopping Tïme for Ships of Différent Types 21 Conclusions 27 10 List.of References 28 il Appendices i 29 9 6 SUMMARY. On the basis of the results from previously interaction performed. modè], tests concerning the between ship and propeller at extreme loads, an analysis of the, influence of ferent parameters were carried out propeller the with difregard / to the stopping distance öf the ship. In addition distance a comparison of the stopping made between types of ships has been most commonly in use today 1. INTRODUCTION. The continuous increase in the size of ships, in the speed and the traffic, epecially in certain straits, has caused a current interest in. investigating the stopping ability of ships. Today a great deal of literature has already been. published the subject and full lists of references are given about in, for instance, Ref. (1], [5] and' (7]. The periodicals give very often the results from the stopping tests of new ships. In this paper some of. the factors being of importance for the stop- ping qualities of shIps will be discussed. It will mainly be a discus- sion about hydÉodynamic factors because the analysis is based results from previously performed model tests with regard on the to the inter- action between ship and propeller at extreme propeller loads, Ref. [4]. Et will be preferablé to use a manoeuvre nomogram (Fig. 1) when the stopping abilities of the ship are investigated, because a manoeuvre nomogram gives a good survey of the. interaction between ship,machinery and propeller. 4 uu 0.. -12 - MOTOF' SHIP Q / m,I ) 16 ' TANT /SPEED AHE4D f /or 150 . FUEL CUT SHIP GOING AHEAD 100 / ì4.. ELERATll FORCE F M PROPELLER Mp) A 4E 50 - (Mp) V SSURE"' . ED SHIP GOIN' ASTERN /\ - NN72 100 URN ASTERN s FfJ:L ON ITI pc,* D:VICE IN ACTION ZERO SPEED V 12 - CONSTANT SPEED ASTERN -: 6O -1 -80 -40 0 40 80 n 1 (REVS./M,N) Fig. 1. Sketch of manoeuvre nomogram för ship with diesel engine going from full ahead to full astern. In most of the earlier investigations of the hydrodynamic conditions of the starting, the stopping arid the reversing of the ship it is assumed that the wake coefficient and the thrust deduction stant during the manoeuvre. It is coéfficient are con- also frequently assumed these investigations that the wake coefficient as well in some of as the thrust de- duction coefficient are equal to zero. By using the manoeuvre nomogram it is also automatically assumed that the thrust deduction and thè wake vary with the thrust loading coefficient of thé propeller. 2. SYMBOLS AND UNITS. The symbols have beén chosen in accordance with the "Standard Symbols", 1972, recOEnmended by the Presentation Committee, ITrC, where applicable. General. = linear acceleration a = force g = acceleration due to gravity length along path s t) = time (or t = time interval Ship Dimensions. L = L = length between perpendiculars B - = breadth on waterline T = draught AM = immersed midship section area S = wetted surfàce (L X mean girth) V = displacement volume LCB = longitudinal position of centre of buoyancy (also used to length of waterline = draught aft, TF = draught forward) (including rudder) denote the distance of CB abaf t amidships Prcp Z 1er dimensions. D = propeller diameter P = propeller pitch A0 = propeller disc area (rID2 AD = developed blade area Einem atió and D,'ncjrrz:c Symbols. V = speed of model VA = speed of advance of propeller R = RT = total resistance RR = residuary resistance T = propeller thrust Q = propeller torque n = rate of revolution F = tow-rope pull ( or t4/2)) head reach S5 SL = lateral reach track reach ST = hydrodynuic cOEnponent of ST S = machine component of ST mass density of water p = kinematic viscosity of water Dimensionless Coefficients and ratios. V = = block coefficient = midship section coefficient V 1/3 V, - longitudinal prismatic coefficient = length-displacement ratio VA nD advance number of propeller = K V nD = torque coefficient pn2D5 R - resistancè coefficient corresponding to IÇ pn2Dk T L (also used as resistance + tow-rope pull coefficient) = thrust coefficient pn2D w= V_VA - Taylor wake fraction WQ = Taylor wake fraction determined from torque identity WT = Taylor wake fraction detirmined from thrust identity T_RT = T - thrust deduction fraction Metric units are uses throughout, however in the speed-length ratio V/IL, V is in knots and L is in féet. 3. DEFINITIoNs. In investigating the ship's stopping qualities some different parameters have been ùsed. To remove any possibility of a misunderstanding thé parameters will be defined in the following. The track reach (fig. 2) ST is the distance travelled by center of gravity of the Ship along the stopping track,from the time the of the order to stop wtil the tïÈe.of zero speed (distance to dead-in-thewater). The head reach. is the distance measured in S the direction the ship' s initial course, from the place of the bow at the time of order to stop to the point most distant of any part of the of, the ship during is the distance perpendicular to thé ship's the stopping procedure. The lateral reach SL initial course line to the point . of the ship most distant during manoeuvre. Omm. "FULL ASTERN" Fig. 2. Definition of track reach and lateral reach SL. 5T' head reach SH the 8 In the presént investigations only and SLO. The effective wake coefficient is considered, i.e. ST = SE ST is determined by the ship propeller acting as a wake meter and integrator, the effective wake velocity being defined as the difference between the veloc.ty of propulsion (V) and the velocity (VA) which in a homogeneous field would enable the propeller at torque the same number of revolutions to create a thrust or to absorb a equal to that measured Dividing these two wake velocities by the model velocity, two coefficients are obtained, referred to as thrust identity wake and torque idendity wake respectively. Thus the wake coefficient is expressed.by: w- VVA VA V v('-) (1) If the number of revolutions of the propeller is kept at the same value, the advance numbers VA = nD can be inserted in equation (1), D the diameter of propeller. (2) and nD n being the number of revolutions and Equation (1) then becomes J' -J (3) J'. Conseqùently the wake can be determined by the use of a propeller. diagram in which 1Ç and KQ curves of the prôpeller behind the ship are plotted and KQ in addition to the corresponding usual curves from the open water experiments. For the sake of completeness it can be mentioned that .KT and KQ are defined by and = K pn2D5 pn2D' where T is the thrust of the propeller, Q mass density. The positive direction of accordance with fig.' 3. (4 the shaft torque, p the V, n, Q and T was chosen in RIGHT- HAND. PROPEL LER Q POS. -----'- (ON SHIP) n POS. - - + - LOOKING FORWARD Fig. 3. Sketch of definition. V POS. TPOS. (ON SHIP) NORMAL - LEADING EDGE DRIVING FACE ..n POS. Q POS. (ON SHIP) The thrust deduction cae fficient tT where K is determined by KrKR (5) T is the propeller thrust coefficient and KR is a coefficient defined by R R when the model is running freely, and R+F R pn2D ASTERN AHEAD R POS. - e F POS. V POS. r pos. Fig 1. F POS.' Sketch of definition. R POS. lo under overload conditions. R the tow rope is the ship resistance, F pull or the force available for acceleration or retardation. tive direction of Thus t R, T The posi- are chosen in accordance with and. F can easily be determined by inserting the fig. 4. in the KR curves propeller diagrams. LI1 MANOEUVRE NOMOGRAM. A Manoeuvre nomogram can best be constructed if the results of complete model test are available. In this casé it means test carried out for all four.possible combinations of and V astern. a overload an sign of the n together with towing tests of the model going both ahead and Corrections to the wake coefficient for the scale effect are best carried out when the results from a complete open water propellér test are available. A manoeuvre nomogram can be drawn as shown in the fig. 1. The abscissa ïs the number of revolutions and the ordinate is the propeller torque. Curves of constant speed have been inserted, as an example,for maximum speed ahead, stationary, maximum speed astern and mediate speeds. The values of on F ("tow rope pull") are given curves for.constant speed, where F inter- some. the. indicates the forces available for acceleration or retardation T(l-t) = F + R or F .T(l-t) - R (9) A further curve is inserted corresponding to free running (F = O).. The time of acceleration or retardation from initial speed V terminal speed V2 and the head reach corresponding to it, 10 can be de- termined by F = ma = m dt. = m dV m dVds -= m dV (V21 a t = (l+k) dV (11) dv (12) J VI ds = m dv s i(l+k) f': 11 in which F = force a = acceleration = mass t = time = displacement (=pV) s = reach V = displacement volume' p = mass density l+k = f àctor, which takes into account the hydrodynamic added mass The factor l+k = 1,05 has been used everywhere in this investigation (see section 7) The stopping time TB and the stopping distance (the head reach) Sa are determined by use of the formulae (11) and (12). In the nomogram correspondïng values of 1/F and Vax to V/F 0. F V and as functions of V can be read can be drawn and and curves indicating integrated from The stopping time and stopping distance can then be deter- mïned by graphic or numerical integration. To the values determined integration there must be added the time required for the by to machinery be reversed and the corresponding head distance. 5, STOPPING PROCEDURE, the Besides depending on the hydrodynamic conditions of the ship, stopping time and stopping distance of the ship will depend on the pulsion machinery as mentioned above. differ Thè reversing characteristiçs of the propulsiPn machinery with type, make and size. pro- For some types only a few seconds will elapse from the order "full astern" until the machinery goes astern at required number of revolutiöns. For other. types and under unfavourable conditions the operation may call for several minutes. Assuming that the machinery manoeuvre lasts only a short time ship speed will only change very little. the Therefore,in the manoeuvre no- mogram (see fig. 1) the operation approximately corresponds to the con- curve for stant speed curve through the point of initial speed on the free running (F=O). The curve is followed until intersection the n-axis (Q=0, the propeller running freely), then to its intersection Q-axis (the direction of rotation of the propeller changing with the from posi- tive into negative) and finally on to the maximum negative number of revolutions. Further stopping öf the ship will then continue at a nearly constant number of revolutions but with the propulsion machinery even less negative torque. giving If this procedure is continued,the ship will stop moving after some time (V=0), whereupon it will start going astern. 12 nega- For many types of machinery there are limits to the maximum tive torque and the maximum negative number of revolutions. It can be suitable to dïvide up the stopping process in two stages: ist stage: The period from the order "Full astern" to final the negative torque or number of revoultions of machinery. number 2nd stage: The period from final negative torque or of revolutions to a speed equal to zero. The reach corresponding to the ist. stage will, above all,depend on the characteristic of the machinery and it would be natural to call this component of the stopping distance, the machine component (S). In the manoeuvre nomogram, shown in fig. 5, which corresponds to fig. i, an example has been given showing the influence of the machinery reversal time of the pro- the reversal on the relation between the propeller torque and the number peller revolutions during "braking". It may be noted that changing time can vary within very wide limits without essentially relation simple. relation which makes the determination of the 2,0 Q CONSTANT SPEEDS. MNm AHEAD cßmis)J / 45 'Án mr DEVICE IN a Fig. 5 flON -Q5 O 0,5 1,0 1,5fl (REVS!5) Sketch of manoeuvre nomogrmn for. ship, when machinery reversal time is varied. this 13 in the 2nd stage the stopping distance will, above all, depend on the hydrodynamic conditions at the ship and propeller and this component wIll be called the hydrynamic còmponent (S). which It will be primarily the hydrodynamic contributions - are treated in. the following. MATHEMATICAL AND PHYSICAL MODELS. For the investigations into the influence of the various parameters from previously per- on the stopping ability of the ships, the results fòrmed model tests have been used. The modél tests in question have been The results have been applied described in ref. [4]. to particular a as stated in appendix 5. ship, here marked Ship "U" with the main data The ship "u" corresponds to a typical middle-sized bulk carrier. Most of the other ships in the investigation are hypothetical. ships with main dimensions determined by statistical way (see appendix 6). By calculating the stopping time and stopping distance las (11) an used (12) were diagrams in connection with the formu- especially constructed for the purpose and to a great extent graphical methods have been used. The performance (the mathematical models) are briefly dis- cussed in appendices 1, 2 and 3. PARAMETERS OF IMPORTANCE FOR THE STOPPING MANOEUVREG From equations (11) and (12) in section 5 (V1 t = - dv F (1+k) and s = I (l+k) (V2v - dv 'v F i and from équation (9) also in section 5 F = TU-t) - R it can be seen which parameters are of importance for the ship's stopping ability. It is obvious that the ship's mass t plays an important part. the full ahead propulsion effect of the ship is reduced so much propeller turns without producing thrüst, the ship will stop on account of the hull resistance. If that the exclusively 14 With a rough estimation O A2"3, which means that t tional to nal with T as well as t and R propor- is will be proportio- ST of increase ST. (1 + k) is the factor which takes intO added mass. and By doubling the displacement it means an A1!3 about 25% of F = -R gives account hydrodynamic the This factor certainly varies from ship to ship and from coithe dition to condition and possible also together with the velocity of Ship. that the is assumed As these variations are not fully known, it say factor is constant, equal 1.05, and it is therefore not possible to anything and about the influence t Ofl added màss of the hydrodynamic SH. In the diagram fig. 6 coasting with propeller winilling near (T = 0) is shown for different ship types. As mentioned above the effect of the displacement' appears clearly and further more it appears that the an play ship typé and consequently the ship form and the initial speed important part in the sequence of events. From the equations (li) and (12) it appears that the ship' s veloan city immediately before thé beginning of the stopping manoeuvre has influence on the stopping distance and the stopping time. By coasting it appears that the influence is immediate: when the velocity If the pro- the stopping distance and the stopping time becomè greater. peller is reversing during the "braking, the influence increasïng, i' will be very drastically camouflaged. This question will be examined in the following. The force F = T(1-t) - R, i.e. the tow force has to be as great as possible in order to give a. and stopping distance. or the short braking force, stopping time R- (R negative during backing) If the resistance of the ship has a great negative value, the stopping time and the stop- ping distance will of course be small.. A large value for F can be obtained going astern by having a large propeller thrust, The necessary prope11er thrust velocity V T at the required for propulsion can be obtained for a single screw ship either by small quickly rotating propeller or a big slowly rotat-ing using a propeller. 15 TANKERS BULK CARRIERS 15 1o00000" 12 - 12 15 V V 10 IO s., 200O0t 000 t 8 p,P::; I-III m 30 000 rn/s 5 4 km 5 200000 t 30000 o - - 3OminAO 20 10 t T o 1000 sec 2000 50 0 3000 ô CONTAINER SHIPS o 30lfl40 20 10 toòo 20b0 50 sec 3000 REFRIGERATED CARGO SHIPS 15 12 50000 t 15 12 s s V V .5 35000 ' t 8 10 10 km rn,5 rn/s / 5 4 LA \\ 5 km l0000t -s 7000t V -----.--- 8 - 0000 bOOt 50000 t 30000 I o A 0 20 10 30 min 40 2000 sec o o 0 t 3000 GENERAL CARGO SHIPS 12 15 2'OOOt V s 10 o 50 30 min 40 20 10 15 - 12 s- s lSIOtA 8 8 i000t \Y14 A km ,-20000t km rn,5 15 000 t 4 5 7 o 30 min 40 10 o moo Fig. 6. 2000 sec o 50 0 3000 0 20000 t - 20 10 30 min 40 0 50 I .................................-.' g sec 1000 2000 Coasting with propeller windmilling and rotating without producing any thrust. 3000 16 An investigation was carried out to find out of the propeller on the stopping the influence of the size time and the stopping ship "u". (dates for. ship "U", see appendix 6). distance for eqLp- The ship "U" was ped with one of the following 16 propellers: The propeller diameters D = 5, 6, 7 and 6 ni ratio P/P 0,4, 0,8, 1,2 and 1,6. ccnbined with the pitch It was assumed that the generalized 35000 PD SHIPU' 30000 5m D 6m V = 1.5 knots hp 7m '8m ,'D, PI 25000 ,, , 20000 ..4br 15000 10000 5000 4 ) - 10 Fig. 7. 20 1 REVSk- 40 Necessary power for shi "U" equipped, with different própeiiers. n Si 17 characteristics of these propellers were the same strörn (61. By generalized propeller characteristics that the characteristics cover all combinations stated as by Nord- meant here it is of speed and revolu- tions both positive and negative. The calculations werè carried out on condition that the machinery was always able to deliver sufficient power to move the ship "U" with a velocity of 1.6.5 knots. Furthermore it was assumed that the machinery might be reversed instantaneously and be able to deliver negative a Going astern the turning mcgnent numerically equal to the ahead moment. moment and the maximum number of revOlutions could not maxim ceeded. be ex- The calculation procedure is discussed in appendix 2 and 3. The necessary power for the ship "U" is shown in fig. 7 as a function of the propeller number of revolutions. As will be seen, there is a very great variation in the requirement power. The result of the calculation is indicated in table 1. It appears from the table that the than the shortest time and the longest stopping distance is about 27% longest stopping time is about greater than the shortest distance. The larger propeller 24% diameter the 5 6 7 8 549 510 485 461 2047 1934 1875 1742 469 471 469 449 1764 1757 1747 1688 471 468 463 442 1741 1715 1682 161]. 498 480 477 1827 1765 1735 D P/D\ t (sec) 0,4 S (m) t (sec) 0,8 S Cm) t (sec) 1,2 S (m) t (sec) 465 - 1,6 S (m) Table 1. Stopping time t and track reach 1695 S for ship "U" equipped with different propellers (16,5 knots). ( greater S) 18 shorter stopping time and stopping distance. Futthermore it noted is that the propeller with the smallest pitch ratio is the poorest in stopratios ping' the ship and that the propellers with the large pitch also poor. The conclusion is: of The optinnun propellers for the propulsion aleo are the ship will of be the most suitable for the stopping the ship. The picture. is quite different during coasting wïth windmilling (Q = 0). prqpeller the For the same ship "U" equipped with the same 16 propellers the time and the run distance were determined when city of the ship was changed from 20 knots to 4 knots. At the velo- greater the pitch ratios the propeller diameter had only a small influence while the change of the diameter from 5 ni to 8 m. caused a reduction distancel of about 10%. in time and At a propeller diameter of 8 rn the change of the pitch ratio from 1.6 to 0.4 showed that the time and stópping the stance would be reduced with about 11% and 14% respectively. The dicon-. clusion is then as expected: When coasting with propeller windmilling the propeller with the largest possible dicvneter cowl the least possible pitch will be mo8t suitable for stopping the ship. ¡t will be seen from Fig. i that the force has the greatest né- F gative value at.the greatest possible number of revolutions During the stopping manoeuvre it is important to torque. or the greatest obtain possible numbers of revolutions or torque as soon as possible. more it turns ot fr Fig.5 Farther- as mentioned before, that the relation b- tween the torque and the number of revolutions is only to Some exteflt dependent on the, reversing time of the machinery. On the other hand this relation will, to a great extent be dependent on the Fig. 8 shows the relation between torque and rate of chosen propeller. revolution the operation, "full ahead" to "full astern" for ship "U" .durin equipped with different propellers. The longer time the operation "full ahead - full astern" lasts the longer will be the loss in velocity of course, but generally it will not be' advantageous to spend much time on this operation as the reach naturally increases. total track 19 150 Q ". "FULL AHEAD" Mp m 100 :0,8u D =8m 7 50 6 5m o 50 loo "FULL ASTERN' -150 -200 -100 Fig. 8. o RPM n 00 Relation between torque and number of revolutions per minute during the óperat ion "full ahead" to "full astern" for ship "U" equipped with different propellers. The term "full astern" may be interpreted in severa.], ways. In the present investigation it was assumed that the engine when going astern could produce a torque equal to that going ahead and that the rate of revolutions can be. the same in both directions. This is not the case with many types of engines. The availablé power with machinery going astern will be only a percentage of the fOrward full power. This influence will be studied in more detail. stoppïng time and stopping distance for ship "U" have 1ers. determined been after having been equipped with one of the above-mentioned 16 The effect of the ship going ahead with avelocity. of has been determined and the corresponding torque Q on the The pröpel16 knots propeller has been used as the starting point. The stopping time and the stopping distance has been determined when the torque -Q, -2/3 Q and -1/3 Q was available when the stopping manoeuvre was started partly with the velocity of 16 knots and partly with an imagined velocity of 2OE knots The 20 calculations were perfàrmed under the condition that. and t = 0,20, and w = 0,20 and t = 0,10 w = 0,40 réspectively. Ftzrtheinore it was assumed that the machinery was arranged in such a way that either the torque or the number of revolutions were constant during the ping manoeuvre. The procedure has been adapted as mentioned dix 2 and 3 respectively. In accordance with the above-mentioned calculatiOns of Q to 2/3 Q and 1/3 Q stop- in appen- the reduction results in the following: When the torque is constant during the stopping,a reduction of the propeller torque from Q to 2/3 Q will get the result that the stopping ti.me will be izcreased wïth about 35% and that the stop-) ping distance will be increased with about 30%. It is nearly same whether the ship is equipped with a large or a the small propel- 1er or with a propeller with a large or small rate of revolutions. When the torque is constant during stopping, propeller torque from Q to a 1/3 Q will mean reduction that the time will be increased with about 110% and that thé of the stopping stopping di- stance will be increased with about 85%. Just like 1) the type of propeller has a very little influence on these relations. When the number of revolutions is constant during stopping, a re- duction of the maximum available trque from the Q to 2/3 Q has effect that the stopping time will be increased with 40% (the average value in this investigation was 67%) and stopping distance will be increased with 25% to 80% value in this invéstigation was 45%). to 120% the that (the average The srna1let propellers will have the minimum increases, while the 8 rn-propellers with a pitch rtio 0,4 will have the greatest. Keeping the number of revolutions constant uxing the stopping, reductioh of the available maximum torque from Q to 1/3 Q a will mean: that the stopping time will be increased 3 tò 4 times (the average value in this investigation was 3.59), that the stopping distance will be increased 2 to 3 times. average value in this investigation was 2.63). (the 21 8. CALCULATED TRACK REACH AND ST9PPING TIME FOR SÑIPs OF DIFFERENT TYPES. For a number of ship models and ship sizes the track reach and the stopping time have been determined under the condition that whole the engine power is available during the stopping manoeuvre.. However, there must be the limitation that neither the torque Q nor the number revolutions n propulsion. In appendix 6 the main dimensions and several numerically must exceed the existing values been given for the ships used in the investigation. of for normal data The method have of thé calculation is explained in appendix 2 and 3. Also here the change from full ahead to full astern is assumed to take place instantaneously. The sequence of the stopping manoeuvre, is illustrated, in the figures 9-14. The abscIssa is here the time and the ordinate is partly the and partly the distance run. the föllow-ing The stopping manoeuvre for velocity types of ships are illustrated: fig. 9 -fig. 10 Tankers Bulk.Carriers fig. 11 Container fig. 12 Refrigerated Cargo Ships f i. 13 Cargo Liners fig. 14 General Cargo Liners Ships In most of the calculated examples it has been ships have only a single screw for propulsion. assumed In the screw ships this has been indicated cn the figure. case that of the twin The dotted line in- dicates that this curve has not been completély calculated. It will be noted that the stopping time and the track reach vary very much from ship to ship and with the initial velocity. On the other hand the relative sequence of the stopping manoeuvre are the same fOr all the models. on the whole 22 TANKERS 15 V:1kflotS V (7,ri%) // - ' " t (2 prop. '.000 t0 t t (2p,tp.) S (823m,4) 500 ''' t (2 prop.) 410 4 3000001 2prop.) km rn/s 1000''' knots 5"000tC2propJ SV A km rn,9 5 o t 1000 sec 1500 o is :18 knots r (D9,9m) 2' :. :':.1t (D 300''OU2pro' lOO'' t(D8.Im) f \\,. , e V5-=2. knots (j, .n)) 4 t(0'(0.3e) 5 2 OD t 1500 S A 200000t(D.9.Im) km mf5 2 iûoösec t 410 0,7) l00000('rB.9rn) o 1500 15 SV A 10 Io 6 500''' t '1000000 t .2prop) (26'%) V 1000 sec 2000 2060 0Ç012O0c t 1000 sec "O 1500 t 2000 Stopping diagrams for tankers. Fig. 9. BULK CARRIERS 3 15 = 14 (yomh) V 3 15 SV knots V51knots ( S 23"v) A .50000t io 210 A -- km 30000 t 400 sec o km m 1 o 2 50,''t 00 t o 800 5 o 200 0 400 sec 600 15 e 3 V5 = 18 \.20knots .Ffl) knots (26"}t) V (0) A lo 50000 t(7,m) 50000 t (Z2m) :. o o \ 'tFi ---c°r - \ S (1' 2 S km A 50''t 30000 t 000 t 200 400 Fig. 10. sec 600 200 400 sec 600 Stoppingdiagrazns for bulk carriers. 23 CONTAINER SHIPS 3 15 SV \S=? !4:25 knots 86'%) ( 3 15 10 5goot 35 210 2 '° 0Pî(t2.. : km t (2 prop. 5 km 5 1 35OOO 200 sec 100 t 300 0 400 200 sec 100 -400 t 300 3 15 s knots V 2 10 km "Vs I 5 S. - 35000(It2..-.) 200 Sec 100 o prop. Fig. 11. t 300 400 Stopping diagrams for container ships. REFRIGERATED CARGO SHIPS 15 V V5o8knots 9.26m,4) V ,Jr .0 JlL 10 lSOsec 200 50 o V5: 22 knot- Oknots Vs S (1429m,4) l0 A l0000t 7000 t 5 45 A' biri00(t o 25 50 lSOsec 200 100 t 250 '.5 15 1.5 4knots S (I1$2Tt)) V 1.5 S (12.35"W V 0 A "I.- t0000t S 70.. 45 - Fig. 12. too l5Osec 200 km A 'Vs 5 50 1.0 km t 250 s 5 0 50 t0000i boot 100 ISO sec 200 t. 250 Stopping- diagrams for refrigerated cargo ships. 24 CARGO LINERS 15 IS 1.5 Vs=leknots V SV A C26m/s) Vs: (9m/) 'knots 15000t . s km m, VTV5 455 5 15000 L. 10 1,0 s S L V 200 séc 300t. A. 200 Sec 00 'O. t 300 1.5 15 4:22 knots V S tm/i) (1 V L Vs: knots S (125'%) L 200001 20000 t 10 %010 1,0 km km 5 5 00Cc 200sec 100 Fig. 13. " o t 300 OES i00 2000Cc 200 sec I00 O o t 300 ¿.00 Stopping diagranis for cargo 1inèrs. GENERAL CARGO SHIPS 5 15 Vs: ßknofs \/Ííri 9.26'%) V Io 5 V 1,0 200001 10000 t t 45 5 00 2 2 knots 11,32 ') so ioo ISO sec oo t S AÌ. 116m) 0001m; 1,0 km 0000 tI 50 lOO Fig. 114. km -10000 t LS 1,5 V IO 10 rTy5 15 V s lO,29"/i) 20000 t 150 sec 200 o o A 1.5 VS :"Oknots .ISOsec 200 t 250 Stopping diagrams for general cargo ships. 25b 25 On the basis of this màterial, the following averages have' been have been found: Torque Variation of velocity Distance run .0 ]_00 o 20 70 40 40 50 65 60 30 85 80 15 95 100 0 100 It will be noted that the characteristics.of thé machinery ignored. On the baSis of the above-mentioned table or the figures 9-14 and with knowledge 6f the òharacteristics of the machinery easy to design curves which give the väriation of velocity and th it is di- stance run during the stopping man9euvre. in the diagram fig. 15 the values of the' track reach (S) the various ships fr fig. 9-14 are ut together with the S. As mentioned in setiôn 5 this is that part of the for distances track reach which depends on the characterIstic of the machinery. The total track reach is thus determined by ST S + SHY Asan example, a tanker with a displacement Of 300.000 tons,with a velocity of 8 rn/s and with the'machinery reversed at 125 s, is expected to have a track reach of about ST = l000 + 3700 = 4700 m In the construction of the diagram it has been. assumed necessary effect for propulsion can vary with ±10%. This that. the scattering in the effect results in a scattering of the SHY_values. This is shown by the hatched Spaces on the diagram fig. 15. A special calculation of the stopping distances and the times has not been carried out for ships running in ballast. stopping A rough esimate can be carried out in the following manner: With the available '-I. P 'D (j] (D cl- (D (D I-i) F-i. e o o M lo 5 REFRIG. BULK CARRI 5000 SHY /p 15 CARII 1000.1 IP I' p 2'O 10 l0O C 00 t 300000t (2P) 5000001 C2P) 2'S 1000000 t (2P) TANKERS 20 001 3'O 15 si V 3 TIME KNOTS rn,5 20 S mil Amin 3 man REV1RSAi"'. 60 s 30s SHIPS 50000 t 35000 t MACHI NEL 2 min CONiAI NE ) 27 engine power the ty y m/s. ship SHY with the displacement x t will obtain the veloci- can be read in the diagram at the velocity ship ôf the same type in question but with a displacement of can be read at the velocity y, using the same curve for y x t. Also as for a full loaded ship. 9, CoNcLusioNs, The type of ship, dimensions, mass and velocity are the parameters of greatest importance for the track reach and the of the ship. The type of the ship has the importance that the stopping effect propulsïon machinery of the ship is thus determined. time of Hereby the also the available effect for stopping is determined. When the parameters mentioned in a. together with the velocity and the machinery of the ship are determined, other factors have only a secondary influence on the stopping qualities of the ship. If shorter stopping times and track reach than usual the ship may be equipped with a special mechanism, are for wanted, instance parachutes or extra propellers. If the propeller is optimum for Ithe propulsion of the ship,it will generally be nearly optimum for the stopping of the ship. If a short stopping time and track reach are wanted, it is sary to have as far as possible the maximum available neces- efféct du- ring reversing. The mode of operation of the regulator put on the propulsion chinery has an influence on the stopping manoeuvre. Thus mathere will be a difference on the track reach and the stopping time, the number of revolutions or the torque are on a if constant level during the last phase of the manoeuvre. In the speçification of the propulsion machinery of ships it is necessary to estimate the time for the reversing of themachinery, for instance as a function of the nthnber of revolutions - torque. a and the 28 10, Lisi OF REFERENCES, [i] Clarke, D. and Weilman, F.: "Thé Stoppïng of' Large Tankers and the Feasibility of Using Auxiliary Braking Devices" ,Transaction of the Royal Institution of Naval Arthitects, London 1971, p. 139. (2] Guidhammer, H.E. and Harvald, 5v. Aa.: "Ship Resistance, Effect of Form and Principal Dimensions",. Akademisk Forla,Copenhagen 1974. Harvald, SV. Aa.: "Wake of Merchant Ships", The Danish Technical Press, Copenhagen 1950. Rarvald, Sv. Aa.: "Wake and Thrust Deduct.ión at Extreme Loadings", Publications of - the Swedish Experimental Tank, nr. 61, State Propeller Shipbuilding Gòteborg 1967. The M9 Panel of the Ships Machinery Committee: "Guide to the Selection of Backing Power" Technical and Research Bulletin No. 3-5,The Society of Naval Architects and Marine Eigineers, New York 1957. Nordstrom, H. F.: "Screw Propeller Characteristics", Meddelanden frân Statens Skeppsprovningsanstalt, Nr. 9, 1948. (7] Norrby, Ralph A.: "A Study of Crash Stop Test with Ships", Chalmers University of Technology, Single Screw Göteborg 1972. 29 11. APPENDICESI APPENDiX 1 Calculating Procedure for Stopping Manoeuvre, Stage 1. Calculation of reach and loss of velocity during the time sary to change the number of revolutions from that neces- corresponding to "full ahead" to that corresponding to "full astern" has been performed as follows: Principal data: Ship (dimensions, form and mass (m)). Propeller (diameter (D) and pitch ratio (P/D)). Ship's speed, sailing freely (V0). Number of revolutions of machinery (n). Change of number of revolutions (an) per unit f time (frr). Diagrams giving ship resistance, propeller thrust and torque as function Of diameter,speed and number of revolutions, wake and thrust deduction coefficients (for instance from "Wake of Merchant Ships" [3]. Figs. 52, 58, 104 and 111 and from "Wake and Thrust Deduction at Extreme Propeller Loadings" [4]). CalcüJ.at Ing procedure: o Sailing freely, V = V0. TT =0 o R0 V0 A diagram R = R(V) R V0 A T0 A diagram T = T(V,n) A n. A diagram Q Q(V,n) T no Q0 1-t0 30 t=t =t Initial calculation. i = + frr o o O =n -n o AVA n1 diagram T = T (V,n) F' = T' 1 (1-t ) 1. F F R 0 1 T; = ½ frr ½ o in i = V + V o V A diagram AV n i R = R(V) R diagram T = T(V,n) A T i FI = T i VA Q 1. t i +tt 2 = n n -R A diagram Q = Q(V,n) n 1 TT -t I) 2 1 AVA n 2 diagram T = T(V,n) T' 2 1 Fri here analogous with E! T = T = T p + (p-1)frr or t 1 p-1 + At =n p-1 p AV A diagram T = T(V,n) p-1 p pp-I (l-t ) - R F'p = T'p p½ Ar F m p Vp =V p-1 T' +Vp ; F p-¼ = ½(Fp-1 + F') p 31 V ¿s. diagràm R = R(V) = T VA (l-t ) p n R - R p A diagram Q = Q,.(v,n) Q The procedure is.continued until the maximum negative number of restopped volutions, or the maximum negatïve manent is reached, or may be np = O even at if wanted. The manent Q may now be mapped as a function of V The speeds n (see. Fig. 5) . F may be indicated on the curve. and the forces phical integration of eq. (12). ratio as a function of V/F gra- of If the reaches are wanted they may be determined by means This is done by drawing a curve of the V. APPENDIX 2 The Calculating Procedure, Stoppi.ng Manoeuvre Stage2. constantly negative value, n variable (free). A regulator being attached to the machinery provides that torque is kept constant.. The calculation of the loss of velocity, reach and the elapsed time at constantly negative torque Q the the (reversing engine) takes place in the following way: T = tq Vq (principal data, see also appendix 1) VqAQAdira1n Q=Q(Vfl)'flq Vq A ng A diagram T = T(V,n) diagram R = R(V) V A F = T (1-t ) - R q q q q q T R q This procedure is executed for the points, in diagram Q = which has the chosen Q and which is placed on the. curves corresponding to a round number of V. 32 The procedure gives F-values for different values of V. The curves for 1/F and V/F can be drawn, and the. stopping tizne and thé stopping di- stance can be determined from the formulae (11) and (12) by making a graphic integration and using a planimeter. APPENDIX 3, The Calculating Procedure of stage 2 of the Stopping Manoeuvre, n constantly negative value. regulator beig attached A to thé number of revolutions is kept constant. machinery The calculation of the velocity, the reach and the elapsed time at cnstantly of 'revolutions V = Vr A loss of negative, number n '(reversing engine) takes piace in the following way: T = Vr A n provides that the (principal data, see also appendix 1) diagram Q = Q(V,n) V A n A diagram T = T(V,n) Vr A diagram R = R(V) Rr F = T (l-t ) - R .r r r r This procedure is executed for the which has the. chosen n to the constant V points in diagram Q Q(V,n), and which is placed on the curves corresponding values. The procedure gives F-values for different values of V. The curves for 1/F and V/F can be drawn,and the stopping time and the stopping distance can be determined by the formulae (il) and (12) by the use of planimeter and graphical integration. a 33 APPENDIX 4. The Calculating Procedure of the Stopping Qualities when Coasting with Propeller Windmilling. The calculation of the loss of velocity, the run distance and the elapsed time when coasting with the propeller wthdmil1ing and rotating wIthout producing thrust has been made in the following way: For a number of characteristic ships (see appendix 6) the curves of resistance have been determined by use of "Ship Resistaric&' ,ref. [2). With regard to other assumptions for the calculatIons, see appendix 1. R=f(V) R F When F has been calculated for a suitable nthnber of yalues of V, the curves för 1/F and V/F can be drawn. Rñn distances and loss of velocity can be determined by use of the formulae (li) and (12) in section 3, and the integràtions can be made graphically and by use of a planimeter. APPENDIX 5. In the investigations on the influeÏce of the vaious parameters on the stopping ability of the ships the results from earlier perfórmed model tests have b'een used (ref. [4]). The -results have been transferréd to a ship marked Ship "U", wIth the following main data: 210m 205m L = B =30,5m =l1,5m pp T L/V = 58.000 rn3 = 5,42 ( = 59.450 t) =0,807 6 pp. L/B = 6,89 B/T = 2,65 LCB/L = -0,Ö20 6 = Ö,787 = 0,997 tp = 0,786 34 APPEÑD'IX 6. The main dimensions and various data for the ships, the model family, used in the investigation are as föllows: Type Displacement t Tanker Bulk Carrier Container Ship Refrigerated Cargo Ship Cargo Liner General Cargo Ship LX B X T mx 6 V - rn/s service Knots 1.000.000 400 )c 96 X 31 0,820 8,23 16 500. 000 315 X 77 X 25 0,804 8,23 16 300.000 265 X 65 X 21 0,809 8,23 16 55 X 19 0,795 8,23 16 4l 0,796 8,23 16 X 200. 000 235 100.000 230 X X 13 50. 000 180 X 33 X 10,5 0,782 8,23 16 30.000 140 X 27 X 10 0,774 8,23 16 200. 000 235 X 55 X 19 0,795 7,72 15 100.000 230x41x13 0,796 7,72 15 0,782 7,72 15 27 X 10 0,774 7,72 15 X 0,556 15,43 30 X 50.000 180 X 33 30.000 140 50.000 255 X 32 35.000 228 X 29 X 9,6 0,538 15,43 30 10.000 130 X].8,7X 7,5 0,535 11,83 23 7.000 115 X16,7x 6,7 0,531 11,83 23 22. 000 163 X 22 X 9 0,665 11,32 22 15.000 147 X 21 X 8,2 0,578. ll32 22 20.000 135 X 22 X 9 0,730 10,29 20 10.000 109 x17,5x 7 0,731 1Ö,2. 20 X 10,5 10,75