Model-Ship Correlation Method in the Mitsubishi Experimental Tank By Kaname Taniguchi*, Member Summary The model-ship correlation method which is developed and used in the Mitsubishi Experimental Tank is presented. From the ship trial analysis, two correlation factors, i. e. the so-called roughness allowance factor and a wake correction factor are analyzed. The analyzed data of these correlation factors are given for more than 50 vessels of miscellaneous kinds. The power estimation of an actual vessel using these correlation factors is the reverse process of the trial analysis. The detailed explanations of the whole system of this method are given. Contents 1. Introduction 2. Model Test 3. Ship Trial Analysis 4. Power Estimation 5. Acknowledgement 1 Introduction It is not an easy matter to make a precise prediction of performance of an actual ship from the model tests. Indeed, the higher the requirement of accuracy of prediction is, the more the difficulty is. This difficulty comes mainly from the lack of our knowledge of the scale effects on the resistance, epropulsion factors and the characteristics of the propeller. The method for correcting these scale ffects, the so-called model-ship correlation method is one of the most important problems for our tank people. It has been an ever hot problem in the International Towing Tank Conference. At the present stage of our knowledge, it is not possible to make a reliable prediction of performance of an actual ship from the model test results and the pure theory only. We have to rely upon the actual ship data and to use the empirical correlation factors which are analyzed from those actual ship. data. Therefore, it is essential to gather the reliable data of such analysis as many as possible, in order to develope a reliable model-ship correlation method. The Mitsubishi Experimental Tank belongs to a shipyard, one of the most powerful shipyards in the world, and has been testing directly every new ship which was built in the shipyard with the large scale model (7 meter as standard). SHP and the related data on the sea trials of these ships have also been measured by experienced staff of our Experimental Tank. So we are in the most favorable situation to investigate the model-ship correlation problem. The necessary conditions for a good model-ship correlation method are as follows : a) The accuracy and reliability are sufficient for the severe practical use. b) The assumptions involved in the method are reasonable and do not conflict with the theory. c) The method must be simple enough to be used in the routine works, and must be applicable to any type of ships, such as a high-speed planing boat. Recieved on December 17, 1962. * Assistant Director of Laboratory & chief, Experimental Tank, Mitsubishi Shipbuilding & Engineering Co. Ltd.
18 d) The method must be elastic to allow a necessary improvement or modification in accordance with the development of our knowledge of the scale effect. Strictly speaking, the method of model-ship correlation involves so many complicated factors in details, that there are many, as many methods as the numbers of experimental tanks in the world. And the international unification of the method is hoped eagerly. Though our model-ship correlation method is not perfect, it satisfies practically all the above conditions and has been used satisfactorily for long years. The author presents this paper, hoping it will be of any service to the concerned circles and that he will be given some useful suggestions as to the further improvement of this method. 2 Model Test Model test is performed with a large scale model, 7 meters in length as standard. Test procedure is conformed to the I. T. T. C. -A1B2C1 method'), i. e. the resistance test and the corresponding selfpropulsion test are carried out on the same day. As for a single-screw ship, these tests are performed with full appendages (bilge keels and rudder), but for multiple-screws ship the resistance tests are performed both with and without appendages. The propeller open-tests are performed immediately prior to the self-propulsion tests for propeller to be used, at two kinds of revolutions. The one corresponds to the standard Reynolds number (Rek= 4. 5 ~ 105) for standard use and the other corresponds to the rated RPM of the ship. The latter characteristics are used for the analysis of the self-propulsion tests. There are, however, usually not so much differences in these two characteristics at two kinds of revolutions. Resistance tests are extended to the low Froude number as low as O. 1, from which Hughes' form factor K is also analyzed. The mean Reynolds number at 0.1 Froude number is approximately (5-7) x 106. From the resistance tests with and without appendages (for multiple-screws ship), we analyze the total appendage resistance coefficient. It is defined as follows : Total appendage resistance coefficient,capp=ƒ R/ƒÏ/2 EƒË 2F where, F=Total wetted area of the appendages, integrating the girth length along ship length (not along the water line). and the corresponding Reynolds number, Rnapp. =ƒë E F/2/ƒË. Capp is plotted on the basis of Rnapp and the general trend of Capp against Rnapp conforms to that of usual friction line against R. From these plottings we analyze the resistance ratio (corresponds to Hughes' ƒá) and apply the same resistance ratio to ship calculation at the corresponding Rnapp of ship and Froude number. Fig. 1 shows an example of this plotting and Fig. 2 shows the similar plottings for the Lucy Ashton's experiments2) including the actual ship's data. From these figures, the validity of our practice to calculate appendage resistance may be allowed. As for the self-propulsion test, we usually conduct the test at the ship point of propulsion. In this case the resistance coefficient of ship is calculated from the following formula : and the appropriate skin friction correction is applied. But in a special case, e. g. in the case of high speed planing boat and of the self-propulsion test in waves, we conduct the test at the model point of propulsion. From the self-propulsion test, we analyze the self-propulsion factors by the thrust identity method using the above stated open-characteristics of the propeller at the Reynolds number corresponding to the ship's rated RPM. It is a generally recognized fact that the self-propulsion
Model-Ship Correlation Method in the Mitsubishi Experimental Tank 19 Fig. 1 Examples of plotting of Cap p against Rnapp Fig. 2 Plotting of Capp against Rnapp (Lucy Ashton)
20 factors are practically independent of the propeller loading within the practical limit. We calculate the DHP of ship from the residual resistance coefficient, propeller characteristics and the self-propulsion factors with appropriate correlation factors as shown later and do not calculate directly from the DHP of model by the mechanical scaling up. Therefore, the propeller loading is not a substantial problem for us, i. e. in our self-propulsion test it is not a matter of substantial importance for us which friction line is to be used or how much the roughness correction is. In the case of ship whose propeller is expected to suffer severe cavitation, we conduct also the cavitation test for her model propeller and measure the cavitation characteristics in the homogeneous flow. We use usually a current-meter to get a more reasonable relative speed to water. The currentmeter is positioned in the centerline plane of model, one ship's length forward of F. P. of model and at 150 mm below the water surface. It is 120 mm in diameter and two-bladed windmill type, supported by one jewel bearing and one plastic bearing and its number of revolution is counted electronically without any gear friction. The wake velocity measured in the test run is approximately +1% of the velocity of previous measuring run. 3 Ship Trial Analysis Sea trials are performed carefully in accordance with the trial code almost same as that of the 41 st Research Committee3) of the Shipbuilding Research Association of Japan. The effects of the wind and tidal current are corrected to the tank test condition by the J. T. T. C.-method4). This method, however, fails in the case of athwartships wind, then we use a more rigorous method') of correction, taking the effect of small speed difference in the up and down runs into consideration. The torque of the propeller shaft is measured with a precision torsion-meter (electric type') or optical type), however, the rigidity of the propeller shaft is not usually measured. We have already many such data, i. e. the modulus of rigidity of 36 intermediate shafts were measured by Dr. Togino and he got7) We use this mean value, i. e. G=8. 31 ~ 10 kg/cm2. Zero line of the torque measurement is determined as the mean of the both readings of the torsionmeter in the dead slow rotation of shaft in normal and opposite directions. From this measurement the stern tube friction may be estimated, but we do not use this value to estimate DHP/SHP, because the stern tube friction at the normal running condition may not be same as that at the dead slow turning condition. From thus measured and corrected data, we make a ship trial analysis as shown in Table 1. In this analysis, the assumptions as for the negligibleness of the scale effect on the following items are made : (a) relative rotative efficiency (b) thrust deduction factor (c) propeller characteristics (d) residual or wave resistance coefficient. In Table 1, in the step (4), we take e7=0. 98 as standard, irrespective of the value of stern tube friction above mentioned. However, it may be more reasonable to deduce the constant torque loss corresponding to approximately 2% of the normal rated torque. In the step (7), we calculate the torque coefficient corresponding to the open-condition in accordance with the thrust identity system. The propeller open-characteristics used in the step (8) and (9) are derived from our standard propeller charts (Rek= 4. 5 ~ 105) with the appropriate correction for area ratio, boss ratio and blade thickness
Model-Ship Correlation Method in the Mitsubishi Experimental Tank 21 Table 1. Ship Trial Analysis ratio. We have found from our long experiences that the much better consistency of the ship trial analysis can be obtained by the use of the above mentioned characteristics than by the use of the individual open-characteristics of the propeller used in the self-propulsion tests. In the step (15), we make the correction for the added air resistance (in still air) corresponding to the difference of the still air resistance between the actual ship and the model. From the ship trial analysis, we get two correlation factors, i. e. e (step (11) ) and cfs (step (20)). The former is the empirical correction factor for the scale effect on the wake and latter is the similar factor for the so-called roughness correction. The steps (18) -(20) may be modified to follow Hughes' methods) and of course, we may modify the step (20) to get (roughness allowance) instead of cfs. In this analysis, the assumption of the negligibleness of scale effects on er, t, and cr (or c) is allowed practically, i. e. the scale effects on these factors are not so much if any. And the Kt-Kg relation of the propeller suffers much less from the scale effects than the case of Kt-J or Ifq-J relations. Therefore, the analyzed cf, (or cf) has a pretty clear physical meaning and universality, though it contains all the residuals from the experimental errors and the assumptions made. But the wake correction factor, ei (step (11)) suffers directly from the scale effect on the K5-J relation. Therefore, it depends upon the Rek of the propeller charts used and the Reynolds number on which the model wake fraction wm is measured. It is essential to check carefully the propeller chart and wm in the case of utilizing the similar correlation factors from the different experimental tank or of comparing such data from the different sources.
22 Figs. 3-6 show the such analyzed results for about 50 single-screw ships, built recently in our shipyards. These vessels are all welded and painted with usual commercial antifouling paint. In our trial analysis method, the problem as to which friction line is adopted as reference is not of substantial importance. We use at present Prandtl-Schlichting's formula. However, it is not difficult to convert the results into those corresponding to other friction formula. Fig. 3 shows such a result for z.cf using the I. T. T. C. 1957 model-ship correlation line as reference friction line and Fig. 4 shows a similar plotting for Cj using Hughes' method. Fig. 5 shows a plotting of et for singlescrew ships and Fig. 6 the correlation of these et and cf (I. T. T. C.). From Figs. 3 and 4, we can see a slight superiority on the consistency of plotting in Fig. 4 (Hughes' method) over Fig. 3 (I. T. T. C. friction line). A general reasonableness of Hughes' method is thought to be shown in this comparison, though the validity to use his form factor K got in the low Froude number into the higher speed region remains some questions. In Fig. 6 we can see a correlation between the ei is. By the simplified assumptions that (a) the velocity distribution in the frictional belt around propeller obeys the 1/7 th-power law and is uniform in the depthwise direction, (b) the magnitude of the frictional wake can be determined by the momentum equation so that the drag due to the momentum loss is equal to the frictional resistance of the model or the ship, we can calculate the approximate relation between cf (I. T. T. C.) and et theoretically. In Fig. 6, thus calculated line is shown for reference.
Model-Ship Correlation Method in the Mitsubishi Experimental Tank 23
24
Model-Ship Correlation Method in the Mitsubishi Experimental Tank 25 Fig. 6 Correlation between ef and et (single-screw ship) For twin-screw ships analyzed et is 0.95-0.98 and there can be seen no difference in CJ between the multiple-screw ship and the single-screw ship. 4. Power Estimation The power estimation is naturally a reverse process of the ship trial analysis. Our method of power estimation is shown in Table 2. It is thought that there remains nothing to be added for detailed explanation except some minor points. In the steps (4)- (7), the modifications have to be made in accordance with the analysis method and the reference friction line adopted. The step (10) is corresponding to the step (15) of Table 1. In the steps (18)- (20), we use the ãkt/j curve against J from the estimated propeller characteristics. These characteristics are also got from the standard series charts of the propeller by correcting the effects of difference in area ratio, boss ratio and blade thickness ratio of the actual propeller from that of the standard series propeller. This process of power calculation is also programmed into the electronic computer. As seen from the Figs. 3-5, the standard deviation of and et are approximately } 0.1 ~ 10-3 and Therefore, the standard deviation (error) of the power estimation is approximately }0. 25 knots for the same power, taking the correlation of cf and et (see Fig. 6) into consideration. However, for usual cases, in which some appropriate type ships can be used, the estimation error of the speed can be expected to approach within }0. 15 knot. This has been proved from many examples during a long period of time. For special cases, in which the severe cavitation is observed, the trial analysis must be performed first in the speed region in which no cavitation occurs. From this analysis, z.c.f and et are estimated and then we extend the power calculation up to the higher speed zone using these cf and ei, assuming that there is no cavitation. From the actual difference of the measured SHP and RPM and such calculated SHP and RPM at the same speed, we can analyze the cavitation effects, from which we
26 Table 2. Power Calculation get the correction factors Kkt and Kerr for cavitation characteristics, including the effect of shaft inclination on the cavitation. The power estimations of such vessels are quite reverse of the trial analysis. We calculate first the power and RPM for the assumed condition of no cavitation and then correct them using Kkt, Kep and the cavitation characteristics of the propeller used. The latter calculation of correction may be performed by trial and error method easily, assuming RPM of propeller at a given ship speed. By this process of power estimation, we get satisfactory results for the naval vessels of Froude number more than 0.5 and also for the high speed planing boat up to about 50 knots. For the calculations of power and revolution in the regular waves, the same method may be applied. In the waves which are met practically the time mean characteristics of a propeller may be thought not to be effected by waves.9)10) And the time mean values of the propulsion factors are also shown'1) approximately equal to those in the still water condition. Therefore, it is only necessary to add the appropriate resistance or thrust augmentation due to waves (and due to wind if necessary) to the step (11) or (14) of Table 2. In the case of irregular waves, approximate time mean augmentation of thrust may be calculated
Model-Ship Correlation Method in the Mitsubishi Experimental Tank 27 as follows : 12) Transfer Function of thrust increase The validity of this approximate method is shown in the analysis of the " SS Nissei-marul3)." 5 Acknowledgement This model-ship correlation method has been developed by the author in these about fifteen years. In this period of time, a lot of assistance and cooperation were given him by the shipyards and the staff of the Mitsubishi Experimental Tank, especially Mr. K. Tamura and Dr. K. Watanabe. The author wishes to acknowledge the assistance given by them and to thank the director of our Laboratory for the permission of publishing this paper. References ( 1 ) 9 th I. T. T. C., Report of the Propulsion Committee ( 2 ) H. Lackenby : B. S. R. A. Resistance Experiments on the Lucy Ashton Part III-The Ship-Model Correlation for Shaft-Appendage Conditions. T. I. N. A., Vol. 97, No. 2, 1955. ( 3 ) The 4 1st Research Committee, Investigations into the Propulsive and Steering Performances of Super Tankers, The Report of the Shipbuilding Research Association of Japan, No. 31, Nov., 1960. ( 4 ) J. T. T. C., Standardization Trial Analysis Code (Draft), Bulletins of the Society of Naval Architects of Japan, Jan., 1944. ( 5 ) K. Taniguchi and K. Tamura : On the New Method of Correction for Wind Resistance-Relating to the Analysis of Speed Trial Results. Jour. of Seibu Zosen Kai (The Society of Naval Architects of West Japan), Vol. 18, Aug., 1959. ( 6 ) K. Taniguchi and K. Watanabe : A New Electric Torsion Meter for High Speed Naval Craft. Jour. of Zosen Kiokai (The Society of Naval Architects of Japan), Vol. 108, Dec., 1960. ( 7 ) S. Togino : The Measurement of the Modulus of Rigidity of Intermediate Shafts. Jour, of Zosen Kiokai, Vol. 95, Nov., 1936. ( 8 ) G. Hughes : Friction and Form Resistance in Turbulent Flow, and a Proposed Formulation for Use in Model and Ship Correlation. T. I. N. A. Vol. 96, 1954. ( 9 ) K. Taniguchi and K. Tamura : On the Performance of a Propeller in waves. Mitsubishi Experimental Tank, Report 221 (Apr., 1955) (10) J. H. McCarthy, W. H. Norley and G. L. Ober : The Performance of a Fully Submerged Propeller. D. T. M. B. Report 1440, May, 1961. (11) K. Taniguchi : Lecture on the Performance of Ship in Waves. J. T. T. C. Symposium on the Ships and Waves. (June, 1961). (12) Lectures on the above mentioned Symposium by K. Taniguchi and by H. Maruo (13) K. Taniguchi and M. Iizuka : On the Motion and the Thrust Augmentation of a Ship in Waves- Comparisons between the Model Tests and the Actual Ship Experiments of the " Nissei-Maru." Jour, of Seibu Zosen Kai (The Society of Naval Architects of West Japan), Vol. 17, March, 1959.