THE UNIVERSITY OF MICHIGAN College of Engineering Department of Naval Architecture and Marine Engineering Final Report RESISTANCE OF CONVENTIONAL SHIP FORMS WITH LARGE BULBOUS BOWS I. Series 60, CB = 0.60 2. Series 60, C = 0.70 B Tetsuo Takahei Finn C. Michelsen J. L. Moss Project Director: R. B. Couch Under contract with: Department of Commerce Mari time Admi ni stration Contract No. MA-2564, Task III Washington, D. C. Administered through: Office of Research Administration July 1964 Ann Arbor

CONTENTS PART I Page Introduction 3 Model and Bulb Designs 4 Test Procedure and Results 5 Conclusions 7 Tables 9 Figures 17 PART II Page Introduction 35 Model and Bulb Designs 35 Test Procedure and Results 38 Discussion of Results and Conclusions 39 Tables 41 Figures 49 Page REFERENCES 71 iii

TABLES PART I PART I I 6. 7~ 8. 9. 10. 11 Parent Model Characteristics, Series 60, CB = 0.60 Existing Bulb Design Data Bulb Characterist ics Model Resistance EHP and EHP/A for LBP = 600 ft Bulbless Parent Model Dimensions and Characteristics Large Bulbous Bow Models, Dimensions and Characteristics Model Resistance, Fu11 Load Condition, 1b Model Resistance, Ballast Condition, lb EHP for LBP = 600 ft, Ful Load Condition EHP for LBp = 600 ft, Ballast Condition v

FIGURES PART I 1. Wave pattern of high speed cargo liner model. 2. Bulb B1 lines. 3. Bulb B2 lines. 4. Bulb B3 lines. 5o Bulb B4 lines. 6. Bulb B5 lines, 7. Sectional area curves, bulbless parent and parent fitted with B1-B5 bulbso 8. CR curves, bulbless parent and parent fitted with B1-B5 bulbs. 9. EHP curves LBp = 600 ft for bulbless parent and parent fitted with B5 bulb, 10. EHP/A curves LBp = 600 ft for bulbless parent and parent fitted with B5 bulb. PART I I 11. Bulbless parent 902A bow lines. 12. Model 902A-B1 bulb lines. 13. Model 902A-B1M bulb lines, 14. Model 902C-B1 bulb lines. 15. Model 902D-B1 bulb lines. 16. Sectional area curves, 902A, 902A-B1, 902A-B1M, 902C-B1, and 902D-B 1 vii

FIGURES (continued) 17. CR curves, full load condition. 18. C curves, ballast condition. 19. EHP curves, full load condition. 20. EHP curves, ballast condition. 21. Wave profile at 4.525 fps, full load condition. 22. Wave profile at 4.08 fps, full load condition. 23. Wave profile at 3.69 fps, full load condition. 24. Wave profile at 4.525 fps, ballast condition. 25. Wave profile at 4.08 fps, ballast condition. 26. Wave profile at 3.69 fps, ballast condition. viii

Part I. Series 60, CB = 0o60

INTRODUCT ION In developing an efficient hull form, the naval architect automatically provides for beneficial interference between the bow, stern, and shoulders transverse wave systems. The addition of a bulbous bow, which generates large divergent and small transverse wave components, is aimed at cancelling the divergent component of the bow wave system. Techniques for optimizing bulb designs are somewhat different for the two following cases: (a) a bulb fitted to an existing hull, and (b) a hull designed with an integral bulb. This part of the report deals with case (a), and the necessary techniques of fitting a bulb to an existing hull are explained. In this case, a series of five bulbs for Series 60, CB = 0.60, hull form were designed and tested. The most serious problem is that the location and amplitude of the divergent wave system of the bulbless hull are unknown. These, however, may be fairly accurately estimated. Wave contour maps are the best means of determining location and amplitude of waves. Simple photographs of wave patterns can be helpful. High quality photographs of wave patterns can be obtained by spreading a thin coating of fine aluminum powder on the water surface. The high reflective qualities of the powder, combined with stroboflash lights, yield distinct pictures of the rapidly fluttering wave pattern. See Fig. 1. A quicker, but more approximate method, is to simply photograph the wave profile along the side of the model. However, the interference between the bow and shoulder wave systems tends to obscure the bow system. Were it possible to represent mathematically conventional ship forms accurately, wave contours could be computed. This would permit more accurate determination of bulb size and location. I

A bulb must be designed for a specific speed, since amplitudes of bulb and hull waves vary in opposite directions when ship speed is changed. However, an optimum bulb for a given speed will be effective, although to a lesser degree, over a wide range of speeds straddling the design speed. Therefore, it is not necessary to operate the ship at the specified speed in order to realize the benefits of the bulb. At speeds considerably lower than the design speed, the bulb is generally detrimental. MODEL AND BULB DESIGNS For this experimental research project on a large bow bulb fitted to a conventional ship hull, the Series 60, CB = 0.60, LBp/ /3 = 6.165, was chosen as being a typical hull form. The particulars of this hull are given in Table 1. Therefore, the design procedure followed is applicable to the design of bulbs for other conventional hull forms. For a given set of principal dimensions, displacement and stability requirements, a hull with an integral bulb may be calculated. However, in this case, as indicated earlier, the quicker but more approximate, alternative method of fitting a bulb to an existing hull was adopted. The data in Table 2 of the characteristics of existing hulls with large bulbs was used as a basis. Five different bulbs were designed and tested when fitted to the Series 60, CB = 0.60 hull form. The characteristics of these five bulbs are given in Table 3 and a description of each bulb follows. Bulb B1 This bulb was designed from the characteristics of C-201-F2 (Fig. 2) and also those of the'rKurenai-Maru" (see Table 2), taking into account design speed and the effects of ship's breadth and draft. 4

Bulb B2 B1 was modified so that no part of the bulb protruded below (Fig. 3) the baseline. In other aspects, B2 is similar to B1. Bulb B3 Tests results with B1 and B2 showed that these bulbs over(Fig. 4) cancelled, i.e., the counter-waves generated were too large. B3 was designed to create a smaller wave amplitude. Bulb B4 The size of B3 was retained, but the center of B4 was positioned (Fig. 5) aft of the FP in order to determine longitudinal location effects. Bulb B5 Both B3 and B4 were found to be still too large so that the (Fig. 6) waves generated over-cancelled. In addition the tests of B4 showed that longitudinal locations forward of the FP, instead of aft, are desirable for the bow in question. Therefore, the volume of B5 was decreased from that of B3 and B4, and its center was positioned forward of the FP but not as much so as in the first three designs. Presumably, further alterations could optimize the bulb design. However, the intention here was not necessarily to find the most desirable bulb, but rather to show typical steps in design and testing in order to find the;:optimum bulb. TEST PROCEDURE AND RESULTS A 14 ft (LBp) parent model was used in the tests. Resistance and propulsion test results have been reported previously. (Ref. l).* Other than the bulbs, the rudder was the only appendage attached. The tests were carried out at constant draft, so that the addition of the bulb increased both wetted area and displacement over that of the * References listed at the end of this report. 5

bulbless hull. Turbulence was stimulated on the main hull by means of a 0.036 in. diameter trip wire placed 5 per cent of LBp aft of the FP, and on the bulb by round studs 0.032 in. in diameter, 0.020 in. in height spaced 0.5 in. apart.* The protruding ends of the studs were squared off. The test results were analyzed by The University of Michigan EHP computer program which makes a small blockage correction. (Ref. 2). The 1947 A.T.T.C. friction extrapolator was used to expand the data to a 600 ft LBp, with a roughness allowance of ACF = 0.0004. Figure 7 shows the sectional area curves for the bulbless hull and the hull when fitted with each of the five bulbs. Figures 8 through 10 give the test results in terms of CR, EHP and EHP per ton of displacement. Table 4 gives model resistance in lb corresponding to the bulbless hull and to the hull fitted with each of the five bulbs. Table 5 gives EHP and EHP per ton of displacement for a 600 ft LBp for the bulbless hull and for the hull fitted with each of the five hulls. In addition, the latter gives the per cent increase in EHP due to the fitting of the bulb as compared to the bulbless hull. It should be pointed out that some ambiguity is introduced regarding CR, since this coefficient is a function of wetted surface which is slightly different in each case. Instead of the wetted surface, the square of the constant characteristic length, either LWL or LBp, could have been used in the expression for CR, but this would have been against accepted practice. Also in the present case, as wetted surface increased, so did displacement, and hence resistance. Only slight discrepancies result when The position of the line of studs on the bulb was determined by the bulb and cone with its apex located at the center of the bulb and apex half angle of 65 deg. This location of stimulation is the same as used on sphere drag tests in order to induce turbulent separation.. 6

using the standard definition of CR. The test results are shown more strikingly in Figure 8. Bulb B5 is shown to decrease resistance, as compared to the bulbless hull, over a much broader range of speed than the other bulbs. However, the performance of B5 at high speeds is not as good as that of the first three bulbs. While bulbs B1, B2 and B3 over-cancelled, mainly because of their large size, B5 appears close to optimum with respect to both size and location. Bulb B5 may under-cancel owing to its small size. Bulb B2 had the lowest resistance at the high speeds, but nearly the same as B5 at the trial speed of 23.54 knots. As shown in Table 5, the reductions in EHP were 5.1 and 5.0 per cent for B2 and B5 respectively at 24 knots. The latter figures reflect differences in wetted surface and displacement not shown in Fig. 8. At the trial condition, both B2 and B5 bulbs enable the ship to attain about one-quarter of a knot higher speed with the same power, assuming the same hull efficiency. CONCLUSIONS The bulb designs and tests reported herein were begun before analytical investigations of the hydrodynamic characteristics of the bulbless hull form were in progress. In view of the information about the bulbless hull form gained through analyses reported under Task 1, bulb B5 appears to be closely optimized within the limitations of the two-dimensional linearized wave-making resistance theory, The next logical step would be to design a hull with an integral bulb based on the configuration of B5. By retaining the principal dimensions and displacement of the bulbless hull, further reduction in resistance in the design speed range should be expected. 7

Table 1 Bulbless Parent Model Characteristics Series 60; C = 0.60 D3 U of M Model No. 912 LWL = 14.235 ft. LB = 14000 ft. B = 1.867 ft. H = 0.747 ft. B/LL = 0.131 H/LwL = 0.0524 LBP/ 1/3 = 6,165 CB = 0.600 Cx = 0.977 C = 0.614 Design SpeedTrial Speedo V/'\L W = 0.894; v/\i 0.268 V/ \T~Z =L 0 o.952; v/ giTw =L 0.285 9

Table 2 Existing Bulb Design Data Ship Main Hull Characteristics *V Bow Bulb Characteristic No. or.....-12 — Model A L B/L H/L CB L/V1/3 l/2 E ao/L 8 V/V7 S/S AB/AX 1 C-101-Fl _I 0.0904 0.068 6.30 12.5 0.85 2.6 2.13 4.41 21.0 2 CFK-101-FF-1 - 0.0904 0.060 0.627 6.66 12.5 o0.85 2.6 2.51 4.89 25.0 3 CFK-101F2 0.0904 0.060 0.627 6.66 12.5 -- 2.8 4.60 6.99 40.5 4 C-201-F2 -- 0.121 0.074 5.52 18.o 0.90 3.3 4.o06 9.96 22.1 5 M44 -BB1 -_ 0.210 0.12 0.548 3.18 26.5 0.95 4.3 4.35 9.60 27.4 6 UF3(x UF7)F1 -- - 0.152 0.060 0.580 4.34 19.0 0.93 3.0 1.95 3.09 20.0 7 Railway Ferry -- 0.157 0.040 0.545 5.02 — 0.90 2.0 2.02 3.18 20.1 8 Ocean. Research Ship 642 147 0.224 0.065 0.486 3.90 13.0 1.00 2.5 1.92 4.64 16.5 9 Kurenai Maru 2,333 262 0.168 0.049 0.526 4.60 11.0 1.10 1.9 1.96 3.88 16.8 10 Jap. Escort Ship 2,890 378 0.116 0.031 0.511 8.13 7.7 | 1.10 1. 87 4.22 25.6. s, per Cent Remarks h/L t/L 4.0 4.0 Streamline form, rocker bottom 4.0 4.0 Streamline form, flat bottom 4.8 5.3 Streamline form, flat bottom 5.4 6.0 Streamline form, rocker bottom 7.5 5.0 Fishing boat 4.2 -2.0 Streamline form, simulated high-speed freighter 3.0 1.0 Modified streamline form 5.0 1.3 2.5 1.9 Passenger coaster 3.1 3.1l L=-LBp=length between perpendiculars, ft B=beam, ft H=mean draft, ft CB=block coefficient 1/2 oCE=half angle of entrance at LWL V=volume of displ. of hull without bulb SV=incr. of volume of displ. due to bulb S=wetted surf. of main hull without bulb S=incr. of wetted surf. due to bulb A=displacement, long tons V=speed in knots ao-mean radius of bulb=(width + height)/4 h=depth of bulb center below LWL e=longitudinal distance of bulb center from FP(+ forward, -aft) AB=transverse sectional area of bulb at its center Ax=main hull midship sectional area 11

Table 3 Bulb Character stics No. ao/L% h/L %.b/L % 6 % $/S% AB/AX% B1 2.05 4.05 2.74 1.91 4.54 19.5 B2 1.95 3.72 2.68 1.95 4.40 17.1 B3 1.84 3.68 1.20 1.42 3.20 16.9 B4 1.90 3.68 -1.90 110 139 14.6 B5 1.44 4.15 0.60 0.79 1.79 11.3 Remarks: Negative values of /L indicates a center of bulb location aft of F.P. L = LB 13

Table 4 Model Resistance |.......Pounds Resistance!-V' v,ft/sec Bare Hull B B2 B 3 B4 B5 0.3 1.912 0.43 0.48 0.54 0.53 0.54 0.52 0.4 2.549 0.82 0.97 1.00 0.96 0.92 0.90 0.5 3A187 1 131 1.53 1.58 1.49 1.45 1.30 0.6 3.824 1.89 2.11 2.19 2.05 2.09 1.92 0.7 4.460 2.55 2.76 2.86 2.73 2.75 2.52 0.8 5.097 3.31 3.58 3.57 3.42 3 49 3.27 0.9 5.736 4.65 5.00 4.96 4.92 4.86 4.59 1.0 6.372 7.02 6.56 6.66 6.79 6.7 6.658... _ o s- _ _....~............, —..... 1.1 7.009 8.80 7.94 8.09 8.03 8.19 8.08 1.2 7.647 -- 9.46 -- -- - 1 Test W8ter Temp. 70 1 772 70 68 F - L = L w 14

Table 5 EHP and EHP/nZ for LBp=600 ft EHP ii EHP/ZA K| V Bare Bare Hull B1 B2 B3 B4 B5 Hull B1 B2 B3 B4 12 0.486 2,250 2,900 3,000 2,930 2,820 2,630 0.0854 0.1080 0.1117 0.1096 0.1059 0. 13 0.526 2,870 3,630 3,790 3,650 3,580 3,300 0.1089 0.1352 0.1411 O. 1?66 0.1344 0. 14 0.567 3,620 4,450 4,620 4,450 4,400 4,000 0.1374 0.1657 0.1720 0.1665 0.1652 0. 15 0.607 4,490 5,390 5,640 5,380 5,380 4,820 0.1704 0.2007 0.1884 0.2013 0.2020 0. 16 0.648 5,450 6,410 6,730 6,380 6,470 5,710 0.2068 0.2387 0.2506 0.2387 0.2429 0. 17 0.688 6,620 7,610 7,980 7,420 7,670 6,780 0.2512 0.2834 0.2971 0.2777 0.2879 0. 18 0.729 7,960 9,070 9,350 8,700 9,o00 8,030 0.3021 0.3378 0.3481 0.3256 0.3379 o. 19 0.769 9,480 10,800 1 10,900 10,530 9,600 0.3598 0.4022 0.4058 0.3817 0.3953 0 20 0.810 11,300 13,090 12,850 12,170 12,380 11,580 0.4288 0.4875 0.4784 0.4554 0.4647 0. 21 0.850 13,780 15,870 15,380 14,700 14,660 14,190 0.5230 0.5910 0.5726 0.5501 0.5503 0. 22 0.891 17,400 19,200 18,480 18,100 17,980 17,540 0.6603 0.7150 0.6880 0.6773 0.6750 0. 23 0.931 22,390 23,100 22,200 22,230 22,200 21,610 0.8497 0.8602 0.8265 0.8318 0.8334 0. 24 0.972 28,000 27,150 26,580 26,600 27,040 26,600 1.0626 1.0111 0.9896 0.9954 1.0151 1. 25 0.012 33,680 31,100 30,850 30,900 31,900 31,400 1.2780 1.1580 1.1485 1.1563 1.1975 1. A Iv__,,' _. - ~, c m.r T r rri_ -01': _ _. % EHP Change Due To Bulb B5 B1 B2 B3 B4 B5,0990 28.9 33.3 30.2 25.3 16.9,1242 26.5 32.1 27.2 24.7 15.0.1506 22.9 27.6 22.9 21.5 10.5.1815 20.0 25.6 19.8 19.8 7.3,2150 17.6 23.5 17.1 18.7 4.8,2553 15.0 20.6 12.1 15.9 2.4,3023 13.9 17.4 9.3 13.0 0.9.3614 13.9 15.0 7.6 11.1 1.3,4360 15.8 13.7 7.7 9.6 2.5.5369 15.2 11.6 6.7 6.4 3.0,6623 10.3 6.2 4.0 3.3 0.8.8136 3.2 -0.9 -0.7 -0.9 -3.5 0015 -3.1 -5.1 -5.0 -3.4 -5.0 1822 -7.7 -8.4 -8.3 -5.3 -6.8 _ /- \=aoispiac me nz 1 intw. (, *y Il 26,34.'26,852 26,863 26,723 26,639 26,557 lI 11 I I I I52 i_ ** + when bulbous bow is inferior, - when bulbous bow is superior Design Speed Trial Speed V =22.08 knots V/ -V=0.894 V,23.51 knots V/V -LO. 952 15

Note: This photograph was obtained using the aluminum powder technique. Fig. 1. Wave pattern of high speed cargo liner model. a.7

LWL FP A Fig. 2. Bulb B1 lines. 19

LWL FP A, Fig. 3. Bulb B2 lines. 21

LWL FP A B Fig. 4. Bulb B3 lines. 23

2 M! 4 FP C Fig. 5. Bulb B4 lines. 25

FP A Fig. 6. Bulb B5 lines. 27

LJ OC iO 6 0 TEN STATIONS - TOTAL Fig. 7. Sectional area curves, bulbless parent and parent fitted with B1-B5 bulbs.

2.4 2.2 2D) 1.8 1.6 )o 1.4 x 1.2 U. _ LEGEND x — PARENT B I - B2 B3 B4 B5 v> /- / - / 0 / l - -I.0 --— o-. _j0' —-- 0.40 0.50 0.60 0.70 0.80 0.90 SPEED LENGTH RATIO 0.15 0.20 0.25 ___ FROUDE NUMBER 10 14 18 22 SHIP SPEED IN KNOTS Fig. 8. CR curves, bulbless parent and parent fitted with B1-B5 bulbs.

34.., 26 22 (A) Q < 18 _ _ _ _ 0 z I, SPEED' IN KNOTS 0.6 0.7 0.8 0.9 0.1 SPE E D L E N GTH RATIO Fig. 9. EHP curves LBp = 600 ft for bulbless parent and parent fitted with B5 bulb.

1. I. 0. 0. O. IO. -- Zo. bJ zo. )n 00. 10 o / 00 __.90 _ _ _ _ _,80 70 60 50,40 30 10 12 14 16 18 20 22 24 26, SPEED IN KNpTS l, | Q. 0. xl 0. 0. 0 0.6 0.7 0.8 SPEED LENGTH RATIO 0.9 1.0 Fig. 10. EHP/A curves LBp = 600 ft for bulbless parent fitted with B5 bulb. parent and 32

Part II. Series 60, C = 0.70 B

INTRODUCTION In the first part of this report the purpose and necessary techniques of incorporating a bow bulb to ship's hulls are explained. In addition, the results of fitting a bulb to an existing hull of conventional form are presented. This report describes a second attempt to design a large bulbous bow for a conventional merchant ship form. In this case the following procedures and conditions were investigated: (a) The two approaches of incorporating a bow bulb, mentioned in the first part of this report, were used in combination. (b) Different size fillets were used behind the bow bulb to fair it into the main hull to ascertain how this would affect form drag. (c) Tests at the ballast load of 60 per cent of full load were carried out, in addition to those at 100 per cent of full load. This was done realizing the importance of ship's resistance in the ballast condition. MODEL AND BULB DESIGNS In this second attempt to design a large bulbous bow for a conventional merchant ship, the Series 60, CB = 0.70, L/Vl/3 = 5.944, was chosen as being a typical hull form. The dimensions and characteristics of the corresponding bulbless parent (U. of M. Model No. 902A, Fig. 11) are given in Table 6. *Model 902A was used earlier at the University of Michigan to investigate a systematic set of variations on the Series 60, CB = 0.70, L/V 1/3 = 5.944 hull form (D.T.M.B. Model No. 4259). These variations consisted of three conventional bulbous bows of three, six and nine per cent area (Model Nos. 902B, 902C and 902D respectively), which were compared with the bulbless parent form of Model 902A. The results of this investigation are reported in the publication of ref. 3. 35

The bow bulb chosen for these experimental investigations was designed by the waveless hull theoryo Its dimensions and characteristics are near the optimum for minimizing the wave resistance of the parent hullo The size of this bulb was characterized by a sectional area at its center (AB) of 11 per cent that of the midship sectional area of the main hull (AX) and a mean radius (a ) of 1.6 per cent of the length between perpendiculars (LBp) of the bulbless parent hullo These bulb features are very close to those of bulb B5 of the first part of this report, which proved to be superior to the four other bulbs tried, with -the Series 60, CB = 0060 hull form~ The same bulb was incorporated in the former model numbers 902A, 902C and 902D of refo 3o The new models 902A-B1 and 902A-B1M were alterations of model 902A, and 902C-B1 and 902D-B1 were respectively alterations of models 902C and 902Do The general characteristics of the new models with their integrated bulb are given in Table 7 and brief descriptions followo Model 902A-B1 (Figo 12)> In this model the bow bulb center was placed forward of the FP and faired into the main hull by means of a regular size filleto Model 902A-B1M (Figo 13)o Here also the bulb center was placed forward of the FP, but as compared to model 902A-B1 it was faired into the main hull using a larger fillet, to ascertain whether the form drag of the bulb could thus be reduced, especially in 36

the ballast condition. Because of its larger fillet, this model had slightly greater volumes of displacement both in the full load and ballast condition as compared to those of model 902A-B1. However, the wetted surfaces for both loading conditions were the same as for the latter model. Model 902C-B1 (Fig. 14):. In this model the bow bulb center was placed forward of the FP and faired into the main hull using a regular size fillet. The volumes of displacement for both the full load and ballast conditions and the wetted surface for the full load conditions were slightly less than those for model 902A-B1. However, the wetted surface for the ballast condition was slightly greater than the corresponding value for the latter model. Model 902D-B1 (Fig. 15): Here the bow bulb center was placed at the FP. The volumes of displacement, both in the full load and ballast conditions, were the same as those of model 902C-B1 and the wetted surfaces for the two loading conditions, while slightly greater, were practically the same as those for the latter. Wave-making resistance is mainly influenced by the geometry of the ship's entrance or by the shape of the sectional area curve forward. Figure 16 shows the sectional area curves for the models described previously, including that for the bulbless parent hull. 37

TEST PROCEDURE AND RESULTS A 12.5 ft (LBp) parent model was used in these tests. Resistance test results for this model were reported previously in refo 3. In the new tests, other than the bulbs, the rudder was the only appendage attachedo Regular resistance tests were carried out with each of the five models of Tables 6 and 7 for two loading conditions, i.e., full load, and ballast at a displacement of 60 percent that of full loado Throughout each condition the drafts were kept constant in all models at the values shown in Table 6 for model 902Ao Because of this, the displacement and wetted surface of the five. models were slightly different during the tests, as shown in Tables 6 and 7. However, the effect of these differences on the resistance results may be justly disregardedo Turbulence was stimulated in the way described on page 6 of the report. Test results were analyzed also in the manner explained on page 6. Figures 17 through 20 give the test results in terms of CR and EHPo Tables 8 and 9 give resistance in lb for models corresponding to their parent bulbless hull and to the four other hulls wi th bulbous bow. Tables 10 and 11 give EHP for a 600 ft LBp for the bulbless hull and for each of the four hulls with integrated bow bul bs 38

Photographs were taken of the wave profi.'le alongside models 902A and 902A-B1M, and comparing these pictures, the d.ifference of wave profile due to the bulb was investigatedo Figures 21 through 2.3 show the wave profile for the full load condition and Figs. 24 through 26 show it for the ballast condition. DISCUSSSION OF RESULTS AND CONCLUSIONS The CR curves of Fig. 17, for the full load condition, shows clearly that 902AB1l is the best of all modelso The reductions in resistance shown by the latter model over the bulbless parent are 28 per cent at the designed service speed and 19 per cent at the trial speed. The other three bulbous bow models, 902D-B1, 902C-B1 and 902A-B1M, show reductions in CR of decreasing magnitude in the latter order. Two facts which follow seem worth mentioning. (a) The order of increasing fullness of the entrance was given by 902D, 902C, and 902Ao The latter fitted with the BI bulb, model 902A-B1, yielded the least CR valueso This fact shows the importance of the proper combination of main hull and bulb. In other words, the optimum configuration of bulbous bow should be figured out from the very first step of the hull design, instead of fitting a bulb to a conventional hull form. (b) Models 902A-B1 and 902A-B1M differ in that the latter' had-a larger fillet to fair the bow bulb into the main hullo It could have been expected that the larger fillet would decrease form drag and thus yield a lower resistance. The test results, however, indicate that with a larger fillet behind the bulb the residuary resistance is 39

increased both in the full load and ballast conditiono The tests, in addition, show that even a substantial hollowness behind the bulb need not produce serious separation drag. The CR curves for the ballast condition (displacement' 60 per cent that at full load) are shown on Fig. 18. None of the bulbous bow models suceeded in getting lower CR values than the bulbless parent hull in this condition. Again, the least resistance of the latter models was given by 902A-B1l The EHP values evaluated for a ship of 600 ft LBP are shown in Figo 19 for the full load condition and on Figo 20 for the ballast condition. The best model, 902A-B1, shows a reduction of EHP in the full load condition over the bulbless parent of 8.5 per cent at the service speed and 6.5 per cent at the trial speed. This trend is reversed in the ballast condition and model 902A-B1 shows an increase of 19 per cent over that of model 902A at a speed corresponding to 19 knots. When considering both the full load and ballast conditions, a somewhat smaller bulb, say 8 per cent as defined on Table 7, seems desi rableo 40

Table 6 Bulbless Parent Model Dimensions and Characteristics Series 60, C8-0,070 U. of M. Model No. 902A, Fig. 11, (see ref. 3) L^W-12.709 ft LBp= 12.5 ft B= 1.786 ft C-:- 0.700 CX=0o.986 C p0.710 FP-1 B/H 3 00 L53p/B= 7 00.-Bp/ V=3- 5.944 aet 1, 60 LE/LBP=0.42 Lx/LBP. 119 LR/LpP=O' 461 C.-0.642 CpR=O. 698 Nome nc lature L llength of entrance Lx-len7gth of parallel middle body L =length o f run CpE=prismatic of the entrance CpRPprismatic of the run Loading Condition Full Load Ballast -Hf -^}- 0.25 Draft, ft H t0. 5950.62 (even keel) at Trim=0. 3125 7V, ft3' 9.298 5.570 S, ft2 28.499 23.037 *Ballast condition is at a displ, of 60' that of FL. Deslgn Speed V/ (fL-0.695 v/ \/gL0. 207 Trial Speed: 7 Vf -) 0.755 v/ l/gLt 0.225; v/ g'wL=O. 9L5

Table 7 Large Bulbous Bow Models, Dimensions and Characteristics Models 902A-B1 902A-B1M(a) 902C-B1 902D-Bl(a) Bulb Features, per cent AB/AX 11.0 11.0 11.0 11.0 aO/LBp 1.6 1.6 1.6 1.6.(b) 1. o(b) 1.0(b) | (c) p/LBP 2.6 2.6 2.6 1.6 h/H 75.5 75.5 75.5 75.5 Hull Features Full Load Cond. 9.353 9.372 9.298 9.298 ft3 Ballast Cond. 5.618 5.632 5.579 5.579 ft Bal~~~asi Cn,11 1,i.. S Full Load Cond. 29.016 29.016 28.874 28.750 ft2 Ballast Cond. 23.422 23.422 23.438 23.443 (a) Large fillets used behind the bulb to fair it into the main hul (b) Bulb center located at station A (see Figs. 12-14). (c) Bulb center located at FP (see Fig. 15). 1. 42

Explanations for Table 7 Notes: 1. Original models 9020 and 902D had the same dimensions and characteristics listed in Table 1 for model 902A, except for S, 1/20(E, and V for the ballast condition. 2. Only the volume of the entrance of models 902A, 902C and 902D was redistributed to obtain models 902A-PB1, 902A-B1M, 902C-B1 and 902D-Bl1 Ship Nomenclature LBp=length between perpendiculars, ft H=draft, ft V =volume of displacement, ft3 S=wetted surface, ft2 A=midship sectional area, ft2 Bow Bulb Nomenclature a =mean radius, ft =longitudinal position of bulb center (+ fwd., -aft from FP), ft p=protruding length, ft h=inmersion of bulb center, ft AB=sectional area at bulb center, ft2 43

Tab 1'.3 Model Resistance - Full Load Condition Pounds Resistance **, I V v, ft/sec 902A 902A-B1 902A-B1M'902C-B1 902D-B1 1 (BTulbless VL.... Parent) ___ ___ 0.34 2.015 0.49 0.55 — 0.54 -- 0.38 2.269 0.61 0.67 0.65 o.64,, o0.42 2.523 0.75 0.30 0.80 0.78 0.76 0.46 1 2.775 0.90 0.93 0.94 0.93 0.89 0.50 3.026 1.06 109 1.09 1.0805 0.54 3.276 1.24 1.26 1.26 1.26 1.22 0.59 3.524 1.45 1.42 1.43 1.43 1.44 0.63 3.771 1.67 1.61 1.62 1.64 1.64 0.67 4.017 1.90 1.81 1.82 1.85 1.84 0.71 4.264 2.14 2.03 2.07 2.07 2.05 71~~~~~~~~~.. 03...lii. 0.75 0.79 4.512 4.763 0.83 5.018 0.88 1 5.278 0.92 5.543 Test Wl!ater Temp. p~;.: 2.42 2.82 3.25 I a 2.35 2.70 3.10 3.62 I — 2.36 2.70 3.12 2.33 2.65 i 2.30 2.60 3.05 I 2.96 3.69 r - 3.65 I — -1 I.....__ -- F I 4.99 72 4. 46 I t. 4.61 4.54 — - -` I 72 74 72 73 I *X

Table 9 Model Resistance - Pallast Condition Pounds Resistance V v, ft/sec!902A 1 902A-Bl 902A-B1M 902C-B1 902D-B1 y j, ( (Bulbless I \VL | [ Parent) I 0.30 1.807 0.39 - -- - 0.33 2.009 0.40 0.49 0.54 1 - -'-'-""''-'- _._...... 0.38 2.262 0.49 0.65 -.69 0.60 0.42 2.514 0.60 0.83 0,74 0.87 0.70 0.46 2.765 0.72 1.05 0.92 1.09 0.92 0.50 3,016 0.84 1.30 1.20 1.36 1.12 0.54 3.265 0.98 1.55 1.46 1.60 1,38 0.58 3.514 1.13 1.79 1.72 1.81 1.64 0.63 3.763 1.30 1.97 1 96 1.90 1.94 0.67 4.01o 1.47 1.98 2.11 1.96 2.15 0.70 4.258 1.69 2.06 2.21 2.06 2.22 0.75 4.507 1.89 2.20 2.35 2.18 2.30 0.79 4.758 2.12 2.37 2.51 2.37 2.44 0.83 5.011 2.43 2.57 2.72 2.61 2.63 0.87 5.267 2.91 3.03 - 2.74 0.92 5.526 3.30 3.39 3.42 3.37 3.38 0,96 5.78 9 3.97 3.82 1.01 6.053 4.81 4.77 5.22 4.56 Test Water Temp. OF 72 72 74 72 73 L=LWL

Table 10 EHP for LB-600 ft - Full Load Condition BJ V V EHP SEHP Kv ^ -_____________________________________ vs 902A 902A 902A-B1 902A-B1M 902C-B1 902D-B1 902A-B1 902A-B1M 902C-B1 902D-B1 12 0.486 2,620.2,700 2,780 2,460 2,340 3.05 6.11 6.11 -10.61 13 0.526 3,380 3,470 3,500 3,380 3,380 2.66 3.55 0.00 0.00 14 0.567 4,270 4,2.83 4,270 4,270 4,390 -0.23 0.00 0.00 2.76 15 0.607 5,390 5,090 5,200 5,230 5,440 -5.57 -3.52 -2.97 0.92 16 0.648 6,670 6,170 6,260 6,350 6,600 -7.~9 -6.15 -4.80 -1.05 17 0.688 8,060 7,400 7,570 7,620 7,700 -8.18 -6.08 5.46 -4. 47 18 0.729 9,660 8,940 9,230 9,100 9,100 -7.45 -4.45 -5.80 -5.80 1910.769 11,880 11,130 11,310 10,990 10,970 -6.31 -4.80 -7.49 -7.66 20 0.809 14,830 13,800 13,990 13,430 13,230 -6.95 -5.66 -9.44 -12.09 21 0.850 18,160 17,000 17,310 16,600 16,250 -6.38 -5.23 -8.59 -10.51.. \...~~~~~~~~~~~~~~~ A 1I 28,632 28,802 28,857 28,632 28,632 I displacement L==LWLr, A~=displacement in S.W. @ 59~F long tons + when bulbous bow is inferior, - when bulbous bow is superior Design Speed VK17.1 knots v/ VL=0.695 Trial Speed VK=18.6 knots v/V-=o0.755 46

Table 11 EHP for Lp-600 ft - Ballast Condition BP! v * EHP 5 EHP V V K |vs 902A 902A 902A-B1 902A-B1M 902C-B1 902D-B 1902A-B1 902A-B1M 902C-B1 902D-B1 12 0.486 2,060 3,730 3,400 4,070 3,000 81.1 65.0 97.6 45.6 13 0.526 2,670 5,100 4,700 5,310 4,570 91.0 76.0 98.9 71.2 14 0.567 3,340 6,420 5,950 6,600 5,970 92.2 78.1 97.6 78.7 15 0.607 4,170 7,750 7,450 7,490 7,490 85.9 78.6 79.6 79.6 16 o.648 5,100 8,380 8,750 8,030 8,720 64.3 71.6 57.5 71.0 17 0.688 6,220 8,700 9,700 8,690 9,770 39.9 55.9 39.7 57.1 18 0.729 7,450 9,610 10,640 9,530 10,440 29.0 42.8 27.9 40.1 19 0.769 8,990 10,800 11,800 10,700 11,280 20.1 31.3 19.0 25.5 20 0.809 10,780 12,130 13,120 12,300 12,540 12.5 21.7 13.7 16.3 21 0.850 13,130 14,040 15,020 14,220 14,250 6.9 14.4 8.3 8.5 A 17,152 17,300 17,341 17,180 17,178 ii i B 1 1i *X —X+ when A -displacement in S.W. e 59~F long tons bulbous bow is inferior, - when bulbous bow is superior 47

/ V\/ l d VV l _DL -___\A / _ iDWL1 l l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.6W.4WL.2WL I1 I 2 FP Fig. 11. Bulbless parent 902A bow lines. 49

lf / I DWL.8WL l I, 2 -5 -I _-\I / I / / j - 1~~ ~ 1 | I- - 1 i 1.0I I I i I I J / I.4 w\A I I -I _.6WL 1^ l / I I -L I - -I l I I i ~ -, i 3kc i-., I I J I - -- I.6 L-.2 WLo~Io I - / —7 I I -.4WL.2WL UFP A k4/~ J --, LI-aE I DWL = -r I I -S M1 Io O I 1II -~C J,- I I z FP A B ( Fig. 12. Model 902A-B1 bulb lines. 51

FP A B 4 Fig. 13. Model 902A-B1M bulb lines. 53

I~ I s FP A B G Fig. 14. Model 902C-B1 bulb lines. 55

;i;l DVVL - - iI ]i.8WL I -1-.IO, i i\ FPr- ___.6WLI.A1.4VVWL.11,.2WLv ( _B -1 I I I x, i, -4~ ~ ~ ~ ~ ~ ~ ~ ~~ ~~~~~~~~~~~~~~~~~~~~' i ~ ZI-11, -r I.4WL' _._._-~ I,.._ —- --- I I \ I- B.2WL /.6CWL E2 2 1 2, I 1 FP A Fig. 15. Model 902D-B1 bulb lines. 57

wt ft f-J 2 z 0 u Lli (U) D z 7z w U ly w a. 90 90 --— B-_" 50 -------- - 902 A-B IM ----------- 902C-BI -------- 902D-BI —---- a.......... TV 902 C-BI & 902 D-BI 30 —— " 2.0 MIDDLE BODY PARALLEL -MIDDLE BODY __^ 902A BULBLESS PARENT _________________I 1 10F 9 8 7 6 5 4 3 2/2 2 STATIONS Fig. 16. Sectional area curves, 902A, 902A-B1, 902A-BlM, 902C-B1, and 902D-B1. \iz I Y/2 F PI B A

2.8 I I I I 1 I I 2.6 H 2.4 2.2 LEGEND 902 A 902A- B — 90ZA- BIM — -- 90C- Bl ----- 902D-B.( —-- --- 7, 2.0 I I, IFL 1.8 - itn I 0 x a U 1.6 /4 a' 1.4 1.2 1.0 0.8 0.6: ).30 0.40 0.50 0.60 0 0.70. 0.90 1.( SPEED LENGTH RATIO..... I I 0.10 0.s5 0.20 0.25 FROUDE NUMBER... a A I B 10 1, Io 16 I a 2o SHIP SPEED IN KNOTS zz Iot Fig. 17. CR curves, full load condition.

3.4 I I 3.2 3.0 2.8 ooos / / _/' I /J /," LEGEND 902 A 902A-1 -- —. 902A-B1M — 902 C-BI - 902 D-BI ---.I I 2.6 2.4 2.2 2.0 I 0 I.B 0 1.8 1,6 1.4 2 II // / / / / / I // I, \ I'N I / OC i I I / t \ \ /I / /,,\ -..:__ _ _ /__ _ _ ____'^ ^ -^ / - --./Of.. 1.2 1.0 0.8 0.6( 30 0.40 0. 50 $PEECD 0.60 0.70 LENGTH RATIO 0.80 0.90 1.00 0.10 0.:15 0. 20 0.26:FROUDE NUMBER' I....i, I.. _1.,,i, ~, a 1o 12 14 SHIP SPEED 16 1l IN KNOTS 22 24 - Fig. 18. CR curves, ballast condition.

18 16 IA 12 m I I) I I I LEGEND, I I 1. 1. I I 90SA FULL LOAD 902A-BI FULL LOAD --- 902A- BIM FULL LOAD 902 C-B1 FULL LOAD -- 902 D- B1 ULL LOAD / I REAR R EMA RKS: I I I I I EHP VALUES W RE FICURPO FOR OF Lgp = 6001t, BASED ON A SCWOCNIrE R LINE ASSOCIATED W ITH ACo -- 0.0004 SHS4PS / /0 I I I I 8 I ^ alo w w 4W U, 0 ~ "'. B 14 Is5 |6 17 8 19 _ SHIP bPrED IN KN OTS 4 2 0 0.6 0:7 SPE:ED LENGTH 0.8 RATIO Fig. 19. EHP curves, full load condition. 62

14 I I t [i.I I I I I -. - I I I I I I LEGEND 902A BALLAST CONDITION 902A-Bl BALLAST CONDITION --------- 902 A -BIM BALLAST CONDITION --- 902 C -BI BALLAST CONDITION --— _ 902D-BI BALLAST CONDITION — _-. _ _,. 1 REMARK S: 1 E H P VALUES WERC FIIUREP FOR SHIP -- o L p = 600G t BASE~ ON - SCHONcMERR LINE As SSOCIATED WrtH ACF-= 0.0004 DISPLACEMENT IC 60 PIR CENT OF FULL LOAD D1SP.L ACrMENT TRIM Is 2j PER CrwN or LBp. t B.Y STERN I / - - / # / 2 / i - - i / o 0 I Id 8.. __. I____ _ ____ __ 9 2, -- ---- —,_........,.... I/. 15 I& 1 7 1e 19 20 SHIP SPEED IN KNIQOTS........ 0.1.. 0.6 0.1 SPEED LENGTH RATIO Fig. 20. EHP curves, ballast condition. 0.6 63

MODEL L.p = 12.50 ft MODEL SPEED = 4.525 fps L -- LWL v/-r =o 0.752 F= FROUDE NO. = 0.224 K I= a L a = A /. = /:20 I * ~ ^ t / \ eco/" / I -- L cr)! I 1+ / I 9A FULL LOAD 0.010 902A FULL LOAD / - O L'~~ \902 A- BIM FULL LOAD ------------------------ |: +1 I X // h ~l"~.':. _s.N /-/I -o. 005 -I j I, I A I I I AP 9 8 7 6 5 4 3 2 I FP Fig. 21. Wave profile at 4.525 fps, full load condition.

MODEL Lap = 12.50 ft MODEL SPEED = 4.08 Pps L= LWL V/<r = 0.678 F=- FROUDE NO.=. 0202 KoL= L/v = /F1=24 U) I +2 z 902A FULL LOAD 902 A-BIM FULL LOAD o: LJ I L3 X +1 0.010 0.005 0 - 0.005 0 -1 I AP 9 8 7 6 5 4 3 2 1 FP Fig. 22. Wave profile at 4.08 fps, full load condition.

MODEL Lbp - 12.50 -Ft MODEL SPEED = 3.69 fps L= Lw. v//p= 0.612 F= FROUDE NO. =0.825 KL= IL/2 = )/F1= 30 Iu o\ ~ co LJ I 902A FULL LOAD 902A-B1M FULL LOAD ------ --------- 0.010 0.005 0 -0.005 0 ul 4 I AP 9 8 7 6 5 4 3 2 1 FP Fig. 23. Wave profile at 3.69 fps, full load condition.

MODEL Lp = 12.50 ft MODEL SPEED = 4.52fp 902A BALLAST COND. --- L= LwL.3 +2 L -0.5 902A-BIM BALLAST COND. — u %,,- V/'^T = 0.752 _ F= FROUDE NO. = 0.224 00 0.010 KoL: ~L/, = / — I, 0 / I\ I + — / "LJ 5,#',' _ ~0.005 I~A 94 0o 0 I -00 ) ^' - -0.005 -IAP 9 8 7 6 5 4 3 2 IP L S902A- BIM] -[ SO92A] L NNIQ~~~~~ / - -~~~~~~~~~~~~0.005 -0. 005 -1 Fig. 24. Wave profile at 4.525 fps, ballast condition.

LJ z -, MODEL LBP = 12.50 Ct MODEL SPEED = 4.08 -fs L = LWL V/lr = 0. 678 F = FROUDE NO.= 0. 202 K0,L= qL/v'I= /F2 = 24 I 902A BALLAST COND.' 902 A - BI M BALLAST COND. I I II II FI L9 t 4: i / \ //f / 0 L 0.010 0.005 0 - 0. 005 L 0.005 0 -.005 AP 9 8 7 6 5 4 3 2 1 FP [ 902A- BIM] - L902 A LJ z z Z +1 r // 0 LL a - I Fig. 25. Wave profile at 4.08 fps, ballast condition.

U 3: 2 I-. I LJ +2 MODEL Lep = 12.50 ft MODEL SPEED= 3.69fps L= LWL V/L r O.60. 612 F= FROUDE NO. = 0.1825 KoL= I.L/, ='/F — 30 902A BALLAST COND. 902A - BM BALL AST CC )ND. +1 0 /, / A I I I I / I /../ I I I I 1 I i I'! %1I 0N \O I 0.010 0.005 0 -0.005 L 0.005 0 -0.005 I AP 9 8 7 6 5 4 3 2 1 u) I z +1 0 [I 902A-BIM) - [L 902A] rj~~~~ -1 Fig. 26. Wave profile at 5.69 fps, ballast condition.

REFERENCES 1. Finn C. Michelsen, R. B. Couch, and Hun Chol Kim, "Resistance and Propulsion Tests on Two Series 60 Models," University of Michigan Report 03509-1-F, April 1961. 2. Finn C. Michelsen, R. B. Couch, and Hun Chol Kim, "Resistance and Propulsion Test Results on Two Models," University of Michigan Report 04652-1-F, March 1962. 3. Hun Chol Kim, "Resistance Tests on Three Series 60 Bulbuous Bow Models," University of Michigan, College of Engineering, Department of Naval Architecture and Marine Engineering, May 1961. 71

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