THE UNIVE RS I TY OF MI CHI GAN COLLEGE OF ENGINEERING Department of Naval Architecture and Marine Engineering Technical Report RESISTANCE TEST RESULTS ON DD HULL WITH LARGE BULBOUS BOWS T. Takahei J. L. Moss Project Director: Ro B. Couch ORA Project 04886 under contract with: BUREAU OF SHIPS NAVY DEPARTMENT CONTRACT NO. NOBS 4485 WASHINGTON, Do C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR September 1962

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii I, INTRODUCTION 1 II. TEST PROCEDURE 2 IIIo MODELS AND BULB DESIGNS 3 IV. TEST RESULTS 5 V. SUMMARY 8 VI. ACKNOWLEDGMENTS 9 SELECTED BIBLIOGRAPHY 10 Appendix A. SEPARATION EFFECTS AND TURBULENCE STIMULATION 35 B, THE WAVE-CANCELLING EFFECT OF THE BOW AND BLUB WAVES 41 C. CAVITATION INVESTIGATION 45 Do COMPARISON WITH JAPANESE RESULTS 47 E. COMPARISON OF EHP USING HUGHES' AND SCHOENHERR'S FRICTION EXTRAPOLATORS 51

LIST OF TABLES Table Page I, DD Hull Characteristics 11 II. Bulb Characteristics 12 D-I. Comparison of Hull Characteristics 48 v

LIST OF FIGURES Figure Page 1. Main hull lines. 13 2. Bulb F1 lines. 13 3. Bulb FlR1 lines. 14 4, Bulb F2 lines. 14 5. Bulb F3 lines. 15 6. Bulb F4 lines. 15 7. Bulb F5 lines. 16 8. Bulb F6 lines, 16 9. Bulb F7 lines, 17 10. Bulb F7. 17 11. Sectional area curves of bulbs combined with DD hull. 18 12. Model resistance with bulb Fl. 19 13. Model resistance with bulb FR1. 20 14. Model resistance with bulb F2. 21 15. Model resistance with bulb F3. 22 16, Model resistance with bulb F4. 23 17. Model resistance with bulb F5. 24 18. Model resistance with bulb F7. 25 19. Ship resistance and power with bulb Fl. 26 20. Ship resistance and power with bulb F1R1. 27 vii

LIST OF FIGURES (Concluded) Figure Page 21, Ship resistance and power with bulb F2. 28 22. Ship resistance and power with bulb F3. 29 23. Ship resistance and power with bulb F4. 30 24. Ship resistance and power with bulb F5. 31 25. Ship resistance and power with bulb F7. 32 26. Comparison of various bulbs, 3 27. Effectiveness of bulb F7 compared with Navy sonar dome F6 34 A-l. Configuration of stimulation on large bulbs. 37 A-2. Effects on model resistance of varying stimulation on bulb F5. 3 A-2. Effects on model resistance of varying stimulation on bulb F6. 39 A-4. Effects on model resistance of varying stimulation on bulb F7. 40 B-l. Amplitude function of bow wave and bulb waves for DD hull.42 B-2. Photographs of wave profiles on 12-foot model 43 B-3. Measured wave profiles on 12-foot model. 44 D-lo Comparison with Japanese model tests. 49 E-l. Comparison of EHP using Hughes' and Schoenherr's friction extrapolators. 53 viii

I. INTRODUCTION Reported herein are resistance test results for the DD hull and for the hull in combination with several different large bulbous bows. The tests were carried out at The University of Michigan from April to August, 1962. Recently, at the University of Tokyo, Professor Inui, assisted by Dr. Takahei, one of the authors of this report,developed a hydrodynamic theory of wave cancellation which utilizes large bulbs. According to the theory, bow and stern waves can be completely cancelled at a specific speed by proper combination of bulb volume, shape, and location with the main hull. Over a wide speed range, wave resistance can be considerably reduced. For hulls whose shape is a known hydrodynamic singularity distribution, direct calculation of optimum bulbs is possible. For conventional hulls, the current practice in optimization is to vary the bulb parameters systematically. Modern naval vessels have, suspended beneath the main hull, larged faired domes in which the sonar transducer is mounted and which adversely effect the total resistance. The design criterion for the sonar housing on the hull tested requires that it be able to accommodate a cylinder 17 feet in diameter and 8 feet high. These experiments were designed to explore for the first time the feasibility of designing a bulb of sufficient size to accommodate the sonar transducer and to have a wave cancelling effect as well. All but two of the bulbs tested were of sufficient size to accommodate the transducer. 1

II. TEST PROCEDURE The model used in these experiments was 12 feet long and made of wood. The bulbs, also made of wood, were firmly attached to the hull and putty was used to smooth out the juncture between main hull and bulb. No other appendages were attached. There are at least two fundamental approaches to bulb-resistance testing; one is based on keeping the displacement constant and the other on keeping the draft constant from one test to another. The constant-draft method involves changing the displacement by using bulbs of different volume. In this way, the hydrodynamic characteristics of the main hull remain unaltered, since all changes are caused by the bulb. In these experiments, turbulence was stimulated in the following manner. For all tests, the main hull was stimulated by means of round studs 0.032 inches in diameter and about 0.030 inches high, the protruding end being squared off. The pitch of the studs was 1/2 inch; the line of studs was vertical and located 5% LWL aft of the F.P. At The University of Michigan, a trip wire is generally used for mainhull stimulation, but because of possible air drawing by a wire on high-speed forms, studs were adopted for this experiment. Most of the bulbs were stimulated with studs of the same diameter and pitch as those on the main hull, but of 0.015 inches height. In some tests over the higher speed range, no bulb stimulation was necessary. A complete discussion of bulb stimulation is included in Appendix A. 2

IV. TEST RESULTS The results of the Inui bulbs are compared with those of the bare hull and the hull fitted with the sonar dome, F6, in Figs. 12 through 25. In Figs. 12 through 18 they are compared on the bases of total model resistance and residuary resistance coefficients, and in Figs. 19 through 25 on the bases of effective horsepower and total ship resistance per ton displacement. In the expression for residuary resistance coefficient, model length squared was substituted for wetted surface area because the latter was different for each bulb design. Had surface area been used, ambiguity regarding the real effects of the bulbs would have resulted. The 1947 A.ToT.C. friction extrapolator and the standard correlation factor of 0,0004 were used throughout, although as discussed in Appendix E, the Hughes' friction formulation compares the bulbs with the basic hull more favorably. Corrections were made for blockage according to routine practice at the Michigan model basin. However, such effects were extremely small as V/LA was only 0.13%, where V is model volume, L is model length, and A is tank cross-sectional area. Brief remarks concerning the performance of each bulb follow. F4 (Figs, 16,23,26) The best results were obtained with this bulb, which reduced CO from that of the bare hull for speeds above the speed/length ratio of 0.8, The maximum reduction was 21% at the speed/length ratio of approximately 0.9, or at a ship speed of 18 knots. Reduction in total resistance per ton, full-scale, over that of bare hull occurs above 16 knots and attains a maximum of 10% at 30 knots. Similar trends in effective horsepower occur up to 604% at 30 knots. Significantly, there is no noticeable increase in effective horsepower at 15 knots. Figure 26 shows total resistance per ton and effective horsepower ratios comparing F4 with the bare hull. For reference the portion of the residuary resistance in the total resistance per ton is shown in Fig. 23. Fl (FigSo 12,19) Although this bulb is similar in design to F4, its larger volume and excess depth made it less effective in reducing wave resistance. The larger volume and surface area also caused increased viscous drag. 5

FlR1 (Figs, 13,20) The results for this bulb show that the separation behind Fl cannot be compensated by increasing fillet size and hence volume, which causes a rather deformed appearance of the main hull. The total resistance is, then, larger than with Fl owing to increased volume and surface area. F2 (Figs. 14,21) From the amplitude function configuration for this bulb, the wave cancellation effect appears to be larger than with F4 (Appendix B, Fig. B-l). Nevertheless, test results show slightly higher resistance than with F4; this is because the transverse-wave component of F2 is too large for the fine DD hull, which is already fairly well designed for inherent transverse-wave cancellation, (See Appendix B for a more detailed explanation of wave cancellation phenomena,) Also, the larger size of F2 contributes to its higher resistance. F3 (Figso 15,22) Although total resistance is not sufficiently low with this bulb, the wave resistance was decreased remarkably over the high-speed range. The resulting decrease in resistance per ton was 10.3% less than that for the bare hull at 30 knots, F5 (Figs. 17,24) Under the condition of sufficient volume to enclose the sonar transducer, F5 has the lowest resistance for speeds up to 24 knots. By decreasing the fillet size from that of Fl, the main hull remained unaltered as much as possible. The results for this bulb indicate that when bulb shapes are faired into main hull forms, often the best procedure is to refrain from emphasizing fairness as one does in usual lines development. In this case, lines bordering on grotesqueness happen to yield lower resistance than lines with more gentle fairing such as those of Fl and FRl. F6 The Navy's present sonar dome exhibited the highest resistance except at the highest speed range of about 30 knots, where the effective horsepower was nearly the same as that of the bare hullo 6

F7 (Figs. 18,25,26,27) As already mentioned, F5 and F7 are very similar. The total resistance of F7 was slightly higher than that of F5 below 24 knots (speed/length ratio of 1.2) and lower above 24 knots. As shown in Fig. 27, the total resistance of F7 is 20% less than that of F6 at 15 knots and 7% less at 30 knots. Since total displacement is nearly the same for both F6 and F7, differences in effective horsepower percentage are about the same as differences in total resistance. Since very few test results utilizing large bulbous bows are available, a comparison of results from the DD hull and those from some Japanese destroyer escort models is included in Appendix D. 7

V. SUMMARY The best bulb from the standpoint of resistance only is F4, which substantially decreased total ship resistance above speeds of 17 knots. When taking into account the sonar transducer dimensions, bulb F7 deserves strong recommendation for further investigation of its performance in waves, maneuverability, etc, In this experiment, the conventional DD hull was used without modification, On the basis of the theory, however, to obtain better wave interference it would be better to alter the forebody directly behind the bulb than to design the bulb to fit the existing bow. By keeping the principal dimensions and displacement of the basic hull constant, approximately 5% further reduction in resistance in the high speed range should be expected. 8

VI. ACKNOWLEDGMENTS The authors wish to acknowledge the cooperation of Dr. Ryo Tasaki in the performance of tests and the analysis of test results. The drafting of Mr. Otto Scherer and Mr. Norman Rabe and the calculations of Mr. Nils Salvesen are also acknowledged. 9

SELECTED BIBLIOGRAPHY *1 "Wave Profile Measurements on the Wave-Making Characteristics of the Bulbous Bow," by To Inui, T. Takahei, and M. Kumano, Journal of Society of Naval Architects of Japan, Vol. 108, 1960. *2. "A Study on the Waveless Bow," Part I, by To Takahei, Journal of Socity of Naval Architects of Japan, Vol. 108, 1960o 35 "A Study on the Waveless Bow," Part II, by T. Takahei, Journal of Society of Naval Architects of Japan, Volo 109, 1961. *4~ "A Study on the Waveless Stern," Part I, by M. Kumano, Journal of Society of Naval Architects of Japan, Volo 108, 1960. 5. "A Study on the Waveless Stern," Part II, by M. Kumano, Journal of Society of Naval Architects of Japan, Volo 109, 1961. 6. "A Study on the Waveless Stern," by M. Kumano, Part III, Journal of Society of Naval Architects of Japan, Vol. 110, 1961, 7. "The Wave-Cancelling Effects of Waveless Bulb on the High-Speed Passenger Coaster M/S KURENAI MARU; Part I: The Model Resistance and Propulsion Experiments, by T. Inui and T. Takahei; Part II: The Full Scale Experiment, by M. Shigemitsu and K. Kai; Part III: Photogrammetrical Observation of Ship Waves," by T. Inui and T. Takahei; Journal of Society of Naval Architects of Japan, Vol. 110, 1961. **8. "A Study on the Large Bulbous Bow of High-Speed Displacement Ships; Part I: Resistance Tests in Still Water," by S. Takezawa, Journal of Society of Naval Architects of Japan, Vol. 110, 1961. **9. "A Study on the Large Bulbous Bow of High-Speed Displacement Ships; Part II: Performance in Waves," by S. Takezawa, Journal of Society of Naval Architects of Japan, Vol. 111, 1962, 10. "Fishing Boat of the Waveless Hull Form" (in English), by N. Yokoyama, Journal of Society of Naval Architects of Japan, Volo 110,, 1961. 11. "Friction and Form Resistance in Turbulent Flow, and a Proposed Formulation for Use in Model and Ship Correlation," by Go Hughes, Transactions of the Institute of Naval Architects, Volo 96, 1954o *Translated into English at The University of Michigan, Dec. 1961. **Translated into English at The University of Michigan, Part I: May 1962; Part II: July, 1962. 10

TABLE I DD HULL CHARACTERISTICS Ship Ownero U, So Navy U of M Model No.: 946 Model Material: Sugar Pine Scale RatioO 32.5 LWL B H Trim Model 12.000 ft 1.260 ft 0.415 ft None Ship 390.0 ft 41,0 ft 13.5 ft None V A 3.076 ft3 191.48 lb at 105,590 ft3 3017.8 L.T. at 59~F S.W. 73~F F.W. Wetted Surface 15.902 ft2 16,796 ft2 Form Parameterso CP CB Cx LCB L/B L/H = 0.605 = 0.480 = 0,792 = 1.2% LWL aft of midship = 9.512 = 28.89 11

TABLE II BULB CHARACTERISTICS AV, V+AV, AV/V, AS, S+AS, AS/S, b/LWL, 1/LWL, f/LWL, p/LWL ABAX, Acceptable Bulb ft3 ft3 ft2 ft2 $ Sonar Dimensions, 1 %_______. _________. _%........................_ _ %Dia. x Ht., ft F1 0.130 3.206 4.22 1.330 17.232 8.36 4.23 2.5 4.5 5.2 55.3 17 x 8 F1R1 0.222 3.298 7.22 1.800 17.702 11.3 4.23 2.5 4.5 5.2 55.3 17 x 8 F2 0.101 3.177 3.35 0.966 16.868 6.07 3.90 2.5 3.5 4.4 40.7 13.5 x 7 F3 0.204 3.280 6.70 1.872 17.774 11.78 4.15 2.5 4.5 9.5 55.3 17 x 8 F4 0.073 3.149 2.37 0,796 16.698 5.00 3528 6.2 3.1 4.6 27.9 10.5 x 7 F5 0.120 3.196 3089 1.024 16.926 6.45 4.90 1.2 4.5 3.7 54.6 17 x 8 F6 0.155 3.231 5.05 10297 17.199 8.15 5.20 -5.0 4.5 -2.3 461 17 x 8 F7 0.162 3.238 5.27 10319 17.221 8.29 4.90 1.2 4.5 4.1 54.6 17 x 8 r) Vno AV S' AS: LWL: b: 1: fp: AB: AX displacement volume of basic hull without bulb = 3.076 ft3 displacement volume of bulb only wetted surface of basic hull without bulb = 15.902 ft2 wetted surface of bulb only length on waterline of basic hull = 12.00 ft maximum breadth of bulb longitudinal distance of bulb center from F.P. depth of bulb center protruding length of bulb from F.P. transverse sectional area of bulb at center basic hull midship section area = 0.416 ft2

Fig. 1. Main hull lines. F I -AB 0 -2 Fig. 2. Bulb F1 lines. 13

1I I i 1,' MAX STA ru

F3 Fig. 5. Bulb F3 lines. F4 I I I Bulb F4 lines. Fig. 6. 15

F5 Fig. 7. Bulb F5 lines. F6 Fig. 8. Bulb F6 lines.

DWL F 7 D~/ 2\~~~~~~~~~ SONAR 17FT. DIA.x8FT. HT. IF l 0 "4" ~ Fig. 9. Bulb F7 lines. IL B Fig. 10. Bulb F7. 17

-TT-n'q cc q( f paUTCIUoO sqT-nq jo sainto val: e -euoTF;^as 1TT *9 I I 1 zo llnH u!eW v CO r-l 9~ XV my o!lem 8~

3.8 3.4 3.0 2.6 2.2 Q. (,) rl 1.8 1.4 x~~~~~~~~/..... \I- Bare Hull is _^ ______ _ F6 Navy Sonar x'< } / - | Bulb 0m \ | l// ---- Bulb F1 \' /I -!^EEE~~~~~/ / f 4 5 6 7 8 9 10 11 I I 4 I 6 118 9 | 1 1.0 8 6 4 2 0.4.6.8 1.0 1.2 1.4 1.6 1.8 2.0 Fig. 12. Model resistance with bulb Fl. 19

3.8 3.4 3.0 2.6 2.2 1.8 -J. Q. 1.4,.-I. cr-c " 1.0,. I cr 8 6 4 2 0 -hi- \ —-— A --- ---— Bare Hull x l\ I\> / | _ F6 Navy Sonar _________ 1 - - --— r < ~~~~~~~BulbFIRI // -_ / /., /.e / en 1-0l^ 000 V (ft/sec) 3 4 5 6 7 8 9 10 11 A f 0 IA I<) I A 1 t. ~/ I. 4. U 0 1. U 1. z 1.4 1.0 1. Z ~. U V//LWL Fig. 135. Model resistance with bulb F1R1. 20

3.8 3.4 3.0 6 2.2 1.8 N.-i cJ X C.4 O 1.0 8 6 4 2 // N/ \ 1 _ /. 1Legend ---- /// - -Bare Hull \.//I / __/ F6 Navy Sonar x ~_ / __ Dome -.. o: _ ______ BulbF2 [ _ _n /X___ /______ / ~ ~~'~' VM (ft/sec) 4 5 6 7 8 9 10 11, t I..1. i. I I I I. i I I I,!, i.4.6.8 1.0 1.2 1.4 1.6 1.8 2.0 V/LWL Model resistance with bulb F2. Fig. 14. 21

3.8 3.4 ----- Cc v/ 1.8 ____ -J CM Qi. O l 1 8 > 1. 4 4 6 8 1.0 1.2 1.4 1.6 V../LWL Fig. 15. Model resistance with bulb F3. 1.8 2.0 22

3.8 3.4 3.0 2.2 1.8 C__ cl > 1.4 |et 1. 0 1.0 II 8 F6 Navy Sonar / / — E/ q tI\ I --- Bare Hull 4 5 _ F6 Navy So na 1.a -- --: -I I ----- -- - Dome(-)_inI'' / Bulb F4 / //!, I ~, I I' - I, I I, / 6 4 2 0.4.0.0 I.U 1. ~z 1.4 V/v/LWL 1. 1.0.U Fig. 16. Model resistance with bulb F4. 23

3.8 3.4 3.0 2.6 2.2 1.8 _, - 1.4 cr ",. ^. 8.6.4 /'70 / \ t\ --— XX-,-f- A ~~ —- Bare Hull \ l __F6 Navy Sonar Dome - _r __Bulb F5 CD I,,, IT.' IE l l l I., l l l / / / VM (ft /sec) 3 4 5 6 7 8 9 10 11 0.4.6.8 1.0 1.2 V//LvWL 1.4 1.6 1.8 2.0 Fig. 17. Model resistance with bulb F5.

3.8 3.4 3.0 26 C 1.8 Is "r 1.4 N 1.0 Legend.... \ 1 7 Bare Hull --- F6 Navy Sonar so /i \I <I -p. BulbF7 -o/ / ---— __ - X ~. ~-~,, VM(ft/sec) 4 5 6 7, 8 9 10 11 4 Lh. L j ii_ i5 j~ 1 1I 8 6 4 2 0.4.6.8 1.0 1.2 V//LWL 1.4 1.6 1.8 2.0 Fig. 18. Model resistance with bulb F7. 25

100 80 60 40 n 20 0 24 20 16 / Legend /1 ---- Bare Hull c/) --- F6 Navy Sonar Dome /.. V^_ V//LWL.5 I 1. 0 1. 5 2. rn aLJ 12 8 4 0 6 1 10 zU Z4 Z8 3IZ 36 4U Vs (Knots) Fig. 19. Ship resistance and power with bulb Fl. 26

100 80 60 <w40 20 0 24 20 16 a 12 I 0U.8 4 0 010 _L- Legend...Bare Hull ---— F6 Navy Sonar Dome ______- Bulb FIRI _ _ 1 /. 1.0- V// WL.5 - 0 1.0 1.5 2. 8 12 16 20 24 28 32 36 40 Vs (Knots) Fig. 20. Ship resistance and power with bulb FR1. 27

100 80 60 40 O)t: 20 0 24 20 16 12 II Legend.|... — Bare Hull __-___ —- F6 Navy Sonar Dome /^ ---- BulbF2.5 - 1.0 1.5 2.0 I~~ ~~~~ L, ]/ ]W ] I 0) I r — 8 4 0 8 12 16 20 24 28 32 36 40 Vs (Knots) Fig. 21. Ship resistance and power with bulb F2. 28

100 80 60 on t 40 20 0 24 20 16 1 12 CL x = 8 1...-.. — Bare Hull -—.- F6 Navy Sonar Dome _ —— __ Bulb F3 4 0 8 16 20 32 36 40 Vs (Knots) resistance and power with bulb F3. Fig. 22. Ship 29

100 80 60 40 C, 2C,1 /'. / ) _____^ ^/-/ dResidual Resistance per Ton /. I 5 Legend 6~'~~ ~~ -— ~ - ____ _Bare Hull --—, F6 Navy Sonar Dome 82 __________ __ II ---- Bulb F 4 _ 8 4~ _,__ _^_10,,,__~. _.. 4. 5 A A e _ ON,_ ll A 0 24 2C 1( t) x aX CL 12 I I 8 1Z 10 ZU Z4 Z8 3Z 36 4U Vs (knots) Fig. 23. Ship resistance and power with bulb F4.

100 / 80 / 60 40 n24 20 / 16 Legend /' ---— Bare Hu ~ / — F6 Navy 12 ---- BulbF5 ~, / - 8 12 16 20 24 28 32 36 x/ LU V/'LWL.S L5 J 1. 0 1.5 8 12 16 20 24 28 32 36 Vs (Knots) Fig. 24. Ship resistance and power with bulb F5. III y Sonar Dome I 40 31

100 80 60 40;20 24 20 Legend.... Bare 16. F6 N / ---- Bulb 12 L, 8 ~' / 1 4 05 IT _ _. _ _,.,_ 5__ _ 8 12 16 20 24 28 32 36 VS (Knots) Fig. 25. Ship resistance and power with bulb F7. Hull avy Sonar Domi F 7 40 32

1.70 1.60 1.50 1.40 1.30 1.20 1.10 1.00.90 22 24 zo zz Vs (Knots) of bulbs to that of bare hull. (a) Ratio of RT/AS 1. 70 1.60 1.50 1. 40 1.30 1. 20 1.10 1.00.90 I,,,.,.,., 1I F6 28 30 V s (Knots) (b) Ratio of EHP of bulbs to that of bare hull. Fig. 26. Comparison of various bulbs. 33

1.00.95.90.85.80.75 1. 00.95.90.85.80 75 I I I I I I I I I I I I I I (,) F7 (RT AS ~I-(^ _ ^ ^ -^j ^.80.90 1.00 1.10 1.20 1.30 1.40 1.50 V/VLWL I,,, I, I., I, -, I, I, I, 16 18 20 22 24 26 28 30 Vs (Knots) (a) Ratio of RT/AS of F7 bulb to that of Navy sonar dome F6..80.90 1. 00 1.10. 20 1. 30. 40 1. 50 VA/LWL I I I I I I I, 16 18 20 22 24 26 28 30 Vs (Knots) (b) Ratio of EHP of F7 bulb to that of Navy sonar dome F6. Fig. 27. Effectiveness of bulb F7 compared with Navy sonar dome F6. 34

APPENDIX A SEPARATION EFFECTS AND TURBULENCE STIMULATION Experience during bulb tests has repeatedly shown the need for taking extreme care when stimulating turbulence. Since the Reynolds number of the bulb with respect to diameter is about that of the critical value where the boundary layer separation changes from laminar to turbulent, difficulty arises in stimulating flow on the model which simulates the flow on the ship. The problem is aggravated by the fact that the critical speed is often included within the speed range over which the model is testedo Initially, comparative tests were run in which various degrees of stimulation were used. The bulb chosen for these tests was of the type which protrudes in front of the main hull but not much below it. By mounting studs on the bulb in a manner to be described, essentially the same resistance record was obtained as for the case in which no studs at all were used. The only exception occurred at very low speeds (model Reynolds number of about one million), where all the data were generally scattered. However, the trend in the low-speed range for the case in which studs were used was towards slightly less scatter and slightly less total resistance. The studs were round, about 0.032 inches in diameter, and the ends were squared off. The height of the studs on the bulbs was one-half the height of those on the main hull, the latter being placed at 5% LWL from the forward perpendicular. The height of the studs on the bulbs was about one-half the boundary layer thickness at the stud location. The position of the line of studs on the bulb was determined by the intersection of the bulb and a cone with its apex located at the center of the bulb. (The half angle of the apex was 65~) (see Fig. A-i). This location of stimulation is the same as that used on sphere drag tests in order to induce turbulent separation. The normal stud pitch was 1/2 inch, Initially, then, it seemed that the stimulation used afforded the most convenience and the least amount of scale effect over the ordinary speed range of Reynolds numbers-about 1,5 x 106 to 10 x 106, In the more recent configurations which have been tested on the DD hull model, the majority of bulbs were suspended below the keel line in contrast with those previously mentioned (see Fig. A-l). When the bulbs were suspended in this manner, the flow seemed to be sensitive to separation in the region beneath the keel line, i.e., the region where there was no hull form immediately behind that portion of the bulb, 35

Figures A-2, A-3, and A-4 show model resistance for three varieties of this type of bulb and include specifications for the different types of stimulation used in various tests with each bulbo As one might expect, the effect of stimulation becomes more severe as the amount of fillet between the bulb and hull is reduced, io.e, over the whole speed range tested, the resistance increases with increased filleto The greater increment of increased resistance corresponds to the lesser fillet size and also to the lower Reynolds number. Similar trends can be seen for cylinder drag when stud dimensions are changed.* Near the critical speed, where the Reynolds number is about 1.5 x 105 with respect to bulb diameter, the dispersion of the measured resistance is much larger than it is beyond the critical speed, and the appropriate bulb stimulation sometimes causes noticeably decreased resistanceo Further investigation by means of dye injection around bulb F5 showed that the flow did undergo transition to turbulent separation near the critical Reynolds number range. Therefore, for bulbs which protrude beneath the keel line, the tendency of resistance deviation dependency upon stimulation closely resembles that of spheres and cylinders, and the differences in resistance found between the two types of bulbs seem to be justified. Extreme care with respect to stimulation must be exercised in testing models with bulbs whose major portion protrudes beneath the keel line. Above the critical range, smooth surfaces without any stimulation are preferable, and below this range the results which yield the least total resistance with stimulation may be considered valid, For models more than 10 feet long, most of the low speeds (below the critical Reynolds number range) are too low to be considered important in an ordinary resistance test, Therefore it seems that test results can best be extrapolated to full scale by using the combination of results described aboveo *Modern Developments in Fluid Dynamics, ed. Sydney Goldstein, Oxford University Press, 1938, Vol. II, p. 433. 36

U of M Model No. 946 Model L= 12' d = 0.415'.65o Stimulation.032" studs 1032" \\\ \\\\ v. 032" x. 032" studs.\.03" rubber band. 032" studs C J4015"' w<W<^f~ Fig. A-1. Configuration of stimulation on large bulbs. 37

.11.10 MODEL NO. 946 F 5 BULB,_ - _.01,I- 00 / / RT V2 009 A_._.08,07.01 V2 O N Stimulation on Bulb - No Bulf Stimulation —. 032' Dia. x. 032' Height Studs, 2 Spacing -.- Studs +. 03" Thick Rubber Band RT x, ACD = A 1 *_-,04.02L 1 S 2 PV (Bulb Sec. Area)... -.00010- *f — O -0 -- - * VM (ft/sec) 2 3 4 5 6 7 8 9 10 I I I I I I I I I I 2 3 4 5 6 7 8 9 10 1x106 RL= v (Model Length)/z/! J I I I I I I I I I 1 2 3 RD = v (Bulb Dia. /z/ 4 5x105 Fig. A-2. Effects on model resistance of varying stimulation on bulb F5.

.11 MODEL NO. 946 F6 BULB 10 A / no A -.0. - Nn Bulh Stimllatinn. uu.07 Av2 V + I... -_A I N- w iii i W ii __.032" Dia. x. 03Z' Height Studs, 2 Spacing A —--. 032" Dia. x. 015" Height Studs, 2 Spacing RT ACD = IA ( --— ) ACD = (1 PV2 (Bulb Sec. Area).02 r J. 02 j — ~="~''.=-_ ___ -— _ — ~ ~~_ __ VM (ft/sec) i I I I I I 1,2 3 4, 5, 6, 7,8 8 9, 10 2 3 4 5 6 7 8 9 10 11 x106,i,__ I RL v (Molel Length)/v I, 1 2 3 4 5x 105 R v (Bulb Dia. )/z Fig. A-3. Effects on model resistance of varying stimulation on bulb F6.

.11 MODEL NO. 946 F 7 Bulb.10 \ R^ + //+ V M.39.08 ____ OAO<^ __ -s_// + No Bulb StimLlation... + o <& <>_0 -.02Da..032 " Dia.x.032" Height ^^**'* —*^^ Studs, 2 Spacing 07 + 0 —..032' Dia. x. 015" Height Studs, - Spacing I- RT o AI A}\ —ACD= (- ) 1 PV2(Bulb Sec. Area) 005 02 RT...._, -~- - A -- - — __ _- - --- ____ V2.005 VM (ft/sec) 1 2 3 4 5 6 7 8 9 10. I I I i I I I I I I 2 3 4 5 6 7 8 9 10 11 x 106 RL= v(Model Length)/v 1 2 3 4 5x105 RD= V (Bulb Dia. )/v Fig. A-4. Effects on model resistance of varying stimulation on bulb F7.

APPENDIX B THE WAVE-CANCELLING EFFECT OF THE BOW AND BULB WAVES Associated with the bow and bulb waves are the amplitude functions A(G) and B(G), respectively, which are opposite in sign. When the bulb is located at the origin of the bow wave, the composite wave remaining after interference is represented by the difference in amplitude functions. In Figo B-l, A(G) was assumed for the DD hull, at a particular speed, in accordance with the hull form. B(G), which is linearly proportional to volume and exponentially inversely proportional to depth, was obtained for three typical bulbs by assuming a sphere of the same Volume as the bulb, F4 worked best because it had the least volume and surface which, from the wave-making viewpoint, were compensated by less depth. The larger the bulb, the deeper it must be for the same effectiveness; but the larger it is, the more the viscous drag is increased. The total wave system is comprised of two fundamental components, the transverse and the divergent wave systems. In the normal course of design the main hull is designed for cancellation between the bow, stern, and two shoulder transverse wave systems. For a conventional ship, the bow bulb might be designed to cancel the bow divergent component. The small transverse component and large divergent component of F4 makes this bulb the best for the DD hull. The relationship between divergent and transverse wave systems can be seen by stereo-photographs of the whole wave system. The transverse system can be more easily observed in regular photographs of the wave profile from which wave height is measured by a grid on the model surface, as illustrated in Fig. B-2. After the bulb is fitted, the difference in wave profiles from the bare hull condition represents the wave generated by the bulb. The measured wave difference in Fig. B-3 agrees quite well with the calculated wave generated by a sphere, or doublet, which is hydrodynamically substituted for the bulb. Hence, the wave interference can properly be evaluated by taking advantage of the aforementioned amplitude function.

F 0.316 V//LWL= 1. 06 1.0 A(&) L.8.6 r) B(O) T.4.4.2 0 20 40 60 80 8 (DEGREES) Fig. B-l. Amplitude function of bow wave and bulb waves for DD hull.

(a) Bare hull., (b) With bulb t7. Fig, B12. Photographs of wave profiles on 12-foot model at model speed of 6.97 feet per second, V/ v/: 1.19, VK 25.6 knots, 43

(a)V/[L -. 971 KoLLg/V2 =12 Vs = 19. 2 KTS Model Speed: Without Bulb 5.684ft /sec With F7 Bulb 5. 681 ft Aec 2 IN 1 0 -1 1 0 -1 -2 2IN 1 0 -1 1 0 -1 -2 2 IN 2 1 0 -1 1 0 -1 -2 191 KoL =9 Vs = 23.6 Without Bulb 6. 968 ft /sec With F7 Bulb 6. 974 ft /sec FP Fig. B-3. Measured wave profiles on 12-foot model.

APPENDIX C CAVITATION INVESTIGATION Calculations were carried out according to inviscid fluid theory in order to investigate the possible occurrence of cavitation on the F7 bulb. A three-dimensional Rankine-body of the same dimensions as the forward part of the bulb was chosen. The maximum velocity, 1.44 times the ship speed (and hence by the Bernoulli equation the minimum pressure), occurs at the maximum section when the ship runs in still water with the bulb center about 17.5 feet deep, Vapor pressure at the maximum breadth is reached at a ship speed of 32 knots, Hence for ship speeds of 32 knots and more, cavitation on the bulb should be expected. If the ship is pitching moderately, so that the bulb is only 5 feet beneath the surface, cavitation could be expected at a ship speed of 28.4 knots, In these calculations, the static pressure assumed corresponded to an undisturbed free surface. 45

APPENDIX D COMPARISON WITH JAPANESE RESULTS In Japan, Dro Takezawa has carried out a series of tests (see Items 8 and 9 of the Bibliography) with large bulbous bows on two destroyer escort ship models having similar hull characteristics as the DD hull. In Table D-I the characteristics of one of the Japanese hulls are compared with those of the DD hull. Direct comparisons cannot be made because the Japanese tests were carried out with all appendages affixed, whereas the tests at Michigan were carried out with no appendages except the bulbs. However, comparison of residuary resistance, with the Schoenherr line used as a friction basis for both cases, is enlightening (see Figo D-l)o In both series of tests, the bulbs compared had been designed by theory to most effectively cancel bow waves; no other design criterion was considered. The curves for the basic hulls show large differences in favor of the DD hull, particularly at the moderate ship speed of around 20 knots. The DD hull is favored even when the additional form resistance of the appendages on the Japanese hull is considered. The significant point, however, is that in both cases the reduction of wave making resistance is of the same trend and magnitude over the whole speed range. Since each test series was carried out independently, the bulbs compared are at least nearly optimum for the hull forms of conventional high-speed destroyers.

TABLE D-I COMPARISON OF HULL CHARACTERISTICS odel 59* 59(7)** 946+ 946F4++ L/B 9.25 9.51 L/H 29.8 28.9 CB 0.511 0.480 Cp 0.620 0.605 Cx 0.824 0.792 AV/v% 1.89 2.37 AS/S% 4.35 5.00 AB/AX% 25.7 27.9 *Japanese destroyer escort without bulb and with all appendages. **Japanese destroyer escort with bulb and with all appendages. +DD hull without bulb and without appendages. ++DD hull with bulb and without appendages. 48

/ / 1 V22 RESIDUARY RESISTANCE COEFFICIENT CR = RR/ P V L | I BASED ON SCHOENHERR LINE I 4.5x10-' 4 3.5 3 2.5 N_-_ Nc 2 1'. a 1.5 II W us( i Japanese Destroyer Escort (Model 59) - Without and With Bulb (No 7) With All Appendages US Navy DD Hull (Model 946) --— Without and With Bulb (F4) Without Appendage Without Bull Model 59 1 0.5 0 0.2 0.4 0.6 0.8 1.0 1.2 V/,LWL 1.4 1.6 Fig. D-1. Comparison with Japanese model tests. 49

APPENDIX E COMPARISON OF EHP USING HUGHES' AND SCHOENHERR'S FRICTION EXTRAPOLATORS In extrapolating test results to full scale, the relative merits of the various bulbs are highly dependent upon the friction extrapolator used. Since the proportion of residuary resistance to total resistance changes as the amount of frictional resistance changes, according both to Reynolds number and the friction basis, it is to be expected that the percentage of improvement in power prediction due to a bulb is affected by the use of different friction lines, The full-scale predictions in this report are all based upon the Schoenherr (1947 ATT.C.) line which, among the extrapolators commonly advocated today, generally yields the lowest proportion of frictional resistance. The Hughes method generally yields the highest proportion of viscous resistance to be extrapolated to full scale, and therefore is particularly suitable for comparative analysis. In 1954, Hughes proposed a model-to-ship viscous resistance correlation method in which the formula Cf =.0o66(loglORn-2.03)'2 was advocated for flat-plate friction. In order to account for the hypothesized increased negative slope of a line connecting the so-called run-in point of geosims of three dimensional forms, Hughes further proposed to multiply the flat-plate formula by the factor (1+K), where K is a form factoro The resulting formula yields a separate total viscous line for each ship form tested; the remainder of the total resistance is due to potential wave making and is expanded by means of Froude's law. From a practical standpoint the form factor, K, is not easily determined but the Japanese destroyer escort model tests (see Items 8 and 9 of the Bibliography) mentioned in Appendix D advocated using a form factor of approximately 0.27. For the DD hull, K = 0.25 was chosen and the resulting viscous extrapolation curve could then be considered as an upper practical limit, Since the Schoenherr curve might be considered a lower limit, comparison of the results using these two extrapolation methods indicates the range within which different extrapolation methods would predict full-scale results. 51

Figure E-1 shows the comparison of bare hull and bulb F4 using the two methods. Because of the converging nature of the Hughes and Schoenherr curves with increasing Reynolds number, and because the Hughes line is higher, one might expect the improvement due to the bulb to look more favorable. Such is the case; at 28 knots the predicted decrease in effective horsepower for bulb F4 is 21% higher when the Hughes rather than the Schoenherr extrapolator is used. Stated another way, the decrease in effective horsepower due to the bulb at 28 knots over the bare hull condition is 9% by the Hughes line and 7% by the Schoenherr line. It should be noted that ACf = 0.0004 was used as a correlation factor in both cases, and also that at corresponding speeds the Hughes line yields lower effective horsepower than the Schoenherr line. 52

23 21 19 17 15 13 L. a) 0 -o Im c 0 11 _ 3 UU!Vu L UL I uU IVtlLI UUO Bare Hull - 9 7 ____/ With Bulb 3 1 6 18 2 2 16 18 20 22 24 Speed in Knots Fig. E-1. Comparison of EHP using Hughes' extrapolators. 26 28 30 32 and Schoenherr's friction 53

UNIVERSITY OF MICHIGAN I3 90' 03526 84ll 3 9015 03526 8484