DINSRDC/SPD 1030-01 IGATION OF THE HYDRODYNAMIC LOADING ON RIBBON TOWCABLE dD ' SSeS on LA mer oma! DAVID W. TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER Bethesda, Maryland 20084 INVESTIGATION OF THE HYDRODYNAMIC LOADING ON RIBBON TOWCABLE WHOI Reece Folb DOCUMENT John Nelligan COLLECTION APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED SHIP PERFORMANCE DEPARTMENT DEPARTMENTAL REPORT January 1982 DINSRDC/SPD 1030-01 MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS DTNSRDC COMMANDER TECHNICAL DIRECTOR: OFFICER-IN-CHARGE CARDEROCK OFFICER-IN-CHARGE ANNAPOLIS SYSTEMS DEVELOPMENT DEPARTMENT AVIATION AND SURFACE EFFECTS DEPARTMENT SHIP PERFORMANCE DEPARTMENT 15 COMPUTATION, MATHEMATICS AND LOGISTICS DEPARTMENT STRUCTURES DEPARTMENT SHIP ACOUSTICS PROPULSION AND DEPARTMENT =a AUXILIARY SYSTEMS DEPARTMENT SHIP MATERIALS CENTRAL ENGINEERING ! ; INSTRUMENTATION DEPARTMENT OB DEPARTMENT TL 0 0301 0037113 4 MBL/WHO! I Geiguinaclons NDW-DTNSRDC 5602/21 (: UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE BERS CoE eo eid 1. REPORT NUMBER 2. GOVT ACCESSION NO./ 3. RECIPIENT’S CATALOG NUMBER DINSRDC/SPD 1030-01 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED INVESTIGATION OF THE HYDRODYNAMIC LOADING ' DEPARTMENTAL ON RIBBON TOWCABLE = 6. PERFORMING ORG. REPORT NUMBER DINSRDC/SPD 1030-01 7. AUTHOR(2) 8. CONTRACT OR GRANT NUMBER(a) Reece Folb and John Nelligan 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK AREA & WORK UNIT NUMBERS David Taylor Naval Ship R&D Center Element 62543N Ship Performance Department SF 43-400-001 Bethesda, MD 20084 DINSRDC WU 1507-101 11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Naval Sea Systems Command January 1982 2 4. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of thie report) UNCLASSIFIED 1Sa. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. DISTRIBUTION STATEMENT (of this Report) APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, If different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse aide if necessary and identify by block number) Ribboned Towcables Ribbon Fairing Loading Functions Towcable Performance Improvement 20. ABSTRACT (Continue on reverse side if necessary and identify by block number) Hydrodynamic loading functions and drag coefficients have been developed for a ribbon towcable. These functions represent a mathematical fit to data measured on a towcable at sea. The functions should be used with caution in predicting the towing configuration of other types of ribbon cable design or other cable diameters because of the difficulty in scaling ribbon character- istics such as material stiffness. DD ans; 1473 EDITION OF 1 Nov 65 Is OBSOLETE UNCLASSIFIED S/N 0102- LF- 014-6601 SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) S/N 0102- LF- 014-6601 SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) TABLE OF CONTENTS TSE OUP JRIKEUINIOS 55 5 5 OG 6 6 ao) 6 0) O10 6 0 1 Oo LOM olso 6 TAIESHE OW AWA S 5 5G 6 6 Go Oo OOO do O LOO 0 0 © iGiidioAmey a. a NOTATION i en fer fo uon foul Fol feito ts! feo) te! Mon ite, | fo Weil Mali Me), MoMereteterton te JASSHORNGIES 6 6 6 0 oO Ga0 6°56 0,0 0.6 610 16 6 Jo) o.80 /NDWIEIESHERVIEIEIAD, IOMIHORMUEIONS 6 6 6 0 a 00050000000 60% 9 LIRTUROUGIILON go 6 6 0 6 6 6 O96 ooo oO LYASIUG (CONSIDNGVMEMONIE 5 6 6 0560600 O Oo oOo OO DESCRIPTION OF EXPERIMENTAL EQUIPMENT . ........2.4+.42.-.2 -. DTS ERG MIO OF INSU RUMINPUMENONG 6 56 606 6006060000000 EXPERIMENTAL ARRANGEMENT AND PROCEDURES . ......-.-.+.-s @ ISIE, ANID) IDIUSGUISISIIONG 5 5 616 6 0 6 9 oo ooo 8 COMO LHISIONS 9.6.0 6 6 050 6 6.6 610 6 6 6 6 46 0 05 6 0 OD OO INGIIRN(GES6 oO 6 5 6 0 0 690 0-6 6 0 0 Oooo Oo ob APPENDIX A -— A COMPARISON OF THE HYDRODYNAMIC LOADING FUNCTIONS WITH kh I Oo rN Du £ I A. 2- A.3- SOME CRITICAL ANGLE TOWING DATA. .......... LIST OF FIGURES DHEMSINIDG IDSDRESECEG o 6 0 6 0 6 6 0 6 465 6 6 0 Oo Oo 6 Danes soynys; ONE IHMC WapymAsceies 5.6 6560000056 560606 Depressor Performance as a Function of Speed... ° 0 0 3(a)-Cable Angle at the Depressor; 3(b)-Cable Tension ae the Depressor Ratpoem Weal, o 6 6000000500000 000 5000 6 Schematic Diagram of the Towing Arrangement. .... . Cable Tension at the Ship as a Function of Cable Scope... Depressor Depth as a Function of Cable Scope ....... Hydrodynamic Loading Functions ....... Bh ce op POL ros he 8(a)-Normal Hydrodynamic Loading Function vs Cable Angle; 8(b)-Tangential Hydrodynamic Loading Function vs Cable Angle Drag Coefficient Cc, as a Function of Reynolds Number... Towcable Tension per Unit Length versus Towspeed for \Weneslors MERCEINIERG 6 0°50 6 6 0060 000000060 50-0 0 0 Towing Angles versus Towspeed for Various Towcables. .... Tangential Hydrodynamic Loading vs Cable Angle ..... iii LIST OF TABLES 1 - Cable and Ribbon Geometry. ........ 2 - Measurement Sensors. . .« »« « « « « « « « » A.1— Ribbon Configurations. | 6. 3 6 5 6 6 w. A.2- Derived Normal Drag Coefficients ..... A.3- Tangential Hydrodynamic Loading Values. . iv > v > i mw oO o v Sy 5S 1) BS) els) fo) tas) ep) Tay Inn eal fe (>) @ r+ e) NOTATION Dimensionless coefficients Normal drag coefficient based on cable diameter Diameter Normal component of hydrodynamic force per unit length Normal hydrodynamic loading function ; Tangential hydrodynamic loading function Tangential component of hydrodynamic force per unit length Tangential component of force per unit length Normal component of force per unit length Cable drag per unit length when the axis is 90° to the flow Reynolds number Cable scope Cable tension Velocity Cable weight per unit length in seawater Density of seawater Towcable angle relative to horizontal Towcable critical angle eas acai Mas Dabo ViNinen), Maven, f ay : a nr Ne et pa ol x Aah pha ‘Seep lore eo C4 > | ' neha ult anthaes § | a Maant Ting 79g banal matty bou gat % SAT F ‘ a ‘ owinech sdiaws yok aaa 6 a os fold of): cs "50 #2 etxs fang Fail 4 eres ABSTRACT Hydrodynamic loading functions and drag coefficients have been developed for a ribbon towcable. These functions represent a mathe- matical fit to data measured on a towcable at sea. The functions should be used with caution in predicting the towing configurations of other types of ribbon cable design or other cable diameters because of the difficulty in scaling ribbon characteristics such as material stiffness. ADMINISTRATIVE INFORMATION The work described in this report was performed in support of a number of projects sponsored by the Naval Sea Systems Command, the Naval Ship Engineering Center and the Naval Air Systems Command. The effort was carried out jointly by David Taylor Naval Ship Research and Development Center under Program Element Number 62543N, Task Area Number SF 43-400-001, Work Unit Number 1507-101 and MAR Associates, Inc. under DINSRDC Contract Number N00600-79-D-2507. J. Nelligan is with MAR Associates, Inc. of Rockville, Maryland. INTRODUCTION Various devices can be attached to round towcables to improve hydrodynamic performance. A streamlined fairing reduces the normal component of drag allowing the towline to span a greater depth per unit of scope, at the same time reducing cable strumming. Fairing, however, is expensive and can be difficult to store and stream reliably, especially in certain applications, e.g., submarine towed systems. Ribbon towcable does not have the hydrodynamic efficiency of streamlined fairing, but it is much more easily stored and handled, in addition to being less costly. Ribbon is used primarily to reduce cable strumming which can be a source of noise or cause early fatigue. In so doing it appears also to reduce the normal component of drag below that of the fully strumming bare round cable. The mechanism by which strumming is suppressed is not fully understood but is thought to involve the disruption of spanwise coherence in vortex shedding and drag damping. A negative in the use of ribbon as with all cable-attached devices is the increase in the tangential component of drag (tension) relative to bare cable. As ribbon towcable has found important applications in fleet systems, particularly in submarine towed communications buoys and various airborne mine countermeasure systems, the need for accurate towing configuration prediction has increased. Knowing the hydrodynamic loading on the ribbon cable is required for configuration prediction. Typically one of two methods is used by the David Taylor Naval Ship Research and Development Center (DINSRDC) to develop the hydrodynamic loading functions. The first involves direct measurement of the hydrodynamic loading on a two-dimen- sional (rigid) model in the towing basin.” In the second technique an at-sea experiment is performed in which certain parameters describing the towing con- figuration are measured and the hydrodynamic loading functions are deduced by a regression analysis process until a match of computed and measured configurations is attained. This latter technique was used to determine the hydrodynamic loading func- tions for a particular ribbon cable. This report describes the at-sea experiment including towcable model, instrumentation, and experimental procedures; presents the results of the sea-trial and loading function analysis; and presents conclu- sions. Comparison of the loading functions with an independent data base is performed in Appendix A. BASIC CONSIDERATIONS The differential equations describing the steady-state two-dimensional towing configuration and forces in a cable-body system are well defined based on certain simplifying eae eOMe.” Solutions can be obtained by numerical inte- Swe: Ae : gration requiring as inputs: dhe Tension and angle at some point on the cable, usually an end condition specified at the towed body termination, 2. The form of the hydrodynamic loading functions, and Bo The characteristic drag coefficient for the towline. The body forces defining the cable end conditon typically are measured quite accurately in towing basins or wind tunnels. Tn complete list of references is given on page 21. Thus the problem of predicting the steady-state towing configuration becomes one of expressing the hydrodynamic force on the towcable. As noted previously, DINSRDC has developed a method for directly measuring the hydrodynamic loading functions in (two-dimensional) towing basin experiments. These measured loading functions must ultimately be verified by at-sea measurements since there are some artificialities introduced with the two-dimensional model. In time, as this verification process proceeds on different designs, confidence in the two-dimen- sional measurements as a basis for loading functions will grow and the need for at-sea verification diminish. The second method is based on an at-sea experiment in which measurements are made of cable tension, body depth, and cable angle, all as functions of cable scope and speed. The computer model is then exercised assuming different values of hydrodynamic loading until an acceptable match of predicted-to-measured con- figurations obtains. This regression analysis method is used here to develop ribbon cable loading functions. A towcable configuration can be defined mathematically by specifying an end condition (tension and angle) and by knowledge of the loading along its span in terms of the normal, Q, and tangential, P, force components expressed as follows: Q F - w sino (1) ae) i] G - w cosd where is the normal component of hydrodynamic force per unit length, F G is the tangential component of hydrodynamic force per unit length, w is the cable weight in water per unit length, and 0) is the cable angle relative to horizontal. The effort of this report is to evaluate these expressions of P and Q for the ribbon towcable. Since the weight of cable is readily measured the task becomes one of determining by regression analysis the normal and tangential hydrodynamic force components which produce a fit of computed-to-measured data and which can be expressed as: £ (o)°R £.(o)"R o (ep) i} where £ Co) is the normal hydrodynamic loading function, £.(o) is the tangential hydrodynamic loading function, R is the cable drag per unit length when the axis is 90° to the flow (R = 450 ,Vd) , p is the density of seawater, CR is the normal drag coefficient based on cable diameter, V is velocity, and d is cable diameter. As seen in Equation (2), F and G are expressed as the products of two terms. Essentially the process of determining the hydrodynamic loading functions is one of assuming various forms of £ Cd) and £.() until, through the regression analysis, a value of Cy (as a function only of Reynolds number) is obtained for which the computed configurations match those measured. Since the fitting process is based on the products £ Co) °R and £ Co) °R, it appears that there could be a family of solutions rather than a unique solution. However a constraint on the range of solutions is that the CR values be plausible. Nonetheless it must be recognized that the derived value of CR may be different from that which would be obtained by physical measurement and, therefore, it is not valid to imply that this CR is a characteristic of the cable independent of the hydrodynamic loading functions. The above caveats notwithstanding, there is confidence in this technique for developing the hydrodynamic loading functions and in applying these functions to the configuration predictions of ribbon towcable provided: 1. the ribbon towcable design is similar, cable diameter is not greatly different from that measured, and 3. the Reynolds number is within the range from 5.2 x 10° to 1.28 x 10. In conformance with established marnodalloasy.." ff) and £.(¢) are represented in this analysis by selected terms from the following trigonometric series: f(¢) = A, + A, cosd + A, sind + A, cos2>o + A, sin2o. 1 2 3 4 DESCRIPTION OF EXPERIMENTAL EQUIPMENT The experimental equipment consisted of a towed depressor body and the experimental ribbon towcable. The towed body is shown in Figure 1; its dimen- sions are given in Figure 2. This depressor weighs 1609 pounds (7204 N) in water and has a variable incidence mid-wing. For this experiment, the wing incidence angle was set at 57 (leading edge down). The hydrodynamic performance of the body as measured in the towing basin is shown in Figure 3. The ribbon towcable consisted of a 1450-ft (442-m) length of 0.78-inch (1.98 cm) diameter, double-armored, electrical-mechanical cable with ribbons attached, as shown in Figure 4. The cable consisted of two layers, reverse lay, of galvanized steel armor strands surrounding a 10-conductor electrical core. The cable weighed 0.688 pounds per foot (1.02 kg/m) in sea water and had a breaking strength of approximately 50,000 pounds (223,880 N). The ribbons were polyurethane strips threaded under the outer layers of armor. Ribbon geometry is given in Table l. TABLE 1 - CABLE AND RIBBON GEOMETRY Cable diameter 0.78 in. (1.98 cm) Cable length 1450 ft. (442 m) Ribbon loop length 9.36 in. (23.77 cm) Ribbon length-to-cable- diameter ratio 6 Ribbon width 0.78 in. (1.98 em) Material thickness 0.015 in. (.038 cm) Spacing (centers) 0.78 in. (1.98 cm) Ribbon coverage 100% The towcable was marked at 100-ft (30.5-m) intervals to permit estimation of cable scope in the water to about + 5 ft (+ 1.5m). 3G) 6 cispaier is oy aber tL Sihee ) tounerqeb: wii ioe biprel let Ay Ss eeOR RY ae | ‘ : - DUE ke Dk Salted i ray et r y cme jue 2 ‘Me a3 tte: youre pening ei de ; ‘el yeu Pent 199 elias 10g ce Bf fringe: hee wong i a hy : my ‘ Th a i cars ah oO (7a YY a ‘ ) y ba ic | eee Gu De =| 4 ra 1a nf f wih M ‘ f | nt a’ ‘ th ties a ety ra pane wig \T i * h ns r bbe ve & _ 4 ; 3 F Ye POG Sees § a tty by f ( . M nt s - ‘ “y : if, fy , * 3} a i ij aul j i PSD 0053/25-10-77 Figure 1 - DINSRDC Depressor 5.6x7 = 2.18’ sae DEPRESSOR WEIGHT IN WATER = 1609 POUNDS DIMENSIONS IN FEET Figure 2 - Dimensions of DTNSRDC Depressor SPEED (m/s) 0 2 4 6 8 90 e 88 [3] ‘= nm ov = lu rs} = = 86 a S 84 0 4 8 12 16 SPEED (knots) Figure 3a - Cable Angle at the Depressor SPEED (m/s) 0 2 4 6 3 2.8 11.6 = SP 256 x< a = «28 10.7 S 2 22 = 2 2.0 $) 9) oO 1.8 1.6 9.0 0 4 8 12 16 SPEED (knots) Figure 3b - Cable Tension at the Depressor Figure 3 - Depressor Performance as a Function of Speed for a Wing Angle of -50 CABLE TENSION (N x 107°) CMSFE Severo it * 79 a 1.08 OL h (atond) 04399 TORSO TGO 29 Fe get ema ideo + de J t ot) 0) rat ‘ ID alt dag TT ke i 4 a7 : erighy = = = ZZ AAA VV\ Vv = SE SS WNININ. Lil PSD 340261 Figure 4 - Typical Ribbon Towcables DESCRIPTION OF INSTRUMENTATION The experimental system was instrumented to measure the following parameters: ike body depth below the water surface, Zs cable tension at the ship, and 3ic towing speed. A watertight instrument housing in the depressor body contained electronics for amplification and remote electrical calibration of the body depth sensor. The housing also contained a voltage-controlled oscillator-type telemetry assembly to transmit the depth signal through the towcable to the graphic and digital recorders aboard ship. The cable tension at the ship sensor was direct wired to a control unit within the ship laboratory which contained the tension sensor amplifier and electrical calibration circuit. Ship speed was measured by the DITNSRDC knotmeter. The sensors and their accuracies are listed in Table 2. TABLE 2 —- MEASUREMENT SENSORS Sensor Measured Measurement Cable tension Dyna-Line 0-10,000 + 200 1b at the ship tensiometer 1b Body depth Diaphragm OSS) ie ap Do wie pressure gage Ship speed DINSRDC knotmeter 0-25 kts ae Wo (Ohl Ise The design of the electrical calibration circuits in this measurement system virtually eliminate the effect of long-term zero drift and sensitivity error within the amplifier and recording electronics external to the sensors. As a result the total readout error is limited to that of each individual sensor. These calibration principles are discussed in detail in Reference 5. The ship- board readout electronics consisted of a 6-channel strip chart recorder providing a time history of cable tension at the ship, depth of the body, and ship speed; an integrating digital voltmeter, and two preset electronic counters provided digital displays of the cable tension, body depth, and ship speed, respectively. A digital recorder was used in conjunction with the digital display units to obtain a printed record of the data. iS} 2 EXPERIMENTAL ARRANGEMENT AND PROCEDURES The experiment was conducted at sea from the R/V PATRICK KILEY in the New Providence Channel off the Bahamas during July 1970. The operational area was selected for minimum sea state conditions to obtain, as nearly as practicable, steady-state towing. The general towing arrangement is shown in Figure 5. A cable dominated system was chosen assuring curvature over a significant portion of the towline. Use of the AN/SQA-13(XN-1) winch and handling system accommodated the large size towcable and simplified system deployment and retrieval. The system was towed in a calm sea at nominal speeds of 6, 8, 10, 12 and 14 knots (3.1, 4.1, 5.1, 6.2, and 7.2 m/s). At each speed, measurements were taken at nominal wetted cable scopes of 200, 400, 600, 800 and 1000 ft (61, 122, 183, 244 and 305 m). Prior to recording data for each new speed and scope, body depth was monitored to assure that the system had established a new equilibrium configura- tion and was no longer influenced by speed change transients. Four separate sets of measurements were taken for each data run. RESULTS AND DISCUSSION The averaged measured values of cable tension at the ship and depressor are shown in Figures 6 and 7. Also shown in the figures are computer model predic-— tions (solid lines) based on a regression-analysis determination of the hydro- dynamic loading functions fo and f. and the drag coefficient Ce: These functions represent the best fit to the data and were obtained through a trial and error process. The values of the functions are: fs = 0.4986 - 0.2499 cosd + 0.2527 sing - 0.2487 cos29 (4) f. = -0.2255 + 0.3417 cosd + 0.2255 sind - 0.0811 sin2¢ (5) Coyne 5.7467 - 0.93 log,, R, (6) These functions are shown graphically in Figures 8 and 9 and apply to the Reynolds number range from 5.2 x 10 to 1.28 x 1028 In assessing the goodness of fit of computed-to-measured data it is seen that tension predictions are generally within 10% of measured values with the body force zeroed out (within 5% with body force included). Body depth predictions are within 5% of measured values except 14 y, | ae au les ss Son a = WATER SURFACE TOWING SHIP RIBBON TOWCABLE _ CABLE ANGLE DIRECTION OF TOW |__==z TOWED BODY Figure 5 — Schematic Diagram of the Towing Arrangement 15 CABLE TENSION (1b) 0 61 7000 CABLE SCOPE (m) 122 183 Speed in Knots (m/s) O 6.06 (3.1 6000 O 8.09 (4. Ool17 (Ss2 A 12.09 (6.2 (we ) 2) ) ) A 14.03 ) 5000 4000 3000 1000 0 200 400 600 CABLE SCOPE (ft) 244 800 1000 Figure 6 - Cable Tension at the Ship as a Function of Cable Scope 16 CABLE TENTION (N X 1072) DEPRESSOR DEPTH (ft CABLE SCOPE (m) 61 122 183 244 305 600 Speed in Knots (m/s) O 6.06 500 O 8.09 (4. 152 © 10.17 A 12.09 AAS 400 | 300 200 100 0 200 400 600 800 1000 CABLE SCOPE (ft) Figure 7 - Depressor Depth as a Function of Cable Scope 17 DEPRESSOR DEPTH (m) SuoTjouny Su~peoyT ofweudporpAy —- 8 ein3sty eTsuy eTGeD SA uot joUNng Sutpeoy ITweukpospsy Tetquesuel - qg san8tTy (6ap) 3J79NV 4 719V9 08 OL 09 0S Or og 02 S) 4 i=) (4) INIGVOT DIWYNAGOUGAH “WILN39t N j=) eT3uy eTGeD SA uoTIOUNg SUT peo] o-weudkpoapAy TeWION - eg oansty (59p) 379NV 379v9 06 08 OL 09 0S Ov O¢ 02 O1 S oO wo oO oO od (2) INIGVOT DIWWNAGOYGAH TVWYON 18 jequny sprousey Jo uotjJoUNg e se JUSTOTFZOOD Beagq - 6 ean3Ty YaEWAN SATONASY GOL X I Ol6o1 66°70 - £9b/°S = OT X I CO jo) oO 4 N a + co (uy) IN319144509 SVUC 19 for scopes of 400 and 200 feet where the average differences are about 6% and 8.7% respectively. The relationships between £0) > £ (>) and CR have been discussed previously. With respect to the problem of fitting predicted-to-measured configurations another factor should be considered. In this methodology the term CR accounts for the effect of Reynolds number on both the normal and tangential components of hydrodynamic force. However, it should not be expected that the Reynolds number effects are physically the same for the normal component at steep cable angles where pressure drag predominates and for the tangential component at shallow angles where frictional drag predominates. The final curve fits shown in Figures 6 and 7, therefore, reflect a compromise in the expression of Cc, with Reynolds number. Ribbon represents a type of "fairing" unlike streamlined rigid fairing in that the geometry changes with speed and with cable angle inclination. It has been observed that at an angle of the cable 90° to the flow, the ribbons stream out normal to the cable axis. At shallow angles, the ribbons have been observed to lay down along the trailing edge of the cable. In addition to cable angle, intuitively such factors as ribbon material stiffness, percent cable coverage, and method of attachment are judged to influence the detailed geometry of the ribbons and therefore the hydrodynamic loading. Some insight into this is given in Appendix A. However, primarily because of a lack of knowledge of how to scale the material stiffness factor, caution must be exercised in applying these loading functions to a cable of significantly different diameter. Scaling should not be attempted outside of the Reynolds number range covered in these tests. 20 CONCLUSIONS As a result of this experiment and the data analysis here and in the Appendix the following is concluded; ibe The derived hydrodynamic loading functions and drag coefficients will support a good estimate of towing configurations for this design of ribbon towcable and for the range of variables covered by the experiment. Dap The functions and coefficients should be applied to other cable diameters and/or ribbon designs with caution since ribbon material thickness appears to be an influential parameter and methods for scaling material stiffness have not been developed. REFERENCES bs Folb, R., "Experimental Determination of Hydrodynamic Loading for Ten Cable Fairing Models," DINSRDC Report 4610, November 1975. De, Pode, L., "Tables for Computing the Equilibrium Configuration of a Flexible Cable in a Uniform Stream," David Taylor Model Basin Report 687, March 1951. Bye Cuthill, E.H., "A FORTRAN IV Program for the Calculation of the Equilibrium Configuration of a Flexible Cable in a Uniform Stream," Naval Ship Research and Development Center Report 2531, February 1968. 4, Springston, G., "Generalized Hydrodynamic Loading Functions for Bare and Faired Cable in Two-Dimensional Steady-State Cable Configurations," Naval Ship Research and Development Center Report 2424, June 1967. 5h Singleton, R.J., "BIAS Buoy Measurement and Depth Control Instrumentation," David Taylor Naval Ship Research and Development Center Report 4451, November 1975. Zl APPENDIX A A COMPARISON OF THE HYDRODYNAMIC LOADING FUNCTIONS WITH SOME CRITICAL ANGLE TOWING DATA Figures Al and A2 show hydrodynamic data on ribbon towcables obtained in critical angle towing tests by DINSRDC. In these experiments long lengths of cable were towed at the critical angle while cable tension at the towpoint, cable angle and speed were measured. From these data a few points can be extracted for comparison with the hydrodynamic loading functions and drag coefficients developed earlier in the body of this report. Two ribbon towcable models were evaluated, the models differing primarily in the thickness of the ribbon material. Models A and B each had a 0.84-in. (21.3-mm) diameter, double-armored electrical cable weighing 1.02 1b/ft (1.51 kg/m) in sea water. Ribbon configurations were as shown in Table A.1. TABLE A.1 - RIBBON CONFIGURATIONS RIBBON RIBBON MATERIAL % CABLE MODEL LENGTH WIDTH THICKNESS COVERAGE A 6D 2D 15 mil (0.38 mm) B 6D 2D 30 mil (0.76 mm) The ribbon material was polyurethane and the ribbon density (or percent cable -coverage) was 50% compared to 100% for the model described in the body of the present report. Note, however, that the latter model and Model A have the same material thickness, namely 15 mil (0.38 mm) which is one-half the material thick- ness for Model B. In reviewing Figures Al and A2, which are the reduced hydrodynamic measure- ments of towcable tension per unit length and towing angle, it can be seen that the Model B cable tows at a more shallow angle and develops a much higher tension than the Model A cable. (In the graphs showing 30-mil (0.76-mm) thick ribbon cable data Model B refers to the curve marked R/S = 50/00. The other curves result from parts of the test in which increasing percentages of the ribbon were clipped off.) 22 dT/dS (lb/ft) (N/m) TOWING ANGLE (deg) cu RIBBON-FAIRED TOWCABLE RIBBON/STUB-FAIRED TOWCABLES 50% RIBBONS, 15-MIL THICK 30-MIL THICK TRIAL 4H8 ye TRIAL 4H8 = = cc R/S% a f= as ae ai i sO a pees S 25/25 as) 13/37 a 00/5007 0 6(3.1) 12(6.2) 0 6(3.1) “12(6.2) TOWSPEED (knots) (m/s) TOWSPEED (knots) (m/s) Figure A.1l -— Towcable Tension per Unit Length versus Towspeed for Various Towcables RIBBON-FAIRED TOWCABLE RIBBON/STUB-FAIRED TOWCABLES 50% RIBBONS, 15-MIL THICK 30-MIL THICK TRIAL 4H8 TRIAL 4h8 TOWING ANGLE (deg) 0 6(3.1) 12(6.2) 0 6(3.1) 12(6.2) TOWSPEED (knots) (m/s) TOWSPEED (Knots) (m/s) Figure A.2 - Towing Angles versus Towspeed for Various Towcables 23) Since these cables are trailing at a constant angle for each speed, each experimental data point yields a set of hydrodynamic loading data points which can be compared with the functions (or coefficients) developed earlier. Con- sidering the normal components of force first, in a critical angle tow the normal component of hydrodynamic force balances the cable weight component normal to the cable axis. Thus Ge), OR & wecosd (1A) from which wecoso C 8 Sea (2A) 2, Gy Gare) where o- is the critical angle. Applying the normal hydrodynamic loading function presented in equation (4), C.'s were computed for the two models from the data shown in Figure A.2 and are presented in Table A.2. TABLE A.2 —- DERIVED NORMAL DRAG COEFFICIENTS Reynolds Model A Model B fo) 5)o 8) x 10° 8.86 x 10° IG ALI/ o5 lop 1.477 x LO? Also shown in Table A.2 is a column designated Cm These values of Ca were computed by equation (6) for the corresponding Reynolds number in Table A.2. It is seen that cn and Cc. for Model A agree rather well. It is concluded that the representation of the normal hydrodynamic force developed in the body of the report is also a good representation for Model A. This is in spite of the fact that Model A has only 50% of the ribbon cable coverage. The reason may be that the data base is comprised largely of shallow angle data. It has been observed that at 24 shallow angles ribbons tend to lie flat along the trailing edge of the cable. This may reduce the effect of percent cable coverage on the normal component of hydro- dynamic force. In the case of Model B the ie eS drag coefficients Cc. are approximately double the values for Model A (and Cc. ) a trend which could be inferred from the data in Figure A.2. It may be that the thicker (stiffer) ribbon material results in a higher projected frontal area to the flow and this accounts for the higher drag co- efficients when based on cable diameter. Or it may be that material stiffness alters the wake to the extent that a different loading function applies or some combination of the two. Regardless, it is clear that the normal hydrodynamic loading function and Ce derived from a 15 mil (0.38 mm) ribbon data base is a poor representation for a towcable with 30 mil (0.76 mm) ribbon. In analyzing the tangential hydrodynamic force components, estimates of tangential hydrodynamic loading function values can be made from the data in Figure A.1 and the following relation: (AT/AS - w sing) Cas snl once alae ta . (3A) Computed values of (Ey are shown in Table A.3. c TABLE A.3 — TANGENTIAL HYDRODYNAMIC LOADING VALUES 25 The computed values of £ (>) are also plotted in Figure A.3. Considering the values of £.(o) as derived from the three data bases, neglecting for the moment the CR values by which they were derived and how the CR values ultimately scale the tangential hydrodynamic force, there is a consistency to the £() values. First, Models A and B both representing 50% ribbon coverage have £($) values which closely approximate a single trend line (Figure A.3). Second, these values are approximately one-half those pertaining to the 100% ribbon coverage cable. So it appears that wetted surface (percent cable coverage) is a key parameter controlling tangential drag as would be expected. However to compute the tangential force CR must be applied. If only the 15 mil (0.38 mm) thick ribbon models are considered, the consistency is maintained and so is the concept of surface area as a key parameter. When the 30 mil (0.76 mm) case is considered with its large CR values the tangential force scales up to where the 30 mil (0.76 mm) ribbon tangential force is twice that of the 15 mil (0.38 mm) ribbon although both have the same wetted surface. Now the concept of wetted surface area having a linear effect on tangential force does not hold. It must be concluded that the characteristics of the ribbon especially material stiffness and possibly method of attachment are influencing hydrodynamic forces both normal and tangential in important ways that are not understood. For this reason scaling this data to ribbon cables of significantly different size must be done with caution. aTZuy eTqeD sA BUTpeoT oTMeUApOIpAH TeFJUesUe] - E*y 21N3TY ‘saaubap) FTONY 318v9 O€ G2 02 SI 01 G 0 , JOVYIAOD NOSSIY %OS S0°0 T'0 ONIYIAOD NOGGIY %OOT Z ULS TI80°0 - PULS GGZz2°0 + SOD LIVE" 0+SS22°0- = oy S1°0 *(g) nb3 NOGdIY TIW-O€ *d 130d0W O NO@aIy TIW-ST ‘VY 1300W O 2°0 QNIGVOT JIWWNAGOYGAH IWILNSONVL 27 ) te | | . OR. i thi computed vabuoe of TAG) Bis alte » pase, 4 bya bade ie ey yuan of s. 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