R-Al21 S12 HYDRODYNAMIC STABILITY AND TOWING ANALYSIS OF THEiiMAGGIE 11 YEHICLE(U) NAVAL COASTAL SYSTEMS CENTER

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UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (Ph" Dat ntefO4_

I READ fISTRUCTIONSREPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM1. REPORT NUMMER .GOVT ACCESSION NO S. RECIPIENT'S CATALOG NUMBER

NCSC TH284-80 1/ /,- _4. TITLE (and Subtitle) S. TYPE OF REPORT A PERIOD COVERED

Technical MemorandumHYDRODYNAMIC STABILITY AND TOWING ANALYSIS Jan 1978 - Nov 1978

OF THE MAGGIE II VEHICLE 6. PERFORMING ORG. REPORT NUM9ER

7. AUTHOR(e) S. CONTRACT OR GRANT NUMER(e)

J. W. Crane

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAN ELEMENT. PROJECT, TASKAREA & WORK UNIT NUMBERS

Naval Coastal Systems Center Work Unit SD78P

Panama City, Florida 32407 Task Number 00078-01

II. 'CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

June 198013. NUMMER OF PAGES

14. MONITORING AGENCY NAME a ADDRESS(If different from' Controllind Ofice) IS. SECURITY CLASS. (at thie rlp tt"

UNCLASSIFIED

1ia. DECLASSIF I C ATION / DOWNGRADING

!SCpAKDULEI

IS. DISTRIBUTION STATEMENT (of thin Report)

This document has been approved for public release and sale;its distribution is unlimited.

17. DISTRIBUTION STATEMENT (of th eb reat entered in Slock 0. II different from Report)

Is. SUPPLEMENTARY NOTES

It. KEY WORDS (Con#hue an revere a4d I nesee, ad Idottl, b week number)

Hydrodynamic stability Identifiers:Towed vehicles MAGGIE II VehicleUnderwater vehicles Towing AnalysisHydrodynamic coefficients Tail sizing

\ Towing cables Cable catenary20. ABSTRACT (Continue en reverse lde If negonearaend Identify by oWek nustber)

, An analysis of the hydrodynamic characteristics and stability of the

MAGGIE II towed vehicle system has been performed. The vehicle's hydro-dynamic coefficients and mass properties were determined from its geometry.The tail surfaces were sized to provide the required stability; the effectsof tail size variations are presented as root locus plots. The vehicle's

motions resulting from a heaving motion of the towing vessel have beenpredicted.

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SECUITY CL.ASSIIlCATION OF THISl PAGE (M Dome E~

TABLE OF CONTENTS

Page

INTRODUCTION. ... ...... ....... ....... ...... 1VEHICLE CONFIGURATION. .. ..... ...... ....... ....

Fixed Tail Surface Sizing .. ..... ....... ....... 1Control Surface Sizing .. .. ....... ....... ..... 5

VEHICLE STABILITY .. .. ....... ...... ....... ... 10Base Case .. ..... ....... ...... .........10Towing Speed .. .. ....... ....... ...... ... 11Pigtail Length .. .. ....... ...... ....... .. 11

STATIC CATENARY. .. .... ....... ....... ........ 11VEHICLE RESPONSE TO UPPER TOW POINT INPUT. .. ..... ........14FLOW VELOCITY OVER AFTERBODY .. ..... ....... ........ 21CONCLUSIONS. .. .... ....... ....... ...... ... 21REFERENCES .. ..... ....... ...... ....... ... 23

LIST OF ILLUSTRATIONS

Figure Page

1 MAGGIE II VEHICLE DIMENSIONAL DRAWING .. .. ....... ... 22 MAGGIE 11 VEHICLE (TOP, SIDE, AND FRONT VIEWS). ... ...... 33 MAGGIE II VEHICLE (OBLIQUE VIEWS) .. ... ...... ...... 44 HORIZONTAL TAIL WITH ELEVATOR. .. .... ....... ..... 9

*5 VERTICAL TAIL WITH RUDDER. .. .... ....... ....... 96 EFFECT OF VARYING TOW SPEED ON VEHICLE STABILITY .. .... .. 12

*7 EFFECT OF VARYING PIGTAIL LENGTH ON VEHICLE STABILITY .. .. .. 138 PROPOSED CABLE CATENARY WITH 600 FOOT SCOPE. .. ..... .... 16

9PROPOSED CABLE CATENARY WITH 800 FOOT SCOPE .. .. ..... .. 1710 PIRESON-SEOWODIT HEAVINGCTOW. PO.. .. .. .. .. ...... 19

12 RESPONSE OF BODY 2 TO HEAVING TOW POINT.. .. ......... .. 2013 PRESSURE DISTRIBUTION OVER MAGGIE II AFTERBODY .. ..... .. 22

LIST OF TABLES

Table Page

1 MAGGIE II VEHICLE GEOMETRIC PROPERTIES .. ... ...... ... 52 MAGGIE II VEHICLE HYDRODYNAMIC COEFFICIENTS .. ..... ..... 6

*3 TAIL SIZE VARIATION. ... ...... ....... ....... 84BASE CASE ROOTS. ... ...... ....... .........10I

5 CABLE CATENARY DATA .. ..... ...... ....... ... 15

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INTRODUCTION

At the request of the Applied Physics Laboratory (APL) at Johns HopkinsUniversity, NCSC investigated various aspects of the MAGGIE II vehicle, partof a second-generation prototype system of towed magnetometers. The follow-ing analyses were performed in the course of this study, the results of whichare documented herein:

(1) Sizing of tail surfaces of a typical MAGGIE II vehicleconfiguration;

(2) Determination of vehicle stability, and specified cable catenaries,including scopes and tensions, for a given configuration;

(3) Estimation of vehicle response to input at the upper tow point;and

(4) Determination of the flow velocity over the afterbody.

VEHICLE CONFIGURATION

FIXED TAIL SURFACE SIZING

NCSC determined the sizing for the tail structure of the MAGGIE IIvehicle; APL supplied the external configuration of the fuselage. Theresulting vehicle is shown in Figures 1, 2, and 3. Mass characteristicscalculated using a weight and balance program developed at NCSC I are givenin Table 1, and hydrodynamic coefficients calculated by means of standardNCSC techniques2 '3 are presented in Table 2.

Three horizontal tail sizes, as detailed in Table 3, were considered.The tail configuration labeled Fin 4 is a modification of Fin 2, in whichthe leading edge has been swept 30 degrees. Fin 4 was selected for thevehicle.

The following characteristics of the tail configuration were consideredin determining the relative effectiveness of the tail size alternatives.

1K.W. Watkinson, "The Midcohv Weight and Balance Computer Program (WrBAL),"Naval Coastal Systems Laboratory Informal Report 22074, September 1974.

2D.E. Humphreys and L.E. Bowen, "Prediction of Hydrodynamic CoefficientsFor Underwater Vehicles," paper presented at 1975 NAVSEA HydromechanicsAdvisory Committee (SEAHAC) meeting, Monterey, CA., October 1975.

3D.E. Huuphreys and K.W. Watkinson, "Prediction of Acceleration Hydro-dynamic Coefficients For Underwater Vehicles From Geometric Parameters,"Naval Coastal Systems Laboratory Technical Report 327-78, February 1978.

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TABLE 1

MAGGIE II VEHICLE GEOMETRIC PROPERTIES

mass = 11.09 slugs

1= 1.61 slug/ft.2

I = 3.93 slug/ft.2

y1= 3.93 slug/ft.2

I = 0.00 slug/ft.2

xz

= 12.93 ft.

Xnose/c.g. = 3.11 ft.

xnose/c.b. = 3.11 ft.

Z c.b. = -0.10 ft.

Cable length = 50.00 ft.

The twin horizontal tails act as endplates on the vertical tail and increaseits effective aspect ratio to range approximately from 2.5 to 3.0.4 Thehorizontal tails also serve as bi-wings, thus effectively doubling theireffective aspect ratio.4 Interference effects at the junction of the verti-cal and horizontal tails were not considered.

CONTROL SURFACE SIZING

MAGGIE II control surfaces were sized to produce a displacement of 5feet vertically and horizontally when fully deflected (±20 degrees). Thenominal case examined was a speed of 8 knots and a cable length of 50 feet.The surfaces used were rectangular, with a chord of 1.33 inches and a semi-span of 4 inches. Planforms of the horizontal and vertical tails are shownin Figures 4 and 5, respectively.

4S.F. Hoerner and H.V. Borst, "Fluid-Dynamic Lift," (Published by the authors,1975) pp. 3-9 to 3-10, pp 20-7 to 20-8.

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TABLE 3

TAIL SIZE VARIATION-

FIN I FIN 2 FIN 3 FIN 4

Width (in.) 14.00 20.00 26.00 20.001

Length (in.) 24.00 24.00 24.00 24.00

Effective Span (in.) 6.50 12.50 19.50 12.50

Area (sq.in.) 156.00 300.00 444.00 248.00

Aspect Ratio 0.27 0.52 0.81 0.60 -

Effective Aspect Ratio Horizontal Tail 0.58 1.01 1.43 1.14

Taper Ratio 1.00 1.00 1.00 0.84

Leading Edge Sweep (deg.) 0.00 0.00 0.00 30.00

*Aspect Ratio Vertical Tail 0.54 0.54 0.54 0.54

Effective Aspect Ratio Vertical Tail 1.85-2.5 2.5-3.0 3.00 2.5-3.0

To determine the magnitude of the displacement when the controlsurface is deflected, the depth (Z) transfer function is examined. The Z

*transfer function is formed from the w and 0 transfer functions and is*given by

U~s) -1 W(s) -0(s)6(Cs) S 6 (s) o 37s)e e e

.0041 (s + 49.45)(s + 10.66)(s2 + 0.170 s + 0.039).

Application of the Final Value Theorem of Laplace Transforms for a step* input in elevator results in steady state depth-change of

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-0.49 ft./deg.

since the maximum elevator is ±20 degrees, final steady state depth changewill be 10 feet. Also, because pigtail restoring forces vary inversely with

* pigtail length, doubling or halving this length will double or half the depthchange. Doubling the elevator area will also double the depth change.

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The Y transfer function is formed from the v and , transfer functionsand is given by

Y = 0.00128 (s + 675.1)r) s + 20.35)(s2 + 0.157 s + 0.040).

The steady state gain for a step rudder input is

Ysteady state = 1.06 ft./deg.

Changing the cable length and the control surface area will have similareffects on the y response.

VEHICLE STABILITY

BASE CASE

The stability of the MAGGIE II towed body and pigtail was examined forvarious speeds and pigtail lengths. The base case used in this analysis was aspeed of 8"knots and a pigtail length of 50 feet. The corresponding longitudi-nal and lateral roots for the base case are given in Table 4. Except for theroots marked roll and surge, longitudinal and lateral roots are similar becausethe vehicle has two almost identical planes of symmetry. Roll roots are moder-ately damped, with a maximum time to half amplitude of 1.9 seconds and a periodof 9.1 seconds. This can be improved by increasing the c.b./c.g. separation.

TABLE 4

BASE CASE ROOTS

Longitudinal wn (rad./sec.)

-1.30, -10.66 1.61 3.71

-0.09 t 0.18 0.45 0.20

* -0.20 ± 0.11 0.87 0.24

4Lateral Roots w (rad./sec.)n .

-1.41, -20.3 2.03 5.35

-0.08 ± 0.18 0.39 0.20

-0.37 ± 0.69 0.47 0.78

* Surge

* Roll

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TOWING SPEED

Towing speed was varied from 2 knots to 14 knots with a constantpigtail length of 50 feet. Results of this analysis are presented in rootlocus form in Figure 6. Examination of the roll roots reveals that natural

* frequency does not vary with speed, due io the fact that wn is a function

of only the c.b./c.g. separation. Damping ratio does, however, increase* with an increase in speed because of the presence of the tail.

K. Surge roots are dependent upon the X' cable derivative and the vehicledrag coefficient; natural frequency varies proportionally with towing speedwhile damping ratio remains constant. Both roll and surge motions aredecoupled from the other motions of the vehicle.

Examination of the remaining roots reveals that the damping ratio ofthe oscillatory pairs continues to be constant while speed increases.Damping ratio of the real roots decreases but remains greater than unity.Natural frequency, varying linearly with speed, increases in conjunction withspeed for the remaining real roots. Notion associated with these rootsconsists of w,q,z,e longitudinal motion and v,r,y,*~ lateral motion.

PIGTAIL LENGTH

Pigtail length was varied from 25 to 300 feet while a constant* speed of 8 knots was maintained. Figure 7 presents the results of this

analysis in root locus form. Examination of the roll and surge roots* reveals that only the surge roots are affected by cable length varia-

tion. Increasing pigtail length drives the surge roots toward theiruntethered values, 0.0 and 0.42, because cable length appears inverselyin the X' derivative in the surge mode.

Base case real roots are only slightly affected by changes inpigtail length. Increasing the length results in a decrease in fre-quency of oscillation while time to half amplitude remains constant.Frequency of oscillation is dependent upon the cable derivatives whichvary inversely with pigtail length, while damping ratio is predominantlyspeed dependent.

STATIC CATENARY

The static catenaries originally proposed by APL were analyzed usingthe three-dimensional cable program developed by Wang.5 Results of this

511.T. Wang, "A Fortran IV Program for the Three-Dimensional Steady StateConfiguration of Extensive Flexible Cable Systems," Naval Ship Researchand Development Center Report No. 4384, September, 1974.

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analysis are presented in Table 5. A typical MAGGIE II cable system isshown in Figure 8.

The depressor used for the purposes of this study was the ClassicThicket,8 with a tail incidence angle of -2 degrees. Lengths of thepigtails were such that the two MAGGIE towed bodies trailed at equaldistances from the tow point at a speed of 8 knots. Lengths of thecable segments were determined such that the first towed body was at adepth of 100 feet, the second body was at 500 feet, and the depressorwas at 600 feet. Indicated cable sections were faired with FathomFlexnose Fairing; otherwise, ribbon or hair fairing was used.

The cable configurations adopted by APL7 are constructed such that100 foot lengths may be added or removed, as is illustrated in Figures8 and 9.

VEHICLE RESPONSE TO UPPER TOW POINT INPUT

To determine the response of the MAGGIE system to a heaving motionat the upper tow point, it was necessary to create a model of the entiresystem of MAGGIE bodies, cable, and depressor. The cables were modeledas five groups of springs and dampers, one group for each cable segmentas was shown in Figure 8.

Input at the tow point was to have a 5-foot amplitude, correspondingto Upper Sea State 3 as indicated in Figure 10, the Pierson-MoskowitzSea Spectra.8 This also corresponded to a frequency of approximately 1radian per second. Response of the system was determined over the rangeof frequencies from 0.01 to 10 radians per second. The output amplitudewas normalized with respect to the input amplitude as is illustrated inFigures 11 and 12 for Bodies 1 and 2, respectively. Response data forfrequencies greater than 1.2 radians per second corresponds to Sea Statesl and 2.

Body I response peak occurs at approximately 0.08 radians per second(Sea State 4). The amplitude of the z response at peak is 1.12 percentof the input, while the 0 or pitch response is 0.4 degree per foot.

8Charles W. Sieber, "Design and Evaluation of a Large Towed WingedDepressor for Project Classic Thicket," Naval Ship Research and Develop-went Center Report No. SPD-487-04, October, 1974.

7B.F. Fuess, "Cable Catenary for MAGGIE II Sensor System," Johns HopkinsUniversity Applied Physics Laboratory Memorandum No. BFD-3-78-002, 30 March1978

8W.J. Pierson and L. Moskowitz, "A Proposed Spectral Form Based on theSimilarity Theory of S.A. Kitaigorodski," Report No. 63-12, GeophysicalSciences Laboratory, N.Y. University, 1963.

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In the range of frequencies from 0.1 to 0.2 radian per second, however,tez response is only 32 percent of the input and the e response is 0.25dereper foot.

The peak responses of Body 2 are not as sharply defined as those ofBody 1. They occur in the range of frequencies from 0.07 to 0.3 radianper second, with a maximum z amplitude of 32 percent of the input, and6 amplitude of 1.20 degrees per foot at 0.08 radian per second. Themaximum z amplitude near 0.25 radian per second is 25 percent of the input.The maximum e amplitude of 0.25 degree per foot is only slightly less thanthe peak 6 amplitude.

Frequencies less than 1 radian per second are outside the operatingenvelope of the vehicle. Motion expected in Sea State 3 for Body 1 is aone percent z response and 0.04 degree per foot 6 response. Motionexpected for Sea States less than 3 will be approximately the same asthose predicted for Sea State 3.

FLOW VELOCITY OVER AFTERBODY

*Figure 13 presents the two-dimensional potential flow solution forpressure distribution over the afterbody of the MAGGIE vehicle. Pressure

* distribution data was obtained by representing the body as a seriesof source panels, and then solving for source strengths which satisfythe local boundary condition of each panel such that the velocitynormal to each panel equals zero.

The local velocity over the afterbody is found from the pressuredistribution data by

V2 =v2 1-C)p

* CONCLUSIONS

Analysis of the MAGGIE 1I vehicle has shown in to be stable and itsfixed tail size to be adequate. Determination of sizing for tail controlI

* surfaces should be based upon the amount of cable to be used in the towtank tests. The proposed cable catenaries have been analyzed and the tensions

* at the winch determined acceptable. Motion of the bodies induced by the upper* tow point was found to be acceptable through Sea State 3.

21

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REFERENCES

1. Watkinson, K.W., "The Midcohv Weight and Balance Computer Program(WTBAL)," Naval Coastal Systems Laboratory Informal Report 220-74,September 1974.

2. Humphreys, D.E. and Bowen, L.E., "Prediction of Hydrodynamic Coeffic-ients For Underwater Vehicles," paper presented at 1975 NAVSEAHydromechanics Advisory Committee (SEAHAC) meeting, Monterey, CA.,October 1975.

3. Humphreys, D.E. and Watkinson, K.W., "Prediction of AccelerationHydrodynamic Coefficients For Underwater Vehicles From GeometricParameters," Naval Coastal Systems Laboratory Technical Report 327-78,February 1978.

* 4. Hoerner, S.F. and Borst, H.V., "Fluid-Dynamic Lift," (published bythe authors, 1975) pp. 3-9 to 3-10.

5. Wang, H.T., "A Fortran IV Program for the Three-Dimensional SteadyState Configuration of Extensive Flexible Cable Systems," Naval ShipResearch and Development Center Report No. 4384, September, 1974.

6. Sieber, Charles W., "Design and Evaluation of a Large Towed WingedDepressor for Project Classic Thicket," Naval Ship Research andDevelopment Center Report No. SPD-487-04, October 1974.

7. Fuess, B.F., "Cable Catenary for MAGGIE II Sensor System," JohnHopkins University Applied Physics Laboratory Memorandum No. BFD-3-78-002, 30 March 1978.

8. Pierson, W.J. and Moskowitz, L., "A Proposed Spectral Form Based onthe Similarity Theory of S.A. Kitaigorodski," Report No. 63-12, Geo-physical Sciences Laboratory, N.Y. Univeristy, 1963.

72

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