—> on) Or en oe tadirmer ce Gis” cite i Si Coast Ena.Re Ctr. i MR 82-11 The Design, Development, and Evaluation of a Differential Pressure Gauge Directional Wave Monitor WHO > b if \ i ( DOCUMENT ' Kevin R. Bodge \. COLLECTION MISCELLANEOUS REPORT NO. 82-11 OCTOBER 1982 distribution unlimited. Prepared for U.S. ARMY, CORPS OF ENGINEERS COASTAL ENGINEERING RESEARCH CENTER Kingman Building Fort Belvoir, Va. 22060 Sx \y> &2—1\ Reprint or republication of any of this material shall give appropriate credit to the U.S. Army Coastal Engineering Research Center. Limited free distribution within the United States of single copies of this publication has been made by this Center. Additional copies are available from: National Technical Information Service ATTN: Operations Divtston 5285 Port Royal Road Springfteld, Virginia 22161 Contents of this ‘report - are not to be _used for advertising p> ; a ae oY aa °eS Citation os tr al endorsement ot products. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE SSS Ga 1. REPORT NUMBER 2. GOVT ACCESSION NO, 3. RECIPIENT’S CATALOG NUMBER H MR 82-11 f 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED THE DESIGN, DEVELOPMENT, AND EVALUATION OF A DIFFERENTIAL PRESSURE GAUGE DIRECTIONAL WAVE MONITOR Miscellaneous Report 6. PERFORMING ORG. REPORT NUMBER | 8. CONTRACT OR GRANT NUMBER(s) 7. AUTHOR(s) Kevin R. Bodge 10. PROGRAM ELEM AREA & WORK U NT, PROJECT, TASK IT NUMBERS 9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of the Army Coastal Engineering Research Center (CEREN-EV) Kingman Building, Fort Belvoir, Virginia CONTROLLING OFFICE NAME AND ADDRESS Department of the Army Coastal Engineering Research Center Kingman Building, Fort Belvoir, Virginia 22060 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) Ei N €31181 12. REPORT DATE | 13. NUMBER OF PAGES Loam eager 15. SECURITY CLASS. (of thie report) UNCLASSIFIED 15a, DECLASSIFICATION/ DOWNGRADING ! SCHEDULE 1 Approved for public release; distribution unlimited. 16. DISTRIBUTION STATEMENT (of thie Report) 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse side if necessary and identify by block number) Waves Directional Wave Spectra Wave Spectra Wave Gage Wave Direction 20. ABSTRACT (Continue am reverse side if necessary anc identify by block number) This report discusses a directional wave gage consisting of one absolute and four differential pressure transducers. The differential pressure gage (DPG) development and field testing at the Coastal Engineering Research Center Field Research Facility pier at Duck, NC, is discussed and data analysis software programs presented. The development of the first nine Fourier directional coefficients from a four-gage pressure sensor array and the first eleven or twenty-one coefficients from a five ‘gage DPG is discussed. FORM DD i jan 7a 1473 EDITION OF 1 Nov 65 1S OBSOLETE UNCL SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) Wave height, period, and directional information as estimated from DPG data is compared with estimates from radar and Baylor gauge data at the field evaluation site. Recommendations for future investigations and development of the DPG sys- tem are discussed. UNCLASSIFIED eine eels eee SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) - iii - PREFACE This report is published to provide engineers with a new technique and instrument to obtain directional wave data for use in coastal engineering design. A portion of the work discussed in this report was carried out under the U.S. Army Coastal Engineering Research Center's (CERC) Littoral Data Collection Methods and Engineering Applications work unit and the Field Research Facility's (FRF) Environmental Measurements and Analysis Work Unit under the Beach Restoration and Nourishment Program and the Coastal Flooding and Storm Protection Program of the Coastal Engineering area of Civil Works Research and Development. The report is published as received from the author; results and con- clusions are those of the author and are not necessarily accepted by CERC or the Corps of Engineers. The report was prepared by Mr. Kevin Bodge while in graduate study at the University of Delaware and under the general supervision of Dr. Robert G. Dean. CERC Technical Monitor for the work done under CERC Contract Number DACW72-81-C-0025 was Dr. Todd L. Walton, Jr. Technical Director of CERC was Dr. Robert W. Whalin, Ph.D., P.E., upon publication of this report. Comments on this publication are invited. Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963. Ye TED E. BISHOP Colonel, Corps of Engineers Commander and Director =) ae & ACKNOWLEDGEMENTS Firstly, I would like to thank Dr. Robert Dean for his guidance and patience throughout this project. I thank the other members of my graduate committee, Dr. Robert Anthony Dalrymple and Dr. Nobuhisa Kobayashi for their continuing interest and guid- ance, and especially Dr. Todd Walton whose assistance in the DPG project is greatly appreciated. I would also like to thank the U.S. Army Coastal Engi- neering Research Center and the Exxon Corporation for their support of the DPG study. I would like to thank the many fine people who contributed to make the DPG project a success. Among them are the personnel of Setra Systems, Blake Cable, Brantner Connectors, Sea Data Corporation, Wilmington Valve and Fitting, and many other firms whose assistance is greatly appreciated. I am especially indebted to Curtis Mason and the excellent staff of the Field Research Facility, CERC, and to Jim Coverdale, Ed Green, and Rolin Essex for their dedicated technical assistance and advice. I would like to give sincere thanks to my colleagues "Chip" Fletcher and Brian Jacobs who helped in the DPG installation and testing. TABLE OF CONTENTS ACKNOWLEDGEMENTS . LIST OF FIGURES AND TABLES . LIST OF SYMBOLS CHAPTER acti. SUN TRO DU CITON Seve) ccheei tele tel ters) Tel ieleas) ve) el V6 CHAPTER II: CONCEPTS OF A DIFFERENTIAL PRESSURE GAUGE SYSTEM. A. DPG Response to Surface Waves . . « » « . 5) 6 6 B. The Differential Pressure Gauge SESS RLCHL (leisy Wlonanintoren ee G5 Yo 5 co Go ‘Osco. Oyo, O20 C. Selection of Transducers and Gage Length. CHAP THR Gist? SSD PG eHASREWARE yep oauen ialemmeliieh ‘ioniletlis) opin iefetet ce) A. Instrument, Service Box, and Cradle . ’ ibs Wbahtaatoyohbicwwakoyay 4 cao 0) 9. ooo fo og ade tn ped 2. The Instrument Fuselage and Nees « DON Gon toate ce eo 3. The Transducers... og Nou od Be Galo 4, The Isolation Sensor hey Maas oo! OO: 6 wo Go 5. The Water-Tight Instrumentation Cylinder. . . Ge hho Cabliemandsocrvalc cmb Oxumemicitemmemmenitelt site as) 1 el MLNee Mike CraalCallaOVSiGe Mel jet Leu vol eel Meliiel kellie jue) bet ve 8. The Instrument Cradle .... ; a CMIRenuien @ ake 9. Biofouling and Corrosion Erovention eee 60 B, Data Retrieval... . =. . ao Ha oO C. Some Considerations of ne Wecarene escent 1. Fuselage Isolation Diaphragms ....++sss-s Dy lelenllonesone iS\eiaisongs} 6 Gulp ob O10. 6-010 0 G0 6 1 Wd CORRES “5 6. 6c OO. OO ed SOM OO (0-60. Gente OLE: 60 CHAP TMA eLVEs =) DEG SORDWARH ie lt ele tet tel eta) isl le Neyer ie] eae) ler te ING “Abianeretoychbyereakonato: (gy oo | Dd O) GOs eo. ba 10! O1.04,00 D Beaehneory, of Analysis, =. 1 6) ( a 00 0 . C. Correction for Centering of Meco rementee Ob 0. Oo ali iValecibals sXelleiot = Wal oo TABLE OF CONTENTS (Continued) D. Program Operation Notes. . . « « «© « «© «© «© «© «© « AMianreoyelbionealOm 5 6 6 0 0 ails Mes Rav alee shateuens . input and Screening of Data. oa Go o 9 Conversion from Voltage to Pressure SSeS Instrument Tilt Approximation. . Tide Calculation... lo Wows O80 - Development of Guevetmce Terms Gf MOL Noe eOsosga) 0 FFT and Conversion to Water Surface Terms. Failure of the Absolute Channel. ... cC Failure of 3 Differential Channels ..... Hifective Period... . 6 oo 66 12. The Directional Fourier Goetel ents 0 13. Block-averaging. . . 610 14. Frequency Bands of Crentest nerey 0 A Gc Bo) ADAG Slubulercsloral Ehavel, Mwaaone 6 5 oo Be Siow O. PR FOO ONAN FWNHE CHAPTER V: LABORATORY DEVELOPMENT, CALIBRATION, AND TESTING OF THE INSTRUMENT .... . 6 6 A. Introduction... 60 0 0.0.0) .0).0° B. Fluid Back-Filling one Sierisorae (GiSreei Worbisticarrlopis)) 4 5 86 6.0.0 6 to 0,0 Ci Benchy Catibrastilionie ss ooo 6 OF"6 1. The Calibration Teennienien BOO bt GD zo 2. Testing for Air Bubbles. . ...+s «sss Be Tatavec Cadibrativon RESuukts) eine te 2, 9) le) le it) UPOWEE SUpplyMoeNSalulnVAucyp lef cemereis Sell ia jr is) elinenite So Mibateralsyohblexsne Dare h Go 0000 08010 oF 0 ayo 6. Temperature Effect ..... a ie aten Wie ae 7. Absolute Sensor Back-Fill peesece ota De cuRCaWavienRanku esc Sausmmentcmeiten trite: iclaeint iments big WdbakraatoyehbyetealOralq) Go soni, san B. NOs Geo Ze eln St alMlattalO ne mater enurceksien ents mi enits Bio Aeswsicenael INeSUlstsy ug So! doliothio oy om Doo oe 0 His) Lhe second) PPG VPRO ypel sl versie) sls, =) “ellis te CHAPTER VI: FIELD INSTALLATION AND EVALUATION. ... AV) installa tronwartysbaew Hive: ei leitsh Wil Meuntsh prt ialleh evn Be Instrument Omen Pascal Omarion tena seoiel mellem cel ten ieiiare Che Siersite Mon thaws sinspec von neue mielmsiita Mev telts: Mell euule Significance of the Signals in Linear Theory . - vii - TABLE OF CONTENTS (Continued) Dee SResulsts) of DEGe Darbar AnauliyiSisiin ss) eater! elt)l's)) i ye! Oo NOU FWN 9. CHAPTER VII: CHAPTER VIII: REFERENCES APPENDIX A: APPENDIX B: APPENDIX C: APPENDIX D: APPENDIX E: APPENDIX F: MLO GUGINO since neal felikevertstiveyatiea ae Time Domain Signal eevarsile BOA bro oe 60" "S Record Length... . oF aol ob OG. oO Capability of the DPG Be cit 5 ooe so OL a! of 6 Directional Spectra Smoothing... 5 0, 60 Redundancy of DP2 and DP4 Meaeurenente. cretenike Energy Spectra from Differential Pressure Gauges. .. . Go (LO sOedsaodd, ao Gkko: beso Directional necimeces without the MbsSolubeyPressuresGaMgern te ie ieee) ell ‘se Arithmetic Development of the Curvature Terms RECOMMENDATIONS . CONCLUSIONS . . Sample DPG Analysis Results; June 8-11, 1982. Typical Strip Chart pe eaaey from Bench Calibration.) .%% : 4 muteiniet weliey ove A Partial List of DPG Dimensions. Assembly and Maintenance of the DPG. . The Estimation of Higher Order Directional Fourier Coefficients. ... Fortran Analysis Program for DPG Data . co 8 200 207 Figure e253} Wt 5 55) T1-4 AES II-6 il TZ AGES) TIT-4 NIE SS TIT-6 Tih= "7 III-8 - viii - LIST OF FIGURES AND TABLES Approach of a long-crested wave to tWOmadsja cent spEESSUeCESeHSORSig suomienenlcn rents Tile Instrument response to a five-foot surface wave in varying water depths ...... Differential pressure transducer response to a five-foot surface wave in twenty-five feet of water with varying deployment depths Schematic representation of the DPG....... Differential pressure response with WEMene *Clenoncl ay ehaxel “amacyalbKeMVeH5 og 6 4b 5 0 dg 0-0 6 6 AROS yD ACs bakshera buyers eS oe lars Code Olan 6 ue ede dc. OF vO ZO The DPG instrument secured to the steel cradle . Rendering of the DPG fuselage, arms, sensors, and water-tight instrumentation cylinder .....-. Assembly drawing of an isolation sensor diaphragm Isolation sensor diaphragms shown attached by flexible and nylon tubing through the top of the water-tight instrumentation cylinder andor ithe: rans duc erSuvjeisiiis: ie enwel uel eu ay ceriteiae Assembled water-tight instrumentation cylinder with sensors penetrating the top plate ..... The transducer stack before insertion into themansteumentaraOrsiciyelan exe ca Mei vew veluieealsn aeieieten te (atreabbaverchiever sell store Mya IDIAG Gg. Geta lo lo8o0 a0 oO. 0 o aS 10 iil 13 19 Za 22 23 ZU 28 30 Bt 34 Vou V2 iS} Iv-4 INE IV-6 INH Iv-8 IV-9 IV-10 IV-11 AN (Sil el OXelee LIST OF FIGURES AND TABLES (Continued) Coordinate system adopted HOM DEG MaMa Sister pm te ee etre tele ell el re tel i Hilowscharv Of sDPGwanadySas programa!) es ltttel Ne Instrument tilt above the seafloor. .... Mou eOots Rometanzent(2O)ie wn aor es Simulated time record of water surface elevation. Raw energy spectra; Simulation Case 1. Illustrates presence of three Glijshicaliaeney qRENAS) eIgesHas\ 6 1G loo) 60a “a lo ho 6) toe) A Non-weighted 7-coefficient Fourier series direc- tional energy distribution. Simulation Case 1. Illustrates presence of three. distinct wave trains with different directions. . Raw energy spectra; Simulation Case 2. Non-weighted 7-coefficient Fourier series directional energy distribution. Simulation Case 2. Illustrates good directional Spectra agreement with slight differences Glbys) eo) leElever a ou o Gl lola) ID loo 6 “o Moola! o 6.6 Non-weighted 7-coefficient directional energy spectra; Simulation Case 3. Illustrates software inablility to clearly define two directions per frequency - waves of equal haight. Non-weighted 7-coefficient directional energy spectra; Simulation Case 4. Illustrates software inability to clearly define two directions per frequency - waves of unequal height Non-weighted directional energy spectra using the first seven directional Fourier coefficients compared to the first five. . AA 68 69 71 72 e 9) 6-1 - x - LIST OF FIGURES AND TABLES (Continued) Schematic representation of differential pressure transducer and isolation sensors. . Cross-section of isolation diaphragm with an object load applied. The DPG bench calibration system. . Strip chart recording illustrating possible existence of air in arm Salolayone ClshG oun Me Ree Be ata as WG DPG transducer calibration curves. Orientation of the DPG during CERC Wave: tankumb OS Sis) oes verte iter loin cutee ius Sample strip chart recording; CERC test. Configuration I. DP3 arm sabia left acca denitadaly, one: fenl case teh te . 9 Sample strip chart recording; CERC test. (OfohanEnenbhaslesloya IDG o-G: 6, o..0 06 0 OO Oc Sample strip chart ee eee CERC test. (CfoyabealfenbaeeheaL Ol ITIL Gago . : : Comparison of DPG absolute pressure gauge and CERC resistance wave probe .... . Site of the DPG field evaluation . Nearshore bathymetry of installation site. Preparing for field installation: the DPG suspended underneath the operator's platform of the CRAB . Orientation sees of the DPG Arms (Table). Gee lise ercl occa etah sag We 78 85 87 89 91 2D 98 100 101 102 108 109 110 114 v1I-4 Wa Vi-8 WaE=9) VI-10 Nai A eee LIST OF FIGURES AND TABLES (Continued) Typical influence of the steel cradle upon the magnetic compasses used for orientation measurements . . Comparison of Tide Level (Table) Portion of time record from DPG signals. DPG analysis results using the full record length of 17 minutes with effective 2 Hertz sampling DPG analysis results using the first 8.5 minutes of the record, (4 Hertz Sehomolstiaer 5 8G Soo go o¢ o.- Golo. 0 20 DPG analysis results using the last 8.5 minutes of the record, (4 Hertz SAMpUbn ee vere Vela veces eee culls os Block-averaged energy spectra of water surface displacement for a 17 minute long record and 8.5 minute long records. Non-weighted directional spectra of peak energy band (11.0 seconds) for a 17 minute long record and 8.5 minute Teyaves: TaXCOPACIS) 4.15 1h¥ Gyo 0 el Oo. oO be D Comparison of DPG Results with FRF Observations) (Rabie) ns clei eae 6 Photographs of CERC radar screen illustrating wave activity from June 8 - June 11, 1982. Non-weighted directional spectra of the first two peak energy bands:ABS, dP2, and dP3 gauge combination and ABS, dP4, and dP3 gauge combination. Well-defined swell Non-weighted directional spectra of the first two peak energy bands:ABS, dP2, and dP3 gauge combination and ABS, dP4, and dP3 gauge combination. Poorly-defined sea. ibALS) AI ZAL 122 126 127 L283 129 130 Bil 132 138 139 VI-14 VI-15 VI-16 - xii - LIST OF FIGURES AND TABLE (Continued) Block-averaged energy spectra of water surface displacement and water surface slope. . . 1... ««- Wave crest approximately aligned Wake ClY2 hag. Gon ig 0 08 6 0 0 6 Oso. 0 Typical portion of time series of dP2 and dP4 "slope" signals with the associated dP4¥-dP2 “curvature” signals. .... Block-averaged power spectra of water surface displacement and curvature terms Comparison of Other Directional Estimates (RaibleN acca ss) ok atelier sania Uae a aie Back-filling the center sensors. . .. .« Back-filling the arm sensors .... ... 144 142 145 147 182 194 195 = xia —- LIST OF SYMBOLS absolute pressure (signal or transducer) directional Fourier coefficients Dn" Jin ln normalized co-spectra inner tubing diameter; distance between gauges differential pressure along arm n complex directional amplitude spectrum full scale water depth wave height Significant wave height number of wave trains present in simulated record Bessel function folding time of sensor response pressure response function current response function wavenumber in the x direction wavenumber in the y direction length of tubing height of sensor above transducer number of sample points analyzed; maximum number of Fourier coeffictent pairs pressure atmospheric pressure - xiv - LIST OF SYMBOIS (Continued) Ppf sensor back-fill pressure Pdyn dynamic pressure Pmean mean pressure of record P, pressure differential in x direction Py pressure differential in y direction Q difference in water column height above sensors; volumetric flow rate in sensor line q normalized quad-spectra R rated capacity of transducer s sensor height above bottom S(S) unidirectional spectral density S(6,@) directional energy spectrum S*(6,0) measured directional energy spectrum t time U current xX x-axis location y y-axis location Zs water column height above sensor” od instrument tilt; transducer diaphragm volumetric change proportionality constant to pressure differential > angle between gauges /on' apparent heading of DPG arm n Pu actual heading of DPG armn OP¢ frictional pressure drop along circular pipe Ot data sampling interval OVe volume displaced by transducer diaphragm Ox gage length € phase angle error in compass measurenent of DPG arm n water surface displacement “x water surface slope in x direction water water water water LIST OF SYMBOLS (Continued) surface slope in y direction surface curvature in x direction surface curvature in y direction surface curvature in x-y direction coefficient of dynamic viscosity specific weight of seawater specific weight of back-filling fluid wave frequency effective frequency spectral frequency wave direction mean direction meas ie ace tits ae CHAPTER I INTRODUCTION The need for widespread wave data of improved quality has been recognized by the ocean science and engineering community for some time. In an editorial in Shore and Beach (October,1974), M. P. O'Brien noted that: Observations and measurements of ocean waves have been made at points along the coasts of the United States => at some locations over a considerable period of time —- but the accumulated data fall short of “the need in geographical distribution, duration of the records, and detail of wave characteristics.... [Data]...suffers from a number of deficiencies, notably the lack of wave direction measurements.... Significant strides have been made in the measurement and recording of wave amplitude and period since Dean O'Brien's commentary, but the success of these systems has not been matched by the development of numerous reliable wave sensors with directional capability. Despite the importance of directional wave information to offshore and coastal engineers as well as ocean scientists, the development of directional wave sensors has lagged behind other ocean | nN ! instrumentation advancements. Indeed, a recent conference of scientists and engineers skilled in wave measurement cited the improvement of the measurement, analysis, and reporting technology of directional wave spectra as the first priority of future ocean wave research and development (Dean,1982). Some directional wave data are available today using both remote sensing and in-situ techniques. Remote sensing, a promising alternative for the future because of its capability to monitor large ocean surface areas, presently suffers from the expense and lack of availability of air and space craft platforms as well as sometimes lengthy and expensive data analysis. Further, the development of remote sensing still requires dependable ground verification. Although in-situ systems are single point sensors, they offer some advantages over remote sensing techniques. In-situ instruments can monitor the sea surface continuously, are composed of less expensive and less complex hardware, and can generally offer relatively inexpensive data reduction that approaches real-time. Although more difficult to install and service, submerged in-situ systems offer advantages over surface riding or piercing instruments in that submerged hardware is less prone to loss, does not interfere with the propagating wave field,. and is more likely to operate without malfunction during extreme wave events. Such underwater systems, however, are generally limited to use in near-shore applications or at a shallow depth from a fixed platform in deep water. 5) Several types of underwater in-situ systems have been suggested; some of which are operational presently. Such instruments include tri-axial current meters (van Heteren and Keyser,1981), bi-axial current meters with one pressure transducer or wave staff (Aubrey,1981; Nagata, 1964; Bowden and White, 1966; Simpson, 1969) , arrays of pressure transducers (Peacock, 1974; Seymour, 1978; Mobarek, 1965; Chakrabarti,1971; Chakrabarti and Snider,1973; Panicker and Borgman, 1970; Ploeg,1972), and measurement of the bi-axial components of the force on a_ sphere together with bottom pressure fluctuations (Suzuki,1969). A review of many procedures that have been used to make directional wave measurements is presented by N. N, Panicker (1974), K. Rikiishi (1977), and more recently within the Proceedings of the National Data from some current meter systems is often suspect after deployment because of the suseptibility of the instrumentation to bias from bio-fouling and corrosion. Bottom-mounted pressure transducers, on the other hand, have been used with considerable success for wave sensing for several years (Forristall,1981). The concept of measuring the directional characteristics of waves is fairly atEaienttorward: If one considers a long wave crest approaching parallel to the alignment of two pressure sensors, as in Figure I-1, it is easy to imagine both sénsors recording the crest passage simultaneously. If the wave crest approaches obliquely to the pressure sensors, as in Figure I-2, one could imagine that one sensor would report the passage of the crest before the other. The difference in pressure over time between the sensors' records can be analyzed by well-known techniques and a first estimate of the wave direction calculated, (Longuet-Higgins,Cartwright,and Smith,1963). There is, of course, a directional ambiguity with only two sensors since a wave approaching as in Figure I-3 would create the same VVave Crest pressure record over time as in Figure 1-2. Such ambiguities may be resolved by additional sensors. Presently, the analysis of data from bottom-mounted arrays | of pressure sensors usually develops pressure differences through the sub- traction of individually meas- ured absolute pressures. However, instantaneous differ- ences in the transducers' records FIGURES I-1,2,3: Approach of a long-crested wave to two due to wave action are typically adjacent pressure sensors. very small when compared to the large pressure values that they -5- are required to record. Hence, the pressure difference across an array is calculated by subtracting two large numbers in order to generate a very small number. Such a system lends itself to inherent inaccuracies. For example, a bottom-mounted transducer in twenty feet of water records the passage of a three foot wave crest of nine second period with a value of 24.78 psia compared to the 23.64 psia reading under still water. A similar transducer placed twenty feet away at a 45 degree angle to the wave crest would report 24.69 psia at the moment the crest passes its neighboring gauge. (Linear wave theory is utilized for this example.) The arithmetic difference calculated between the transducers, 0.09 psia, is less than one half of one per-cent of the still water value each transducer would record or less than nine percent of the dynamic pressure caused by the passing wave. The difference can be improved by increasing the distance between transducers -- at the expense of a more physically unmanageable array, greater error in the assumption of linear water surface slope, and introduction of directional ambiguities for the higher frequencies present. It is the contention of this thesis that the accuracy of the directional wave spectrum calculated from such small differences between large pressure values is questionable. The accuracy and physical size of the pressure sensor array can be improved by utilizing differential pressure transducers designed to record small pressure differences between two points. This thesis will document ation the design, installation, and performance of such an instrument as carried out at the University of Delaware and the Coastal Engineering Research Center's test and field research facilities in Fort Belvoir, Virginia, and Duck, North Carolina. Since the majority of industries and machinists associated with the project's instrumentation work in the English system of units in the United States, the English system was used in the development and reporting of this project. CHAPTER II CONCEPTS OF A DIFFERENTIAL PRESSURE GAUGE SYSTEM A. DPG Response to Surface Waves As previously mentioned, it is the difference in pressure between points that must be considered in the determination of wave direction. Differential pressure transducers generate an electrical voltage proportional to the fluid pressure ciererones on opposite sides of a mechanical diaphragm. Absolute (or gage) pressure transducers report only the fluid pressure at one point. Using absolute (or gage) transducers, the difference in pressure between two points must be arithmetically created by subtracting the pressures reported at each of the two points of interest. Since the differential transducer measures pressure differences directly, the differential gauge can be considered to be an inherently more effective instrument for determining wave direction. Furthermore, the response with depth of the differential pressure is a maximum over a range of frequencies that is more representative of typical ocean gravity waves. For a pressure transducer located at height s 248) 2 above bottom, the dynamic pressure at the sensor can be expressed over time t as: H Payn (Xr¥ Sit) ah ays cos (kx + KY - ot +€) Ga) cosh ks cosh kh and H = wave height k,= k cos@ = wavenumber in the x-direction ky= k sin@® = wavenumber in the y-direction © = wave direction O = wave frequency h = water depth Y = specific weight of water € = phase angle The components of differential pressure differs in phase and by a factor of wavenumber: H cos 9 dP (x,t,s;t) Fy a ison K_sin(k x + ky sin 6| P = Y @22) Ox - ot +e) -9- A current meter similarly located at a depth s will record a Signal under waves such as: a del af Uixepyy Sat) = By Kk cos (kx ote Ho! ene ae )) (33) where : K = cosh ks u sinh kh Although the magnitude of both the pressure and current decreases steadily over increasing frequency, the differential pressure signal reaches a maximum at an intermediate frequency. This is illustrated graphically in Figure II-1, which depicts the dynamic response of pressure and differential pressure gauges located near the bottom with a wave crest of 2.5 foot amplitude. In the upper-most curves, the differential gauge is assumed to sample _ two points separated by three feet coincident with the wave ray. The lower curve represents the difference in pressure monitored by two absolute pressure gauges separated by twenty feet along the wave ray. Each curve is normalized by typical values of the rated capacity of the instruments, (35 psia for the pressure transducer, and +0.5 psid for the differential transducers). Figure II-1 represents a water depth of fifteen feet, while Figures II-2 and II-3 represent twenty and twenty-five feet water depths respectively. In each case, the transducers are located three feet off the seafloor. It is clear that the differential pressure signal utilizes a greater portion of Ors PERIOD (secs J 4 - PERCENT INSTRUMENT RANGE UTILIZED FREQUENCY (rad/sec } Qa uw N : Ww 9g Zz & pe Zz ii = =} & Q Zz A ‘ Zz ui & 17] a FREQUENCY (red/sec ) FIGURES II-1,2: Instrument response to a five- foot surface wave in varying water depths. Sensors are three feet from the seafloor. ihe PERIOD (seco } : 4 : 200 3 PERCENT INSTRUMENT RANGE UTILIZED 9.00 8.00 200 1.50 2.00 FREQUENCY (rad/sec ) FIGURE II-3: Instrument response to a five- foot surface wave,, (continued from previous page). PERIOD (seco ) q oF Le SENSOR HEIGHT ABOVE BOTTOM 200 9 : 8.00 PERCENT INSTRUMENT RANGE UTILIZED FREQUENCY (rad/sec ) FIGURE II-4:; Differential pressure transducer response to a five-foot surface wave in twenty-five feet of water with varying deployment depths. = ih) the instrument's dynamic range and reaches its greatest response level for waves between four and six second periods. Sensitivity to longer period waves increases with increasing water depth. Differential pressure response increases as the transducers are raised off the seafloor, as expected, and the greatest sensitivity shifts to waves of higher frequency (Figure II-4). In Figures II-1 through II-4, the response of the differential transducer was developed over a pressure sample spacing of only three feet -- less than one-sixth of the gage length of conventional pressure sensor array systems. Typical arrays generally develop two orthogonal measurements of water surface slope by sampling points separated by twenty to thirty feet. The differential pressure gauge concept, then, suggests that more efficiently measured directional information can be obtained with a considerably smaller instrument than is presently used. B. The Differential Pressure Gauge Directional Wave Monitor To test the effectiveness of an array using differential pressure transducers, the Hefeorentian pressure gauge directional wave monitor (DPG) was developed. Using small distances between differential pressure sampling points, it was possible to design a system which directly measures the water surface slope yet is physically smaller, more manageable, and potentially more accurate S48) 6 than conventional pressure sensor arrays. FIGURE II-5: Schematic representation of the DPG. The DPG samples the pressure about its center using an absolute pressure transducer and simultaneously samples the differential pressures on the bow, port, aft, and starboard sides of pestis the instrument center using four differential pressure gauges, (Figure II-5). The differential gauges directly infer water surface slope, and since there are two such measurements along two axes through the instrument center, it is possible to arithmetically develop the water surface curvature along each axis. It’ will be demonstrated in Chapter IV that these measurements permit’ the estimation of the first seven Fourier coefficients of the directional wave spectrum. Conventional analysis from submerged pressure sensor arrays arithmetically develops one measurement of the water surface slope along each of two axes. Typical surface riding buoys similarly measure the slope along each of the two axes. This data, along with the water surface displacement record, permits the generation from these systems of the first five directional Fourier coefficients. The cloverleaf buoy, a cluster of three surface riding buoys, is capable of estimating the first nine Fourier coefficients, (Mitsuyasu,1973; Cartwright and Smith,1964). It can be shown that it is possible to generate up to the first M(M-1)+1 directional Fourier coefficients for an array with M number of gauges (Borgman,1969). Using this technique, pressure sensor arrays such as the Scripps Sxy gauge (Seymour,1978) could generate the first nine directional Fourier coefficients. The DPG, in the configuration described, could develop the first eleven coefficients. The DPG could potentially develop the first twenty-one coefficients with the same number of transducers in a different configuration. This analysis technique is discussed in Appendix E. C. Selection of Transducers and Gage Length The selection of the gage length between the two points to be compared by the differential pressure transducers is dependent upon three criteria: (1) the characteristics of the transducer, (2) the error in approximating the water surface slope as a linear function between two sampled points, and (3) reasonable size limitations of the instrument. The third criterion limits the gage length per transducer to a maximum of about five feet if one imposes a design constraint of easy instrument manageability. At such small spacings, the maximum error in linearly approximating the water surface slope between sample points is less than one and one-half percent for the shortest waves of interest, (say, 3.2 seconds). Having satisfied the second and third criteria, the first criterion remains. In the selection of the differential transducers, one must consider the physical size, ruggedness, cost, and " " availability of a transducer that can measure. small wet bidirectional pressure fluctuations. The desired rated capacity of the transducer is a function of the maximum wave height expected and the ability of the transducer to detect and report a pressure difference of a minimum wave condition beyond the ambient and electrical noise level. One might determine the rated capacity by BeGo-= first selecting an instrument deployment depth according to the site and the wave frequencies that are of most interest or are most likely to be encountered -- remembering that deeper installations require more sensitive transducers. A maximum wave height at the most sensitive frequency for the chosen depth is then considered with the manageable gage length restriction in mind. The maximum differential pressure is then calculated from Equation 2.2. The result is an estimate of the rated capacity of the transducer needed. This estimate is then used to select a transducer available from industry. One next considers the noise level of the system to determine whether the selected instrument is capable of reporting the minimum differential pressure of interest, (i.e., a small amplitude wave of frequency higher or lower than that of the instrument's most sensitive range at the chosen depth). Satisfied with the results, the gage length, ax, is fine-tuned based on the rated capacity of the transducer, R, and the maximum wave of interest. From Equation 2.2, R oa V¥) Heke cosid (2.4) The instrument's response to a minimum wave condition is checked again using the newly calculated gage length to ensure that a reasonable signal to noise ratio is maintained for small amplitude, long period waves. = 1S The installation site of the DPG was proposed as the United States Army Corps of Engineers Field Research Facility (FRF) at Duck, North Carolina, operated by the Coastal Engineering Research Center (CERC) . The instrument was to be placed near and hard-wired to the Facility research pier. After examining the bathymetry near the pier and considering the high cost of underwater cable, a nominal deployment depth of 20 feet was selected. This indicated that the instrument would be most sensitive to waves of about 5 second period, (Figure II-2). This was considered acceptable at the time since the mean monthly nearshore wave periods for this site were reported between 4.8 and 6.5 seconds (SPM, Figure 4-11, 1977). (It was discovered much later that this estimate was poor. A better estimate is given as about 7.5 seconds from Birkemeier, et.al., (1981).) A design wave height of 16 feet was chosen and considered with a gage length of five feet. This suggested the use of a +0.6 psid transducer which was unavailable. A +0.5 psid transducer was selected instead, mandating a gage length of 4.15 feet (1.27 meters) using Equation 2.3. The overall dimensions of the final instrument, then, became 9 feet - 9 inches (2.97 m) along each axis (including protective caps on the ends of each arm) and 40 inches (1 m) in height to accomodate the electronics package. 2 Ais The response of an instrument of this configuration in varying depths of seawater is illustrated in Figure II-6. The contours represent lines of equal transducer response per Dfeet of wave height normalized by the rated capacity of the transducer. The fields of highest value indicate the environmental conditions conducive to greatest instrument performance. The absolute transducer was selected with a rated capacity of 50 psia (because of cost and availability) which provides the DPG the capability to measure a pressure head of over 75 feet. (feet) SEP 12.5 aon FREQUENCY (rad/sec) 3.0 2.5 2.0 1.5 1.0 0.75 0.5 0.35 15 INN SS neg S Cee We \ == 20 18 17.5 16 20 AA Ve 22.5 10 25 8 27.5 6 30 2 / 32.5 \ 2 2.5 3 4 5 GH 7a ot OW 42h 14 etGan18 PERIOD (secs) FIGURE II-6: Differential pressure response with water depth and frequency. Contours are lines of equal dP response normalized by the rated capacity of the instrument, (1.0 psid). (Sensors are 3.875 feet from the seafloor, differenial gage length = 4 feet along wave ray; wave height = 5 feet.) =) Bo) CHAPTER III DPG HARDWARE A. INSTRUMENT, SERVICE BOX, AND CRADLE 1. Introduction The in-situ instrumentation is contained in a _ poly-vinyl chloride (PVC) structure that is secured to a steel cradle moored to the seafloor. The PVC structure, or "instrument'', as it is hereafter called, consists of a central tube, or "fuselage", and four "arms" that extend from near the top of the facets A plexiglass service box, also attached to the cradle, provides storage for eighty feet of unarmored cable at the installation site. Figure III-1 illustrates the instrument and Figure III-2 depicts the steel cradle with the instrument in place suspended under the Field Research Facility's CRAB vehicle. This chapter describes the DPG system as installed at the FRF, Duck, N.C. Several components of the system were altered from the original design during DPG assembly and laboratory testing. The discussion of these modifications is presented in Chapter V. =e Ot ‘juemnsjysul 54d eu *T-III FunoId - 22 - (aVUd) AZ3ng st AjTquasse "AYTTTIeY Yoreesey prety IuFD ey] Aq peyesado snotqtydwy yoreasey ,ejseo) ey] y}eaueq pepuedsns ayL “eTperd [99}sS ay} Oj paiInoess JueMNIysUT D5qq eUL *@-III aunotd = 23) = FIGURE III-3: Rendering of the DPG fuselage, arms, sensors, and water-tight instrumentation cylinder. - 2h — 2. The Instrument Fuselage and Arms The fuselage section of the instrument is ten inches in diameter and forty inches in length, (Figure III-3). It secures a circular plate with five pressure-sensing "isolation" diaphragms and a water-tight cylinder that contains the pressure transducers. Both ends of the fuselage are covered by plexiglass plates to prevent large marine animals from entering the inside of the instrument. The top plate contains a number of 5/8 inch holes to allow the fuselage to flood and ensure that the pressure-sensing diaphragms therein are communicating with the outside. The bottom plate has a one inch wide slit cut across its radius to allow the cable entry to the fuselage and water-tight cylinder. Both plates are secured to the cylinder by titanium bolts attached to PVC blocks on the inside of the fuselage. The blocks are made fast to the fuselage by. adhesives and nylon screws. Each of the four arms penetrate the fuselage and are held therein by a PVC "spider." A spider is a common plumbing junction which connects four pieces of tubing at ninety degree angles tto one another. Four bolts are tapped through the spider to secure the arms. In this way, any or all of the arms can be disconnected for greater ease in transportation, or potentially, a change in arm orientation. = 25 - The arms are three-inch diameter PVC pipe and fifty-two inches in length. Each contains a pressure-sensing diaphragm near its end. The extreme end of each arm is covered by a_ threaded Ppipe-cap which can be removed to inspect the diaphragm and replace copper scouring pads placed near the diaphragm to reduce biological fouling. The arms are punctured with 11/16 inch diameter holes about their ends to allow diaphragm communication with the environment. Each arm is labelled with strips of white cloth tape to identify the differential transducer channel corresponding to that arm. 3. The Transducers A typical differential pressure gauge senses the pressure difference between the diaphragm at the end of an arm and one of the five diaphragms mounted inside the fuselage. The differential pressure transducers are located inside the water-tight cylinder. The differential transducers are Setra Systems Model 228. They are a high line, low-differential wet-wet capacitance type sensor with infinite resolution and a +0.5 psid range. Transducer output noise is rated as below 100 microvolts RMS. Burst pressure is 2500 psid (either side) such that there is less danger of catastrophic failure during construction or- installation. The differential transducers require 28 volts DC nominal excitation and feature O to 5 volt positive output. The transducer circuits have internal protection against reversed excitation voltage for at least 5 minutes, 5 B62 short-circuit of signal output leads, and short duration power line transients up to 150 volts. Each is supplied with independent remote zero adjustment, although this feature is not used in the present DPG model. The fifth pressure-sensing diaphragm in the fuselage supplies a signal measured by an absolute pressure transducer also located inside the cylinder. The absolute gauge is a Setra Systems Model 205-2 of 50 psia range. It also operates on 28 volt DC nominal excitation for a 0 to 5 volt positive output. 4. The Isolation Sensor Diaphragms The stainless. steel diaphesene of the transducers are protected from the harsh marine environment by the nine "isolation" diaphragms located within the fuselage and eee (Figure III-4). The isolation diaphragms are made of 13 mil DuPont Fairprene® elastomer mounted on an acrylic housing. Fairprene® is a durable nylon material, coated with neoprene, that is flexible perpendicular to the plane of the fabric. The elastomer is sealed to its acrylic housing by a 90-10 copper-nickel alloy ring. The 90-10 alloy was picked for its anti-fouling properties. Bio-fouling across the diaphragm ring could puncture the elastomer or restrict its ability to deflect and thereby introduce a bias. The rings are designed to last at least Five years assuming a corrosion rate of 1.0 mpy, (Dexter,1979). The ring is secured to the diaphragm housing with six Monel 1/4 inch - 27 - bolts. Diaphragm housings are 2-7/8 and 3 inches in outside diameter within the arms and fuselage respectively, and 2-5/16 inches long, including the Cu-Ni ring. The diameter of the elastomer exposed by the ring is 1-5/8 inches on all diaphragms. The acrylic housings behind the elastomers are hollowed to a conical shape that funnels to PIE, neg? a PRS TT Till ( (lay alee bd . hh bees FASS wan o Acrylic Housing Cu-Ni Ring Elastomer Diaphragm Tubing & Connector FIGURE III-4: Assembly drawing of an isolation sensor diaphragm. =" 26 = FIGURE III-5: Isolation sensor diaphragms shown at- tached by flexible and nylon tubing through the top of the water-tight instrumentation cylinder and into the transducers. - 29 - a small opening in the back. This opening mates with 1/4 inch (1/8 inch I.D.) flexible teflon tubing which leads to the sensing ports on the pressure transducers inside the water-tight cylinder. The flexible tubing, manufactured by Cajon®, is armored with stainless steel braid. Specifically, it connects to the back of the isolation diaphragm chamber and is fastened to the top of the water-tight cylinder with Swage-Lock® connectors, (Figure III-5). The connectors penetrate the top of the cylinder and connect to nylon tubing inside. Nylon tubing is used inside the cylinder because of its partial flexibility and transparency. (Nylon is easily impregnated and hardened by seawater and is used outside the cylinder only as a permanent fastener, (Dexter,1979).) The nylon tubing is heated and bent to shape to mate with the transducer pressure ports. The housing and tubing assembly is filled with fluid which transmits the deflections of the elastomer to the stainless steel transducer diaphragms. The fluid is dyed with food coloring for ease of identification and inspection for air bubbles that might be seen in the nylon tubing or acrylic housings. During assembly, the isolation diaphragm housings are drawn through the arms and secured inside them by brass screws which penetrate the arm walls from the outside. The five isolation diaphragms inside the fuselage fit snugly through three-inch holes in a circular plate positioned just above the spider. A two-inch hole is cut in the center of the plate for ease in assembly. | b l i FIGURE III-6: Assembled water-tight instrumentation cylinder with sensors penetrating the top plate. FIGURE III-7: The transducer stack before insertion in- to the instrumentation cylinder. = BYE = 5. The Water-Tight Instrumentation Cylinder The water-tight cylinder, located underneath the spider, is an anodized aluminum pressure-tested housing developed by Sea-Data Corporation. Four sacrificial zinc anodes are positioned about the top of the cylinder. All of the pressure tubing penetrates the top (removable) section of the cylinder, while the power and data cable connects to the bottom via Brantner underwater XSL-20 connectors, (Figure III-6). The cylinder is held in place within the fuselage by PVC blocks bolted to the fuselage walls with Monel fasteners. The transducers are held inside the cylinder by a series of five wafers separated by acrylic rods. The bottom two wafers support two of the differential transducers, the middle two support the remaining two differential and one absolute transducer, and the upper attaches to the underside of the cylinder top and suspends the wafer assembly. The wafer and transducer stack is shown in Figure III-7. 6. The Cable and Service Box The instrument is cabled to shore for power requirements and data delivery. Eleven hundred feet of Blake BC 4960-1 double armored cable is laid between the instrument and the land-based recording facilitys The cable is an eighteen conductor (18 gage - tin/copper) strand wrapped around a polypropylene filler. The conductors are water-blocked, wrapped in mylar tape, and sheathed under a I 3} polyurethane jacket with double steel armoring and an external polyurethane jacket. The cable weighs 0.98 pounds per foot in air. Eighty feet of the seaward end, stripped of its armoring, is stored in an 18 inch square by 9 inch plexiglass service box just before mating with the instrument. The top plate of the box is removable by unthreading four titanium nuts. This accesses the spare cable if the instrument is tc be moved or taken to the surface. IGE the instrument requires service in the boat or on shore, the cable may be disconnected above water, sealed with a dummy connector, and released. A dummy connector is then attached to the instrument for safety. For re-installation at some later time, the cable is recovered, re-connected in the boat, and the instrument is brought underwater. It is hoped that operating the underwater connectors only above water will help alleviate some of the flooding and corrosion problems experienced in the past with underwater-pluggable connectors. 7. The Electrical System Fourteen of the available twenty conductors are utilized. Ten carry the five transducers' signal outputs, two carry the positive excitation voltage (one for back-up), and two carry the negative excitation ground, (one for back-up). Each of the transducers share the excitation positive and negative leads. A simple RC network can be installed at the landward end of each signal 3 Pin numbers are internal AMP 16 and BRANTNER XSL 20 Connectors Resistors are 100 ohm (1/8 watt ) FIGURE III-8: Wiring diagram for the DPG. = 35) — output as a passive low-pass filter. The network is easily designed for 3 dB attenuation at 50 cycles per second with the aim of eliminating 60 hertz noise from the power supply and local electrical systems. Such high frequency noise would alias into the calculated water wave spectra and bias the analysis results. An active filter is, however, more strongly recommended. To guard against the possibility of unwanted output oscillation caused by the capacitance introduced by the long cable to shore, 100 ohm resistors are installed in series in each of the output leads inside the water-tight cylinder. Since the electrical circuitry of the transducers is equivalent to a 4-terminal network which can be grounded at only one point, it is essential that the negative output leads of the transducers not be commoned since the negative excitation leads are already commoned inside the instrument. A complete wiring diagram is presented in Figure III-8. 8. The Instrument Cradle Both the instrument and the service box are mounted onto a steel cradle secured to the seabed. The cable is constructed of C4x5.4 steel channel and 3/4 inch thick steel plate, two inch steel pipe legs and Lixlxl/8 angle iron’ stringers. The channel is connected primarily by the steel plate. A break is made in one plate to allow the cable to slip through the structure when the instrument is pulled out of the cradle. This is closed by a plate which bolts 2 36 Me over this area to retain structural integrity after the instrument is installed. The legs are welded onto the underside of the channel such that they balance the cradle about its center when no instrumentation is installed upon it. Onto the bottom of the forty inch legs are welded i0 by 12 inch thin steel plates to reduce burial into the seafloor. The cradle is secured to the bottom using 5/16 inch galvanized chain that attaches underneath each channel and cinches tight with a chain binder to one of four screw anchors driven into the seafloor. The instrument arms lay into the steel channel and the fuselage slips into the center of the cradle. The Bes are made fast to the cradle with heavy electrical cable ties. The sevice box is mounted onto the cradle by four titanium bolts secured through the bottom of the box. Attaching plates and rings are welded throughout the cradle for buoy markers, flotation devices, pingers, diver-assist lines, and weights to balance the asymmetrically placed service box if necessary. 9. Biofouling and Corrosion Protection The cradle was sandbilested: primed, undercoated, and then covered with anti-fouling paint. All surfaces of the plexiglass service box and the PVC instrument structure (with the exception of the fuselage end-cover plates) were sanded and also coated with anti-fouling paint. The paint used was red PETIT BIOGUARD 1665 with - 37 - 19.14% active ingredient bis(tributyltin)adipate. B. Data Retrieval At the FRF installation site, the cable interfaces with Facility equipment at the seaward end of the pier. The power supply board is located inside a trailer at the seaward end and the transducer output leads are hard-wired down the length of the pier and recorded on a NOVA computer system located inside the facility's main building on shore. The computer digitally records the transducer signals at 1/4 second sampling for a 17 minute period every six hours. C. Some Considerations of the Hardware Design 1. Fuselage Isolation Diaphragms The absolute pressure measurement and one side of each of the differential pressures are all to be taken at the instrument center. Five individual diaphragms in the fuselage are employed for this task. Since not all of the diaphragms can occupy the center of the instrument in one plane, there is a small error inherent when saying that the differential measurements are exactly adjacent and share an endpoint with the absolute measurement. The midpoint of the fuselage isolation diaphragms are each about two inches (7.1 cm) from the = 38) = actual fuselage center. Further, the arrangement of the dP3, dP2 and dP4 diaphragms. within the fuselage is such that they are not precisely aligned with the x- or y- axes respectively. This design was the result of space allocation problems within the top of the fuselage. The errors are such that the sensor alignment of dP2 is 91°, 178° for dP3, and 269° for dP4 with respect to dP1 = 0°. It was considered that these one and two degree errors were negligible for the present investigation. 2. Height of Sensors Once again due to practical space allocation, the instrument was designed such that the center isolation diaphragms are nine inches (22.9 cm) above the arm diaphragms. The pressure response function is developed during data analysis for the mean of these two elevations above the seafloor. In 20 feet of water, the error between the pressure response function for the actual sensor height and the mean sensor height is less than two-and-one-half percent for the highest wave frequencies of interest (periods of 3.14 seconds) and less than one percent for wave periods greater than four seconds. — oa D. Cost = The hardware used to construct and install the final DPG prototype at the Field Research Facility cost approximately $13,000. Machine shop fees for the entire project were $3090. The total project cost, including design, development, laboratory testing, hardware, travel, computer time, salaries, and indirect costs was approximately $31,000. = Iho) = CHAPTER IV DPG SOFTWARE A. Introduction The theory of data analysis and computer software for the original design of the DPG were developed during the drafting and machining stages of the project. The complete theory and software to directly develop the first seven directional Fourier coefficients for a fully functioning 4-arm DPG are presented in this chapter. After initial evaluation of the instrument's first sets of field data, it was considered that only one differential pressure gauge on each axis was reliably accurate. Hence the software package, as used at the FRF installation site, analyzes only two orthogonal differential pressure channels along with the absolute signal. The FRF package, then, is an abridged version of the program described herein. Ite develops only water surface slope in the x and y directions and vertical displacement, and the first five directional Fourier coefficients. sti es B. Theory of Analysis Selecting the x-y coordinate system in the horizontal with the origin at the instrument's center as in Figure IV-l, the DPG is assumed to faithfully record the water surface displacement 7 (x,y,t) at the center, the slopes yn, at A and C and Ny at B and D. The curvatures ny, and N\,,, across the center can be arithmetically approximated by (nx(A) - 1x (C))/ox and (ny(B) - ny (D))/ay respectively. With the present DPG configuration, it is not possible to arithmetically create the cross curvature term Nxy: An additional measurement would be necessary to define such a term. FIGURE IV-1: Coordinate system adopted for DPG analysis. = (NB) The analysis procedure follows from Longuet—Higgins, Cartwright, and Smith (1963). The water surface displacement is expressed in terms of the complex directional amplitude spectrum, FCG; easi: eae i (ot-k_x-k n(x,y,t) = | | F(o,8)e" 2 an yy) 96 30 (4.1) -0 O where O = frequency © = direction (assuming © measured counter-clockwise from the positive x-axis) ky = keosQ, wave-number in the x-direction ky = ksin@, wave-number in the y-direction, - and (a= =e The water surface slope and curvature follow from (4.1) as: oo 27 an i = i Ox (x,y,t) = | | -~ik cos 9 F(c,@)e™ roe Les ae Jo (4.2) -~ 40 an eager i(ot-k_x-k gy yet) = | | - ik sin 6 F(a,8)e x KY) 96 96 (4.3) =O (6) 2 oo 27 nN 7 —_ —_ Hay Care) = | | EUKk> cos] Gu(Gheye | isk aay) elo God - 43 - 2D co 27 ; 22 (x,y, t) = | | SO UARE 6) BG Ge Se OO BE Ges oy -0 “OQ Ei Information providing a partial description of the directional energy spectrum S(6,Q), (equal to |F(6,e) |” Vine ats contained in the auto- and cross- spectra of the water surface displacement, slope, and curvature terms. These spectra are obtained through Fast Fourier Transform procedures using: 27 2 Suen (C)e = | lE(o78) |= de nn (4.6) 0 27 5 S (0) = - ik | cos6|F(o,6)|~ de Ga nn 0 x 27 5 So! (co) = Sk | sind|F(o,6)|~ 46 (4.8) nn y 0 a Ae 2 S (5) =k | siné cosé|F(c,6)|~ dé (4.9) 4 Ea Sys (@) 27 Ss (o)} = ae | cos76|F(a,6) |? dé (4.10) mea} Wok Q Es Mills, 27 Sat (co) = a | sincé(F(o,6)|> dé (4.11) nyty 0 27 S (c) = ik? | cos*e|F(a,0)|* dé (4.12) Mex ) 277 2 1. os ike | sin?6|F(o,8)|* 49 (4.13) Sf Ay 0 The directional spectrum at a frequency 6 is then expressed as a partial Fourier series in terms of the wave direction © as: N N S(o,0) =a + } a, cos n 6 + ) b_ sin n 6 (4.14) n=1 ioeail: The Fourier coefficients are determined in the usual manner asé 1 27 ay (9) 2 Se |. S(o,8) dé (4.15) 1 27 a (Oo) = x | S(a,8) cos nO dé (4.16) n 27 O = 45 = 1 20 b (0) = 1] S(o,9) sin nO dé (Coz) 0 The first seven Fourier coefficients in the Fourier series representation of the directional spectrum, Equation 4.14, (i.e., N=3), are obtainable from the auto- and cross-spectra, (Equations 4.6 through 4.13): ay = OT Sa (4.18) - il a) = ink ai (4.19) aa an eiiec (o) - § (o)] 2 5) nn en (4.20) 1k x xX y y 4 E D (4.21) An = —k' s (o) +S | : pee = ee Tse By seals j (4.22) by eae Ison (o) ] eS Tyas 2 b, = may iS 5 (o) J] (4.23) Tk x y - 4 Bue? b, = SoG) ees (Sl (4.24) 3 Hoe Sm 4 of] The truncated Fourier series directional spectrum is now easily developed from Equation 4.14. If two measurements each are accurately made of Ul and 1), it would be possible to generate all of the first and third coefficients four different ways and the second coefficients two different ways using various combinations of the differential gauges in auto- and cross-spectra. The instrument software, (re-printed in Appendix F), generates each of the possible coefficients. There are _ two advantages here. The program will use the mean value of each calculated angular Fourier coefficient in generating the directional spectrum if it is decided that each transducer is working correctly. If it is concluded that a transducer is malfunctioning during a sampling interval, the program will disallow that transducer's signal during the final coefficient calculation. The redundancy of the transducers' measurements, then, would offer a potentially more accurate estimate of the directional Fourier coefficients as well as a first-stage failsafe mechanism if one of the differential Sey = “ transducers fails. This was indeed the case in the field evaluation. (Ge Correction for Centering of Measurements The analysis theory used herein assumes that all of the water surface measurements are taken about one point in the generation of the first five directional Fourier coefficients. However, the physical orientation of the instrument is such that the water surface slopes are each taken about a point midway along each arm (approximately two feet from the instrument center in the present design). This analysis difficulty can be overcome by averaging the two slope measurements along each axis and using the resulting mean slope values in the analysis. This is done in the present program if both transducers along an axis are deemed operational. The measured slope values could be transferred to the center of the instrument using a complex response function. If one considers, for example, the absolute pressure signal to be monitored at the instrument center (x9,yo), and an x-axis differential pressure signal measured at Casas the water surface and displacement terms could be expressed (from Equations 4.1 and 4.2) as: So 27 ; Men) is | | Ficje “kor yo 96 do (4.25) —_0O (@) 5 hey = SP sige i (ot-k_x,-k n_(x,,y,,t) = -ik cos@ F(o)e ig dl y‘1 Schlag: e!G 36 30 (4.26) The cross-spectrum of water surface displacement and slope as measured, then, would be 27 F Seo) Seal | cos0|F (0,0) [76 + Ky, 1-%0) +k, (v4 Vo) 1a, (4.27) 277 (@)) So sie | cos0|F(o,6) |7 dé (4.28) Hence, the measured spectrum is corrected using 27 ss ilk. (x,-x,)+k_ (y.-y_)}] S) ute) oa (oc) | e Sdn LNT KO) idl: AO dé (4.29) x) (0) Similarly, the correction for a slope measurement along the y-axis at. (x9,¥) would be 2a ye Sra (Oc hse ne (o) | et Uk, o-X 9) tk (Ya-Vo)] ae (4.30) - 49 - and for the cross-correlation of slope: 27 40k (x,-x. 4k (y,-y1)] Ss once ioen peelGe) | Sig bes Dy dldeeay en abe (4.31) where the starred spectra are those measured by the instrument. The transfer function alters only the phase, not the amplitude, and is a function of wave frequency, direction, and gage length of the instrument arms. The corrections require one to know the wave direction of each frequency component a priori. These can be calculated (if two transducers along an axis are functioning properly) using the simultaneous solution of a set of equations such as: 27 stk. (x,-x,) +k. (y,-y,)] s (o) = S* (o) | Ceipcc uel On te Vansele Oia OO nny nn * 1 27 ; (4.32) S (co) =*s*. (0) | pile a5 XG) amo) tae mee nis 0 3 or Resi oat y+k_ ( )] (oc) = S*_ (0) | Sa SO OW ye 20201) de): aT OS 0 rofl Ne ai a (4.33) J Ge st Gh | et lk, (x, xtk WA Yo) 3 ae = 50) = where (x,,y,), (xg,y3), and (x,,y2), (x4,y,) are the known positions of the Xe and y-2@xis slope measurements, respectively. Alternatively, the analysis could be carried out with the non-corrected spectra, the directions at each frequency estimated, and the process repeated using spectra corrected by the previously estimated direction to yield continually more accurate directional information. This analysis, however, can correct only for the principal direction. Such corrections are assumed small enough to be neglected in the present analysis. For the worst case of small period waves, (say, 3.2 seconds), the phase shift is less than 1 degree. D. Program Operation Notes 1. Introduction The FORTRAN analysis program, presented in Appendix F, accesses and analyzes the five raw digitized voltages recieved from the DPG data storage tape. A crude flow chart of the program is shown in Figure IV-2. = c J racy | # data points for analysis. sanpling interval ¥ freq. bands to block-ave:uge ent-off frequency for analysis atmospheric pressure neawater specific gravity DRG critical dimensions INPUT DETATIS ASPUr SOCAN DATA: 1. Calculate record mean RAW TATA. x and standard deviation 2, T'runcate unreasonable values 3. Ke-calculate record Mean & subtract from signals in record Convert to psi or psid ESTIMATE CALC. DEPTH REVERSE SIGNS INST. ELT AND TIDE FROM OF dPi & aP2. POM DIFF. ABS. PRESSURE PRESSURE MEAN. MEAN CALCULATE PRESSURE FFT CREATE * RESPONSE FUNCTION (Ky) EACH CURVATURE TERM AND WAVENUMBER (k) HRCORD - RECORD - FOR EACH FREQUENCY BAND i CALCULATE SIGNIFICANT WAVE HEIGHT FROM ABS. POWER TERMS DIVIDE EACH CHANNEL'S FOURIER COEFFICIENTS BY K, & SEAWATER SPECIFIC GRAVITY CiKEATE POWER SPECTRA GEYFRATE j if CAILUTATE ESTIMATE DIRECT IONAL EFFECTIVE DIRECTION USING, FOURTER TERICT FOR DIFF. GAUGES COEFFICIENTS PACH CHANEL CNLY BINCK -AV ERAGE DIRECTIONAT, COEFFICIENTS , POWER SPECTRA, & OTHER DIRXN'I ESTMATES. IDENTIFY FREQUENCY RANLS OF HIGHEST ENERCY DEVELOP THE UIRBCTIGNAL-FREQ. SPECTRUM FOR HIGHEST ENERGY BANLS CUTPUT: 1. hecord date and time, 2. Integrity of raw data 3. Tide | - 4, Ponsible Instrument tilt 6. Effective Period 7. Highout Energy Bands! 4) relative magnitude il) directional spectrum peak 5. Sleniticant Wave Rotent | ‘ FIGURE IV-2: Flow chart of DPG analysis program. = BP = 2. Input and Screening of Data A preliminary scan of the voltage records is made to calculate the mean and standard deviation of each. In each record, sampled points that are greater or less than 3 standard deviations from the mean are truncated to the average value of their two neighboring points. The number and magnitude of high and low truncations made in each record are reported at the terminal. If an unusually large number of alterations are necessary for a record, the operator may choose to disallow the particular record from further spectral analysis. The mean of each record is recalculated and is then subtracted from each of the transducer signals. 3. Conversion from Voltage to Pressure Signals The differential signals are converted from volts to pounds per square inch differential (PSID) which corresponds to P(arm)-P(center). These values are then divided by the distance between the sensor positions for each arm to yield the pressure differential per inch of length along an arm. To maintain a consistent sign convention among the pressure differences across the instrument, the signs of the dPl and dP2 signsals are reversed. The four differential channels’ signals are now in the form: dP1 = (P(center) - P(arml)) / axl dP2 = (P(center) - P(arm2)) / ax2 dP3 (P(arm3) - P(center)) / ax3 dP4 = (P(arm4) - P(center)) / ax4 aS) im With this convention, the program as written will generate the directional distribution with the greatest energy concentrated about the compass heading to which the waves are moving towards with DPG arm 1 = 0 degrees. (The heading is later adjusted to represent the compass direction from which the waves propagate with respect to true north.) The absolute signal is then reduced to pounds per square inch absolute (PSIA). 4. Instrument Tilt Approximation The mean of each differential pressure record is compared to the zero-wave condition tare as determined in the laboratory. If the mean of a differential record is assumed to represent a zero-wave condition in the field, then a discrepancy between the mean and the laboratory tare could indicate instrument tilt above the seabed. An approximation of the tilt of each arm is calculated using this difference between the mean and tare for each transducer record. Tee the arm tilts about the horizontal an angle G, as shown in Figure IV-3, then a pressure difference between the sensors is _ detected. This pressure differential is converted to a pressure head, Q, and the tilt c& approximated from the arctangent of Q/ax. Specifically, ee AP ae eS mtan Gc aya | (4.34) = oh, — where AP = dP(record mean) - dP (horizontal) and Ax = gage length of arm. The specific gravity of the fluid back-filling the sensor Pieris Vor must be dif- ferent than that of the surrounding sea- water, Y. If both differential trans- ducers along an axis are operating cor- rectly, the angle of tilt calculated for colinear arms should agree with opposite signs. The direction FIGURE IV-3: Instrument tilt above the sea- floor. of tilt is defined after considering the manner in which the differential pressures are reported by the instrument, (i.e., dP = P(arm)-P(center)). An increase in the mean value of a differential transducer indicates that the end of the corresponding arm is slanting upwards (neglecting any changes in temperature). = 55) = If it is decided that the instrument is stable over time, (i.e., there is no further settlement), then changes in the mean of the differential gauge signals could be used to calculate the ambient seawater temperature. This estimate could then be used to develop the temperature-corrected specific gravity of the seawater and back-fill fluid. (This calculation is not included in the present software package.) Temperature estimates could not be made if the back-fill fluid volumes on both sides of the differential pressure transducers were equal. (See Section V.C.6.) 5. Tide Calculation The mean voltage of the absolute transducer record is converted to pressure and is used to calculate the tide level. The total average water column above the sensor, z,, can be found from lip aS ~ y\*mean Pea i Yor be r Pop) (4.35) where Pmean = mean absolute pressure Patm = atmospheric pressure Y = specific weight of seawater Yp¢ = Specific weight of back-filling fluid ne = height of sensor above the transducer Ppp = back-fill pressure. > Both the specific fluid weights should be temperature corrected. The ey 56 & difference between z, and the measured water column abcve the sensor at mean water represents the average tide level during the record. 6. Development of Curvature Terms As the next step, the curvature terms are created by subtracting the colinear slope terms and dividing by the distance between the center of the slope measurements. 7. Significance of the Signals in Linear Theory The absolute pressure transducer signal can then be considered to be in the form: H a P : Saye e te (psia) (4.36) Gay) VS iS cos (kx + ky ot) Pp and the differential signals in the form: H ee ‘ P (x,y,t) = - y oy ss x, sin (kx + KY - ot) (psid) (4.37) H : ; P (xryrt) aoe oy Kk Ky sin (kx + KY - ot) (sid) (4.38) - 57 - The wavenumber, k, and the pressure response function are generated for the frequencies (GE a (n-1) fil 3S DrBpoooli/2 (4.39) where N is the number of sample points analyzed and at is the sampling interval. The water depths used in the calculations include the tidal variation computed earlier. 8. FFT and Conversion to Water Surface Terms The absolute record, the four differential records, and _ the two curvature records are processed by the Fast Fourier Transform (FFT) and the resulting Fourier coefficients divided by the pressure response function and specific weight of the seawater. Frequency bands greater than 2 rad/sec (wave periods less than 3.14 seconds) are disregarded because of the error inherent in dividing these high frequency bands by their respectively small K values. The absolute record is then comparable to: q n(x,yrt) = 5 cos (kx + oy - ot) (in.) (4.40) and the differential records to: = 3 = BS aE a Ginis/ainr i GEG) ny (x+y ,t) 5 k cos 6 sin (kx + Ky ot) and H 5 j n, (&ryt) =O 5 8 Gin @ sin (k,x - KY - ot) (in./in.) (4.42) while the curvature, or acceleration, terms are as: Meal 2 i al Nyy (Yt) = 5 k” cos’ 0 cos (kx + ky ot) (in>') (4.43) and No Gynt) =Hs= Eee eine cos(k_ x - k y - ot) (ins!) (4.44) yy 2 x y Twice the sum of the squares of the modified Fourier coefficients represents the power spectrum of the displacement, slope components, and curvature components. The significant wave height is determined from four times the square root of the sum of the absolute channel's power spectrum: H SS (4.45) Bo) = 9. Failure of the Absolute Channel If it is decided that the absolute transducer has failed, the water surface displacement and power spectrum can theoretically be estimated from the x- and y-axis differential transducers that are deemed as operational. This procedure necessarily assumes that there is only one wave direction per frequency. The record of the absolute transducer has been developed in the time domain to that of Equation (4.40): es i n(x,y,t) = 5 cos (kx + ey ot) so that the power spectrum of the absolute transducer is as: 20 sess ees 2 = ee is acBs Se) ==, [cos (kx + no ot) = 8 (4. 46) and the power spectrum of the x and y differential gauges are correspondingly: 2 H 2 2 Ss eee aka (o) 3 Kk cos’é (4.47) x xX 2 H 2 S (o) =—k §sin 6 8 nny, (4. 48) The power spectrum of the absolute record, then, might be developed from the sum of the x and y differential power spectra divided by the + (60) = square of the wavenumber. Such a module, however, is not part of the software as presented in Appendix F. Theoretically, it is also possible to estimate the principal wave direction without the absolute transducer signal similarly assuming that there is only one wave direction per frequency. From Equations 4.9, 4.10, and 4.11 the differential cross-correlations are as: 2 a2 =k §@=—k 28 Ss Ss, 698 5 Sint + cos 26) (4.49) x xX sia Tig Lee 2 Sh es k an sin 6 = 5k cane - cos 28) (4.50) Vawvs 2 a ee? : S Sey US} sin@é cosé ==k S_ (sin 26) (4.51) Meath n 2 nn for some frequency 6, so that an estimate of the wave direction might be found from: -s (4.52) for some frequency 6. There exists four roots in the arctangent of 2 , as can be seen in Figure IV-4. It can be shown that two of these roots are associated with maxima (and separated by 180°) and the suGay < other two (also separated by 180°) are associated with minima and separated from the first two roots by 90°. Two of these roots can be FIGURE 1V-4: Four roots of tangent (20). eliminated by considering the signs of the numerator and denominator. The remaining two might be resolved by considering the physical environment of the deployment site. One does not expect, for example, incident swell to approach a straight shoreline at angles much greater than 45 degrees to the shore normal. This directional estimate is calculated in the software package and displayed optionally. 620 10. Feilure of 3 Differential Channels If only the absolute and one differential pressure channels are considered operational, another estimate of the wave direction might be made with a 180 degree ambiguity. With the power spectra of the absolute and differential channels in the form of Equations 4.46 through 4.48; So that (4.53) or similarly (4.54) for some frequency 6G. - 63 - ll. Effective Period The non-block-averaged frequency band corresponding to the centroid of each power spectrum is then calculated from: => | in ORaS hacer merrier mee aaa (4.55) where Sxx (6) is the auto-spectrum of a transducer signal. This is an estimate of the "effective wave period" during the record as determined by each transducer. 12. The Directional Fourier Coefficients The directional (or angular) Fourier coefficients are calculated for each frequency band using Equations 4.18 through 4.24. The coefficients are taken as the mean of all those calculated with different combinations (or cross-spectra) of operating channels. These angular coefficients, as well as the water surface displacement power spectrum, are block-averaged over a specified number of adjacent frequency bands. Since an ocean wave time series is composed of random functions, the Fourier COCEE LCL eAtE of each channel must not be block-averaged before generation of the angular coefficients. The average of a random function exhibits. zero correlation with the average of another, so et the angular coefficients “must be calculated from the raw cross-spectra terms and SA then averaged. Similarly, the directional estimates obtained from Equations 4.52, 4.53, and 4.54 are block-averaged. 13. Block-Averaging The stability of the generated spectra is enhanced by block-averaging over adjacent frequency bands. If the water surface displacements are assumed to be Gaussian, the Fourier coefficient spectral estimates are distributed according to the chi-square distribution with two degrees of freedom. The block-averaged, or smoothed, Fourier coefficient spectral estimates are represented by the chi-square distribution with the number of degrees of freedom equal to two times the number of adjacent frequencies averaged (Borgman,1972). When the analysis program operates upon records from computer simulation or a controlled laboratory environment, each spectral estimate is considered separately; that is, there is no block-averaging. This is equivalent to two degrees of freedom and is done to retain the highest resolution possible for the narrow spectra and shorter time records generated in simulation and the laboratory. When the program operates upon a record from the ocean environment, each signal is block-averaged over four to eight adjacent spectral frequencies to yield eight to sixteen degrees of freedom respectively. It is assumed that the frequency resolution thereby lost in the block-averaged analysis of the ocean's broader spectra is balanced by the increased stability of the record. = 65 = 14. Frequency Bands of Greatest Energy The block-averaged frequency bands of maximum energy are then identified from one of the operative channels (generally the absolute) and the amount by which each exceeds the average energy in the spectrum is calculated. The truncated Fourier series directional spectrum (Equation 4.14) is then calculated for each of these high energy bands. The direction of peak energy for each spectrum is reported as that band's direction of wave propagation -- adjusted accordingly to instrument orientation relative to true north. The "mean direction" of each band can also be calculated as: a lb Tiny 7 > = tan = (4.56) where n=1,2,3. (If no water surface curvature terms are developed, then n=1,2.) There exists a directional ambiguity for n>l since there exists more than one peak in sin n@ for n>l (from which the bn terms are developed). Since the ultimate intent of the DPG as a tool is to report predominant wave characteristics at the installation site, the presentation of wave information at the dominant energy levels is considered to be the preferred data display. BAS E. DPG Simulation and Error A simple simulation program was utilized to test the capabilities of the software. A directional wave-pressure field over water depth h, at transducer depth s, was considered using Eee ps 2 ae K, cos Ok otk y ot) (4.57) J P(x,y,S;t) = yh ap ) =i) j where J = number of wave trains present. Multiple wave trains of different frequencies and/or directions were simulated by superimposing all of the dynamic water surface elevations at (x,y,t) onto the static water column, h. The pressure at those (x,y) points corresponding to the five DPG diaphragm locations were generated over time. (It was assumed that the five diaphragms in the center of the instrument occupy the same point.) From these values, four differential signals and one absolute signal were developed at at intervals for a record length of Nat to simulate DPG in-situ performance. Non-linear wave-wave interactions were not considered in this simple model. The integrity of the FFT analysis was first tested by simulating a single wave train at a principal frequency of the FFT. Results of the analysis of the simulated record indicated acceptable FFT performance since all of the energy was indeed found to be - 67 - concentrated at the simulated wave frequency. The ability to discriminate a number of different wave trains was next tested. Two wave trains of frequencies within one spectral bandwidth of one another and of different energy and direction were superimposed upon a train of lower frequency. Analysis was carried 20 .00 -00 40 .00 50 .00 TIME (seconds } -00 FIGURE IV-5: Simulated time record of water surface elevation. Case 1. H=4 ft., 9 = 46 deg., 7.98 sec. pda; H=3 ft., © = 180 deg., 6.33 sec. pd.; H = 4 ft., © = 300 deg., 9.00 sec. pd. out for 512 sample points of 0.25 second interval. A portion of the simulated time record of the water surface displacement generated over each of the five sampling points of the DPG is shown in Figure TW =5\ The raw spectral energy distribution, or energy spectra, presented in Figure Iv-6, illustrates the presence of three distinct frequencies well. Although the simulated lowest and highest frequency waves were of the same wave height, the higher frequency wave dewonstrates a smaller energy spike due to the spectral leakage between the lower frequency bands. The non-smoothed 7-coefficient AR SIMULATION 5.98 seca, H=4 ft» 46 deg| 6.33 secas H=3 ft» 180 deg 9.00 secss H=4 fts 300 deg 320 .00 240.00 280.00 160.00 200.00 ~~ vi) v w N c wt —_ > © Y uJ = uJ 420 .00 80 .00 ENERGY-SPECTRA ef DISPLACEMENT TERM 0525) s0.50)5 10.75) 4.00 25) 450) 475) e200 FREQUENCY (red~sec ) FIGURE IV-6: Rawenergy spectra; Simulation Case 1. I1- lustrates presence of three distinct wave trains. Be 69 a SIMULATION 5.98 secse H=4 fio 6.33 secse H=3 ft» 180 deg —-—- 8.00 seces H=4 fts. 300 deg 9.143 sec. band 6.400 sec.band ENERGY (in? sec ) 420 4180 DIRECTION (deg) FIGURE IV-7: Non-weighted 7 coefficient Fourier series directional energy distribution. Simulation Case l. Illustrates presence of three distinct wave trains with different directions. = AO) = Fourier series directional distribution was plotted over two degree increments for the three bands of highest energy and is presented in Figure IV-7. The analysis program demonstrates its ability to define each wave train's direction accurately by presenting the maximum energy at the correct simulated wave direction. The half-power directional width of each is approximately 60 degrees. These curves, of course, do not contain all of the simulatedgwave energy since only three major spectral bands are plotted. Two wave trains of different frequency but with identical height and direction were next simulated over 512 points of 0.25 second interval. The frequency of each was selected to fall exactly between two spectral frequencies. The higher frequency bands were 0.1184 rad/sec apart and the lower were 0.464 rad/sec apart. The raw energy spectra, shown in Figure IV-8, depicts the two wave trains' energy distribution over frequency. Slight differences in leakage between the two simulated wave frequencies can be detected. The non-smoothed directional distributions of the two waves, shown in Figure IV-9, agree well with each other as expected. The very slight differences are the result of differences in spectral leakage for each wave. The analysis procedure, however, is unable to differentiate between two waves of identical frequency and different direction. Two waves of the same height and non-spectral frequency were simulated with a 130 degree difference in direction. The =A = SIMULATION 53.506 secs» H=4 ft» 60 deg 10.888 secs, H=3 ft» 60 deg ENERGY (in? sec) 80 .00 ENERGY-SPECTRA of DISPLACEMENT TERM 40 .00 8 C5 ~COO.2S. 0.50 0.75 1.00 4.25 4.50 1.75 2.00 FREQUENCY (rad/sec ) FIGURE IV-8: Rawenergy spectra; Simulation Case 2. - 72 - SIMULATION —— 5.506 secs, H=S fts 60 al aonsse 10.888 seco, H=4 f+. 60 dea 180.00 240.00 300.00 360.00 Vv) v 5.565 sec. band Bee ie 10.667 sec. band ca “I of & w 8 za 23 S| ee g 8 -120 00 G 60 420 480 240 DIRECTION (deg) FIGURE IV-9: Non-weighted 7-coefficient Fourier series dir- ectional energy distribution; Simulation Case 2. Illustrates good directional spectra agreement with slight differences due to leakage. ENERGY (1n2 =e SIMULATION 9.50 secs» H=3 fits 80 deg $3.90 secs» H=3 ft» 195 deg Se a aT 6 T Q 60 120 180 240 300 360 DIRECTION (deg } FIGURES IV-10,11: Non-weighted 7-coef- ENERGY (in? sec) ficient directional spectra; Simu- lation Cases 3 and 4. Illustrates software inability to clearly define two directions per frequency, (waves of equal and unequal height). SIMULATION 200 secse H=3 ft» 80 deg secs», H=4 ft» 195 deg T a SIoa4 ers 4120 180 240 DIRECTION (deg} el, non-smoothed seven-coefficient Fourier series directional distribution, presented in Figure IV-10, demonstrates a wide peak of 80 degree half-power bandwidth. The distribution suggests omnidirectional wave power, but with a maximum at the mean of the two simulated directions, 80 and 195 degrees. The identical case was re-simulated with the 80-degree wave retaining its three foot height and the 195-degree wave assuming a four foot height. The directional distribution, shown in Figure IV-1l, is asymmetrical with peak energy at the weighted average value of the two wave directions. Inclusion of higher order terms in the partial Fourier series representation of direction should increase the accuracy of the series representation. Figure IV-12 illustrates the heightened directional resolution of a simulated wave train at a peincipal frequency using the first seven directional Fourier coefficients, (N=3) , compared to the first five, (N=2). The non-smoothed half-power bandwidth for seven coefficients is 66 compared to 76.3 for five. In the simple simulation analysis, the software appears to be non-sensitive to wave direction —- at least for the presence of only one wave train. Four waves of equal energy and frequency, but different direction, were each simulated individually over the DFG. The directional distribution for each was overlaid upon one another =e 5 and excellent agreement readily seen. SIMULATION 8.00 secs H=4 ft 3 224 deg UV vu " N c Sal —_ > © Y uJ Zz Li 4180 240 DIRECTION (deg J FIGURE IV-12; Non-weighted directional spectra using the first seven directional Fourier coefficients compared to the first five. Single simulated wave of spectral frequency. S16 CHAPTER V LABORATORY DEVELOPMENT, CALIBRATION, AND TESTING OF THE INSTRUMENT A. Introduction Some modifications to the instrument were made during the fluid back-filling of the sensors. These changes, as well as the static bench calibration of the DPG instrument are documented and discussed in this chapter. The preliminary wave-tank tests carried out at the Coastal Engineering Research Center (CERC), Fort Belvoir, Virginia, are also described. B. Fluid Back-Filling the Sensors System Modifications Certainly the most difficult problem encountered during the assembly of the DPG was. the fluid back-filling of the sensing diaphragms. The frustration and numerous failures during the very intense six-week period of back-filling attempts led to two changes each of the type of fluid and tubing used. - 77 - The original design called for 1/16 inch inner diameter stainless steel tubing between the water-tight cylinder and isolation diaphragms. The fuselage, or center, tubings were 14 inches in length, while the arm tubings were 44 inches in length. Methanol was first tried as the back-filling fluid, but then discarded because of the poisonous hazard it presented. Standard automobile transmission fluid was next used as the back-filling agent. Although much safer, it easily contaminates laboratory tools and work areas. Hundreds of attempts were made to back-fill the sensors and eliminate all air in the system. An air bubble of appreciable size could compress under a dynamic load and thereby prevent the transducer from sensing the full pressure exerted upon the isolation diaphragm. The back-filiing fluid itself is assumed incompressible so that with no air in the system the fluid transmits the pressure sensed by the isolation diaphragm immediately to the transducer. The final technique used to back-fill the DPG is outlined in Appendix D. Once satisfied that air was removed from the system, more problems arose’ when the transducers, sensing through the 1/16 inch I.D. tubing filled with transmission fluid, failed to respond to a iioaa faster than five to twelve seconds. It was decided that the Pectoral head loss caused by the high viscosity of the fluid and long, small diameter tubing might be responsible for such large response times. It was also considered possible that small bubbles might still be lodged in the system or that impurities in the fluid Sen Transducer Diaphragm = Pressure at Sensor n Transducer Chamber Pressure FIGURE V-1: Schematic representation of differential pressure trans-— ducer and isolation sensors. = Ys) = may have blocked the transducer filter screens and diaphragm. The frictional pressure gradient along the inside length 1 of a circular pipe is (Peerless,1967): ari aaea Go) where AP- = frictional pressure drop v = coefficient of dynamic viscosity Q = volumetric flow rate inner diameter of tubing. Figure V-1 presents a schematic representation of the differential transducer and sensors. The fluid flow along each arm, Q, and Q), that results from difference in pressure between the system's sensors May be expressed from Eq. 5.1 as: Q) = B, (P) = fee (5. 2a) eG paves Me) (5. 2b) where a5) 4 n ————— nN 108 ee (Gr?) raya) SG) Re-writing; Nite aa Onan (5.4a) 2 (5.4b) And, from continuity; ei 5 2a pee G5) (5.6) The transducer diaphragm displaces a volume ¥, proportional to the change in pressure across the transducer chamber: c o) (e7)) Re-writing Equation 5.7 and expressing the change in volume in terms of the fluid flow Q;3 ut aie ee AER Fey hE ai AY = J Q dt (5.8) Seoul Differentiating both sides; e) =" 10; (AP) (5.9) Substituting (Equations 5.8 and 5.9 into 5.6, one obtains: il el BIE iy tay an aR arse CG B) ae (5.10) where AP is the difference in pressure between the two sensors. If the change, AP, occurs instantaneously, it can be shown that the solution to Eq. 5.10 is ) (5.11) substitution into Eq. 5.10 yields: als all — heute = — ee D AP AP. + TE + B Kp AP e (5.12) where Kaw is the "folding time" of the response. Solving, ~ RA 4 . ona a(By + B.) D Bee 4 4 128 a My Uy Xa oo) Dy : Dy 1 Die De Mea Say5 (5.13) If the fluid and tubing diameter are the same on both sides of the transducer, Eq. 5.13 reduces to: ‘ 4 AL AASK Toh TU Ry he ca a8 ae D s pt oat Le : The form of Eq. 5.11 was verified qualitatively by examining the strip chart output of a differential transducer and sensor system loaded in an approximately instantaneous manner. S83) = It is clear that the response time is proportional to the fluid viscosity and inversely proportional to the fourth power of the tubing diameter. Changing the tubing length was not considered since the lengths were pre-determined by the DPG configuration as descirbed in Chapter II. It was first thought that the response time could be sufficiently decreased by reducing the fluid viscosity. A number of fluids were considered but all discarded because of their degrading effects on the system's materials, (i.e., acrylic, neoprene, Buna-n, nylon, and stainless steel). After two hundered and eighty hours of nearly continuous laboratory work, it was decided to use gin as the back-filling fluid. It is inexpensive, easily obtainable, safe, and has a dynamic viscosity coefficient one and one half orders of Magnitude less than transmission fluid. The transducers and sensors were drained of transmission fluid and flushed briefly with hexane, then methanol, then back-filled with gin. A 50-50 combination of 40 proof McCalls and 80 proof Gilbeys gin was used. The water content of the gin required that the fluid rest in the system for twenty-four hours during rising temperatures so that air released from the water could be collected and removed. Although the system response time improved, it remained unacceptably high. It is crucial for each of the five DPG transducers to respond quickly and simultaneously to ensure proper instantaneous measurement of the sub-surface dynamic pressure. a ei, Otherwise, an artificial phase lag may be introduced between the sensors' readings. It was next decided to double the diameter of the long arm tubings. This tactic decreased response time to about 0.12 seconds, but the new 1/8 inch I1.D. tubing was quite rigid. It was mated to the original connectors by Swage-Lock® reducers with very short 1/16 inch I.D. tubings. The severe handling of the arm tubings during back-filling and instrument assembly eventually led to the fracture of at least two, and possibly three, of the reducers. Before the failures occurred, the instrument was calibrated (Section V.C), assembled (Appendix D), and brought to CERC under the pressure of time for initial wave-tank testing. When the DPG was returned to the laboratory at the University of Delaware, the arm tubing failures were confirmed and all of the connectors and external tubing were replaced with flexible 1/8 inch I.D. line and again back-filled with gin. The 1/16 inch I.D. nylon tubing within the water-tight cylinder was not replaced. Response time was recorded consistently as an acceptable 0.12 seconds, (Section V.C), and the flexible tubing proved very easy to work with. aor C. Bench Calibration 1.. The Calibration Technique An extremely simple calibration was first considered to statically determine the static response of the transducers to a known load. The isclation diaphragms were positioned facing upwards and were loaded with known weights. This technique was ineffective because of the physical nature of the dia- phragms. The bottoms of the weights were rarely in full contact with the elastomer, as is depicted graphically in Figure V-2, so that the ap- plied pressure FIGURE V-2: Cross-section of isolation dia- to the sensor phragm with an object load applied. could not be easily calculated. If the weight was too heavy and large, some of the force of the weight would be exerted upon the top face of the =1e6S acrylic housing and not upon the fluid. (Intuitively, one would expect this to happen even in the ideal case of force applied by the dynamic water column —- if the exposed elastomer area was so _ small that it could not deflect.) A slightly more sophisticated calibration system was then designed. The system, as drawn in Figure V-3, consists of two pressure chambers which secure around each isolation diaphragm of a differential transducer, (only one is used with the absolute transducer). Each chamber is equipped with its own pressure transducer and a bicycle tire valve stem. The chambers are connected by tubing with a valve in the center to isolate, bleed, or allow the chambers to communicate with one another. The chambers are built of short steel cylinders with a plate welded on one end. Each chamber is secured to a sensor diaphragm with a short length of motorcycle tire inner tube that is glued to the chamber and hose-clamped to the isolation diaphragm housing. The system is pressured with a bicycle tire pump and the pressure sensed in each chamber and by the DPG transducer is reported on a multi-channel strip chart. The DPG transducers’ response was interfaced with the strip chart using a short "bench cable" that mated with the instrumentation connector located within the DPG transducer stack. = (e772 The instrument was calibrated twice; once with the 1/8 inch arm and 1/16 inch I.D. center inflexible tubing used at CERC, and two weeks later, with the 1/8 inch I.D. flexible tubing used on the Strip Chart Recorder ———— Bench Cable DPG Transducer Stack PrasctinevGhambanrs FIGURE V-3: The DPG bench calibration system. One pair of sensors shown for clarity. final instrument installed at the FRF, Duck, NC. Early during the first calibration, one of the chamber transducers failed. This meant that only one side of a differential transducer could be loaded at a = 88) = time, while the other side was essumed to remain at atmospheric pressure. The calibration technique, then, was not able to simulate differential pressure loading while both sides were subjected to a pressure head as would be felt on the seafloor. (Both chambers leaked somewhat, so that it was not feasible to pressure each side to a particular head and then begin the differential loading.) The calibration technique described herein entailed static loading whereas the operating instrument would be subjected to dynamic loading. This was not of great concern, however, since the in-situ loading is of relatively low frequency. The calibration technique could be improved by using an oscillating pump to pressure the chambers sinusoidally over time. 2. Testing for Air Bubbles Theoretically the calibration system can be used to check for the presence of air bubbles in the transducer sensor lines. Firstly, air in a line will compress under a load and bias the pressure value that the transducer will report. Secondly, it is hypothesized that the loading and unloading of the air bubble will delay the response time of the system. If this is true, then it may be possible to detect an air bubble by loading each side of a differential transducer equally, then unloading them simultaneously. The side with the greater air volume will lag in response. (It is assumed that the inherent lag in arm-side response due to the longer arm =tSou= tubing length is negligible for large tubing diameters ( > 1/8 inch inner diameter). The length of small diameter nylon tubing is the same for each side of a transducer.) This effect was never tested exhaustively in the laboratory, but one possible such occurence is aes 2222 stleroelenselece sertercotooertiveedoan seottorsoleceedeneedonee seocleceetians (0.04 psid/mm) = FIGURE V-4: Strip chart recording illustrating possible existence of air in arm side of 4dP4. A) arm sensor loaded; B) arm and center sensors communicate to establish zero differential pressure; C) both sensors bled simultaneously, arm side shows slight lag. Chart speed: 5 mm/sec. = 90) = shown in Figure V-4. The chamber on the arm sensor of dP4 was loaded (A) and then allowed to communicate with the center sensor chamber (B). The differential transducer correctly reported zero difference in pressure. When the entire system was bled (C), the transducer briefly indicated a greater pressure on the arm side. The arm was re-back-filled to be safe. 3. Static Calibration Results The t iaueation results for each of the four differential pressure and the absolute pressure transducers as found during the pre-FRF calibration are shown in Figures V-5 (a) through (e). Differential transducers dP2, dP3, dP4, and the absolute transducer each demonstrated acceptable one-to-one reporting of the loads applied. DP1, however, is significantly biased. The problem was attributed to the transducer itself, since a similar error appeared during the first calibration. The zero-differential value of dPl was also consistently high (5 to 7 volts as compared to 2.5 volts, as ordered); and unlike the other transducers, it demonstrated sensitivity to excitation voltage as is discussed in Section V.C.4. This malfunction did not appear until just before the scheduled testing was to begin at CERC and time limitations did not allow for its immediate repair. The calibration results of the first investigation for the absolute transducer and dP2, dP3, and dP4 are identical to those of the second. 2 LL Lu o © oO ao a1 O 1 LL LW an U ao iol dl =5 z Apsid dP1 apsid REF O =| = O apsid dPS FIGURE V-5 (a) through (e): 5 Gil 2 2 Apsia ABS Apsid REF ia -1 O apsid dPe 4 LL LU af U - oO Qa qd rae O Apsid dP4 DPG transducer calibration curves. — - 92 - The calibration curves were generated from the strip chart output pe pronubed in Appendix B. The calibration chamber was pressured, allowed to leak slightly, and the chamber and DPG transducer readings taken from the strip chart at the point before the system was loaded again. The response time for the DPG transducers was determined by measuring the passage of time between loading events as reported by the chamber transducer and the DPG transducer on the strip chart. Each transducer appears to respond in an acceptably similar short time period. 4. Power Supply Sensitivity Each of the transducers demonstrated satisfactory insensitivity to power supply voltage fluctuations except dPl. Whereas the absolute and dP2, dP3, and dP4 transducers were unaffected by voltage changes from 20 to 26 volts, the output of dPl decreased in an unexplained manner at excitation voltages below 22 volts. 5. Transducer Drift The absolute and dPl, dP2, and dP3 transducers proved steady in output with steady loading. However, dP4 intermittently and erratically drifted during the second set of bench calibration tests. It is assumed that such drift will be simply interpreted as a long period wave by the FFT analysis of the data. But the inability of =, fs} — the transducer to establish a zero-differential tare value invalidates any calculations of instrument tilt or ambent temperature using dP4 signals (Section IV.C.4). 6. Temperature Effect All transducers are temperature sensitive to some degree. The thermal sensitivity specifications of the DPG's Setra absolute and differential pressure transducers are less than +0.02% FS/°F and +0.03% FS/°F thermal zero shift with thermal coefficients of sensitivity of less than +0.015% FS/°OF and +0.02% FS/OF respectively. The transducer and sensor systems in the DPG are slightly more or less sensitive than the factory specifications because of their fluid back-fill. As the DPG environment changes temperature the back-filling gin expands or contracts. Moreover, a temperature change induces a slight differential pressure across the differential transducers because of the greater volume of fluid in the (longer) arm sensors. Since the volumetric expansion of a fluid is linearly proporfional to the change in temperature and initial volume of fluid, the expanded volume in the arm sensors will be four times that of the center sensors, (since the arm tubing is four times the length of the center tubing.) But since penperature changes under twenty feet of ocean water are typically small and of low frequency, it is assumed that any thermal transducer drift during a sampling interval will be interpreted as a very long period wave or as a mean which changes oh, 5 from record to record. Such thermal effects accordingly affect the mean of a pressure record. This could be mistakingly interpreted as instrument tilt if two differential records taken at different ambient temperatures are compared (Section III.C.4). It could also affect the tide calculation by altering the back-fill pressure tern, Pog » Of the absolute sensor in Equation 4.35. Future development of the DPG should more thoroughly investigate the effects of temperature on the transducers and sensors. 7. Absolute Sensor Back-Fill Pressure The absolute pressure sensor back-fill pressure, Por» is obtained in the laboratory by either of two ways. (1) The instrument is positioned such that there is no fluid head above the transducer and the absolute pressure reported above the atmospheric is recorded. (2) The instrument is oriented upright and the absolute pressure that is reported beyond the atmospheric and sensor fluid head is recorded. D. CERC Wave Tank Tests 1. Introduction The first DPG prototype was laboratory tested at the large outdoor wave tank at the Coastal Engineering Research Center, Fort Belvoir, Va. The instrument and cradle proved themselves easily maneuverable -- both above and below water. Although three of the - 95 - four differential pressure channels failed and/or were distrurbed by the wave tank, the analysis of measurements from the absolute and one differential pressure channel suggest satisfactory performance of the DPG. Dea ins tal lation The cradle was secured to a small flatbed trailer and the instrument mounted upon it. The trailer was easily pulled and delivered to the CERC wave tank by a light vehicle. The outdoor wave tank is a long, 15 foot wide, 20 foot deep facility with a large piston-type wavemaker. The cradle was lowered on its side over the PISTON RETURN FLOW PIPES WAVE PROBE BREAKWATER not to scale FIGURE V-6: Orientation of the DPG during CERC wave tank tests. ConfigurationI: 6=55°; Configuration II: 9=35°. tank wall by ropes and dropped slowly into the water. It was positioned by two divers under 10.2 feet of water at approximately = 96 = mid-length of the tank. The cradle, in the center of the tank, was then secured by ropes to large U-bolts on return-flow pipes that terminated at this location, (Figure V-6). It was not clear whether the outflow of the pipes during testing would influence the DPG. The instrument, carried upon the shoulder of one deck-hand, was then positioned on a trestle over the tank and lowered into the water by another rope slung through an arm on the trestle. Care was taken to keep the instrument arms away from the trestle and tank walls using two lateral control lines that were held on each side of the tank. The instrument was received by a diver, guided and positioned into the cradle, and secured with cable ties. The orientation of the instrument was checked by measuring the distance from the wall to each of the cradle legs with a tape secured along a wooden "'T." The top of the "'T'’ was held against the wall to ensure that the measurement was taken perpendicular to the wall. A 100 foot length of unarmored cable, earlier mated to the instrument above water, was interfaced with a power supply and strip chart recorder in a trailer alongside the tank. Despite the poor underwater visibility, (less than six inches), the entire installation took less than two hours and required only two divers and one deck-hand. To remove the equipment, the procedure was _ reversed. The cradle was lifted from the water by securing a rope between it and a van, then the van was driven away and the cradle hoisted up along the wall. - 97 - Diver entry and exit was made using a long flat aluminum ladder tied to the top of one of the tank walls. 3. Tests and Results The facility was, at the time, in the final week of testing rubble mound breakwater structures. So the DPG tests conveniently "piggy-backed" with the regularly scheduled tests. Sets of eleven waves of 1 meter nominal height (3.28 feet) and 5 second period were run every 4 to 5 minutes. Wave height and period were monitored by resistance probes and recorded on a strip chart located inside the trailer. Initially, the three differential channels monitored appeared ill-behaved (Figure V-7). The fourth, dP2, had already been confirmed inoperative due to a broken arm tubing connector. It was then discovered that the end-cap on the dP3 arm had accidentally been left on. The instrument was assembled for the CERC tests with the arm isolation diaphragms flush with the end OE the PVC arms. With the arm plugged, the diaphragm could communicate with the ambient water only through a thin crescent part-way around the diaphragm housing. It is assumed that such a small gap dampened the dynamic pressure field of the passing waves. *a/Ptsd 79 pue a/etsd oT ‘tuorzesqrye ‘oes /wu Z speeds jyazey9 ‘uo 4jzeT Aj{Tejueprosce deo_-pus wie €dd ‘I woryein3rzyuoj) °4S89} QYaD +Burprosez yareyo drzqys eydmeg :/-a qundId rr = Sod Cia weber aa is = sea Bs eaccees PE = Hy t bo pt Ha ul TTT aa - 99 - Once the end-cap was removed, the third channel demonstrated sinusoidal output with the expected tr/2 phase difference to the absolute signal as predicted by Equations 2.1 and 2.2. The unexpected characteristics of the first and fourth differential channels, however, remained unexplained. Both channels indicated the passage of a trough, as expected, but did not report the actual crest passage -- instead suggesting the passage of two crests mm/4 before and after the actual passage. This phenomenon was noted in both orientations of the DPG tested. It is thought that the unexpected characteristics of these differential channels could have been due to the poor positioning of the sensors at the unprotected ends of the PVC arms. It is also possible that the arm tubings were broken at the time of the tests or that the sensitive differential gauges were adversely influenced by the return flow pipes to which the cradle was attached. The instrument was originally positioned such that the dPl and dP3 arms were aligned approximately 55 degrees from the centerline of the tank, or wave ray. The cradle and instrument were next rotated about 20 degrees such that arms 1 and 3 were approximately 35 degrees from the wave ray. Figures V-8 and V-9 are strip chart recordings from each of the configurations, respectively. The rotation of the DPG was restricted between these two positions because of the pipes that surrounded either side of the cradle. These pipes, however, offerred the only structure to which the cradle *a/ptsd 7°09 pue a/etsd o[ suotqzerqryeg ‘oes/wu z ipaeds qzey)d “][ wotjyein3rzuoyj *3S89}3 DQYqD ‘{3urpzoocex qyaeyo drajs aydwes :8-a qundIa = i \ if - 100 - ae ert \ Lat} early F VAY ( = aL(Oak *A/ptsd Z°Q pue a/etsd QT iuotjeaqtyje) ‘“ses/wm 7 speeds yrzeyD “TI wotyeanSrzuoyd *4se}] QuAD ‘+Butproses yareyo dtrays aydwes %6-pA JUNI L“SEAGZ sy AG‘z 23 qs Wet Ww Vasil = 102 = WAVE STAFF UPCUUAUATAAENAA AAA LTT IOCAUUNTERLUALAA TAAL ANNEAL ANA fUTEAATAA 4 Ko mah erates ABS. PRESS. GAUGE 0.2 psi/mm 0.05 m/mm Chart: 5 mm/sec Comparison of DPG absolute pressure gauge and CERC resistance wave probe. FIGURE V-10: 5 sh03) 5 could be secured. Figure V-10 compares the absolute pressure transducer signal with that of the tank's resistance wave probe located about sixty feet upstream of the DPG site. The resistance probe describes the waves' non-linear profile featuring peaked crests and long shallow troughs. Wave period is 5.0 seconds and the height is between 3.0 feet (0.925 m) and 3.36 feet (1.025 m) from crest to trough. The absolute transducer also reports a period of 5.0 seconds and a wave height of about 3.2 feet as calculated using stream function theory (Dean,1974). Stream function theory is used because of the great non-linear appearance of the wave form. The calculated wave height is only about 2.8 feet if linear theory is assumed. From Eq. 2.1, Beal tee ] crest | _ trough Er ICHOS | scan] Go STeee | (5.15) " Rea Here, y = 62.23 lb/cu.ft. (13 C), and Kp is approximately 0.874 and 1.068 for the wave crest and trough respectively from stream function theory (Dean,1974). This was calculated for a wave of five second period in water depth 10.2 feet and absolute sensor height above the bottom of 4.25 feet. The intimation of static water level is also good. The no-wave tare value was steadily reported as 18.23 psia, which corresponds to a water height above the sensor, from Eq. 4.35 of 5.91 feet. = 10h = 2 7 P mean 7 Wee S27 Patm 7 Poe) /Y (4.35) where Vpr = 55.6 lb/cu.ft. Loe = 18.5 inches ae) i] 14.74 psi Me) i] 0.34 psi = i] 62723 b/icustt. A value of 5.95 feet is expected from the difference of the tank water depth, 10.2 feet, and the sensor's height above bottom, 4.25 feet. An estimate of the wave direction was attempted from the signal of dP3 using wave parameters as predicted by stream function theory. The average magnitude of the channel's signal was estimated and the maximum differential pressure expected along the wave ray calculated from stream function theory. The angle O between the wave ray and the dP3 arm is then: 4 | CdP/dxJ) measured (5.16) Sha CO lil Teeyeniern The wavenumber k was calculated using stream function theory for a 5 second wave in the water depths stipulated earlier. The pressure response function Kp was similarly estimated for a depth equal to the mean of the center and arm sensor vertical positions above the bottom. The gage length dx was 3.5 feet. For configuration I, the estimated angle, 51.3°, compares well with the 55° angie expected. For configuration II, the estimated angle is 35.4° compared to an expected value of 35°. The experiment at CERC, although plagued with arm _ sensor failures and highly non-linear waves, demonstrated the capability of the instrument to measure wave direction. The tests also served the purpose of defining several important modifications required to improve the performance of the DPG system. E. The Second DPG Prototype The DPG was returned to the University of Delaware laboratory and partially disassembled to install the new hardware modifications. The fracture of the arm lines of dPl, dP2, and dP4 were confirmed. All of the stainless steel tubing exterior to the water-tight instrument cylinder was replaced with flexible tubing and back-filled, and the system was calibrated as described in Section C of this chapter. New PVC arms were machined to house the flexible tubing and isolation diaphragms and the instrument was reassembled as described in Appendix D. Care was taken to ensure that the sensors’ elastomer diaphragms were well back from the ends of the PVC arms and exposed to the holes in the sides of each arm. Some dimensions of - 106 - the instrument, reassembled for the field evaluation, are specified in Appendix C. =/a07 = CHAPTER VI FIELD INSTALLATION AND EVALUATION A. Installation at the FRF The newly re-assembled instrument and cradle were towed on a trailer to the Coastal Engineering Research Center Field Research Facility at Duck, North Carolina, in early May of 1982. An installation site was chosen approximately 735 feet directly south of the seaward end of the 1890 feet long research pier. This site fell safely between the FRF's regular bathymmetric profile lines, allowed a reasonalbe safety margin of length for cable deployment (18%), exhibited a relatively stable 20 foot depth contour over time, and was considered to be sufficiently far from the large scour hole at the end of the pier to avoid any related refraction effects. The geographic location and typical nearshore bathymetry of the site are illustrated in Figures VI-1 and VI-2. It was decided to install the DPG using the facility's Coastal Research Amphibious Buggy (CRAB) marine vehicle. The CRAB is a three-wheeled tripod vehicle capable of driving across the beach - 108 - Woy 7 2a . A EX \ 72 ue \ 43 2 " ‘ a 25 54 2 " & \ 28 3 “Nu iN \ FIELD RESEARCH FACILITY 2 é ~ 36°10'S4.6"N 75°45'5.2°W aBon MS am" \ a2 & een Ooch 10\ \3 a AY AY \e\\ Sea Crest OWN Nance 38 0 1 2 3.4 KILOMETERS ° ‘ 2 LES Depths in Feet FIGURE VI-1: Site of the DPG field evaluation; (from Birkemeier, et.al., 1981). = i109) = (W) SINULSIT 850 650 DISTANCE (M) 450 FRE BATHYMETRY 3 N FIGURE Vi-2: OV 81 METERS CONTOURS IN Nearshore bathymetry of installation site. FIGURE VI-2: > LO: = find hy ph Lh, a ES ae ee = seh pen ? sn a 7 Session tans the 1on s platform tallat ield ins ing.) fon), 46 Prepar 3 DPG suspended underneath the operator the CRAB FIGURE VI of = alalal face and through the surf zone. The instrument was secured to the cradle and hoisted underneath the top (operator's) platform, (Figure VI-3). The cable and service box were then brought to the end of the pier. On May 14, 1982, the wave activity settled sufficiently to attempt the installation. The CRAB was driven offshore with the instrument and positioned about 200 feet south of the end of the pier. Three divers and a boat operator entered the surf in a Zodiac and motored underneath the pier. The service box, with its 80 feet of unarmored cable secured inside, was lowered into the Zodiac and then motored towards the CRAB -- pulling the cable behind it. The service box was carried by a diver below the rear of the CRAB and brought underneath the center of the vehicle. In what became the only difficult phase of the operation, the service box was pushed up into the cradle oe the cable mated to the instrument. Large, long period swell made this maneuver both frustrating and often dangerous -- as the sharp corners of the cradle feet pcsed a hazard to _ the divers. The cable was secured to the bottom of the CRAB using a prussick knot and the vehicle was driven towards the installation site -- pulling out the cable. Floats were placed every 80 feet along the cable from the end of the pier. = Ill = Once at the site, originally marked by a buoy, the instrument was lowered into the water. Divers manevvered the instrument between the two rear legs of the CRAB to the seafloor, detached the lines from the CRAB to the cradle and cable, and the CRAB drove away a short distance. A four-foot screw anchor was turned into the sandy bottom approximately three and a half feet from the end of each arm and chain was attached from each arm to its respective screw anchor. The chains were secured taut by a chain binder and each rested at about a 45 degree angle to the seafloor. A fifth screw anchor and buoy was next installed twenty feet away from the DPG and a heavy line secured between this anchor and the cradle. Satisfied with the instrument installation, the buoys were released from the cable and work commenced at the pier. The cable had to be secured under the pier and prevented from chafing on the cement piling jackets. The cable descended from the pier deck inside a stainless steel case along the northeastern-most piling. A steel cable was looped around the base of this piling and attached to a wire jacket that cinched the cable under tension. To prevent chafing about the south pilings among which the cable passed, a long pipe was jetted between the two southeastern-most pilings and a similar steel line and wire jacket attached between the pipe and cable. The cable began to bury itself into the sand within hours of the deployment. = isi The cable leads were interfaced with FRF power and data-logging equipment and regular data recording commenced that evening. B. Instrument Orientation The orientation of the instrument with respect to magnetic north was determined using a submersible digital compass and conventional diving compasses. The digital compass was mounted at the end of a five-foot length of aluminum angle. One diver recorded the value indicated by the compass while another diver held two feet of the free end of the angle onto the top of each PVC arm of the instrument. In this way, the digital compass was at least six feet from the steel cradle. Compass headings were recorded for each arm twice -- once by each of the two divers -- and then averaged. The orientation of each arm was also measured by securing a diver's compass around the end of an arm using the compass wrist strap. . Measurements were taken three times for each arm using two different compasses and then averaged. All of the values recorded for each technique along each arm agreed reasonably well within a technique. The wrist compass, strapped around an arm, indicated the heading perpendicular to the arm. Accordingly, ninety degrees was subtracted from each wrist compass reading to give the heading of the arm. 5 tall, = As an experiment, the divers' compasses were placed on an arm above the end of the steel channel that holds the arm. The compass was then slid towards the end of the arm. The heading changed as the compass was slid across the end of the steel channel and then remained relatively stable. It was therefore thought at the time that the readings taken at the ends of the PVC arms were sufficiently far from the steel cradle to avoid any bias of the divers' compasses. However, aS can be_ seen from Table 6.1, this was not true. Since each arm is perpendicular to its neighboring arm, each of the compass readings are restrained to be 90 degrees apart. Although the digital compass measurements approximate 90 degree separation, those of the wrist compasses clearly do not. TABLE 6-1: ORIENTATION HEADINGS OF THE DPG ARMS WRIST COMPASS DIGITAL COMPASS RESOLVED apparent actual apparent actual average 241.75 151.75 61.75 331.75 i Headings are with respect to magnetic north, 6/15/82. = diese This directional anomaly was resolved using a_ technique suggested by Dr. Robert Dean (personal conversation). The apparent (biased) direction, 8, , indicated by the compass for each arm n, can & Compass needle FIGURE VI-4: Typical influence of the steel cradle upon the magnetic compasses used for orientation measurements. - 116 - be expressed in terms of the actual orientation of that arm, 3p » and the error associated with that arm, e, , that is introduced by the metal mass of the cradle: he eget (6.1) Since the compasses were placed upon each arm at about the same distance from the center of the instrument, and if one assumes that the effect of the metal mass upon the compass readings is the same for each arm (i.e., radially inward), then the errors associated with each of two collinear arms should be equal and opposite in _ sense. (See Figure VI-4). Accordingly, the sum of the errors associated with the reading for each arm should equal zero; 4 ene 0 (6.2) If one expresses the actual orientation of each arm in terms of the orientation of the arm with the smallest value of apparent direction, Equation 6.1 may be written as: Eh Saas (6.3a) 4 (6. 3b) = NG) Bay = ebe, ft eOo ie 1 i (6.3c) eS B, ae ATMOS" tr E5 (6.34) 2 The sum of Equations 6.3 a through d is: a Rigid lace € «4 n=1 ‘ 3 n=1 . From Equation 6.2, 4 1 v 8, a a } BF (6.5) n=1 and the corresponding orientation for each of the other three arms may be found by subtracting Equations 6.3 from 6.1. The corrected orientation headings for each arm and for each type of compass used ere listed in Table Bei Somewhat surprisingly, the agreement between the corrected averages of the arm headings as found using the expensive digital compass and the simple wrist compasses is very good -- within 0.14 degrees of one another. The final orientation of each - 118 - DPG arm was taken as the average of the corrected values found from the digital and wrist compass measurements. The values of each correspond to the heading towards which the end of each arm points with respect to magnetic north. The values were corrected to true north using the 1982 value of the variation for Cape Hatteras, N.C. This investigation indicates the importance of careful redundant checks of instrument orientation when working near a steel structure. The analysis technique outlined here requires at least one pair of compass measurements made on opposite sides and equidistant from the appoximate center of the metal structure. The investigation suggests that simple wrist compasses may be adequate for determining instrument orientation if special care istaken during the measurement and interpretation of the results. C. First Month's Inspection The instrument was re-inspected on June 15, 1982 -- one month after installation. The cradle and instrument had settled into the seafloor only four or five inches with minimal disturbance to the bed around the gauge. The cable had buried itself deeply immediately outside of the service box. The system's anti-fouling agents had thus far worked excellently. Slaten D. Results of DPG Data Analysis 1. Introduction Multiple sets of data were analyzed to determine the integrity of the gravity wave information obtained from the DPG. Although output was available from the facility's HF radar system, there were no other functioning in-situ directional wave monitors at the FRF during the weeks after the instrument installation. Hence, DPG directional information was compared with visual and radar estimates. Wave height and period could, however, be compared with CERC Baylor gauge data from near the end of the pier. The data were also inspected for irregularities in the time domain that could signal system malfunction. 2. Time Domain Signal Analysis The five transducers' records corresponding to a single set of wave data were input to the DPG software package and scanned for signals beyond three standard deviations from the mean of the record. The means were then re-calculated and subtracted from the records which were then converted to pressure signals. (See Sections IV.D.1-3.) = 1h 2Q0) = In each data set analyzed, the number of points beyond the three standard deviation limit was satisfactorily small -- less than one percent of the record, as expected. The mean of channels dP2, dP3, and the absolute agreed well between data sets, (possibly indicating minimal instrument tilt over time due to settling -- see Section IV.D.4). The means of dP1l and dP4 often varied between sets, however. It was expected that the mean of dP4 might vary given the signal drift observed during bench calibration. Similarly, it was not surprising to encounter difficulty with dPl after considering its irregularities on the bench. The mean values of the absolute records predicted tide levels reasonably well as is shown in Table 6-2. DPG tidal calculation is compared with that determined by a stilling well located near the middle of the pier. Differences might be attributed to temperature effects upon the absolute sensor, (see Section V.C.6). Atmospheric pressure fluctuations were accounted for. The mean values of dP2 and dP3 differ significantly from these two channels' tare values recorded on land. In-situ mean values are 2.31 V and 2.56 V for dP2 and dP3 respectively, and 0.60 V and 0.71 Von land. Both subaerial.and subaqueous checks were made with the same 1100 foot long cable. The subaerial tare values were checked on a hot afternoon and the ocean was some 8°C cooler. But it was not likely that this rise in mean voltage was due to temperature changes since one expects a voltage drop with a decrease > ALZAL TABLE 6-2: COMPARISON OF TIDE LEVEL oF 1982 AMBIENT CONDITIONS DATE TIME P (mb) 5/18 0700 1300 5/19 0700 1300 5/20 0700 1300 5/21 0700 1300 5/22 0700 1300 5/23 0700 1300 5/24 0700 1300 1018.0 1020.0 1018.3 1015.5 1013.2 1019.5 1018.0 NOTES : FRF data is from stilling well at Tide elevations are referenced to DPG Ppe(abs) = 1.32 psi. TIME is Eastern Standard. Temperature is for sea-water. in temperature in the present DPG configuration, (Section V.C.6). The difference could indicate slanted installation of the instrument. The changes in mean voltages suggest that arms 2 and 3 could be tilted 9.57. andy lleseabove= the horizontal, respectively; (from Equation 4.34). This could be confirmed by comparison with dPl and dP4; however, neither of these channels show a clear trend in the change of mean value between land and sea. A portion of the time record of one data set is shown in Figure VI-5. The mean value has been removed from each record and the signs of dPl and dP2 have been reversed. The dPl signals have been multiplied by the channel 1 calibration factor of 1.65. The FIGURE VI- Portion of time record from DPG signals. 0.00 00 200 -00 ~ 40.00 50 .00 TIME (seconds } - 123 - absolute record corresponds to pounds per square inch and the signals of the differential records to pounds per square inch differential per inch of gage length. It is immediately obvious that the signal of dPl is extremely erratic with high frequency energy that would alias into the energy spectrum.At other times, it agrees in form with dP3 satisfactorily although it is shifted downwards because of the large mean value subtracted from the record. This large mean is apparently the result of the large positive-valued high frequency oscillations. This disturbance is intermittent and does not appear in all of the records from dPl. These high frequency oscillations have never been observed on the strip chart output at the FRF, and so it is possible that the problem lies within the digitization of the signal. The records of dP2 and dP4 agree well as expected for two collinear gauges. There are slight phase and amplitude differences as would be expected since the two gauges are separated in space a finite amount. There is reasonable phase agreement between the dP2, dP3, and dP4 signals with those of the absolute gauge -- as best as can be seen. Again, one expects a ninety degree phase difference between the absolute and differential signals. 2 ie The "graininess" of the absolute gauge signal is due to resolution limitations of the transducer and digitizer. It is reasonable to conclude from inspection of the raw data, then, that the dPl records should not be included in the spectral analyses, and that less faith should be placed in dP4 because of its tendency to drift (as is exhibited by its changing mean). If these two channels do not provide valid data, it is not possible to generate the water surface curvature terms as described in Chapter IV with any confidence. 3. Record Length In beginning the conversion of the data to the frequency domain, it was discovered that the DEC-10 computer system could not handle the 17 minute long four-samples-per-second data records, (4096 points). So the data size was halved by averaging two adjacent points in the time. series. The Fast Fourier Transform, then, operated upon a 17 minute record with an effective sampling rate of two Hertz. (The corresponding Nyquist frequency was still safely above the two rad/sec cut-off frequency used in the analysis program.) The number of data points in the time series was halved after the initial scan for bad points and calculation of the record mean. = 125 = It was discovered that this modification was very important. The results of the analysis of DPG data varied considerably between a 17 minute long record with an effective sampling interval of 0.5 seconds compared to the analysis of an 8.5 minute long record with 0.25 second sampling. Further, there are considerable differences between the analysis results of the first 8.5 minutes of a record compared to the last 8.5 minutes. This variability may be due to sampling and the confidence limits on the spectrum. Figures VI-6 through VI-8 are copies of the analysis output for one data set analyzed with a 17 minute record, the first 8.5 minutes of the record, and the last 8.5 minutes, respectively. The 17 minute record with 0.5 second sampling interval block-averages 8 adjacent frequency bands compared to 4 bands for the 0.25 second sampled records. The spectra developed from the 17 minute long record, then, is more stable than for the 8.5 minute long record, yet retains the same frequency resolution. Figure VI-9 and Figure VI-10 illustrate the energy and non-smoothed peak-energy directional spectra for each case. The analysis results most closely match other observations made at the FRF when the full 17 minute long record with effective 2-Hertz sampling is utilized. Table 6.3 lists the results of each type of analysis and compares the results with independent FRF observations over a period of four days. = 1126 - UNIVERSITY OF DELAWARE DEPARTMENT OF CIVIL ENGINEERING DPG DIRECTIONAL WAVE MONITOR / FRF, DUCK, N.C. DEV YR MO DAY TIME Nett 8 2 Ge Ait 7 10) 121 82 Giratal 7 O 141 82 6 elit 7 (0) 4096 POINTS ANALYZED AT .50 SECOND SAMPLING 8 BANDS BLOCK AVERAGED GAGE NUMBER 2 8 LOW truncations; 6 HIGH truncations Mean= 2.299 S.Dev= 0.09652 Lower Limit= 2.010 Upper Limit= 2.589 GAGE NUMBER 3 O LOW truncations; 8 HIGH truncations Mean= 2.039 S.Dev= 0.19138 Lower Limit= 1.465 Upper Limit= 2.613 GAGE NUMBER 5 O LOW truncations; 1 HIGH truncations Mean= 2.364 S$.Dev= 0.03900 Lower Limit= 2.247 Upper Limit= 2.481 TIDE LEVEL IS 0.824 FEET. POSSIBLE INSTRUMENT TILT (deg) DP2 DP3 -0.061 -3.365 Significant Wave Height (ABS gage) = 4.32 feet. Effective period = 7.817 seconds. Maximum Energy located at bands: 11.070 exceeds average energy by 715.00 % 10.189 exceeds average energy by 266.13 % 12.118 exceeds average energy by 194.16 % 13.386 exceeds average energy by 159.03 % 8.790 exceeds average energy by 115.97 % 8.225 exceeds average energy by 108.46 % Compass heading from which waves propogate Band 11.070 secs: Greatest Energy at 73. deg Band 10.189 secs: Greatest Energy at 71. deg Band 12.118 secs: Greatest Energy at 67. deg Band 13.385 secs: Greatest Energy at 69. deg Band 8.790 secs: Greatest Energy at 69. deg Band 8.225 secs: Greatest Energy at 75. deg FIGURE VI-6: DPG analysis results using the full record length of 17 minutes with effective 2 hertz sampling. Mean= Mean= Mean= WIDE VEE, POSSIB DP2 -0.065 Effective period = Max imum Compass Band Band Band Band Band DPG DIRECTIONAL WAVE MONITOR / FRF, DEV YR abe 232 UUs 23 141 82 GAGE NUMBER 2 7 LOW truncations; 2.299 S.Dev= GAGE NUMBER 3 O LOW truncations; 2.037 S.Dev= GAGE NUMBER 5 O LOW truncations; 2.360 S.Dev= EL LE DP3 Ses = 127 UNIVERSITY OF DE LAWARE DEPARTMENT OF CIVIL ENGINEERING MO 6 6 6 0.10032 0.18856 0.03693 IS 0.743 FEET. DAY TIME 11 U 0 vi 7 fe) 11 7 Oo 2048 POINT 2 HIGH truncations Lower Limit= 4 HIGH truncations Lower Limit= 4 HIGH truncations Lower Limit= INSTRUMENT TILT (deg) DUCK, N.C. S ANALYZED AT 4 BANDS 1.998 Upper Limit= ee 4aat Upper Limit= 2.250 Upper Limit= Significant Wave Height (ABS gage) = 4.24 feet. 7.206 seconds. Energy located at bands: 11.011 exceeds average energy by 435.16 % 12.047 exceeds average energy by 343.94 % 8.192 exceeds average energy by 233.40 % 10.139 exceeds average energy by 138.87 % 9.394 exceeds average energy by 136.97 % 6.872 exceeds average energy by 127.69 % heading from which waves propogate 11.011 secs: Greatest Energy at 77. deg 12.047 secs: Greatest Energy at 77. deg 8.192 secs: Greatest Energy at 71. deg 10.138 secs: Greatest Energy at 81. deg 9.394 secs: Greatest Energy at 61. deg 6.872 secs: Greatest Energy at 61. deg Band FIGURE VI-7: (4 hertz sampling). .25 SECOND SAMPLING BLOCK AVERAGED 2.600 2.603 2.471 DPG analysis results using the first 8.5 min- utes of the record, Zon UNIVERSITY OF DELAWARE DEPARTMENT OF CIVIL ENGINEERING DPG DIRECTIONAL WAVE MONITOR / FRF, DUCK, N.C. DEV YR MO DAY TIME Aidit 182) Swi 7 fe} 121 82 Gira it 7 oO 141 82 Saati 7 O 2048 POINTS ANALYZED AT .25 SECOND SAMPLING 4 BANDS BLOCK AVERAGED GAGE NUMBER 2 O LOW truncations; 4 HIGH truncations Mean= 2.300 S.Dev= 0.09259 Lower Limit= 2.022 Upper Limit= 2.578 GAGE NUMBER 3 O LOW truncations; 4 HIGH truncations Mean= 2.041 S.Dev= 0.19418 Lower Limit= 1.458 Upper Limit= 2.623 GAGE NUMBER 5 O LOW truncations; O HIGH truncations Mean= 2.367 S.Dev= 0.04066 Lower Limit= 2.246 Upper Limit= 2.489 MBDEVEEVEE MIS On904) REET: POSSIBLE INSTRUMENT TILT (deg) OP2 DP3 -0.058 Sonic Significant Wave Height (ABS gage) = 4.43 feet. Effective period = 8.245 seconds. Maximum Energy located at bands: 11.011 exceeds average energy by 931.01 % 10.139 exceeds average energy by 301.30 % 13.299 exceeds average energy by 291.62 % 8.752 exceeds average energy by 199.04 % 7.699 exceeds average energy by 185.02 % 12.047 exceeds average energy by 118.44 % Compass heading from which waves propogate Band 11.011 secs: Greatest Energy at 73. deg Band 10.138 secs: Greatest Energy at 63. deg Band 13.299 secs: Greatest Energy at 67. deg Band 8.752 secs: Greatest Energy at 75. deg Band 7.699 secs: Greatest Energy at 71. deg Band 12.047 secs: Greatest Energy at 35. deg FIGURE VI-8: DPG analysis results using the last 8.5 min- utes of the record, (4 hertz sampling). = 20n= 6711”82 o700 EST 200 47 MIN RECORD —— j 8.5 MIN,» 1st HALF —---- 9.5 MIN, 2nd HALF ——-— ENERGY -SPECTRA of DISPLACEMENT TERM ENERGY (in? sec) re 4.50 8.00 8 4 i Dee.° 0.25 0.50 O75 4.00 41.25 41.50 4.95 2.00 | euler ais ¢ wlPREGUENCY Mrad/sec Qi. ck ul | FIGURE VI-9: Block-averaged energy spectra of water surface displacement for a 17 minute long record and 8.5 minute long records. 2130) = 6714782 0700 EST 17 MIN RECORD ——— 8.5 MIN» 1st HALF —-—- 8.5 MIN» 2nd HALF ----- g wo 4.50 3.00 -~ 1) YU Si) N € wv wy > © [a uJ Zz uJ 180 DIRECTION (deg) FIGURE VI-10: Non-weighted directional spectra of peak energy band (11.0 seconds) for a 17 minute long record and 8.5 minute long records. =) ign COMPARISON OF DPG RESULTS WITH FRF OBSERVATIONS 8 June - 11 June, 1982 FRE record RECORD OBSERVATIONS 59° Ba) (50°) 1.30 ; fenton 8.19 . 8.00¢ 59° St eae L626 Lose 6.39 : 9-57 ¢ 65° 1 Ge |. 10.14 69° iL pil bah 5h oul? 1.74 12505) 7M 1.35 ibal: Ok NOTES: "dirs" listed is the principal direction (peak energy), TN. "Hsig"” is the significant wave height in meters. "period" corresponds to the frequency band of greatest energy. @CERC Radar (+ 2° ) bViswal estimate from the end of the pier “CERC Baylor Gauge near the end of the pier | 9 June 82 O800 EST ei ita re , ae : a FIGURE VI-11: Photographs of CERC radar screen illustrating wave activity from June 8 - June 11, 1982. Distances indicate offshore range of radar. - 133 - 10 June 82 0740 EST 11 June’ 82 OGIOIESik a7A=) amie FIGURE VI-11 (Continued). = Ae 4. Capability of the DPG System The DPG results shown in Table 6.3 were generated using differential channels 2 and 3 and the absolute channel. These results lend encouraging evidence that the DPG is capable of accurately detecting wave direction. The radar pictures to which the DPG results were compared are shown in Figure VI-11. One can appreciate that it is often difficult to accurately resolve an approximate direction from the radar images; nea City.) faites impossible during low wave activity or in the absence of capillary waves of appropriate frequency. Hence, the small differences between the reported wave direction from the DPG and the estimate from radar is likely attributable to the poor resolution of the radar images. It is instructive to note the accuracy of the visual estimates of wave direction. Anyone who has tried to visually resolve the direction of a wave train, especially that of short-crested waves, appreciates the difficulty in making visual directional estimates. The significant height and period of greatest energy reported by the DPG and the Baylor gauge near the end of the pier agree well. Slight differences may be attributed to the different locations, measurement Buechiiauest and analysis details of each of the two instruments. Analysis of the Baylor gauge data is carried out upon a 17 minute long record of one-quarter second sampling. = i135) = 5. Directional Spectra Smoothing The analysis results of six data sets from the DPG over a four day period are presented in Appendix A. The analysis was carried out using the absolute pressure gauge and differential gauges dP2 and dP3. The smoothed directional spectra of the six peak energy bands are illustrated for each data set. In the development of these results, the directional spectra is expressed as the partial Fourier series in terms of the wave direction © as in Equation 4.14: N N = i .) S(o,8) W369) + ) Wan cos n@ + } Wop. sin n n=1 n=1 where N=2. This is smoothed by the weighting function Sie a ; 3 Cos 58 - 6) (6.6) such that wo = 1,.w, = 2/3, and Wy = 1/6. Such smoothing eliminates negative energy side-lobes in the directional spectra by imposing an always-positive function of the same angular frequency upon. the directional distribution (Longuet-Higgins, Cartwright and Smith, 1963). The function A eee” bé (6.7) - 136 - is first considered, and then expressed in complex form: eibe ie -ipe}* Expanding, ‘ n, [ace by este) ope). ABS 0)| Equation 6.7 can be written as: B = glcos 4b8 + 4cos 2b0 + 3) Letting b=1/2, and factoring 3, the function becomes: 3 4 at = g BQ + 3 cos @ + 3 cos 26) The weighted angular distribution must satisfy the requirement 277 S(o) =| S(o,8) dé to retain the original energy calculated in the must equal 8/3. and 1/6 in accordance with the definition of the Fourier (6.8) (6.9) (6.10) spectra. Hence, B The coefficients Wo, wy, and wy are taken as 1, 2/3, coefficients - 137 - described in Equations 4-18 through 4-24. If the first seven directional Fourier coefficients, (i.e., N=3), were developed, then the directional spectra might be smoothed by a weighting function 16 eae e Ce Bee &) (6.11) such that wo = 1, w, = 66/77, wo = 15/28, and w3, = 5/21. 6. Redundancy of dP2 and dP4 Measurements If differential pressure gauges dP2 and dP4 work correctly, then the results of directional analysis of wave data using either of these two collinear gauges should be nearly identical. To check this, a number of wave records were analyzed using the signals from the absolute pressure channel, dP3, and dP2, and then the signals from the absolute, dP3, and dP4 channels. Two of the results are shown in Figures VI-12 and VI-13. Figure VI-12 illustrates the energy spectrum and the non-smoothed directional spectra of the first two peak energy bands for one data set using both combinations of gauges. The energy spectrum, taken from the signals of the absolute gauge, is the same for either gauge combination. There is good directional agreement in this case of well-defined swell. Figure VI-13 illustrates the energy spectrum and non-smoothed directional spectra of the first two peak energy bands for another data set. The s11138"= 6/03/82 0700 EST ENERGY (in?/sec ) : 7 DIFF GAUGES 2 & 3 —— DIFF GAUGES 3 & 4 ENERGY (in? sec) 420 480 DIRECTION (deg) FIGURE VI-12: Non-weighted directional spectra of the first two peak energy bands using ABS, dP2, dP3 gauge combination and ABS, dP4, dP3 gauge combination. Case 1: Well-defined swell. Block-averaged water surface displacement energy spectrum shown in inset. - 139 - 5714782 1900 EST 0.70 Si4ve2 1900 EST 0.60 0.50 ENERGY (1n?/eec } 0.40 0.30 ENERGY (in?. sec) 0.20 0.410 epi alg ca 0 60 420 480 240 360 DIRECTION (deg) FIGURE VI-13: Non-weighted directional spectra for the first two peak energy bands using ABS, dP2, dP3 gauge combination and ABS, dP4, dP3 gauge combination. Case 2: Omnidirectional sea. Block-averaged water surface displacement spectrum shown in inset. = allio agreement between different combinations of gauges is not as good for this set that represents a "ragged" sea state. This is most probably because each of the two gauges, separated a finite distance, independently measure more slightly different wave activity than in the first data set shown. For such a confused sea state of relatively short period waves, it was not possible to verify which channel, dP2 or dP4, gave the more accurate estimate of wave direction (if indeed there was any one principal direction). Accurete radar and visual observations are practically impossible during such conditions. As expected, the omnidirectional energy spectra generated from the DPG data for this confused sea _ state agrees in form with that of the computer-simulated case of one wave frequency with two directions as shown in Figures IV-10 and IV-11. 7. Energy Spectra from Differential Pressure Gauges Figure VI-14 illustrates one record's wave energy spectra generated from the absolute pressure gauge and the water surface slope energy spectrum from each of the two perpendicular differential pressure gauges dP2 and dP3. The record was taken during wave activity from the northwest -- the direction in which DPG arm 3 is oriented towards. Accordingly, one observes that there is considerably more energy contained in the slope spectrum from 4dP3 than from dP2. This is because there are relatively small slope (and pressure) differences along the wave crests and troughs which are iit < 6709/82 0700 EST DISPLACEMENT —--—- SLOPE (dP3) i OlORERmGdia2:) ENERGY (sec - wv) v a“ nN c wi —_ > 2) a uJ Zz uJ O250' - Gs) 32.00) 254025) 12.50 FREQUENCY (rad/sec ) FIGURE VI-14: Block-averaged power spectra of water surface disp- placement (developed from the absolute pressure gauges) and water surface slope (developed from differential pressure gauges dP2 and dP3). - 142 - aligned with arm 2 whereas there are relatively large slope (and pressure) differences along the wave ray -- aligned with arm 3. (See Figure VI-15.) As is illustrated in Figure VI-14, one expects that the _ wave frequencies of greatest energy should be the same for both the water surface displacement and slope terms. It is instructive to note, however, that greater energy appears in the higher frequency bands of the slope spectra than in those of the wave rycyprF vI-15: Wave crest ap- 3 : proximately aligned with spectrum. This too is an expected apoeaee result since the energy spectrum of of slope (developed from a differential pressure signal) differs from that of water surface displacement (generated from the absolute pressure signal) by a factor of wavenumber-squared. The energy spectrum of the water surface displacement is developed through the frequency-by-frequency division of the dynamic pressure energy spectrum by the specific gravity of seawater (squared) and the square of the pressure response function, Kp. The water surface slope energy spectrum is similarly developed through the division of the differential pressure energy spectrum by the squares of the specific gravity of seawater and the pressure response function. The energy - 143 - spectrum of the water surface displacement is then as Equation 4.46: s no Dae (4. 46) and the energy spectra of the water surface slopes are as Equations 4.47 and 4.48: 2 iS) (o) = ce cone (4.47) ae H- 2 2 s (o) = =k’ sind (4.48) non 8 aay; Since wavenumber increases with wave frequency, energy leaked into the higher frequency differential pressure bands is enhanced in the generation of the water surface slope spectrum relative to the displacement spectrum. It is for this reason that the frequency bands of greatest energy are selected for directional analysis from the water surface displacement spectrum. (Spectral leakage is the "spilling" of energy from the frequencies that are actually present in the record to other frequencies. It occurs naturally in the analysis of a finite length of record due to the inability of the FFT to exactly resolve the spectral content of a time record on the frequency axis.) = ib From Eqns. 4.46, 4.47, and 4.48, one might expect that the sum of the orthogonal slope energy spectra divided by the square of the wavenumber would be equivalent to the water surface displacement spectra for some frequency of frequencies, (Section IV.D.9). However, this would be true oniy for an idealized narrow wave spectra with no frequency or directional leakage. 8. Directional Estimates without the Absolute Pressure Gauge Estimates made of the wave direction without the absolute pressure gauge are generally unreliable. Typical results calculated using Equation 4.52 and the dP2 and dP3 signals for the data sets illustrated in Appendix A are listed at the end of the appendix. Equations 4.52 and 4.54 are valid if there exists only one wave direction per frequency. When waves of one frequency arrive at slightly different directions and spectral frequency bands are contaminated by leakage, the validity of Equations 4.52 and 4.54 fails. As a general statement, it can be said that these equations do not usually provide reliable estimates of the principal wave direction in typical ocean wave analysis. The estimates might be improved by some sort of data conditioning. = ibis 9. Arithmetic Development of the Curvature Terms For investigative purposes, it was attempted to create the water surface curvature terms as described earlier. Typically, this was only done along the y-axis using the dP2 and dP4 signals since DP2»DP4 20.00 30.00 40 .00 50.00 60.00 70.00 TIME (seconds ) 0.00 10.00 FIGURE VI-16: Typical portion of time series of dP2 and dP4 "slope" signals with the associated dP4-dP2 "curvature" signals. Signal of dP4 is dashed line. the digitized x-axis signal of dPl was erratic. The terms were arithmetically created in the time domain through the difference of the dP2 and dP4 signals after adjacent values in each channel's record were averaged and the number of points in the 17 minute long - 146 - record halved. A portion of the resulting y-axis curvature term in the time domain is shown in Figure VI-16. The time series was processed by the FFT and the energy spectra developed. Figure VI-17 illustrates the energy spectrum of the curvature term compared to that of the displacement term. The wave frequencies corresponding to peak energy levels of the data set correspond well between the spectra. The curvature spectrum contains greater energy in the high frequency bands than the displacement spectrum. This is expected since the curvature spectrum differs from the displacement spectrum by a factor of the fourth power of the wavenumber. Despite the reasonable appearance of the curvature spectra, the directional Fourier coefficient b3, developed using the water surface curvature along the y-axis, was at least an order of magnitude larger than the other directional coefficients for each case tested. The dominance of this term would create three high energy peaks in the dirctional spectra and invalidate directional estimates. The curvature terms were also developed in the time domain before adjacent values in the record were averaged. The results were similar. The inability to generate higher order directional Fourier coefficients through the arithmetic creation of the water surface curvature terms is not surprising. The DPG was developed upon _ the - 147 - 5719/82 0700 EST sec ) ENERGY (in2 sec) N \ c ~=i —_— > re) (a4 LJ =z uJ 0525 90.50) -O.¢S) 1.00). 1,25" 4.00 FREQUENCY (rad/sec ) FIGURE VI-17: Block-averaged power spectra of water sur- face displacement and water surface curvature terms. = 148 - premise that there is inherent error in the creation water surface slope terms through the subtraction pressure values. Similarly, the attempt was made create the very small-valued water surface curvature of small-valued of two in this terms the subtraction of two small differential pressure values. large case to through = Wie) = CHAPTER VII RECOMMENDATIONS During the design, development, testing, installation, and evaluation of the DPG directional wave monitor system, some problem areas and phenomena of interest were cited for further investigation and/or development. Foremost, thorough comparisons should be made of the DPG analysis results with those of other in-situ directional wave monitors at the Field Research Facility -- particularly those ee eeuments! that typically Penetate water surface slope terms through the subtraction of signals from adjacent pressure sensors. Also, the digitization of the dPl signals from the DPG should be checked and/or differential transducers 1 and 4 should be repaired or replaced. There are certain design characteristics of the first DPG prototype that might be investigated and improved. One might re-design the fuselage to align the differential pressure sensors exactly upon the x- and y- axes. In the first prototype, as installed at the FRF, the dP2, dP3, and dP4 sensors are misaligned by one to two degrees as discussed in Section III.C.1. The instrument = ils) = might be re-designed such that the arm and center sensors are also at the same elevation above the seafloor. However, for the first DPG prototype, the nine inch difference in height between the sensors leads to very small error in the calculation of an average pressure response function used in the development of the water surface slope terms. (See Section III.C.2.) In water depths as shallow as 10 feet (3.1m), the error is still small -- less than three percent for waves of three second period. The instrument might be re-designed such that the lengths of each tubing used in the sensor systems are identical. This would help ensure that the response time of each channel is identical and that there is no difference in response time for the loading of an arm sensor compared to a center. sensor. This would eliminate differential pressure drift induced by changes in ambient temperature, thus disabling the instrument to measure ambient water temperature. The arrangement of the transducers inside the water-tight cylinder might be re-designed to allow servicing of individual pressure transducers without the need to bring the entire instrument to the surface. Such a design change could, however, add additional problems to the dependability of the transducers since this would most probably require the addition of underwater-pluggable connectors for each transducer. The present instrument utilizes one such connector that is mated only above water in routine maintenance. Sahai For DPG operation in water depths of 20 feet, the absolute pressure transducer should be changed from 50 psia rated capacity to 30 or 35 psia to improve resolution. Different designs of the isolation sensor diaphragms could be considered in order to create a sensor that is easier to back-fill and less difficult to machine. When calibrating the sensors, an oscillating pressure pump used in conjunction with the calibration system described in Section V.C.1 might better estimate the system's dynamic loading characteristics. Temperature effects upon _ the transducers and their respective sensors should be investigated more thoroughly during instrument calibration. The effects of vortex shedding about the sensor diaphragms might be investigated. The sensors could be re-configured within the PVC arms and fuselage to minimize vortex shedding effects if they are found to be of sufficient magnitude for some application of the DPG. Tests in the large wave tank at the Coastal Engineering Research Center suggest that the configuration of the sensors within the arms is important for accurate directional estimates, (Section V.D.3). Although a tripod was at one time considered for the instrument cradle, the four-legged cradle used for the DPG at the Field Research Facility proved stable and easy to maneuver in the installation and first weeks of operation in the field. Future DPG systems may retain this four-legged cradle or experiment with a > 152 = tripod. Any sharp corners on the cradle should be rounded and smoothed for safety. The DPG might be better protected against high voltage transients, (i.e., lightning), by bonding the steel armor of the cable to the water-tight instrumentation cylinder at the seaward end and to the ground system of the FRF at the landward end of the cable, Gi Anderson Plumer, Lightning Technologies, 1G NS5 5 personal conversation). Various configurations of the DPG arms used for differential pressure measurements might be considered for investigative purposes. Intuitively, one might expect that the most effective directional measurements made by the DPG would be for the case of a maximum signal reported by each differential pressure transducer. This requires that the differential transducers be oriented 45 degrees to the wave ray or crest. In this way, the peak signals from each transducer would be of the same amplitude, and for sufficiently large wave activity, above the noise level of each transducer channel. ise the incident wave direction at a site was normally distributed about the shore normal, then one might expect the most effective directional measurements to neumade by a DPG with its arms oriented 45 degrees to the shore normal. The DPG prototype was placed at the FRF (with little consideration for orientation) such that the x-axis (dP1 and dP3) arms and the y-axis (dP2 and dP4) arms are 17 and 73 degrees from the shore normal, respectively. Various configurations lh SB of the arms with respect to one another might be considered. The angle between arms might be varied to "tune" the DPG to the incident wave field -- much the same as a directional antenna. Changes in arm orientation could also permit the estimation of higher order directional Fourier coefficients, (see Appendix E). In future versions of the DPG system, wave data could be transmitted to ship or shore by telemetry -- eliminating difficult cable installations. Data might also be integrated in-situ and reported in concise segments by telemetry or on tape. Present coastal field measurements are often made over long periods of time, where the results of such measurements represent coastal processes that are essentially integrated over time. In such cases, specific hour-by-hour wave data may not be necessary or even desirable. Concise, integrated wave information is just as useful. Software capability on site with the DPG could be developed to integrate large amounts of wave data and report one or two numbers (say, measures of i 5 Os Sxy) to characterize the wave climate over time, (Robert Dean, personal conversation). A technique has also been considered to directly measure water surface curvature using differential pressure gauges. This measurement technique could be developed and evaluated in the hope of accurately developing higher orders of directional Fourier coefficients from directly measured data. = eh = Various types of directional data analysis schemes should be investigated. Among them are the Maximum Likelihood Method, (Clarke and Gedling,1981; Jefferys, et.al.,1981; Goda,1981; LaCoss,1971). and the estimate of higher order directional Fourier coefficients as alluded to in Section II.B.1 and discussed in Appendix E. Proper conditioning of DPG data might also allow directional estimates made without the signal of the absolute pressure gauge. In all future developments of the DPG, as with any well-designed ocean instrument, careful consideration must be given to the problems of corrosion, biological fouling, scour and instrument settlement into the seabed, installation and maintenance, electronics failure and noise, and interference from local marine activity. The limitations of directional wave spectra analyses should always be recognized when dealing with the data obtained from the instrument. =D as CHAPTER VIII CONCLUSIONS This thesis has presented a description of the design, development, and evaluation of a new type of directional wave monitor. The work undertaken in the preparation of this’ thesis indicates that differential pressure transducers used with an absolute pressure transducer, as employed in the DPG directional wave monitor, appear capable of generating accurate estimates of wave direction using the first five directional Fourier coefficients as determined from direct measurements of water surface displacement and slope. This conclusion is based upon the comparison of analyzed data from the DPG with estimates from the CERC radar located at the CERC Field Research Facility, Duck, N.C. The relatively small dimensions and light weight of the DPG system, (two-fifths the size and less than one-seventh the weight of conventional pressure sensor arrays), allowed a smooth, relatively simple field installation. The DPG, as designed, should similarly allow for easy retrieval and re-deployment of the instrument for maintenance purposes. = 156 oa It has been demonstrated that the differential pressure transducer can be considered to be an inherently more effective instrument for determining wave direction. The design is well suited to the measurement of water surface slope and the response of surface slope with depth is a maximum over frequencies that are more representative of typical ocean gravity waves than the response of conventional absolute pressure transducers. In the development of the DPG system, it was discovered that careful attention must be given to the diameter of the tubing and to the nature of the back-filling fluid used in the transducers’ sensors. This is to ensure a small response time for each transducer. The DPG prototype, as installed at the CERC Field Research Facility, utilizes gin and 1/8 inch I.D. flexible tubing in its sensor systems. Ambient temperature changes induce differential pressure changes as measured by the transducers since the tubing used in the arm sensors is four times the length of that of the center sensors. A simple bench-calibration device was developed to monitor the response of the transducers and sensor systems to applied loads. It is important that the load be distributed uniformly across the sensor diaphragm. Bees a Experiments conducted with the first DPG model in the t!arge wave tank at the Coastal Engineering Research Center were plagued by highly non-linear waves and the failure of three differential pressure channels. However, results from the absolute pressure gauge and one differential pressure gauge indicated the ability of the DPG to estimate wave height, period, and direction. The tests were also valuable in defining several important modifications required to improve the performance of the DPG system. Measurements of the orientation of the instrument were discussed and the importance of careful consideration of compass readings in the vicinity of steel structure was stressed. Although it initially appeared that diving compasses were placed upon the instrument sufficiently far from the steel cradle to avoid its Magnetic effects, redundant measurements of the instrument orientation indicated that the compass readings were biased. The error was resolved using a simple technique outlined in the thesis. It was suggested that measurements from simple wrist compasses, when taken and interpreted carefully, may be adequate in determining instrument orientation. The DPG utilizes four differential pressure gauges placed to the bow, port, stern, and starboard of an absolute pressure gauge such that there are two adjacent differential gauges along each of two perpendicular axes. The DPG system develops the first five directional Fourier coefficients using signals from the absolute = 158) < pressure gauge and one differential pressure gauge along each axis. The other differential transducers on each axis were installed for redundancy and for the generation of higher order directional Fourier coefficients. The absolute pressure transducer and one differential pressure transducer along each axis (dP2 and dP3) appear to work satisfactorily. The redundant differential pressure gauges dP4 and dPl intermittently exhibit drift and high frequency oscillation, respectively. The failure of either gauge invalidates reliable generation of higher order directional Fourier coefficients by conventional techniques as discussed in this paper. Accurate, reliable generation of the higher order (N=3) directional Fourier coefficients through the subtraction of collinear differential pressure signals -- similar to the generation of lower order directional coefficients through the subtraction of adjacent absolute pressure signals -- remains questionable. For well-defined swell, directional spectra generated from the signals of dP2, dP3, and the absolute gauge correspond well with the directional spectra generated from the signals of dP4, dP3, and the absolute gauge. There is less Abie for poorly-defined sea. Directional estimates made without the absolute pressure gauge signals are generally unreliable using techniques discussed in this paper. - 159 - Estimates of wave direction developed from DPG data agree best with those of. the CERC radar for a 17 minute long DPG record with 2 Hertz effective sampling and 16 degrees of freedom. Analysis results for an 8.5 minute record with 4 Hertz sampling and 8 degrees of freedom differ from the results of a 17 minute record depending upon which half of the record is analyzed. Possible modifications to the instrument design and recommendations for future DPG development have been outlined. The configuration of the DPG arms and the manner in which the data is processed, transmitted, and analyzed might be altered to obtain more accurate or effective directional wave data. The DPG directional wave monitor prototype has thus far provided reliable, accurate directional wave data through the use of a smaller and lighter instrument than conventional pressure sensor arrays. It generates directional wave spectra using data enaone directly measured instead of arithmetically created and could potentially develop higher order directional Fourier coefficients than conventional arrays. Overall, the DPG appears to be a promising advancement in the technology of directional wave measurement. = 160 = REFERENCES Aubrey, D.G., "Field Evaluation of Sea Water Directional Wave Gauges (Model 635-9),'' Woods Hole Oceanographic Institution No. 81-28; May 1981. Birkemeier, W.A., DeWall, A.E., Gorbics, C.S., and Miller, H.C., "A Users Guide to CERC's Field Research Facility," Misc. Report No. 81-7, p. 10,40; October 1981. Borgman, L.E., ''Confidence Limits for Ocean Wave Spectra," Geology Dept. Research Report 72-1, University of Wyoming; September; 1972. Borgman, L.E., "Directional Spectra Models for Design Use," Proc., Ocean Technology Conference, Houston, Texas; 1969. Bowden, K.F. and White, R.A., "Measurements of the Orbital Velocities Of Sea Waves and their Use in Determining the Directional Spectrum,'' Geophys. Journal Royal Astro. Soc., 12, pp.33-54; 1966. Cartwright, D.E. and Smith, N.D., "Buoy Techniques for Obtaining Directional wave Spectra," Buoy Technology, Marine Tech. Society; Washington, D.C., pp. 112-121; 1964. Chakrabarti, S.K., "Wave Train Directional Analysis," Jour. Waterways, Harbors, and Coastal Eng. Diverse AS CER Oi DP Use Peers Usy7ike Chakrabarti, S.K. and Snider, R.H., "Two Dimensional Wave Energy Spectra,"' Underwater Technology, 2, pp. 80-85; 1973. Clarke, D. and Gedling, P., 'MLM Estimation of Directional Wave Spectra," Proc., Directional Wave Spectra Applications, Berkeley, (Cevlaiteg OS GEHL 10. Wile No sie 14. Ney< 16. Uo 18. 19. Zlis 22 - 161 - Dean, R.G., "Evaluation and Development of Water Wave Theories for Engineering Application, Volumes I and II," Coastal Engineering Research Center Special Report No. ie November, 1974. Dean, R.G., "The NRC Workshop on Wave Measurement Technology: A Summary," Proc., Directional Wave Spectra Applications, Berkeley, Calne pp. 22052322) 1982". Dexter, S.C., Handbook of Oceanographic Engineering Materials, JohnyiWiley and. Sons, N-Y.,; p. 83, p. 178s 1979). Forristal, G.Z., "Subsurface Wave Measuring Systems," Proc., National Research Council Workshop on Wave Measurement Technology; 1982 Goda, Y., "Simulation in Examination...," Directional Wave Spectra Applications, Berkeley, Calif.; 1981. Jefferys, E.R., Wareham, G.T., Ramsden, N.A., and Platts, M.J., "Measuring Directional Spectra with the MLM," Proc., Directional Wave Spectra Applications , Berkeley, Calif.; 1981. LaCoss, R.T., "Data Adaptive Spectral Analysis Methods," Geo- physics! 36, pp. 66l=6/753), 1971). Longuet-Higgins, M.S., Cartwright, D.E., and Smith, MEIDES "Observations of the Directional Spectrum of Sea Waves Using the Motions of a Floating Buoy," Ocean Wave: Spectra, Proceedings of a Conference, Prentice-Hall, Inc., Englewood Cliffs, N.J.; 1963. Mitsayasu, H., et. al., "Studies on Techniques for Ocean Wave Measurements (1),"" Bulletin Res. Inst. Appl. Mech., Kyushu Univer No. 939; pp. 105-1815) 1973. Mobarek, I.E., "Directional Spectra of Laboratory Wind Waves," Jour. Waterways and Harbors Div., 91, ASCE; pp. 91-116; 1965. Nagata, Y., "The Statistical Properties of Orbital Wave Motions and Their Applications for the Measurement of Directional Wave Wave Spectra,'' Journal of the Oceanographical Society of Japan, 19, pp. 169-181; 1964. ort eee O'Brien, M.E., "An Urgent Need," Shore and Beach, Vol. 42a No 2 pe 2s October, 1974. Panicker, N.N., "Review of Techniques for Directional Wave Specirass) ) buock,, International Symposium on Ocean Wave Measurement and Analysis, New Orleans, pp. 669-688; 1974. 23). 24, Ke 26. Dike 28. 29. 30. Shils 32%. 83% = 1162) — Panicker, N.N., and Borgman, L.E., "Dtretional Spetra from Wave-Guage Array sin) l2nOCks Twelfth Coastal Engineering Conference, Washington, D.C., pp. 117-136; 1970. Peacock, H.G., "CERC Field Wave Guaging Program,'' Proceedings of the International Symposium on Ocean Wave Measurement and Analysis, New Orleans, La.; September 1974. Peerless,S.J., Basic Fluid Mechanics, Pergamon Press, Oxford, p. TRS WSYey7hG Ploeg, J., "Some Results of a Directional Wave Recording Sittaitiiont: Proc., Thirteenth Coastal Engineering Conference; Vancouver, B.C., pp. 131-144; 1972. , Proceedings of the National Research Council Workshop on Wave Measurement Technology; 1982. Rickiishi, K., "A Study on the Measurement of the Directional Spectrum and Phase Velocity of Laboratory Waves," Res. Inst. for Applied Mechanics, Kyushu Univ., Fukuoka, Japan; 1977. Seymour, R.J, and Higgins, A.L., "A Slope Array for Estimating Wave Direction," Proc. of a Workshop on Coastal Processes Instrumentation, June 16, 1977; avila amGallvist mmm nays. of Calif., San Diego. Sea Grant Publ. No. 62; Institute of Marine Resources Ref. No. 78-102; 1978. , Shore Protection Manual, I, Coastal Engineering Research Center, figure 4-11; 1977. Simpson, J.H., "Observations of the Directional Characteristics of Sea Waves," Geophysical Journal of Royal Astronomical Soc., IVC PP. 93nl20; 2 1O6or Suzuki, Y., "Determination of Approximate Directional Spectra for Coastal Waves," Rep. of the Port and Harbor Res. Inst., 8, pp. 43-101; 1969 van Heteren,J., and Keyser, H., "Directional Spectra: Comparison of Three Methods," Proc., Directional Wave Spectra Applications, Berkeley, Calif., ASCE; 1981. = 163 = APPENDIX A SAMPLE DPG ANALYSIS RESULTS June 8 - 11, 1982 - 164 - UNIVERSITY OF DELAWARE DEPARTMENT OF CIVIL ENGINEERING DPG DIRECTIONAL WAVE MONITOR / FRF, DUCK, N.C. -50 SECOND SAMPLING 8 BANDS BLOCK AVERAGED DEV YR MO DAY TIME 111 82 6 8 7 (e) 2s ee 6 8 7 (e) 144 82 6 8 7 (e) 4096 POINTS ANALYZED AT GAGE NUMBER 2 9 LOW truncations; 10 HIGH truncations Mean= 2.301 S.Dev= 0.06192 Lower Limit= 2.115 Upper Limit= 2.486 GAGE NUMBER 3 5 LOW truncations; 5 HIGH truncations Mean= 2.211 S.Dev= 0.22893 Lower Limit= 1.524 Upper Limit= 2.898 GAGE NUMBER 5 1 LOW truncations; O HIGH truncations Mean= 2.423 S$.Dev= 0.03973 Lower Limit= 2.304 Upper Limit= 2.542 IDES MEVE LENS tid) coon EE POSSIBLE INSTRUMENT TILT (deg) DP2 DP3 OOS, OPS Pe) Significant Wave Height (ABS gage) = 4.55 feet. Effective period = 7.425 seconds. Maximum Energy located at bands: 8.225 exceeds average energy by 606.14 % 8.790 exceeds average energy by 371.26 % 9.438 exceeds average energy by 371.10 % 7.728 exceeds average energy by 297.40 % ©.189 exceeds average energy by 190.45 % 7.288 exceeds average energy by 164.24 % Compass heading from which waves propogate Band 8.225 secs: Greatest Energy at 58. deg Band 8.790 secs: Greatest Energy at 61. deg Band 9.438 secs: Greatest Energy at 61. deg Band 7.728 secs: Greatest Energy at 61. deg Band 10.189 secs: Greatest Energy at 59. deg Band 7.288 secs: Greatest Energy at 55. deg = GR = ree SSeS SSE EL N ' | nm | ee eat | re | 4 Laat H uv! 8 8s Q it 3 2 | | ea L6 = g eS S r al @ | = rN =I ao | | tu ig | 5 i9 : i lf? 2 i | =e ie | id ‘ =| [seas i 8 e i=} aA fe) nt a % Rr Sz" 00°S S2°E oc*2 So" t 90°0 (29% 243} ADYANSA ce ee ceeneaamememnmenl - 166 - 6708/82 0700 EST v uv n N c w — > O a4 LJ Zz Lu 120 180 240 DIRECTION (deg J = 167 = UNIVERSITY OF DELAWARE DEPARTMENT OF CIVIL ENGINEERING DPG DIRECTIONAL WAVE MONITOR / FRF, DUCK, N.C. .50 SECOND SAMPLING 8 BANDS BLOCK AVERAGED DEV YR MO DAY TIME Hine 82) 6 Gy) ae) 2 l2ny fe 6 Ss) 2 144 82 6 (JS AS) 2 4096 POINTS ANALYZED AT GAGE NUMBER 2 11 LOW truncations; . 9S HIGH truncations Mean= 2.306 S.Dev= 0.05554 Lower Limit= 2.139 Upper Limit= 2.473 GAGE NUMBER 3 7 LOW truncations; 26 HIGH truncations Mean= 2.191 S.Dev= 0.23225 Lower Limit= 1.495 Upper Limit= 2.888 GAGE NUMBER 5 7 LOW truncations; 5 HIGH truncations Mean= 2.344 S.Dev= 0.03559 Lower Limit= 2.237 Upper Limit= 2.450 IDE EEVEE TS. O;369) (FEET. POSSIBLE INSTRUMENT TILT (deg) DP2 DPS =©)1023 =2 383 Significant Wave Height (ABS gage) = 4.19 feet. Effective period = 6.784 seconds. Maximum Energy located at bands: 8.790 exceeds average energy by 722.92 % 9.438 exceeds average energy by 545.18 % 8.225 exceeds average energy by 163.39 % 7.728 exceeds average energy by 122.59 % 0.189 exceeds average energy by 106.14 % 5.936 exceeds average energy by 91.64 % Compass heading from which waves propogate Band 8.790 secs: Greatest Energy at 59. deg Band 9.438 secs: Greatest Energy at 61. deg Band 8.225 secs: Greatest Energy at 57. deg Band 7.728 secs: Greatest Energy at 55. deg Band 10.189 secs: Greatest Energy at 61. deg Band 5.936 secs: Greatest Energy at 57. deg - 168 - ae i oe Were} hee te tee | . | S| ig : sean eo) fe | | 1320 EST 6708/82 U vw} a SS S oa Cj >| O Zz uJ ai (o] Lu Oo u| 00° OF s2°8 os*2 Sz" o0°s Sd" os*z (>? 743) AQYANS 8 —- 9.44 secs 300 of 9 secs 8.28 secs | —- 7.73 secs «34 secs } | | | | | | — 10.19 secs 240 DIRECTION (deg) 4320 EST 180 - 169 - 6/08/82 00"b os*€ o0"€ os*z 00°Z os*t 00° T os*o 00°0 622% 745) ADASNA = 1710) = UNIVERSITY OF DELAWARE DEPARTMENT OF CIVIL ENGINEERING DPG DIRECTIONAL WAVE MONITOR / FRF, DUCK, N.C. DEV YR MO DAY TIME ihm 18:2 6 ) 7 ie) T2482 6 ) 7 O 141 82 6 i) 7] 0) 4096 POINTS ANALYZED AT .50 SECOND SAMPLING 8 BANDS BLOCK AVERAGED GAGE NUMBER 2 6 LOW truncations; 11 HIGH truncations Mean= 2.300 S.Dev= 0.06456 Lower Limit= 2.106 Upper Limit= 2.494 GAGE NUMBER 3 O LOW truncations; 5 HIGH truncations Mean= 2.146 S.Dev= 0.22337 Lower Limit= 1.476 Upper Limit= 2.816 GAGE NUMBER 5 O LOW truncations; 1 HIGH truncations Mean= 2.397 S.Dev= 0.03837 Lower Limit= 2.282 Upper Limit= 2.512 MIDEVEEVELIEES ie 1) Sieh BEE. POSSIBLE INSTRUMENT TILT (deg) DP2 DP3 -0.058 -2.676 Significant Wave Height (ABS gage) = 4.38 feet. Effective period = 7.418 seconds. Maximum Energy located at bands: 9.438 exceeds average energy by 641.68 % 10.189 exceeds average energy by 481.35 % 8.790 exceeds average energy by 282.71 % 8.225 exceeds average energy by 191.30 % 7.288 exceeds average energy by 123.66 % 7.728 exceeds average energy by 89.83 % Compass heading from which waves propogate Band 9.438 secs: Greatest Energy at 67. deg Band 10.189 secs: Greatest Energy at 63. deg Band 8.790 secs: Greatest Energy at 63. deg Band 8.225 secs: Greatest Energy at 63. deg Band 7.288 secs: Greatest Energy at 65. deg Band 7.728 secs: Greatest Energy at 51. deg Gh) ee 4.75 | i { | ae | ( : : R te i | y igi “3 5 S| gf 14 >| g ~ 2 ip Gi * &! a | 1° | eo Ww ! 2 | o a : ° 00° OT s2°s os" ce"s 00°s S2°¢ (29% 743) AQYANA SGD 6709’82 0700 EST 8 zs se beet lente Sra a whe MR SS I) Pant Seine — 9.44 secs | B —— 10.19 secs | rw) —— 8.79 secs | — 8.23 secs } —- 7.29 secs | 8 — 7.73 secs o 3 INIIN v vu rr oo 9 | San | j > 1 eS | | to re) | ' | : : | g ae a | 60 420 480 240 pe DERECIEOND Gdeo i = 1173. = UNIVERSITY OF DELAWARE DEPARTMENT OF CIVIL ENGINEERING DPG DIRECTIONAL WAVE MONITOR / FRF, DUCK, DEV YR MO DAY TIME Ualake = t322 Se) 7 10) VA 4322 BG Alo) 7 10) 141 82 6 10 7 1) 4096 POINTS ANALYZED AT N.C. -50 SECOND SAMPLING 8 BANDS BLOCK AVERAGED GAGE NUMBER 2 14 LOW truncations; 9 HIGH truncations Mean= 2.302 S.Dev= 0.06642 Lower Limit= 2.103 Upper Limit= 2.501 GAGE NUMBER 3 3 LOW truncations; 18 HIGH truncations Mean= 2.104 S$.Dev= 0.19050 Lower Limit= 1.532 Upper Limit= 2.675 GAGE NUMBER 5 O LOW truncations; 5 HIGH truncations Mean= 2.381 S.Dev= 0.03698 Lower Limit= 2.270 Upper Limit= 2.492 (PUES BEVEL TS) 1) 245) FEET. POSSIBLE INSTRUMENT TILT (deg) DP2 DP3 -0.048 -2.962 Significant Wave Height (ABS gage) = 4.05 feet. Effective period = 8.073 seconds. Maximum Energy located at bands: 10.189 exceeds average energy by 704.75 % 9.438 exceeds average energy by 448.02 % 11.070 exceeds average energy by 385.94 % 8.790 exceeds average energy by 196.96 % 8.225 exceeds average energy by 182.72 % 7.728 exceeds average energy by 117.25 % Compass heading from which waves propogate Band 10.189 secs: Greatest Energy at 65. deg Band 9.438 secs: Greatest Energy at 61. deg Band 11.070 secs: Greatest Energy at 67. deg Band 8.790 secs: Greatest Energy at 69. deg Band 8.225 secs: Greatest Energy at 63. deg Band 7.728 secs: Greatest Energy at 69. deg - 174 - | | [ane al A a ie ea hey ee be Be | any al lds eal a | | | H | eal 0700 EST eR S| q | U m WY TaN lee 5| (8 ~| g pes az 5 10 ui a Ln = rn) 19 @ [avg oOo WwW ny t=) | ' & [=] 00° OF G2°s oc" 2 ce2°s o0°s G2°E oc°’g (?°* 743) AOSYANA - 175 - | Witenes Ses 6 te aoe Soe ee { vuUUUdSZY ¥odoeoeg¢gevdsed db | anne & agar OA OOK = —— 10.19 0700 EST DIRECTION (deg) 80 6/10/82 120 ee ee 00°» os’€ oo"e os"z 00°2 os’ o0"t (?°* 743) ADASNS DEV YR MO da 322 6 12a 2 6 144 82 6 GAGE NUMBER 2 6 LOW truncations; Mean= 2.272 S.Dev= 0.2 GAGE NUMBER 3 3 LOW truncations; Mean= 2.116 S.Dev= 0.2 GAGE NUMBER 5 O LOW truncations; Mean= 2.368 DEV EEVEERES Sr OnsSonFicics. POSSIBLE INSTRUMENT TILT DP2 DP3 -0.285 SG )7/ 9] Significant Wave Height (A Effective period = 8.412 Maximum Energy located at 11.070 exceeds average energy by 9.438 exceeds average energy by 10.189 exceeds ave 12.118 exceeds ave Compass heading from which Band 11.070 secs: Great Band 9.438 secs: Great Band 10.189 secs: Great Band 12.118 secs: Great Band 8.790 secs: Great Band 8.225 secs: Great §$.Dev= 0.05197 Bb 176 = UNIVERSITY OF DELAWARE DEPARTMENT OF CIVIL ENGINEERING DPG DIRECTIONAL WAVE MONITOR / FRF, DAY TIME 10 #13 10) NO) = als) () 10 13 ie) 4096 POINTS ANALYZED AT 8 BANDS BLOCK AVERAGED 55 HIGH truncations 1523 Lower Limit= 41 HIGH truncations 6262 Lower Limit= 2 HIGH truncations Lower Limit= (deg) BS gage) = 5.60 fe seconds. bands: rage energy by waves propogate est Energy at (35), est Energy at 87. est Energy at 83. est Energy at 83. est Energy at OMe est Energy at 85. 1016. 377. 349. rage energy by 248. 8.790 exceeds average energy by 184. 8.225 exceeds average energy by 93. 1.62 1.32 Pa GCsh} Asia 6 9 2 Upper Limit= Upper Limit= N.C. .50 SECOND SAMPLING Qed 2.904 Upper Limit= 2.524 4.79 | | | 2 | ey et j iv a i i | en ie a| ; ry | i=) Py 0) go a i A =) { i <>! F nN O| 3 S lo Gl G we =F Pr) =T 2a ee ee ee me — SS Oo LW Se 2 s ros) | Ls ro) go° oT c2°8 og*2 Go°s oo°s G2°s os’z So" Tt C222 52745) ADSENSE S18 a a a a A Ee I he A ec | ofS secs | | | | { { | | — —— 11.07 secs —- 9.14 secs —— 10.19 secs —— 12.12 secs »23 secs | aS nS 1300 EST 480 240 0 DIRECTION (deg) 6710782 120 = 00°¢ os*é o0°e os*2 00°2 os’? 00° y os" oO 00°9 G22 724%) ADYSNS - 179 - UNIVERSITY OF DELAWARE DEPARTMENT OF CIVIL ENGINEERING DPG DIRECTIONAL WAVE MONITOR / FRF, DUCK, N.C. DEV YR MO DAY TIME Vidas 22 a) 7 fe) 2h 82: Catt i, fo) 141 82 Gy alal ri fe) 4096 POINTS ANALYZED AT .50 SECOND SAMPLING GAGE NUMBER 2 8 LOW truncations; 6 HIGH truncations 8 BANDS BLOCK AVERAGED Mean= 2.299 S.Dev= 0.09652 Lower Limit= 2.010 Upper Limit= 2.589 GAGE NUMBER 3 © LOW truncations; 8 HIGH truncations Mean= 2.039 S.Dev= 0.19138 Lower Limit= 1.46 GAGE NUMBER 5 O LOW truncations; 1 HIGH truncations Mean= 2.364 S.Dev= 0.03900 Lower Limit= 2.24 TIDE LEVEL IS 0.824 FEET. POSSIBLE INSTRUMENT TILT (deg) DP2 DP3 -0.061 -3.365 Significant Wave Height (ABS gage) = 4.32 feet. Effective period = 7.817 seconds. Maximum Energy located at bands: 11.070 exceeds average energy by 715.00 10.189 exceeds average energy by 266.13 12.118 exceeds average energy by 194.16 13.386 exceeds average energy by 159.03 8.790 exceeds average energy by 115.97 8.225 exceeds average energy by 108.46 Compass heading from which waves propogate Band 11.070 secs: Greatest Energy at 73. deg Band 10.189 secs: Greatest Energy at 71. deg Band 12.118 secs: Greatest Energy at 67. deg Band 13.385 secs: Greatest Energy at 69. deg Band 8.790 secs: Greatest Energy at 69. deg Band 8.225 secs: Greatest Energy at 75. deg 5 7 Upper Limit= 2.613 Upper Limit= 2.481 - 180 - 0700 EST 6/11/82 00° OT : | | : | | | : | | c2°8 os*2 Sz"3 00°S c2°s os*z (>°* 743) ASYANS A A A A 4.25 4.50 1.75 2.00 4.00 ve eS 0.25 0.50 0.75 FREQUENCY (road/sec } - 181 - ah #a &@R vuvuv Vv eo¢vo?dsd gd? an 2 Hh GH KROnN Sadak& AONN DD ada ol 0700 EST DIRECTION (deg). ee a Te RR a RI te Com 6/11/82 oo" os’s o0o°s os*é ~90°Z OS°t oo’ tT os*o co"o | (296 744) AQYNINA TABIE A-1: =. Wisy2) COMPARISON OF OTHER DIRECTIONAL ESTIMATES June 8 - 11, 1982 MEAN DIRECTION SPECTRAL ESTIMATE i i PERIOD PEAK dP2-dP3 tan'2t tan 132 (secs) (deg) (deg) (deg) (deg) 222 “79 Ab 79 Ay 223 Ab 19 79 19 AL 65.3 65.7 68.3 62.1 65.0 62.1 799 73.8 74.8 7.5 65.9 78.4 Lay 120.5 110.9 94.2 88.0 76.8 8 8 2 8 9 8 2 10 8 fae [e) ro rE FO G | ed (QyNo) — ht a NO ONO EXD nreE WANN OOM OFF - 183 - APPENDIX B TYPICAL STRIP CHART RECORDINGS FROM BENCH CALIBRATION Results from Calibration Test Performed 1 Week before Field Installation. - 184 - Se TT 2 Se eT TAPAT FO TT ETT TTI = ATTATAPNUTTTTTTTTTTTTTTT) LAAT) STITT 2 TTT = z wfc BU) 2 SMe ITUINUAUUOUDSENAUTAOAUNUENATAETA ULEAD SETAE ST eT = =SoeTNAVAVAVENDOAVAN VAY ST ATT = FE eT TTT = Fe I 2 Ee TT 2 SS ee eT 2 : paved 0 TTT = Fe ee eT 2 FT TTT TTT) SA ee TTT) SAU TTTTTTTTTTTTTTT) & TATTTTTTTTTATTTTTTTIT) Mee TITINLUNNNOHNASAUAUTAVATNUATAEAY SANTA HEE a TET TMNT = 2 Het nd EAM HITUOVANATRA STUN AA ATA =A TATUUAUUAONAUADSUUTHNTHRAUEARAUAOOAY SSI UAUEREAEATES AURA Fe TMI 2 STE TTT = =A LANNY RTE Fee TTT TTT) 2 SMe UUITULOAONE?STUOYUEAUAYRAYAEULATAALAA UENO Aa ULTAOOLUOS SONU UANEAAREEEAUEATEYALA EAHA SA TNTTANY INYO UAUAAOAAOTLACEALLUAYTALEAT SUEY ER TVAAAN ANN AVENE ANYTA ATU HAE ST TTT TINCT) Se TT SD TTT ST TATA = EM IALNUUANNUUAAUANRAUAURALAETAAA UL ESLER Chamber Pressure Xdcr. ABS. Calib. Factor: 0.1 psi/mm Calib. Factor: 0.1 psi/mm Chart Speed: 5 mm/sec ~ 185 - = = Lot —— = = = ======== = _———~F — = = a3 = _———I = == eS ES | == hi CTI i= =: Pe Peta == mo === vat = =a = = === = ——) 2553 it =| — ———I ae PRINTED IN U.S.A. = ———"t ry = = B22 == === SS ==2=] == =S===2== == —— ——F ss = —— mae es ———} = a ——I = =, —_ 7 = == == == Chamber Pressure Xdcr. Calib. Factor: 0.1 psi/mm UUW UU WU Uo COCO CUO UG a) uu CUO UG) UG uo CUCU UCU UCU UCU GU uuu) oJ SOOO UCU UU UG) uuu UCU UL 235855 2 SS S748 === == S2258 I LI | oo == SS _— ae == = == —b : A B 2 === cao = va HE 2S = i = =a = == == = eae = ———F = a3 = 3 —— = 53 SS — = E43 =— es I ESSe3 == H et ry = 1 —————J iT a Ej = = ———J es = = === == 2222 222 = 22 = = = = -— —— —— eet as — ae eS = = eS = —_——— —— = -— Bes = = = == ee = = —s — Sore Ss — = = eas 1 ———! | Ss ————) ——! | a ———= + ——T} AOL RL tecefeceebonetocendenes Te PLL Oe ee troclovceteeboeeston reeoleceal) II aPt Calib. Factor: .02 psid/mm Chart Speed: 5 mm/sec Al CT TE IL LE TT i ETT TTT ETN TT pore mob | TTT val LNA TOALUAUAAUAUUELUALAAUU AAT Wa CTT aHTnTOUTnatiig I il TI ICCC HAA = = == = <== L —_ ZS —— ———F = =| — =S== = == SS 55 === == = ————-3 = = = = J 30-02585 —— = — = = —— = = = = = = = —— <= ——! = a os SS=======>== ====SS=2=2=S== == SS5== == === =====S==S>=SSS= === SS55==S=5 === =S=====S========2===== 2555555 ================== ===! ==== 1 =SS=5 = ===========—==S===2/===2==== =S=f>>==================2!==== === —— i = — i == SOs =========22=== =====s/:====s=== ct ~ 7 Ci (= SS SS SS SS SS aa r) SnNiod0934 5) & | 3409 SIOKINOI JIHdVES a == S============== =====2========= ====>>======>=>==== =============== ================= SS SS SSS SS ====================== ======—SS=— ==—===========—== =======——==—— rh ae Zi =— —S a SS SSeS SS — = P4) Se ——— ta SS SS SS SS SS SS SSS SS SaaS —=—2ZaSSaaeS==S====— =555===== 525 == ===5=======2======== == === 2 = eS == SS SS SS SS Se eS eS SS esa a eee ee 2 255 2555 =) S55 == S=S5 22S == SS==S==a SES = SS SS SSS eS SS Se SS Se 2S BS eS eS 2S 2S 2S == 3345) 3 >YOA M3N ‘O1W4SNB = =NOILVYOdNOD SIOYLNOD il ee = ==5========= SSeS 2 | 2222 Se 222 22 222 SES 2 S255 52 22 So2 Se oe ae SS aaa ee eeeee === = =5e==SEEEEEEEEEEEG=ES Se eee aeoe eee ee eee ce Pee eeeeeee eS a a eee ee ee eee 3555552558222 == ===" = === =a====== ===========5= SSS SS SS SS S555 SS S55 555 = SSS S= SSS ==SSSSn== SS SSSSSSSSSa==SSSSS SSS SS SSSSSSSSSS= vesbecvatensadeveetessafsooedsasebeceadovesbevssfoccatoocoteasotevencoetecoetoccetsovefaaeeteroadecsetsavebecsedoceetacootocsaDevssfesec{ecsdverstveetesseloveafooobrosstoeeed .02 psid/mm apy. .05 psi/mm Calib. Factor: Chart Speed: 5 mm/sec Chamber Pressure Xdcr. Calib. Factor: = Aes) = APPENDIX C A PARTIAL LIST OF DPG DIMENSIONS = i160) = LENGTH, ARM To KEM. 9/9" (2.9%) HEILAT OF INSTRUMENT ~ 40.5" (/.03 -) Dee JS CRADLE : 57.5" (1-31 m) ARM 4 APPROX. WEIGHT IN 41R INSTRUMENT; Bo Les C36 kg) CRADLE : Zoo UBS C(F| ky) DFE. PRESSURE GAGE LEPCTH det. 44.25" 8 AGS Hse If3 3.47.95" dPd : 53.8715" CON)UCURATION OF CENTER SterSo€s ELASToOMER DEPTH BENEATH FUSELAGE MvER PLATE = 0.43715" Hole DIAMETER IN FUSELAGE CouEk PLATE = 0.625" ELASTOMER DISTANCE BEHIYD ARMA Wotes = |, 5425" ARA HOLE DIAMETER > 0.6875" TRECISE ORLEMTANLOA CE DIFE. PRESSURE GAUGE MEASUREMENTS art. 0.000° A72: 91. 013? 373° 182.100° dry: 269.00° FUSELAGE CAC AEANCE FIOM LEVEL EARTH = {1” BACK-FILL PRESSURE CABS. GACE) = |. 32 pn CLENLTH 2F aGS. GALE TUG (8.5 inches) INsTRUMENT SecuREeD CRADLE AC 1 - 191 - APPENDIX D ASSEMBLY AND MAINTENANCE OF THE DPG A. = ep = INSTRUMENT ASSEMBLY AND MAINTENANCE Initial Assembly 1. The transducer stack is created by placing the transducers within the plexiglass wafers and attaching the acrylic stand-off rods between the wafers. 2. The stack is attached to the bottom of the water-tight cylinder (can) end-cap. 3. Nylon tubing is connected between the the bottom of the end-cap and the transducer pressure ports. 4. The wiring is then completed terminating to a 16-pin connector positioned just below the can end-cap. 5. The exterior stainless steel tubing and acrylic diaphragm housings are attached to the top of the end-cap. 6. The center housings are larger in diameter and should connect to the slightly "elevated" Swage-Locks on the transducers. B. - 193 - Fluid Back-Filling 6. The center differential lines are fal Ved ay camsit The transducer stack is laid on its side with the bottom slightly elevated. Two center bleed ports face up. The line to be filled is flexed up so that the housing is above the stack. Fluid is poured in to the housing until a steady flow streams from _ the bleed port. The port is then closed. (Figure D-1.) 7. Enough fluid must be poured into the housing so that it forms an inverted meniscus about the o-ring. The elastomer diaphragm is slid horizontally over the fluid until its holes line up with the threaded holes in the housing. The copper-nickel ring is then lowered carefully onto the elastomer and secured to the housing with Monel screws. Each housing, elastomer, and ring is labelled as a set. The labels should fall in line so that the holes in each of the three match. 8. The process is repeated for each of the center differential lines. 9. The arm sensors are filled next. 10. A large plate is attached to the bottom of the stack using the threaded ( 6-32) holes in the stand-offs. 11. The stack is inverted (end-cap down) on top of a _ stand or = Gl, = BLEED s» respectively, then the cross-spectral density, normalized by the unidirectional spectral density S(G) can be expressed as: . . Oey 1} ~ QU US J, (KD) ate ) (a, cos nf +b. sin nf) 7 (i) J, (kD) (F.1)} n=1 for some frequency 6. J, (argument) and J,,(argument) are Bessel functions. In terms of real and imaginary parts, Eq. F.1 can be written: = ZR. c' = J (KD) - 27 J, (kD) (a, cos 28 + b. sin 28) + 27 J, (kD) (a, cos 48 + b, sin 48) 27 J, (kD) (a¢ cos 68 + b- sin 6f) at ena ofl sa hy J, (kD) (a, cosB + by sin 8) — 20 J, (kD) (a, cos 38 + b, sin 38) + 27 J; (kD) (a, cos 58 + b, sin 58) The Fourier series can be accurately truncated to N if J (kD) is negligible for n>N or if a, and by, are negligibie for n>N. There is a set, then, of 2N equations; N equations from each of the real and imaginary parts of Equation F.1, and each with the unknowns an and bn. The maximum nossible value of N is determined by the number of different mon-ambiguous cross-correlations possible from the gauges in the array. If there are no ambiguous cross-correlations between the gauges, the number of possible combinations for M gauges is = 203) = M(M-1)/2. This is the number of coefficient pairs N that one can develop. It is suggested that one does not develop all N pairs, but stops at least two pairs sooner so that there are more equations than unknowns. The coefficients may then be fitted by least squares analysis. As an example, four pressure gauges positioned at the axes of an irregular three-faced pyramid could potentially develop six coefficient pairs (or the first thirteen directional Fourier coefficients). It could more effectively develop four coefficient pairs (or the first nine coefficients) using least squares analysis to Fit the coefficients. Signals from four pressure gauges positioned at the corners of a square, such as in the Scripps Sxy gauge (Seymour, 1978), develop only four non-ambiguous cross-correlations and thusly could generate the first four coefficient pairs (or the first nine coefficients). There are two other possible (ambiguous) correlations that can be utilized to fit the first nine coefficients by least squares analysis -- just as the pyramid-shaped array does by excluding the development of the last two coefficient pairs. Since the DPG utilizes differential pressure gauges, the relations for the cross-spectral densities differ from Equation F.1. The cross: spectral density for two colinear differential pressure signals can be shown to be: (Gelareit = —- [J (kD) Cres N 50) + 2 ) (a. cos n6 + b. sin nB) Tid (KD) a n n n n= ae J, (kD) 7 cos 2B N } (a,cos(n+2)8 + b_sin(n+2)8) i" “J. (kD) n=1 I+ q n-2 ) (a_cos(n-2)8 + b_sin(n-2)8)Ti J (KD) ] eal 8 n n-2 I+ for some frequency 0. The cross-spectral density of the absolute pressure signal and x-axis and y-axis differential pressure signals are respectively: kom aie =y/k [J (kD) cos B (FS) x a ; n+l + lee tae + b sin (n+1)6) mi J 41 (BP) n= A mil ~ eae +b sin(n-1)8)Ti “J__, (kD) 1 n= - 205 - CF.4) ee a =" [9 (kD) ‘sin 6 0) y N + a (asin (n+1)6 - bcos (n+1)8) mi * a, | (kD) A al + nu (b cos (n-1)8 - asin (n-1)8) Ti" Jy-1 (KD) I for some frequency 0. The cross-spectral density for the signals of two perpendicular differential pressure gauges is: GES) iS) N ie S i be pelt + L (a_ sin(n+2)B bo cos (n+2)8) Ti J 42 (KD) ‘ .n-2 - 2 sin(n-2)6-b_ cos(n-2) 8) Ti J-2 (KD) | For the configuration of the DPG prototype, five non-ambiguous cross-correlations are possible. This suggests that the first five directional Fourier coefficient pairs (first eleven coefficients) could be developed from Equations F.2 through F.5. Five additional ambiguous cross-correlations are possible so that these eleven coefficients might be better fit by least squares analysis. If the configuration of the DPG arms was altered such that the angle between each of the arms was unique, it is theoretically = 206 - possible to develop the first twenty-one directional Fourier coefficients with no least squares fit; or more practically, the first fifteen or seventeen coefficients.: = Aone = APPENDIX F FORTRAN ANALYSIS PROGRAM FOR DPG DATA 00050 00100 00150 00200 00250 00300 00350 00400 00450 00500 00550 00600 00650 00700 00750 00800 00850 00900 00950 01000 01050 01100 01150 01200 01250 01300 01350 01400 01450 01500 01550 01600 01650 01700 01750 01800 01850 01900 01950 02000 02050 02100 02150 02200 02250 02300 02350 02400 02450 02500 02550 02600 02650 02700 02750 02800 02850 02900 02950 03000 @HRARHR) PQ) PIPAAMAP) LP.) PG MARUY aeaqnngagangaanaaon - 208 - This program is designed for use with the University of Delaware DPG Directional Wave Monitor as installed at the FRF on 14 May, 1982. The instrument and software were designed by Kevin R. Bodge under the direction of Dr. Robert G. Dean. The program, as utilized by the FRF, uses only differential pressure channels dP2 and dP3 with the absolute gauge. It generates the directional spectra using the first 5 directional Fourier coefficients. The program as listed utilizes alli four differ- ential gauges with the absolute gauge and is capable of generating the directional spectra using the first seven directional Fourier coefficients. English units are used throughout. DIMENSION dp1i(4100),dp2(4100) ,dp3(4100) ,dp4(4100), abs(4100) ,dpxx(4100).dpyy(4100) DIMENSION d1i(2050) ,d2i(2050) ,d3i( 2050) ,d4i(2050), abi (2050) ,dxxi(2050) ,dyyi(2050) DIMENSION d1(2050) ,d2( 2050) ,d3( 2050) ,d4(2050), ab( 2050) ,dxx( 2050) , dyy( 2050) DIMENSION prsp( 2050) ,wvnr(2050), freq( 2050) ,maxfrq(20) DIMENSION thtai(400), thta2(400), thta3(400),pd(20) DIMENSION aO(400),a1(400) ,a2(400),a3(400), b1( 400) ,b2(400) ,b3(400) DIMENSION dir1(400),dir2(400) ,dir3(400),dir4(400), ang1(400),ang2(400) ,ang3( 400) ,ang4(400) INTEGER bik OPEN(unit=18,device=’dsk’,file=’DP1.dat’ ) OPEN(unit=19,device=’dsk’,file=’DP2.dat’) OPEN(unit=20, device=’dsk’,file=’DP3.dat’) OPEN(unit=21,device=’dsk’,file=’DP4.dat’) OPEN(unit=22,device=’dsk’,file=’DP5.dat’ ) OPEN(unit=17,device=’dsk’,file=’PWR.DAT’ ) OPEN(unit=14,device=’dsk’,file=’RAW.dat’ ) OPEN(unit= 3,device=‘dsk’,file=’DIR.dat’) OPEN(unit= 4,device=’dsk’,file=’FRF.dat’) INPUT ANALYSIS DETAILS: ATM = Atmospheric Pressure (mb) GAMMA = Seawater Specific Gravity (1b/cu.ft.) N = # of sampled points to analyze (power of 2) K = such that 2**K=N dT = sampling interval (secs) BLK = ¥# of freq. bands to block-average # of peak energy bands to identify # of non-block-averaged cut-off freq. Zz S 7 7 nou ATM = 1013.0 ATM = ATM*O.0145038 03050 03100 03150 03200 03250 03300 03350 03400 03450 03500 03550 03600 03650 03700 03750 03800 03850 033900 03950 04000 04050 04100 04150 04200 04250 04300 04350 04400 04450 04500 04550 04600 04650 04700 04750 04800 04850 043800 04950 05000 05050 05100 05150 05200 05250 05300 05350 05400 05450 05500 05550 05600 05650 05700 05750 05800 05850 053900 05950 O6000 HAI QNALOLOrOiOiQiQuMrQique) c DPG PHYSI ORICNT SGAGE DXini DX in2 DXin3 DX in4 ARM13 ARM24 Pbof = ORIENT = SGAGE DX ind DX in2 DX ing DX in4 ARM13 ARM24 Pof = Piles twopi = 2 ews 0 oy “ ete ol ie) = 08) = 64.18 GAMMA/ 1728. CAL DETAILS: = compass heading of a mean depth of sensors length of arm 1 diff. length of arm 2 diff. length of arm 3 diff. length of arm 4 diff. distance between DP1 = distance between DP2 fluid back-fill pressur “ont nt won 3.14159265 SOUT Di Format(i4) WRITE(4,819) rm 3 w.r.t. true north below mean water (ft) measurement (in) measurement (in) measurement (in) measurement (in) & DP3 measurement (in) & DP4 measurement (in) e on absolute (psi) Format(//,40X, ‘UNIVERSITY OF DELAWARE’ ,/, 1 36X, ‘DEPARTMENT OF CIVIL ENGINEERING’ ,/, 2 29X,’DPG DIRECTIONAL WAVE MONITOR / ’, 3 JERE DUCK, .NEGe? aA.) Load data arrays with zeroes for cleanliness. 3055 DO 115 I= DP1(i) DP2(i) DP3(i) DP4(i) ABS(i) = 1,most 0.00 0.00 0.00 0.00 0.00 ou ou ou CALL INPUT (dp1,dp2,dp3,dp4,abs) WRITE(4,3055) N,dT Format(/, 35,15,’ POINTS ANALYZE D AT ‘,f4.2,’ SECOND’, - 214 - 18050 READ(19,900) dev,yr,mo,day,hr,min 18100 WRITE(4,901) dev,yr,mo,day,hr,min 18150 n=1 18200 DO 202 j=1,410 18250 READ(19,905) (A(i),i1=1,10),LAST 18300 DO 102 i=1,10 18350 DPV2(n) = A(i)/200.0 18400 102 n=n+1 18450 202 Continue 18500 18550 READ(20,900) dev,yr,mo,day,hr,min 18600 WRITE(4,901) dev,yr,mo,day,hr,min 18650 n=1 18700 DO 203 j=1,410 18750 READ(20,905) (A(i),i=1,10),LAST 18800 DO 103 i=1,10 18850 DPV3(n) = A(i)/200.0 18900 103 n=n+1 18950 203 Cont inue 19000 19050 READ(21,900) dev,yr,mo,day,hr,min 19100 WRITE(4,901) dev,yr,mo,day,hr,min 19150 n=1 19200 DO 204 j=1,410 19250 READ(21,905) (A(i),i=1,10),LAST 19300 DO 104 i=1,10 19350 DPV4(n) = A(i)/200.0 19400 104 n=n+14 19450 204 Continue 19500 19550 READ(22,900) dev,yr,mo,day,hr,min 19600 WRITE(4,901) dev,yr,mo,day,hr,min 19650 n=1 19700 DO 205 j=1,410 19750 READ(22,905) (A(i),i=1,10),LAST 19800 DO 105 i=1,10 19850 ABSV(n) = A(i)/200.0 193900 105 n=n+1 19950 205 Continue 20000 20050 20100 890 Format(//,15X,’ DEV YR MO DAY TIME’) 20150 900 Format(6i4) 20200 901 Format(15x,6i14} 20250 905 Format(10i15,11) 20300 20350 Return 20400 End 20450 20500 Cc 20550 20600 SUBROUTINE PERIOD (ab,d1,d2,d3,d4,n,icut,dT,prsp,wvnr, 20650 1 freq) 20700 Cc Computes the centroid of the power spectra 20750 (Q and reports the corresponding frequency 20800 Cc as the “effective period". 20850 20900 DIMENSION ab(2050),d1(2050) ,d2(2050) ,d3(2050) ,d4(2050), 20950 1 prsp(2050),wvnr(2050), freq( 2050) 21000 21050 21100 21150 21200 21250 21300 21350 21400 21450 21500 21550 21600 21650 21700 21750 21800 21850 21900 21950 22000 22050 22100 22150 22200 22250 22300 22350 22400 22450 22500 22550 22600 22650 22700 22750 22800 22850 22900 22950 23000 23050 23100 23150 23200 23250 23300 23350 23400 23450 23500 23550 23600 23650 23700 23750 23800 23850 23900 23950 24000 Cc aANAaNAaAa = B15 = twopi = 6.283185 N2 = N/2 DATA sumabk,sumik,sum2k,sum3k,sum4k,sabsk,sik,s2k, 1 SIKES4K/O=RORHO! HORMOM, O4nOn (On On On, DO 420 J=2,icut SUMABK = sumabk + ab(j) + SUM1K = sumik + di(j) SUM2K = sum2k + d2(j) SUM3K = sum3k + d3(j) SUM4K = SUM4K + d4(j) SABSK = SABSK + AB(j) * freq(j) S1K = sik + di(j) * freq(j) S2K = s2k + d2(j) * freatj) S3K = s3K + d3(j) * frea(j) S4kK = sdk + d4(j) * freq(j) 420 Continue Tabsk = twopi * sumabk/sabsk T1ik twopi * sumik/sik T2k twopi * sum2k/s2k T3k twopi * sum3k/s3k T4k twopi * sum4k/s4k tom ow ow Report the effective period from the absolute gage. WRITE(4,929) Tabsk 929 Format(’ Effective period =’,f7.3,’ seconds.’ ) Return End SUBROUTINE SURF (icut,d1,d2,d3,d4,dp1,dp2,dp3,dp4, 1 atid21 dai .d4i dirt, dinr2 dirs, diinr4 jolk, 2 orient) DIMENSION d1i(2050) ,d2( 2050) ,d3(2050), 1 d4(2050) DIMENSION dp1( 4100) ,dp2(4100) ,dp3(4100) ,dp4(4100), 1 d1i( 2050) ,d2i1(2050) ,d3i (2050) ,d4i (2050) DIMENSION dir1(400),dir2(400),dir3(400),dir4(400) INTEGER bik Generates directional estimate without absolute gage. DIR1 uses gages DP1 and DP2; DIR2 uses gages DP3 and DP4; DIR3 uses gages DP2 and DP3; DIR4 uses gages DP1 and DP4. DO 435 J=2,icut if(dpi(j).ne. if(dpi(j).eq. if (dp2(j).ne. if (dp2(j).eq. if (dp3(j).ne. if (dp3(j).eq. .O)tant=atan2(dii(j).,dpi(j)) .)tani = 0.0 .0) tan2=atan2(d2i(j).dp2(j)) .)tan2 = 0.0 .O)tan3 =atan2(d3i(j),dp3(j)) .)tan3 = 0.0 o00000 12050 12100 12150 12200 12250 12300 12350 12400 12450 12500 12550 12600 12650 12700 12750 12800 12850 12900 12950 13000 13050 13100 13150 13200 13250 13300 13350 13400 13450 13500 13550 13600 13650 13700 13750 13800 13850 13900 13950 14000 14050 14100 14150 14200 14250 14300 14350 14400 14450 14500 14550 14600 14650 14700 14750 14800 14850 14900 14950 15000 Cc Cc Cc Cc Cc 67 lee DYY(i) = 2.0*(dpyy(i)**2 + dyyi(i)**2) Continue Store the raw power spectra, if desired 4003 4007 1 GO TO 4003 WRITE( 17,4007) WRITE( 17,3098) DO 4003 i=2,icut WRITE(17,914)freg(i),ab(i),d1(i1),d2(i),d3(i), d4(i),dxx(i),dyy(i) Cont inue Format(’ RAW POWER SPECTRA’ ) Calculate significant wave height from absolute gage. 405 E=0.0 DO 405 j=2, icut E = ab(j) + E— Hsig = (4.*sqrt(E))/12.0 WRITE(4,921) Hsig Format(/,’ Significant Wave Height (ABS gage) =’,f6.2, ’ feet.’,//) Determine effective period from all gauges. CALL PERIOD (ab,d1,d2,d3,d4,n, icut,dT,prsp,wvnr, freq) Estimate direction without absolute gage. 6002 GO TO 6002 CALL SURF (icut,d1,d2,d3,d4,dp1,dp2,dp3,dp4, d1i,d2i,d3i,d4i,dir1,dir2,dir3,dir4,bik, orient) CALL SURF2(ab,d1,d2,d3,d4,ang1,ang2,ang3.ang4, icut, wvnr ,b1lk,orient) Cont inue Generate the directional Fourier coefficients On — CALL FCOEFS(ab,abs,abi,di,dp1,d1i,d2,dp2,d2i,d3, dp3,d3i,d4,dp4,d4i,dxx,dpxx,dxxi,dyy,dpyy,dyyi, wvnr, freq, thtal, thta2, thta3, aQ,a1,a2,a3,b1,b2,b3,b1k, icut) Store the block-averged power spectra 3097 3098 1 1 WRITE(17,3097) bik WRITE( 17,3098) Format(/,’ BLOCK AVERAGED BY’,i3, ‘ BANDS’ ) Format(’ freq . ab . dif .'d2. d3-. d4’, VN Tob Sd Nahant WVAVePnci/A)) ‘ DO 77 1=2,icut i ae) rare Lo 1 15050 WRITE(17,914) freq(i), ab(i),d1(i),d2(i),da3(i), 15100 1 d4(i),dxx(i),dyy(i) 15150 UY Continue 15200 914 Format(f11.3,f11.5,4F14.9,2F20. 18) 15250 15300 15350 Cc Identify bands of highest energy 15400 15450 Call MAXSIG(ab, icut,maxfrgq,n,dT,nuff, freq) 15500 15550 15600 Cc Generate directional spectra for highest energy bands 15650 15700 Call DIRXSP (AO,A1,A2,A3,81,82,B3, freq,n,dT,nuff, 15750 1 maxfrq,orient) 15800 15850 15900 Cc GO TO 93gs99 15950 16000 WRITE(4,910) 16050 DO 666 nn=1,nuff 16100 LKM = maxfraq(nn) 16150 PD(nn) = twopi/freq(1km) 16200 IF(thta1(1km).1t.0O.)thtai(1lkm)=360.+thta1(ikm) 16250 IF(thta2(1ikm).1t.0O. )thta2(1km)=360.+thta2(ikm) 16300 IF(thta3(tkm).1t.0O. )thta3(1lkm)=360.+thta3(1km) 16350 WRITE(4,913) PD(nn), thta1(1lkm),thta2(1km), 16400 1 thta3(1ikm),diri(ikm),dir2(1lkm),dir3(ikm),dir4(ikm), 16450 2 angi(1km),ang2(1ikm),ang3(1km),ang4(1km) 16500 666 Continue 16550 910 Format(/,5x,’ MEAN DIRECTION OF PROPOGATION’ ,6x,’ESTIM’, 16600 1 “ATE W/OUT ABSOLUTE GAGE;’,12x,’WITH 1 CHANNEL’, 16650 2 ‘ AND ABSOLUTE’,/,’ Period’ ,5x,‘n=1’,7x, ’n=2’, 16700 iS) aN OS al Di Ox SAM Gh 2 = SG ier tae 16750 4 11x, ’dp1i’,6x,'dp2’,6x, ‘’dp3’ ,6x, ’dp4’) 16800 913 Format(f6.2,3f10.2,4f9.1,5x,4f9.1) 16850 16900 16950 9999 END 17000 17050 c 17100 17150 SUBROUTINE INPUT(dpv1,dpv2,dpv3,dpv4, absv) 17200 17250 DIMENSION dpv1(4100) ,dpv2(4100),dpv3(4100), 17300 1 dpv4(4100) ,absv(4100),M(4100) 17350 INTEGER dev,yr,day,hr,A(10) 17400 17450 WRITE(4,890) 17500 17550 READ( 18,900) dev,yr,mo,day,hr,min 17600 WRITE(4,901) dev,yr,mo,day,hr,min 17650 n=1 17700 DO 200 j=1,410 17750 READ( 18,905) (A(i),i1=1,10),LAST 17800 DO 100 i=1,10 17850 DPVi(n) = A(i)/265.0 * 1.65 17900 100 n=n+i 17950 200 Continue 18000 06050 06 100 06150 06200 06250 06300 06350 06400 06450 06500 06550 06600 06650 06700 06750 06800 06850 06900 06950 07000 07050 07100 07150 07200 07250 07300 07350 07400 07450 07500 07550 07600 07650 07700 07750 07800 07850 07900 07950 08000 08050 08 100 08 150 08200 08250 08300 08350 08400 08450 08500 08550 08600 08650 08700 08750 08800 08850 08900 08950 03000 aan Cc Cc Cc Cc Cc Cc 3056 Scan each record, unreasonable points, SZ) ‘ SAMPLING’ ) WRITE(4,3056) bik Format(57x,12,’ BANDS BLOCK AVERAGED’ ) calculate std.deviation, calculate and subtract report them, convert to psi. Call SCAN(dp2,n,ngage,avg2,dxin2) Call SCAN(dp3,n,ngage,avg3,dxin3) mean from record, NGAGE = 1 Call NGAGE = 2 NGAGE = 3 NGAGE = 4 Call NGAGE = 5 Call N = N/2 N2 = N2/2 SCAN(dp1,n,ngage,avg1,dxin1) SCAN(dp4,n,ngage,avg4,dxin4) truncate SCAN(abs,n,ngage,avgabs,dxin4) Reverse signs on DP1i & DP2 for sign convention. 1057 Record portion 1056 4096 bo DP1(jj) = DP2(jj) = Continue if desired. GO TO 1056 DO Continue 1057 JuJ=1, N 1056 I=1,600 WRITE(14,4096)i, dp1(i),dp2(i),dp3(i),dp4(i),abs(i) Format(i6,5f14.7) of pressure signals in scratch file Calculate tide and water depth. Neglect temperature changes on back-filling fluid. UNG DEPTH = TIDE = Format(/, ‘ WRITE(4,717) TIDE ((AVGABS*10.-Pbf-atm)/qgamma }/12. (DEPTH - SGAGE) TIDE LEVEL IS’,F7.3,’ BEES) Compare record mean and no-wave condition tare instrument tilt. to approximate TARE1 = 7.5 TARE2 = 2.31 TARES = 2.56 TARE4 = 3.825 t1 = (avg1i - t2 = (avg2 - t3 = (avg3 - t4 = (avg4 - g1 = gamma * g2 = gamma * tare1)/5. tare2)/5. tare3)/5. tare4)/5. dxini dxin2 = Zilal 039050 a3 = gamma * dxin3 09 100 9g4 = gamma * dxin4 09150 09200 TILT1 = atan2(t1,gi) * 360./twopi 09250 TILT2 = atan2(t2,g2) * 360./twopi 09300 TILTS = atan2(t3,g3) * 360./twopi 09350 TILT4 = atan2(t4,94) * 360./twopi 09400 09450 WRITE(4,119) tilti,tilt2,tilt3,tilt4 09500 119 Format(/, ’ POSSIBLE INSTRUMENT TILT (deg)’,/, 09550 1 5x, ‘DP1’,6x, ‘DP2’ ,6x, ‘DP3’ .6x,’0P4’,/,4f9.3,/) 09600 09650 G Create acceleration terms 03700 DO 56 I=1,N 09750 DPXX(i) = (DP3(i) - DP1(1I))/arm13 09800 DPYY(i) = (DP4(i) - DP2(i))/arm24 09850 56 Continue 09300 09950 DO 7034 I=1,600 10000 WRITE(14,7033) dpxx(i),dpyy(i) 10050 7034 Continue 10100 7033 Format(2f16.9) 10150 10200 GALE RETGdp 1, dilik, 0) 10250 CALL FFT(dp2,d2i,k,0) 10300 CALL FFT(dp3,d3i,k,0) 10350 CALL FFT(dp4,d4i,k,0O) 10400 CALL FFT(dpxx,dxxi,k,O) 10450 CALL FFT(dpyy,dyyi,k,O) 10500 CALL FFT(abs,abi,k,O) 10550 10600 10650 (6; Generate Pressure Response Function and Wavenumber 10700 Cc using the calculated water depth. Sensors are average 10750 Cc height of 3.79 feet above bottom. 10800 10850 boitom = depth + 3.79 10900 DO 762 i=2,icut 10950 sigma = twopi/(N*dT) * (i-1) 11000 freq(i) = sigma 11050 call WVLEN (bottom, sigma, www) 11100 wvnr(i) = www/bottom 11150 762 PRSP(i)=cosh(wvnr(i)*(bottom-sgage) ) 11200 1 /cosh(wvnr(i)*bottom) 11250 11300 11350 Cc Divide Fourier coefficients by pressure response 11400 Cc function and seawater specific gravity. 11450 11500 CALL HYDRO(icut,prsp,wvnr,abs,abi,dpi,dii,dp2,d2i, 11550 1 dp3,d3i,dp4,d4i,dpxx,dxxi,dpyy, dyyi, gamma) 11600 11650 Cc Create power spectra 11700 DO 67 I=2,icut 11750 AB(i) = 2.0*(abs(i)**2 + abi(i)**2) 11800 Di(i) = 2.0*(dpi(i)**2 + dii(i)**2) 11850 D2(1) = 2.0*(dp2(i)**2 + d2i(i)**2) 11900 D3(i) = 2.0*(dp3(i)**2 + d3i(i)**2) 11950 D4(i) = 2.0*(dp4(i)**2 + d4i(i)**2) 12000 DXX(1) = 2.0*(dpxx(i)**2 + dxxi(i)**2) - 216 - 24050 if (dp4(j).ne.0.0)tan4=atan2(d4i(j),dp4(j)) 24100 if (dp4(j).eq.0.)tan4 = 0.0 24150 tanu = tan2 - tan1 24200 tanv = tan4 - tan3 24250 tanw = tan2 - tdan3 24300 tanz = tan4 - tani 24350 D1i2 = sgrt(di(j))*sqrt(d2(j)) * (cos(tanu)+sin(tanu) ) 24400 D34 = saqrt(d3(j))*sqrt(d4(j)) * (cos(tanv)+sin(tanv) ) 24450 D23 = sqrt(d3(j))*sqrt(d2(j)) * (cos(tanw)+sin(tanw) ) 24500 D1i4 = sart(di(j))*sqrt(d4(j)) * (cos(tanz)+sin(tanz)) 24550 znum = -2*Dit}2 24600 denom = di(j) - d2(j) 24650 DIR1i(j) =ORIENT- (180./3.14159)*0.5*atan2(znum,denom) 24700 Znum = 2*D34 24750 denom = d3(j) - d4(j) 24800 DIR2(j) =ORIENT- (180./3.14159)*0.5*atan2(znum,denom) 24850 znum = 2*D23 24900 denom = d3(j) - d2(j) 24950 DIR3(j) =ORIENT- (180./3.14159)*0.5*atan2(znum,denom) 25000 znum = 2*D14 25050 denom = d1(j) - d4(j) 25100 DIR4(j) =ORIENT- (180./3.14159)*O.5*atan2(znum,denom) 25150 25200 25250 IF(diri(j).1t.0O. )diri(j)=diri(j)+360.0 25300 IF(dir2(j).1t.0. )dir2(j)=dir2(j)+360.0 25350 IF(dir3(j).1t.0O. )dir3(j)=dir3(j)+360.0 25400 IF(dir4(j).1t.0. )dir4(j)=dir4(j)+360.0 25450 25500 435 Continue 25550 25600 CALL BLOCK(icut,diri,maxblk,bIk) 25650 CALL BLOCK(icut,dir2,maxblk,blik) 25700 CALL BLOCK(icut,dir3,maxblk,blk) 25750 CALL BLOCK(icut,dir4,maxblk,bI1k) 25800 25850 25900 Return 25950 End 26000 26050 Cc 26100 26150 SUBROUTINE MAXSIG (R, icut,maxfrq,n,dT,nuff, freq) 26200 Cc Locates "nuff" number of peak energy bands 26250 ¢c and reports their location and relative magnitude. 26300 26350 Dimension R(2050), maxfraq(20).freq(2050),PD(20), 26400 1 exceed(20) ,A(2050) 26450 NN = Icut - 1 26500 TOT = 0.0 26550 26600 Cc Identify average energy in spectra 26650 DO 440 1=1, icut 26700 A(1) = R(1) 26750 440 TOT = A(1) + tot 26800 AVRG = TOT/nn 26850 263900 Cc Identify "nuff" number of peak bands. Calculate each 26950 Cc peak band’s magnitude beyond the average. Set band = O 27000 ( after identification as a maximum in the temporary array. 27050 27100 27150 27200 27250 27300 27350 27400 27450 27500 27550 27600 27650 27700 27750 27800 27850 27900 27950 28000 28050 28100 28150 28200 28250 28300 28350 28400 28450 28500 28550 28600 28650 28700 28750 28800 28850 28900 28950 29000 29050 29100 29150 29200 29250 29300 29350 29400 29450 29500 29550 29600 29650 29700 29750 29800 29850 29900 29950 30000 one enene) 450 445 ss WN= BWHhH - Paley, oo DO 445 m=1,nuff maxfraq(m) = 14 egymax = 0.0 DO 450 j=i1,nn if(A(j+1).1t.EGYMAX) GO TO 450 EGYMAX = A(j+1) maxfrq(m) = j+1 Continue k = maxfrq(m) EXCEED(m) = (A(k)-avrg) / avrg * 400.0 PD(m) = 6.28318/freg(k) A(k) = 0.0 Continue WRITE(4,945) Format (//,’ Maximum Energy located at bands:’) WRITE(4,946) (pd(m),exceed(m) ,m=1,nuff) Format(f15.3,’ exceeds average energy by’, Gea G VA) Return End subroutine FCOEFS (ab,abs,abi,di,dpi,dii,d2,dp2, d2i,d3,dp3,d3i,d4,dp4,d4i,dxx,dpxx,dxxi,dyy, dpyy ,dyyi,wvnr,freg, thtai, thta2,thta3, aO,a1,a2,a3,b1,b2,b3,b1k, icut) Finds the first nine directional fourier coefs for a few selected frequencies. This uses only one possible equation for each coef, but calculates each coeficient with all possible combinations of gages for that equation. DIMENSION ab(2050).abs(4100),abi(2050), di(2050) ,dp1(4100),d1i(2050), d2( 2050) ,dp2(4100) ,d2i1(2050) DIMENSION d3(2050) ,dp3(4100) ,d3i(2050), d4(2050) ,dp4(4100) ,d4i(2050), dxx (2050) , dpxx(4100) ,dxxi(2050), dyy( 2050) ,dpyy(4100) , dyyi(2050) DIMENSION wvnr( 2050), freq( 2050) DIMENSION thtai(400), thta2(400) ,thta3( 400) DIMENSION aO0(400),a1(400),a2(400),a3(400), b1(400) ,b2(400) ,b3( 400) INTEGER bik DIMENSION aid1(400),a1d3(400) ,a2d1d2(400), a2d1d4( 400) ,a2d3d2( 400) ,a2d3d4( 400) ,a3d1(400), a3d3(400) ,b1d2(400) ,b1d4(400), b2d2d1(400), b2d2d3( 400) ,b2d4d1(400), b2d4d3(400), b3d2(400), b3d4(400) pi = 3.14159 twopi = 6.283185 DO 510 I=2,icut 42050 42100 42150 42200 42250 42300 42350 42400 42450 42500 42550 42600 42650 42700 42750 42800 42850 42900 42950 43000 43050 43100 43150 43200 43250 43300 43350 43400 43450 43500 43550 43600 43650 43700 43750 43800 43850 43300 43950 44000 44050 44100 44150 44200 44250 44300 44350 44400 44450 44500 44550 44600 44650 44700 44750 44800 44850 44900 44950 45000 aqaqan0 QOL Or@ ome) = AZ 2 = DO 58 i=2,icut PK = prsp(i) * gamma abs(i) = abs(i) / PK abi(i) = abi(i) / PK a(i) = a(i) / PK bi) = oi) O/ceK c(i) = c(i) / PK d(i) = d(i) / PK e(i) = e(1) / PK f(i) = f(1) / PK g(i) = g(i) / PK h(i) = h(i) 7 PK PCDR=spGi) eek a(i) = q(i) / PK r(i) = r(i) / PK si) -=as\Gih/eK 58 Cont inue Return End Subroutine DIRXSP (a0O,a1,a2,a3, 1 b1,b02,b3,freq,n,dT,nuff,maxfrq,orient) We weight the fourier series directional coefs with cosine**2s factors. Here, s=2. Then we create a matrix of the frequencies of interest analyzed at incremental degrees. DIMENSION a0(400),a1(400) ,a2(400),a3(400),61(400), 1 b2(400) ,b3( 400) , freq( 2050) ,maxfrq(20), 2 $(20, 186) ,deg( 186) ,pd(20) DEGINC is the increment in degrees for which the directional spectra is calculated over. DEGINC = 2.0 Weighting factors to smooth directional spectra and eliminate negative side energy lobes: Wi = 66./77. w2 = 15./28. WSi= ame orion Weighting factors for non-smoothed directional spectra: W1 = 1. W2 = 1. W3 = O. Print out the directional Fourier coefficients, if desired. The header follows: WRITE(4,438) 438 Format(/,’ PERIOD’, i6x,’AO’,14x,‘A1’, 14x, ‘A2’, 14x, 1 ONS! NAM BAL 14x. CBO 4s BOL iaue Otexs 2 POSTE NIC Se Gaede ee ed eine oe eee ICN PAIS 3 PUA ean es) Continue 45050 45100 45150 45200 45250 45300 45350 45400 45450 45500 45550 45600 45650 45700 45750 45800 45850 45900 45950 46000 46050 46100 46150 46200 46250 46300 46350 46400 46450 46500 46550 46600 46650 46700 46750 46800 46850 46900 46950 47000 47050 47100 47150 47200 47250 47300 47350 47400 47450 47500 47550 47600 47650 47700 47750 47800 47850 47900 47950 48000 aa0 Cc Cc Cc 439 604 601 1 o— - 223 - DO 601 NN=1,nuff save = 0.0 I = maxfrq(nn) PD(nn) = 6.2831/freq(i) WRITE(4,439) pd(nn),a0(i),ai(i),a2(1),a3(i), bi(1),62(1),b3(1) Format(f6.2,’ secs’ ,7f16.4) DO 604 m=1,181 deg(m) = save as = aO(i) + ai(i)*wi * cosd(deg(m) ) + a2(i)*w2 * cosd(2.0*deg(m) ) + a3(i)*w3 * cosd(3.0*deg(m) ) bs = bi(i)*wi * sind(deg(m) ) + b2(i)*w2 * sind(2.0*deg(m) ) + b3(i)*w3 * sind(3.0*deg(m) ) S(nn,m) = as + bs save = save + deginc Continue Continue Determine the direction of greatest energy for 612 613 976 1 each band and convert to true north heading from which waves propogate. WRITE(4,6002) DO 613 NN=1,NUFF mBIG = O BIG = 0.0 DO 612 m=1,187 IF(S(nn,m).gt.BIG)mBIG = m IF(S(NN,M).gt.BIG)BIG=S(NN,M) BIGDEG = mBIG * deginc - deginc BIGDEG = ORIENT - BIGDEG IF(BIGDEG.1t.0O. )BIGDEG=BIGDEG+360.0 WRITE(4,976) nn,BIGDEG Continue Format(’ Band’,i2,’: Greatest Energy at’,f7.2, , deg’ ) Record the directional spectra for each band. Directions correspond to angle from which waves propagate with respect to true north. WRITE(3,969) (pd(i), i=1,nuff) DO 615 m=1,181 DEG(m) = ORIENT - DEG(m) IF(DEG(m).1t.O. )DEG(m)=DEG(m)+360.0 WRITE(3,970) deg(m),(S(nn,m),nn=1,nuf Ff) Cont inue Format (//,’ DIRECTIONAL - FREQUENCY SPECTRUM’ ,//, ’ dirxn’ ,9x,6f17.3, secs’ ,/) Format ( f8.1, ’ deg’,3x,6f17.3) Format(/) 36050 36 100 36150 36200 36250 36300 36350 36400 36450 36500 36550 36600 36650 36700 36750 36800 36850 36900 36950 37000 37050 37100 37150 37200 37250 37300 37350 37400 37450 37500 37550 37600 37650 37700 37750 37800 37850 37900 37950 38000 38050 38100 38150 38200 38250 38300 38350 38400 38450 38500 38550 38600 38650 38700 38750 38800 38850 38900 38950 39000 CALL BLOCK(icut,ab,maxblk,blk) CALL BLOCK(icut,aO,maxblk,blk) CALL BLOCK(icut,a1,maxblk,bIky CALL BLOCK(icut,a2,maxblk,bik) CALL BLOCK(icut,a3,maxbIk,b1k) CALL BLOCK(icut,b1,maxblk,blik) CALL BLOCK(icut,b2,maxbIlk,bIk) CALL BLOCK( icut,b3,maxbIk,blk) CALL BLOCK(icut,thtai1,maxbIk,bIk) CALL BLOCK(icut,thta2,maxblk,bIk) CALL BLOCK(icut, thta3,maxblk,b1k) CALL BLOCK(icut, freg,maxblk,b1lk) CALL BLOCK(icut,d1,maxblk, blk) CALL BLOCK(icut,d2,maxblk,b1k) CALL BLOCK(icut,d3,maxblk,blk) CALL BLOCK(icut,d4,maxbIk,b1k) CALL BLOCK(icut,dxx,maxblk,bIk) CALL BLOCK(icut,dyy,maxblk,blk) ICUT = MAXbIk Return End SUBROUTINE FFT(FR,FI,K,ICO) DIMENSION FR(4100),F1I(4100) N=2**K IF(ICO.EQ.0) GO TO 10 DO 8 I=1,N - FI(I)=-FI(1) Cont inue MR=O NN=N- 14 DO 2 M=1.NN L=N L=L/2 IF(MR+L.GT.NN) GO TO 1 MR=MOD(MR,L)+L IF(MR.LE.M) GO TO 2 TR=FR(M+1) FR(M+1)=FR(MR+1) FR(MR+1)=TR TI=FI(M+1) FI(M+1)=FI(MR+1) FI(MR+1)=TI Continue i) IF(L.GE.N) GO TO 7 ISTEP=2*L EL=L DO 4 M=1,L A=3.1415926535*FLOAT(1-M)/EL WR=COS(A) WI=SIN(A) DO 4 I=M,N,ISTEP J=I+L 39050 39100 39150 39200 39250 39300 39350 39400 39450 39500 39550 39600 39650 39700 39750 39800 39850 39300 39950 40000 40050 40100 40150 40200 40250 40300 40350 40400 40450 40500 40550 40600 40650 40700 40750 40800 40850 40900 40950 41000 41050 41100 41150 41200 41250 41300 41350 41400 41450 41500 41550 41600 41650 41700 41750 41800 41850 41300 41950 42000 Cc* c* aagagn0 12 IF(ICO.EQ.1) GO TO 11 TR=WR*FR(JU)-WI*FI(J) TI=WR*FI(JU)+WI*FR(J) GO TO 12 TR=WR*FR(JU)+WI*FI(J) TI=WR*FI(JU)-WI*FR(J) FR(J)=FR(I)-TR FI(JU)=FI(1)-TI FR(1I)=FR(1I)+TR FI(I)=FI(1)+TI L=ISTEP GO TO 3 Continue AN=N IF(ICO.EQ.1) GO TO 6 DO 5 I=1,N FR(1I)=FR(1I)/AN FI(1I)=-FI(1)/AN RETURN END SUBROUTINE WVLEN(DPT,SIG, XKH) THIS SUBROUTINE CALCULATES LINEAR WAVELENGTH BY NEWTONS METHOD PI=3. 14159265 TWOPI=2.0*PI XKHO=SIG**2*DPT/32.2 IF(XKHO-6.3) 2,1,1 XKH=XKHO GO TO 9 XKH=SQRT (XKHO) SH=SINH(XKH) CH=COSH(XKH) EPS=XKHO-XKH*SH/CH SLOPE =-XKH/CH* *2-SH/CH DXKH=-EPS/SLOPE IF (ABS(DXKH/XKH)-0O.0001) 9,9,4 XKH=XKH+DXKH GO TO 3 XLENTH=TWOPI*DPT/XKH RETURN end subroutine HYDRO (icut,prsp,wvnr,abs,abi,a,b,c,d,e, f.9,.h,p.g.r,s,gamma) Divides through by pressure response function and gamma. Operates on the a(n)’ and b(n)’ terms from each of the five gages’ FFT results. DIMENSION prsp( 2050) ,wyvnr(2050) DIMENSION abs(2050), abi{2050), a(4100),b(2050), c(4100) ,d(2050) ,e(4100), f (2050) .g(4190) ,h( 2050), p(4100),q(2050) ,r(4100),s(2050) 4001 WN - 218 - wvnor(i) = wynr(i)/12.0 : = atan2(abi(i),abs(i)) IF(DP1(1I).NE.0.0) TAN1 = atan2(DiI(1I),DP1(1)) if(dpi(i).eq.0.0) tani = 0.0 if (dp2(i).ne.0.0) tan2 = atan2(d2i(i),dp2(i)) if(d2i(i).eq.0.0) tan2 = 0.00 if (dp3(i).ne.0.0) tan3 = atan2(d3i(i),dp3(i)) if (dp3(i).eq.0.0) tan3 = 0.0 if (dp4(i).ne.0.0) tan4 = atan2(d4i(i),dp4(i)) if(d41(1).eq.0.00) tan4 = 0.00 if (dpxx(i).ne.0.0) tanxx = atan2(dxxi(i),dpxx(i)) if (dpxx(i).eq.0.0) tanxx = 0.0 if (dpyy(i).ne.0.0) tanyy = atan2(dyyi(i),dpyy(i)) if (dyyi(i).eq.0.0) tanyy = 0.0 tanab = -1.0/(pi * wvnr(i)) * saqrt(ab(i)) * = -1.0/(pi * wynr(i)) * saqrt(ab(i)) di(i))/(wvnr(i)**2*pi) di(i))/(wvnr(1)**2*pi) d3(i))/(wvnr (1) **2*pi ) d3(1))/(wynr(i)**2*pi) AO(i) = ab(i) / (2.0 * pi) tanM = tani - tanAB tanN = tan3 - tanAB A1idi(i) sqrt(d1i(i)) * sin(tanm) A1d3(i) sqrt(d3(i)) * sin(tanNn) A2did2(1) = -(d2(i) A2d1id4(i) = -(d4(i) A2d3d2(i) = -(d2(i) A2d3d4(i) = -(d4(i) GO TO 4001 tanO = tanxxX - tani tanP = tanxx - tan3 tanQ = tani - tanAB tanR = tan3 - tanAB A3d1(i) + 0.75 * wynr(i)**2 * sqrt(ab(i)) * saqrt(d1(i)) = 4.0/(pi * wynr(i)**3) * (-saqrt(di(i)) * sart(dxx(i)) * sin(tanO) * sin(tanQ) ) = 4.0/(pi * wvnr(i)**3) * (-sqrt(d3(i)) * saqrt(dxx(i)) * sin(tanP) A3d3(1 + 0.75 * wynr(i)**2 * sqrt(ab(i)) * sqrt(d3(i)) ) * sin(tanR)) Continue tans tanT Bid2(i B1id4(i tanu tanv tanw ) ) tan2 - tanAB tan4 - tanAB = -1.0/(pi * wynr(i)) * saqrt(ab(i)) * sqrt(d2(i)) * sin(tans) = -1.0/(pi * wvnr(i)) * sqrt(ab(i)) * sqrt(d4(i)) * sin(tanT) tan2 - tani tan2 - tan3 tan4 - tani 33050 33100 33150 33200 33250 33300 33350 33400 33450 33500 33550 33600 33650 33700 33750 33800 33850 33900 33950 34000 34050 34100 34150 34200 34250 34300 34350 34400 34450 34500 34550 34600 34650 34700 34750 34800 34850 34900 34950 35000 35050 35100 35150 35200 35250 35300 35350 35400 35450 35500 35550 35600 35650 35700 35750 35800 35850 35900 35950 36000 - 219 - tanx = tan4 - tan3 B2d2d1(i) = 2.0/(pi * wvnr(i)**2) * sqrt(di(i)) * sqrt(d2(i)) *(cos(tanu)+sin(tanuU) ) B2d2d3(i) = 2.0/(pi * wvnr(i)**2) * sqrt(d3(i)) * sqrt(d2(i)) *(cos(tanv)+sin(tanv) ) B2d4di(i) = 2.0/(pi * wvnr(i)**2) * sart(di(i)) * saqrt(d4(i)) *(cos(tanW)+sin(tanw) ) B2d4d3(i) = 2.0/(pi * wvnr(i)**2) * sqrt(d3(i)) * saqrt(d4(i)) *(cos(tanx)+sin(tanx) ) Cc GO TO 4002 tany2 = tanyy - tan2 tanz2 = tan2 - tanab tany4 = tanyy - tan4 tanz4 = tan4 - tanab B3d2(i) = -4.0/(pi * wvnr(i)**3) 1 * (-sqrt(d2(i)) * sart(dyy(i)) *sin(tany2) 2 + 0.75 * wvnr(i)**2 * sqrt(ab(i)) * sqrt(d2(i)) 3 * sin(tanz2)) B3d4(i) = -4.0/(pi * wvnr(i)**3) 1 * (-sqrt(d4(i)) * saqrt(dyy(i)) * sin(tany4) 2 + 0.75 * wynr(i)**2 * sqrt(ab(i)) * sqrt(d4(i)) 3 * sin(tanz4)) 4002 Continue 510 CONT INUE DORSAL 2eecut (© IF ALL GAGES ARE WORKING, USE THIS LOOP: GOSTOM?7 Ai(i) = (A1tdi(i) + A1d3(i))/2.0 A2(i) = (A2d1id2(i) + A2d1d4(i) + A2d3d2(i) 1 + A2d3d4(i)) / 4.0 A3(i) = (A3d1(i) + A3d3(i))/2.0 Bi(i) = (B1id2(i) + B1d4(i))/2.0 B2(i) = (B2d2d1(i) + B2d2d3(i) + B2d4d1(i) 1 + B2d4d3(1))/ 4.0 B3(i) = (B3d2(i) + B3d4(i)) / 2.0 is Cont inue Cc IF ONLY TWO DIFFERENTIAL CHANNELS ARE WORKING, USE: Cc GO TO 3077 Ai(i) = A1d3(i) A2(i) = A2d3d2(i) A3(i) = A3d3(1) Bi(i) = Bid2(i) B2(i) = B2d2d3(i) B3(i) = B3d2(i) 3077 Continue Cc Calculate MEAN direction for n=1,2,3 THTA1(i1) = atan2(B1i(i),A1(i)) * 180./3.14159 THTA2(i) = atan2(B2(i),A2(i)) * 180./3.14159 THTA3(i) = atan2(B3(i),A3(i)) * 180./3.14159 511 Continue 48050 48100 48150 48200 48250 48300 48350 48400 48450 48500 48550 48600 48650 48700 48750 48800 48850 48900 48950 49000 49050 49100 49150 49200 49250 49300 49350 49400 49450 49500 49550 49600 49650 49700 49750 49800 49850 428900 49950 50000 50050 50100 50150 50200 50250 50300 50350 50400 50450 50500 50550 50600 50650 50700 50750 50800 50850 50300 50350 51000 Cc Cc Cc Cc Cc Cc - 224 - Return End Subroutine SCAN(X,N,NGAGE,AVG,DXINCH) Dimension X(4100), HIGH( 1000) Real LOW(1000), LOLIM Integer HISTOP Calculates the mean and std.deviation (N-1 weighting) for the record. RUN = 0.0 SUM = 0.0 DO 119 IT=1,N ale) SUM = X(i) + sum AVG = SUM/N DO 130 I=1,N 130 RUN = (X(i)-AVG)**2 + RUN DEV = saqrt(RUN/(N-1)) Reduce those points beyond 3 std.deviations to 3 std. deviations beyond record mean or the average of neighboring points. HILIM = AVG + 3.0*DEV LOLIM = AVG - 3.O*DEV Khi = 0 Klo = 0 X(1) = AVG DO 300 I=2,N IF(X(1).LE.HILIM .and. X(i).GT.LOLIM) GO TO 300 IF(X(i).GT.HILIM) GO TO 150 IF(X(i).LT.LOLIM) Klo = Klo + 1 LOW(Klo) = X(i) IF(X(i-i).1t.LOLIM.or.X(i+1).1t.LOLIM) 1 X(i) = LOLIM IF(X(i-1).ge.LOLIM.or.X(i+1).ge.LOLIM) 1 X(4) = (XCi1-1)4+X(141))/2.0 GO TO 300 150 Khi = Khi + 1 HIGH(Khi) = X(i) IF(X(i-1).gt-HILIM.or.X(i+1).gt.HILIM) 1 X(i) = HILIM IF(X(i-1+).1e.HILIM.or.X(it+1).1e.HILIM) 1 K(1) = (XC i-1)4+X(14+1))/2.0 300 Continue Print out truncated points 9 aagagga - 225 - LOW(K1o0+1) = 900. HIGH(Khi+1) = 900. LOSTOP oO HISTOP 10) WRITE(4,875) NGAGE WRITE(4,890) Klo,Khi,Avg,Dev,Lolim,Hilim WRITE(4,900) GO TO 400 DO 400 I=1,N IF(LOW(1).eq.900.) LOSTOP=1 IF(HIGH(i).eq.900.) HISTOP=1 IF(LOSTOP.eq.O .and. HISTOP.eq.0O) 1 WRITE(4,901) LOW(i),HIGH(i) IF(LOSTOP.eq.1 .and. HISTOP.eq.0O) 1 WRITE(4,902) HIGH(1) IF(LOSTOP.eq.O .and. HISTOP.eq. 1) 1 WRITE(4,903) LOW(i) IF(LOSTOP.eq.1 .and. HISTOP.eq. 1) 1 GO TO 410 400 Cont inue 410 CONT INUE Average 2 adjacent points to halve the record size. N2 = N/2 DO 480 I=1,N2 J=1*2-1 X(1) = (X(§)+X(j+1))/2.0 480 CONT INUE Re-calculate mean. 405 SUM = 0.0 DO 440 I=1,N2 440 SUM = X(i) + SUM AVG = SUM/N2 Subtract mean from record and convert from volts to PSI. Divide diff records by distance between sensing points to give pressure differential per length of arm. DO 450 I=1,N IF(NGAGE.ne.5) X(i) IF (NGAGE .eq.5) X(i) 450 Cont inue ((X(Ci)-AVG)/5.0)/DXINCH (X(i)-avg) * 10.0 875 Format(/, 10x, ‘GAUGE NUMBER’, i2) 890 Format(i6,’ LOW truncations;’,i6,’ HIGH truncations’ ,/, 1 4x, ’Mean=’,f6.3,’ S.Dev=’,f8.5,’ Lower Limit=’, 2 f6.3,’ Upper Limit=’,f6.3) ~ 900 Format(4x, ‘LOW’ ,7x, ‘HIGH’ ) 901 Format(F8.2,F10.2) 902 Format(8x,F10.2) 903 Format(F8.2) Return End 140 Estimates direction using only absolute gage and one 300 ~ 226 = SUBROUTINE BLOCK(n,X,maxbik,b1k) DI MENSION X(4100) INTEGER BLK,STOP (N-BLK) DO 100 IJ=2,stop,blk SUM=0.0 MJ=IuU+BLK- 1 KU=Iu DO 130 KKU=kj,mj SUM=SUM + X(kkj) X(nm) = SUM/BLK NM=NM+14 Continue SUM=0.0 DO 140 kkj=ij,n SUM=SUM + X(kkj) X(nm) = SUM/(n-mj ) MAXBLK=nm Return End SUBROUTINE SURF 2(ab,d1,d2,d3,d4,ang1,ang2,ang3,ang4, icut, DIMENSION ab(2050) ,d1(2050) ,d2( 2050) ,d3(2050) ,d4(2050), ang1(400) ,ang2( 400) ,ang3(400), wvnr,blk,orient) wvnr (2050) INTEGER bik differential channel at a time. pi = 194159 DO 300 j=2,icut z = 1./wvnr(j) * sart(d1i(j)/ab(j)) IF(Z.LE.1.)ANG1(j )=ORIENT-acos(Z)*180. Z = 1./wynr(j) * sart(di(j)/ab(j)) IF(Z.LE.1.)ANG2(j )=ORIENT-asin(Z)*180. Z = 1./wynr(j) * sqrt(d3(j)/ab(j)) IF(Z.LE.1.)ANG3(j )=ORIENT-acos(Z)*180. Z = 1./wynr(j) * sqrt(d4(j)/ab(j)) IF(Z.LE.1.)ANG4(j )=ORIENT-asin(Z)*180. IF(angi(j).1t.0. )angi(j )=angi(j)+360. IF (ang2(j).1t.0O. )ang2(j)=ang2(j)+360. IF(ang3(j).1t.0.)ang3(j)=ang3(j)+360. IF (ang4(j).1t.0. )ang4(j )=ang4(j)+360. 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