EXPERIMENTS WITH A FREE FLOATING WAVE BUOY by Albert J. R. Galus v. United States Naval Postgraduate School THESIS EXPERIMENTS WITH A FREE FLOATING WAVE BUOY by Albert J. R. Galus June 1970 Thi& document haA be.cn approved ^oh. pubtlc dLUtU-biution _ k . Letting e ° = .1 and z = 300 feet (the depth of suspension for the sensor in the measurement made in this study), pressure measurements from waves with wave numbers greater than .0077 feet" , or frequencies greater than .079 seconds" will not be in error by more than 10$. Gaul and Brown [1] give more detail in the theory of a free floating wave buoy. 11 III. DESCRIPTION OF THE INSTRUMENT SYSTEM The instrument system has a transducer-buoy package, a signal conditioning deck unit, and recording units (Figure 1 ) . The transducer-buoy package (Figure 2) consists of a sensitive pressure transducer, small diameter (.060 in.) sea cable, and buoy hull, which contains a modulator, radio transmitter, batteries, and antenna. The transducer detects pressure changes by means of a vibrating wire whose frequency varies directly with the applied hydrostatic pressure. The sensitivity and frequency response are discussed in Section IV. The transducer and buoy electronics convert frequency changes into an FM signal with a center frequency of approximately 27 MHz. The components of this package are designed to minimize water and wind drag. The transducer has a .streamlined torpedo shape of length 30 cm. and diameter 3 cm. The buoy is circular with a 60 cm. diameter in horizontal section, and has an elliptically shaped vertical cross-section of depth 14 cm. The signal conditioning deck unit consists of a modified citizen's band radio receiver, a discriminator, a d.c. amplifier, and a band pass amplifier. The deck unit condi- tions the signal from the buoy so that a ten foot peak-to- peak wave results in a five volt peak-to-peak signal. The output signal does not represent absolute pressures; it reflects changes from the static pressure. 12 r- '"I h O i P 1 Fh cd u CD C CD | •H Fh •H • -H 1 • cp ' CD 6 •H \ O CP • tH 1 O -H • H CD 73 iX Fh > > Fn Q H 1 o ca cd O o P. i £ Eh O co e 1 < CD —. ■H < K ■p Q 1 •H 1 1 c ■ m> / \ y k A •^ o I CD 1 \ r 1 O 1 1 Fh co Fh 1 CD CO CD 1 > cd -h I •H CD 73 «H i 1 O C >H H 6 CD cd a 1 cd CD 1 (X m e < 1 \ t Fh hi) i— 1 cd P CO 1 1 0 tH C >s i Fh S* P CO 0 "^v S CD •H CO CO L-\- _^ __l p xr>__j cd P CD ( \° ° c ^ c Fh X5 V )H c cd CD c Cd Fh V ^ ^ ^ P 6 \ * -C o v«, ^ C Fh cd 3 O O CD 0 O Fh xo-, < CD p

, Ql co T5 CD co Fh C CO Fh CD o >3 M rH o| cd a Ph cd W CD •H CQj 1 £ D ■ 1 ol Fh g Eh O O CO m, h fc MD O cd Fh >»; c o Fh b£ p CD i-l a ^ — ' P 1 CO H Pi 3 cd, g T3 ml fe V O g . 1 , 1, rt C HP CD 3 y v | Fh 1 C5 L. 1 13 >) 60 cm 1 T 30 cm 300 feet 1 3 cm Figure 2. Transducer-buoy Package 1H The recording unit provided with the instrument is a Leeds & Northrup Speedomax H chart recorder. In addition to the chart recorder, the output signal from the deck unit was sent through a d.c. amplifier and recorded on a Sangamo 3500 1^-track magnetic tape recorder. A signal generator was also used to put a 60 Hertz reference signal on a track other than the data track during the period of recording in order to identify the data to be processed. A double-beamed oscilloscope was linked to the playback outlets of the tape recorder in order to verify that the data and reference signal were being recorded. More detailed information about the instrument can be found in Gaul and Brown [2] . 15 IV. CHARACTERISTICS OF THE SYSTEM This section discusses four characteristics of the instrument: frequency measurement limitations due to size of float, calibration dial characteristics, frequency response of the transducer-buoy electronics, and the response factor of the instrument. A. FREQUENCY MEASUREMENT LIMITATIONS DUE TO SIZE OF FLOAT The accuracy of pressure measurements, In part, depends upon the ability of the buoy to follow the surface of a wave The buoy does not respond to waves with a length less than twice the diameter of the float (2.33 feet). Therefore, let the minimum observable wave length, L , equal ^.66 feet, and utilize the deep water equation Lo 5-12 where T is the period of the wave in seconds and L is in ^ o feet. From this equation, T is 0.95^ seconds or frequency is 1.05 sec" . Therefore, theoretically, the buoy does not respond fully to passing waves with frequencies greater than 1.05 sec" (i.e. ~ 1 sec. waves). B. CALIBRATION DIAL CHARACTERISTICS The deck unit has a calibration dial used to maintain a 5 mvolt peak-to-peak output signal, which is equivalent to full scale deflection on the chart recorder for the same maximum wave height when the transducer is used at various 16 depths. For example, a dial setting of 500 when the trans- ducer is at a depth of 300 feet gives a 5 mvolt peak-to-peak signal when a ten foot peak-to-peak wave passes. Figure 3 shows the dial setting for various depths to get full scale deflection for 10 foot waves. Figure 4 and 5 show dial settings vs. peak-to-peak voltages at constant depths for 10 foot waves. C. FREQUENCY RESPONSE OF THE TRANSDUCER-BUOY ELECTRONICS Table I on frequency response of the transducer-buoy electronics was obtained from the manufacturer of the system, Bissett-Berman Corporation, Hytech Marine Products. The table indicates that the pressure transducer is more respon- sive to pressure changes as the absolute pressure increases. By applying increments of pressure at various absolute pressures with a piston-type pressure gauge tester, it was concluded that the instrument does not record the magnitude of the pressure changes with sufficient sensitivity unless the absolute pressure is greater than HO to 60 psi. There- fore, the instrument does not function properly in water with a depth less than 100 feet. This characteristic made it impossible to calibrate the meter by direct comparison with meters placed at near shore locations. D. RESPONSE FACTOR OF THE INSTRUMENT An attempt to compute the response factor of this instru- ment was made by obtaining power spectra of a known input and its response. The piston-type pressure gauge tester was 17 300 250 Depth (feet 200 150 100 50 < . :: ' ~t it : ; ■ ^ . _^ i , ■ XT. L ":;_+__ , ~h "^ f ~i— r ^ 1 r |— ! _i_ i ! 1 M p it U t\z . x .„ 4: X _+. ^ _+- _j_. 1 . _i [_ n ; U i . ! i [i 1 JT' ± i . I t- + \ _4_ \ \ 1 . \ 1 \ . _ . . .1 ... L.-.^4- \ \ y \ I 1 V i \ .J ZT_,_ 4 - \ -t 4-T \ \ i \ \ \ \ r \ \ \ ■ :r ± ■ ~ \ : \ r \ A"\ ) , ^_ VJ/ ! i ik I \ •" \ - -4- _j. _| 1 . \ \ 1 \ x i inr ± \ j ~4-4- - ±± , :t V *^ ^x \ i \ V i iV~ ! S i i 1 \ \ ! MM 1 \ 1 1 i i 1 \ /» ) i vIX , -^ ^~ " \ \ 1 1 \ I \ i ' ' ' \ \ X - 4 [ it : " \ , _, _u_ ^_ ; ; . V i i 1 , ; ; - \ 200 4oo 600 Dial Setting 800 1000 Figure 3, Depth vs , Dial Setting for 10 foot Wave 18 \ \ \ 1 1 \ \ \ L\ . \J/ Y \ \ Y \ 1. . .. \ \ Vn VjJ V lL \jl \ \ \ \ \ A"\ \V \ \ \ ! 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After the Impulse, the pressure was held steady for approximately 20 seconds . Three separate trials were made for which the input, as constructed from visual readings of the pressure gauge and stopwatch dials, is essentially as shown in Figure 6. The power spectrum analysis of this input and the analyses from the three outputs are compared in Figure 7. Variations in the spectra of these three responses were due to the dif- ficulties involved in creating three identical pressure impulses with the pressure gauge tester. Pressure 2 psi t t + 2 At= 2 sec. t = "* ' time 20 sec Figure 6. Input from Pressure Tester. 22 I /// /// / / - *-*/ ,//f _- — 1 •" 1 >> to fn -P cd «H p £> •H .O < CO m CD CO .-— -> CO H O CO a X5 CO C CD o K o cd T3 o CO C OvJ "--' cd >5 p o 3 C ft CD C 3 H cr CD P m Ph CO rH fo CD Eh O cd p O o rH CD * ft CO 23 The response factor was computed by the following formula: R ■ / AREAin AREA out R = Response Factor Area. = Area under input spectrum in stated frequency band Area , = Area under response spectrum in same band The results of this analysis were: 1. For frequencies greater than .15 sec" , the response factor was equal to 1.00. 2. For frequencies between .10 sec" and .15 sec" , the response factor was equal to 1.21. 3. For frequencies between .05 sec" and .10 sec" , the response factor was 1.63. Therefore, these results suggest that the instrument over- responds to low frequency (.05-. 10 sec" ) waves. Frequencies less than .05 sec" were not considered because the instru- ment wasn't designed to measure frequencies that low. There is uncertainty in this analysis due to the uncertainty in the slope of the input pressure curve. 2H V. FIELD OPERATIONS This section deals with the problems and techniques involved in handling the instrument system at sea. The main difficulties at sea occurred in handling the sea cable. The sea cable has a tendency to coil and kink whenever it is not under tension. When a severe kink or puncture in the insulation occurs, the sea cable does not conduct the signal properly. Furthermore, the sea cable becomes difficult to handle when wet because of its small diameter. In addition to these problems, the 90 lb. test sea cable may snap with sudden jei'ks. These problems were solved by taping a small diameter steel cable foot by foot to the sea cable. The rigidity of the steel cable prevents the sea cable from coiling and the tape enables the operator to get a good grip on the line. Furthermore, the steel cable increases the safety margin against losing the transducer. The field operations described here were made from the U.S. Naval Postgraduate School's 63 foot oceanographic research boat. This boat is well-suited to operations involving this instrument because the launching and recover- ing of the buoy could be done by hand. A larger vessel would need a water level platform or smaller boat in order to handle the buoy easily. It would be difficult to use a hoist because of the delicate nature of the instrument and the large antenna mounted on top of the buoy. 25 In launching the floating package, the first step is to secure the buoy end of the safety line. With the boat engines stopped, the transducer and sea cable are then lowered in a hand-over-hand method, care being taken not to allow the sea cable to scrape against anything. This is best accomplished with the transducer lowered on the wind- ward side of the boat. Then the sea cable and safety line are attached to the buoy, which is lowered by hand into the water. To obtain a vertical alignment with the trans- ducer, the buoy is pulled away from the boat. An audible tone from the receiver indicates that the system is in operation. It is recommended that the boat maintain a position 30 to 60 yards downwind from the buoy in order to insure strong reception of the buoy signal and to keep the buoy in sight. After the boat is in position and the equipment is functioning properly, the reference signal generator is turned on to indicate which portion of the magnetic tape has data to be processed. The recovery of the buoy is similar to the launching operation. The buoy is easily brought aboard, by hand, with the base of the antenna serving as a handle. The sea cable and transducer are then hauled slowly aboard hand-over-hand. These techniques for handling the instrument were satis- factory for waves as high as 12 feet with white caps present For higher seas, different techniques in handling the instru- ment may be required. 26 Further detail of the operation of the instrument can be found in the Bissett-Berman Manual [3]. 27 VI. RAW DATA Four wave records were made under varying sea and wind conditions. All four records were made in an area centered 10 miles WNW of Monterey Harbor. All measurements were made in water with a depth in excess of 800 fathoms. Table 11 describes the characteristics associated with each wave record . The Douglas Sea State Code taken from Fairbridge [4], describes codes 2, 3, and 4 (used in Table II) as follows: State 2 small wavelets, crests of glassy appear- ance, not breaking; State 3 large wavelets, crests begin to break, scattered wh i t e c ap s ; State H moderate waves taking longer form, many whitecaps, some spray. CD *~> -P CO TJ Cd -P o rH o CEO H OJ viD rH •H -H C 1 1 1 1 ^ -p ^ ir- C— ^T ir- CO -— ' rH w CO cd (D rH cd -P bO cd cd on ^3- C\J on 3 CO -P O 00 P rH Cd rH O o o C C cd o O o o •H C «H C o o o o cd O hO hC o o o o 6 co on > >> CD CD CD cd cd C a -P s S 3 3 cd h> h> P V s / p c N > r . — ■ Jjl ) ^ / > !: > ^ > > / X ^ ■*< r -- ^ V ^ ^J ) > s \ >- ,> ^ *> i i-- ^ s \ n s^ — ,-> ^ > <. 7^ < r X •-, ^ <^ ^— -, j^~ Cf~" T ^> -r*= - ^ > C^ •\ — — x ^— -^ r^ iT^ ^ ~^--_^ _— — ^ fi£< ^ ~^^~— — __-— - ^^ 2 c *s ■P o CU Cm O £ -P co -p c CD co CD Fh (D M c o •H co •H > •H Fh O •1-3 Oj 6 31 record by playing back the data at a speed increased by a factor of 32 times the recording speed. Under these con- ditions, one second of real data was represented by I.56 mm on the chart paper. Due to the fixed sampling rate of the digitizer, the sampling interval, At, was . 163 seconds. According to the Nyquist criterion, the maximum allowable At is: At max 2f max With f equal to 1.05 cps from Section IV, At = . ^4 76 max H J F ' max seconds. Therefore, the actual sampling interval, .163 seconds, successfully meets the Nyquist criterion. The power spectrum was obtained by utilizing IBM sub- routine RHARM. This subroutine computes one-dimensional Fourier coefficients by using the fast Fourier transform. The power spectrum was smoothed over by averaging every 20 Fourier coefficients resulting in approximately 40 degrees of freedom. The entire procedure was performed by program "Spectrum" in Appendix B. 32 VIII. COMPARISON OF RESULTS WITH THEORETICAL WAVES Figures 9-12 in Appendix A give the power spectra of the four records taken by the wave meter. These spectra were compared with visual observaitons and with waves expected from storm areas indicated by weather maps obtained from Fleet Numerical Weather Central. Significant height estimates were obtained by observing by eye (with two different observers) and recording the vertical movement of the buoy from trough to crest of a large number of successive waves. The average of the high- est one-third of these observations gives the significant height. From the power spectra, the significant height was calculated by H1/3 = 2.83 V^T where E = 2(Variance) = area under power spectrum Table III and Figure 13 give the results of these computa- tions. The results suggest that the meter may have responded accurately to both principle spectral bands. This is not in agreement with the analysis concerning the known input and its response from Section IV. However, Figure 13 is only suggestive because of the. limited number of records taken . The power spectra were compared to the reports from the Fleet Numerical Weather Central of the combined sea 33 Number of Waves Observed Visual Hl/3 (feet) Variance Meter Hl/3 (feet) May 11 125 5.10 1.85 3.85 May 20 75 8.35 9.15 8.55 June 1 288 2.21 1.45 3.40 June 2 261 1.55 2.03 4.05 TABLE III RESULTS FROM SIGNIFICANT HEIGHT ANALYSIS 10 Visual Hl/3 (feet) s 11-- / / / / o / o/ / / / 2- / / / 8 10 Meter H-,,, (feet) Figure 13. Eye Observations vs. Meter Observations of Significant Height 31 height, which gives contour lines representing significant sea height. All the combined sea height analyses for the appropriate days indicate a significant height of approximately three feet in the vicinity of the mouth of Monterey Bay (Figures 14-17 in Appendix A) . This roughly corresponds to all the reports except the one taken on the 20th of May. However, the combined sea height analysis may not be too reliable because it is based on a small number of reports for the area along the coast of California. In addition, sea surface atmospheric pressure analyses were used to locate and investigate the generating areas of the dominant frequency bands for the swell recorded by the instrument. Taking the peak frequency from the power spectra, the group velocity of the dominant swell was com- puted using c = 1*5.- g 2f c = deep water group velocity in knots f = peak frequency in sec" . Then, the distance traveled by the dominant wave was computed by using the difference between the time of the sea surface pressure analysis and the time the wave record was taken. A line was drawn on each sea surface pressure analysis (Figures 18-21 in Appendix A) to represent the starting location for the swell observed at Monterey Bay. These lines appear to 35 lie in each case within the possible generating area of the dominant frequency swell. Computations were also made to determine whether, accord- ing to a commonly used wave generation model, winds in these possible generating areas produced the recorded dominant frequencies. The geostrophic wind speed was calculated from the pressure field using V = r 1 1 &? = 9.53 AP g L 2ftpsin 4> J AN sin* AN where V = geostrophic wind speed in knots ft = angular velocity of earth = latitude AP = pressure difference in millibars AN = latitude change (60 miles » 1 degree of latitude) The surface wind speed, V , is then approximated closely enough for present purposes by; V = . 8V s g With values of surface wind speed and estimated fetch, the maximum periods which these generating areas were capable of producing was estimated by using co-cumulative spectra for wind speeds as a function of fetch, as given by Pierson, Neumann, and James [51. In all four cases, the generating areas apparently were capable of producing the dominant frequency swell recorded by the meter. Table IV gives the results of the computations made. 36 TABLE IV RESULTS FROM GENERATING AREA ANALYSIS Peak Freq. (sec-1) Period (sec) Travel Time (hrs. ) Miles Traveled V s (knots) Fetch (miles) May 11 .08 12.5 Hi 900 14.7 200 May 20 .11 9.1 35 550 8.2 200 June 1 .08 12.5 65 19^0 9.4 200 June 2 .08 12.5 65 19^0 13.0 200 Furthermore, the surface pressure analysis seemed to indicate that secondary peaks in the power spectra are due to local wind conditions. For example, it is noted that a large secondary peak not present on 1 June occurs at approximately .25 sec" on 2 June. From Section VI, it was recorded that there was a large increase in the wind over that 2k hour period. This suggests that the secondary peak was due to the local winds. 37 IX. CONCLUSIONS The portable free floating wave buoy provides a rela- tively inexpensive method for gathering wave records. The evaluation of the records suggests that the main spectral bands, the swell and the local wind waves of the wave system, are properly resolved by the meter. However, further dynamic and static calibration is suggested in order to resolve the discrepancy in amplitude measurements between the input-response analysis and the significant height analysis. Comparison of the buoy's wave records with the simultaneously made records of well-calibrated wave meters on Flip would be a desirable future project. Also, further comparisons with weather analyses would be profit- able in evaluation of the meter. The portable nature and ease of operation of the free floating wave buoy provide the opportunity for deep water wave forecast verifications to be made by organizations which are financially limited. 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Xn„ ia the subroutine o 1 2N-1 computes Fourier coefficients, a , a-,, b, , ap , bp,... aN— rs kj\T -i j a in the equation + I aN(-l)J where j = 0, 1, ... 2N-1 Therefore, with N inputs from a time series, output contains : aQ — , bQ = 0, ais bx, a2, b2, ... aN/2, bN = 0 to get the power spectrum, Program Spectrum gives the spec tral estimate, S, equal to: M N 1 ■I S = Z N=l 1N k=2 a, + b, k k 2 h where T = record length. 56 BIBLIOGRAPHY 11.. Gaul, R. D. and Brown, N. L . , A Comparison of Wave Measurements from a Free-Floating- Wave Meter and the Monster Buoy, paper presented at 2nd International Buoy Symposium, Washington, D.C., 1967. 2.. Gaul, R. D. and Brown, N. L., A Free-Floating Wave Buoy paper presented at Conference of Electronic Engineer- ing in Oceanography, London, 1966. 3. Bissett-Berman Corporation, Instruction Manual: Free- Floating Wave Buoy, Model 1854, October, 1968. 4-.. Fairbridge, Rhodes W., ed. The Encyclopedia of Ocean- ography , p. 790-791, Reinhold Publishing Corporation, 1966. 5. Pierson, W. J., Neumann, G., and James, R. W. Practical Methods for Observing and Forecasting Ocean Waves by Means of V/ave Spectra and Statistics, p. 38-44 , U.S. Naval Oceanographic Office, i960. 57 INITIAL DISTRIBUTION LIST No. Copies 1. Defense Documentation Center 2 Cameron Station Alexandria, Virginia 2231^ 2. Library, Code 0212 2 Naval Postgraduate School Monterey, California 939^0 3. Department of Oceanography 3 Naval Postgraduate School Monterey, California. 939^0 4. Assoc. Professor J. B. Wickham 1 Department of Oceanography Naval Postgraduate School Monterey, California 939^0 5. Assistant Professor E. B. Thornton 1 Department of Oceanography Naval Postgraduate School Monterey, California 939^0 6. LT(jg) Albert J. Galus , USN 1 2072 Starling Way Fairfield, California 9^533 58 UNCLASSIFIED Socuntv Classification DOCUMENT CONTROL DATA -R&D Security classification ot title, body ol abstract and indexing annotation must be entered when the overall report is classitied) originating activity (Corporate author) Naval Postgraduate School Monterey, California 939^0 IEPORT SECURITY CLASSIFlO Unclassified 26. GROUP IEPOR T TITLE EXPERIMENTS WITH A FREE FLOATING WAVE BUOY DESCRIPTIVE NOTES (Type ol report andjnclusive dates) Master's Thesis; June 1970 S AU THORISI (Fust name, middle initial, last name) Albert J. R. Galus , Lieutenant (junior grade), United States Navy REPOR T D A TE June 1970 la. TOTAL NO. OF PAGES 58 76. NO. OF REFS 5 ta. CONTRACT OR GRANT NO. PROJEC T NO 9a. ORIGINATOR'S REPORT NUMBER(S) 10. DISTRIBUTION STATEMENT This document has been approved for public release and sale its distribution is unlimited. 11. SUPPLEMENTARY NOTES 12. SPONSORING kR Y AC Tl VI " Naval Postgraduate School Monterey, California 939^0 13. ABSTRACT A free-floating wave meter was used to obtain a time series of wave-induced pressure variations in deep water. The meter's response was roughly checked against a piston- type pressure testing apparatus. Techniques in the operation of the meter were developed involving a slight modification in the suspension of the sensor. Power spectra of the pressure variations were obtained from the digitized wave record via the amplitude spectra given by the fast Fourier transform. Characteristics of the power spectra of the metered waves were used to evaluate the meter by comparing them with the waves that might be anticipated (on the basis of theory) from the existing surface wind field and with visual observations of the metered waves. DD,?„"v".s1473 ,PAGE" S/N 0101 -807-681 1 UNCLASSIFIED 59 Security Classification UNCT.ASSTFTF.P Security Classification KEY WORDS FREE FLOATING WAVE BUOY WAVE MEASUREMENTS WAVE METER DD,FN°oRvM651473 (back, UNCLASSIFIED 60 Security Classificati Th Gl c. Thes i s G1409 c.l 143 Galus Experiments with a free floating wave buoy. 7 1 1945V 30CT74 2275U Thesis G1409 c.l 4 *> 3149 Galus Experiments with a free floating wave buoy. thesG1409 Experiments with a free floating wave bu 3 2768 002 01016 7 DUDLEY KNOX LIBRARY