TR No. 22 TURBULENCE MEASUREMENTS IN A TIDAL CURRENT by: A. T. Massey NAVAL UNDERWATER WEAPONS ace i ew Te RESEARCH AND ENGINEERING STATION WATER © ec) Uae NEWPORT, RHODE ISLAND a GL ee been approved 3313 | / SZ aa am Ar ‘m3 UNCLASSIFIED y UNCLASSIFIED NAVAL UNDERWATER WEAPONS RESEARCH AND ENGINEERING STATION August 1968 Task Assignment No. NEWPORT, RHODE ISLAND TECHNICAL REPORT TURBULENCE MEASUREMENTS IN A TIDAL CURRENT Prepared by: At Msaey— Ae aie Gs, Go es Technical Director M. J. WINTON Commander, USN Commanding Officer R360-FR-107/219 1/R011-01-01 This document has been ‘approved for public release and salé; its distribution is Unlimited. TR No. 22 UNC LASS TIFIED FOREWORD This report was submitted to the Department of Meteorology at the Massachusetts Institute of Technology in partial fulfillment of the requirements for the degree of Master of Science. All work was performed under Task Assignment No. R360-FR-107/219 1/Rol1-01-01. TR No. TR No, 22 ABSTRACT Measurements were made of the component of turbulent velocity along the axis of a 3-knot tidal current 1.5 meters below the water surface using a ducted impeller current meter. Values of the one-dimensional energy spectra were computed on a digital computer at wave numbers from 0 em-l to 0.157 cm=), The composite energy spectrum obtained from the individual spectra was of the -5/3 power law form predicted by the Kolmogoroff hypothesis for wave numbers from 0.01 cm=! to 0,026 cm-l. At higher wave numbers the energy spectrum decreased more rapidly than predicted because of attenuation of the turbulent velocity variations caused by the relatively large size of the current meter. The average variance for the field of turbulence was 55.6 cm2 - sec~* 425.0 (standard error), and the average rate of energy dissipation by viscosity was es- timated using the Kolmogoroff hypothesis as 0.84 em? - sec”, ii TR No. 22 ACKNOWLEDGEMENTS Gratitude is expressed for the assistance of Miss Diane Riley, Thomas Conrad, John Sabulis, and Robert Gunning of the Naval Underwater Weapons Research and Engineering Station in the data processing, and for the assistance of Wilfred Buckley in making the measurements. Much thanks is due Dr. David Shonting for the valuable assitance given in connection with the instrumentation and data analysis. The astute guidance and interest given by Professor Eric Mollo-Christensen is greatly appreciated. In particular, I wish to thank my supervisor, Raymond J. Grady, for the encouragement and useful suggestions he has provided throughout. iii Abst ract TABLE OF CONTENTS etooeeoooeondgeeteonvnooseentso0d go0o0oeoedveo0o06800068 Acknowledgements .csoococcecerooccoescesegrnsnsnacoee List of IBLE EO OOO DDC ODOCOOOODODOO000NO000000000006 List of MAME Ob O000.00 GOCO0O00 00000000 0000000000000 NOMeNCLA GUC iororoveoreleve/ ele) efelclelolerelelelololelolorelalelevelersiclcievayelclolele MBI WALONG GHOGOODODDOOOOOORODDOGOOOGCOD00dD000000 TMNSEGUMENtATHOri co eaicie c\clelc elele\e erclelclelelelcro 6 Description of the Ducted Impeller Current Meter. Calibrationcsseccce Response Time oscere Sensitivity.-coresc: Output .eccsecssccee AVTAS ING 5c. ¢ 6160 6416 06 Field ObservationsS...-..¢ e o ° o e Data ANG SUS crovercicyolelevote/slecrerorolets a a2ee o ry a ° 2 2 Analog to Digital Conversion... ¢¢r oe of @ 2 eae oe ° o @ J] 9 8 6 eseceteecetnac@asaesd ° 6 ¢ 6 ® TR No, 22 6 6 e 2 e Computation of Autocovariance Series & Energy Spectra Location of Samples.. Results and Discussion... 2 INOHSSrcroretavelcrcreretenovalene Statistical Variations Among Samples € i.) t.) coese eceese ocaoes 0 ees ee tec 200978 @oveed eeetaec Copalwe Cn, ogadsoesoooagdncoqacoeadooeen Planned IRSEISEWEA 6 BO COC OUO00000 GO D00G00CE € o¢ eocecenea 6 e ° e 6 6 iJ e e e6 chet platen oe vi eo Viil 9° ix o8 Al 2° 4 00 h oe 4 2° > es f 2° 7 26 8 25 16 33 12 see gar ‘aha! sa alle 4 20 20 to 22 50. BS sree TR No. 22 Page No. RERETENCES) wellereleleveotenel cle eusleveellelierolelels\eileek=s/(eiis S0000' pe0Db0 OS 506.0010 6.00 29 Appendix A Response of Current Meter to Accelerated Flow...... A-1 Appendix B Computer Programs............-. SaG0DDGOcEOMOD OCC OuUDO B-1 Appendix C Numerical Tabulation of Results........ socoooodddaa Gal TR No. ILLUSTRATIONS Ducted Impeller Current Meter, 3/4 View Ducted Impeller Current Meter, End View Waveforms of Outputs of Current Meter and Schmidt Trigger Waveforms of Outputs of Current Meter and Binomial Counter Calibration Curve for the Current Meter Calibration Coefficient vs Angle between Axis of Current Meter and Direction of Flow Wind Tunnel Calibration Curve for the Current Meter Section of C. & G S. Chart No. 353 Showing the Area within Which Measurements Were Made Lower End of Mounting Strut and Current Meter Mounting Strut on Bow of Boat NUWS Torpedo Retriever Block Diagram of Analog to Digital Conversion Process Typical Digitized Velocity Data Typical Digitized Velocity Data Typical Digitized Velocity Data Typical Digitized Velocity Data Typical Digitized Velocity Data Autocovariance Series Corresponding to Figure 13 Autocovariance Series Corresponding to Figure 14 Autocovariance Series Corresponding to Figure 15 Autocovariance Series Corresponding to Figure 16 Autocovariance Series Corresponding to Figure 17 Energy Spectrum Corresponding to Figure 13 Energy Spectrum Corresponding to Figure 14 vi 22 TR No. 22 ILLUSTRATIONS - cont'd Cole 26. Calas 28. 29. 310), Buk Bee 33. 3h. Energy Spectrum Corresponding to Figure 15 Energy Spectrum Corresponding to Figure 16 Energy Spectrum Corresponding to Figure 17 Variance vs Downstream Distance from Channel Buoys Composite Energy Spectrum Composite Energy Spectrum with Noise Correction Braincon Corp Type 430 Ducted Impeller Current Meter, 3/4 View Braincon Corp Type 430 Ducted Impeller Current Meter, End View Modified Cox Company Turbine Flow Meter, 3/4 View Modified Cox Company Turbine Flow Meter, End View Current Meter Mounted in Wind Tunnel for Measurements of Response Time Instrumentation for Measurements of Response Time Response of Current Meter as a Function of Time for Step Function Change in Wind Tunnel Velocity Response Time as Function of Mean Velocity vii TR No. 22 TABLES Page mevolley il, AUHLGlEML (Ciuaartcahey eho Sieehwaloml. Lio 5 5 boo Oo Oot Oo MD Table 2. Representative Section of the Computer Printout Of the DigitrzedeViellocdtyeWataueg mal voce LA. alec) vel ety Gouueuam eevee Mable. (3. ". POSTtIONS .Of Samplesiist sud eibn ce timia ost es 8 de ee oem es tees ee ELS Vali TR No. 22 NOMENCLATURE three-dimensional energy spectrum function (cae) =2 energy of the turbulence per unit mass (cn =sec ) rate of dissipation of energy by viscosity (encesaens) one-dimensional energy spectrum (em3=sec™*) =] wave number (cm ) wave number at which the maximum in the energy spectrum is located (cm=1) wave number at which the maximum in the dissipation spectrum is located (cm) time (sec) component of velocity along axis of current relative to boat (cm-sec™+) velocity of towing along axis of current (emesec™!) distance of advance of the current meter relative to the water along axis of current (cm) distance along axis of current relative to channel buoys (meters ) component of current along axis (meters-sec™=) component of turbulent velocity along axis of current; u(x) = U(x) + u'(x) (cmesec™) intervals at which data is spaced; x =k Lyn i = 0), als 1 een (em) lag (cm) intervals at which values of the autocovariance series are computed; =n AX x. m= Ly 2.7355 leaioreen at Gem) 1% L ae 35 Tt Ty Ra(k AS ) on S Vaio) Ry(k O§ ) TR No. 22 maximum lag at which a value of the autocovariance series is computed (cm) length of sample (cm) Nyquist wave number (cm=1} time from start of run to beginning of ith rotation of impeller (sec) period of rotation of the impeller (sec) period of ith rotation of impeller (sec) apparent autocovariance function (cm@=sec™*) hanning lag function (non-dimensional) hanning spectral function; the Fourier transform of fy( & ) (cm) =) aes ; : 2 = modified apparent autocovariance function (cm“=sec aliased, modified, one-dimensional energy spectrums the Fourier transform of the autocovariance series ee ASS) (om3-sec™-) velocity of water flowing through current meter (cm=sec=1} angular velocity of impeller (rad-sec71) diameter of impeller (cm) advance diameter ratio; J = u/(@) D) (non-dimensional) moment of inertia of impeller (gram-cm®) calibration coefficient of the current meter (cm) resultant driving torque on impeller (dyne=cm) angle between axis of current meter and the direction of towing (degrees) TR No. 22 constant component of velocity (cm-sec~1) «© varying component of velocity (cm-sec71) constant component of impeller angular velocity (rad-sec71) varying component of impeller angular velocity (rad-sec~1) response time (sec) response distance (cm) highest frequency at which the current meter is responsive to variations in velocity (Hz) wave number corresponding to Prax (em _) average value of the instantaneous velocity u(x) over the interval A x(cm-sec™~) kinematic vicosity (cm@-sec~1) density (gram-cm73) vector position of point in space (cm) vector displacement with respect tox (cm) ith component of turbulent velocity (cm-sec71) Fourier transform of the autocorrelation series; P on © K) divided by the variance R,(0) (cm) a error in the ith value of uj(cm-sec™+) error in the kth value of the autocovariance series (cm2-sec72) variance of the ith sample (cm@-sec™2) value of the eampued energy spectrum for the ith sample (cm3-sec"*) ? san(K) divided by the variance of the ith sample (cm) final, constant value of the step function change in the velocity (cm-sec~t) angular velocity corresponding to uf (rad-sec7l) initial period of rotation of the impeller (sec) é final period of rotation of the impeller (sec) eal TR No. 22 INTRODUCTION The important problems in the theory of turbulence are; the determination of the energy spectrum function, E(K, t), and hence the total kinetic energy of the turbulence, E, and the rate, € , at which the energy is dissipated by viscosity; the change in E(K ,t), E and with decay. A limited number of theoretical predictions are available concerning the form of the energy spectrum function in the low wave number range of the spectrum, the reason being that the structure of turbulence in the low wave number range is, in general, inhomogeneous, anisotropic and strongly dependent on the mean flow from which the energy of the turbulence is derived. Such characterisitcs result in an intractable theoretical analysis. The structure of turbulence in the high wave number range of the spectrum, however, has been hypothesized (Kolmogoroff, 1941) to be homogeneous, isotropic and statistically independent of the mean flow. The Kolmogoroff hypothesis states that at sufficiently high wave numbers the statistical structure of turbulence has a universal form and is uniquely determined by the parameters€ and V, the kinematic viscosity. The range of wave numbers for which the preceding is applicable is known as the universal equilibrium range, Within this range it can be shown through dimensional analysis that the energy spectrum function can be written as HY iG E(Ge | ek ay), (1) where Fk/k,) is a universal function and as (2/25 (2) is the wave number (approximately) at which the maximum in the energy dissipation spectrum is located. TR No. 22 It has further been hypothesized (Kolmogoroff, 1941) that if there exists within the equilibrium range of wave numbers a range (the inertial subrange) where dissipation is negligible, then E(/X, t) is independent of Y and therefore of Ky 3 and consequently F(K/ky must be a constant, Therefore, within the inertial subrange, BR Se BORO RIE Ra (3) The necessary condition fcr the existence of an inertial subrange of wave numbers has been shown (Batchelor, 1) to be that condition in which the Reynolds number of the turbulence is large enough so that the Wave numbers corresponding to the maximum dissipation of energy and to the maximum energy are considerably separated on the wave number scale. This condition is satisfied (Grant, Stewart and Moilliet, 2) in large scale oceanographic flows, wherein the wave numbers corresponding to the Maximum energy are several orders of magnitude smaller than those cor- responding to the maximum dissipation of energy. (The wave numbers cor- responding to the maximum dissipation of energy are of the same order of Magnitude for oceanographic turbulence as for laboratory turbulence. ) Measurements of the turbulent velocity component parallel to the axis of a tidal current were made by Grant, Stewart and Moilliet (2) using a hot film anemometer mounted on the front of a heavy, towed body. The instrument was towed from the research vessel C. N. A. Ve OSHAWA at a depth of 15 meters in Discovery Passage, adjacent to Vancouver Island. One-dimensional energy spectra were derived from samples of the data using analog filtering techniques over the range of wave numbers from 0.01 em™*+ to 35 em™1, ‘The spectra followed the -5/3 power law predicted by the Kolmogoroff hypothesis from wave numbers of around 0.01 em™t to emt, thus indicating the extensiveness and importance of the inertial subrange in oceanographic turbulence, Similar measurements have been made by Grant and Moilliet (3) of the turbulent velocity component perpendicular to the axis of a tidal cyrrent (Discovery Passage south of Cape Mudge). Although a calibration of the hot film anemometer was not obtained, the spectra were of the -5/3 power law form when represented on an arbitrary scale, The first set of measurements allowed the energy dissipation spectra to be calculated, from which values of € and hence the universal constant K could be determined. TR No. 22 Additional measurements have been made by Grant and Stewart (5) of the turbulence spectra in a tidal current (Georgia Straight and Juan De Fuca Straight) near the water surface in the presence of sur- face waves and noise. The results of the previous measurements were used to determine values of € , although the energy dissipation spectra could not be calculated because of the interference. Complementary measurements to those of Grant et al were made over the low wave number anisotropic range of the spectrum from approximately 0.01 meters™+ to 2.0 meters~1 by Bowden (6) and by Bowden and Howe (4). The jactrument used. was an electromagnetic flowmeter. Although the Kolmogoroif hypothesis does not apply to the low wave number range, the spectra obtained from the measurements by Bowden and Howe were reported to follow a power law similar to that predicted by the Kolmogoroff hypothesis, but with an exponent of the order of -1.3 instead of -5/3 for wave numbers from approximately 0.001 om=+ to 0.01 em7+, Shonting (8, 9, 15, 16) has used a ducted impeller ocean current meter to make measurements of the particls motions in ocean waves to frequencies of 2,5 Hz. The results demonstrated the potential of the current meter for measuring relatively high frequency and/or wave number oceanographic turbulence. The hot film anemometer used previously (2,3,5) is a complex instrument requiring considerable electronic equipment to obtain an output suitable for data analysis. In addition, difficulties are encountered in using the hot film anemometer probe at sea because of the corrosive and electrolytic properties and the high level of contamina- tion of sea water. The advantages of the ducted impeller current meter in comparison are simplicity, sturdiness, and reliability, desirable characteris- tics in an oceanographic instrument; the output of the current meter is of the appropriate form for digital spectral analysis with respect to wave number. The objectives of the measurements reported herein, then, are to; (1) obtain, using the current meter, additional turbulence spectra from a tidal current which can be compared with the spectra obtained using the hot film anemometer in order to determine the applicability and/or the limitations of the current meter for measuring oceanographic turbulence; (2) provide additional experi- mental confirmation of the Kolmogoroff hypothesis. w Figure L Ducted Impeller Current Meter, 3/4 View TR No. Ce. TR No. 22 INSTRUMENT ATION The ducted impeller oceanographic current meter (figures 1 and 2) consists of a six-bladed impeller axially mounted in the center of a brass cylinder approximately 8.5 cm in diameter and 15 cm long. The impeller is manufactured of micarta (laminated phenol formaldehyde). The impeller shaft is terminated at either end with carbide pins which rest in quartz V-bearings mounted in neoprene; it is supported at either end by three struts spaced 120 degrees apart. A miniature Magnet (weighing around 5 grams) is imbedded in the tip of each blade, and a coil is potted with epoxy resin in a housing mounted externally on the cylinder. In operation, the instrument is aligned with the water flow which, impinging on the blades of the impeller, is defiected with a resultant force exerted on the blade surface causing the impeller to rotate. When a constant angular velocity has been achieved, the angular velocity is directly proportional to the water current over the specified linear operating range of the instrument; the constant of proportionality is the calibration coefficient, k, for the current meter. The rotation of the impeller, and consequently the passage of the magnets in the tip of each blade past the coil, induces a series of voltage pulses which are trans-= mitted through a two-conductor waterproof cable to appropriate recording instrumentation. The frequency of the pulses generated thus becomes a measure of the water velocity. The waveform obtained from the current meter is shown in figures 3 and 1, Calibration The current meter was calibrated in a water tank by towing the instrument at various known, constant velocities and measuring the fre- quency of the pulses generated. For the calibration, the axis of the current meter was aligned with the towing direction. The calibration curve is shown in figure 5, from which the calibration coefficient, the slope of the calibration curve in the linear range, was determined as 3.12 cm. Thus, (LC) (me Pas) 2 SD (red ee BS cm ie (4) Figure 2 Ducted Impeller Current Meter, End View TR No. 22 TR No. Figure 3 Waveforms of Outputs of Current Meter and Schmidt Trigger 22 22 TR No. Waveforms of Outputs of Current Meter and Binomial Counter Figure 4 SLOPE = 1/2nk 4 = 0.0510 ROTATIONS/cm IMPELLER ANGULAR VELOCITY, (2 (RPS) 0 20 40 60 80 WATER VELOCITY, U (cm/SEC) Calibration Curve for the Current Meter Hieure 5 TR No. 1.0 k (0)/k(0) 0.8 0.6 0.4 0.2 0 20 40 60 80 100 ®@ (DEG) (® = MEASURED VALUES; ... = COSINE 8) Calibration Coefficient vs Angle Between Axis of Current Meter and Direction of Flow Figure 6 TR No. 22 Additional tests were performed to determine the variation of the calibration coefficient with flow direction. For these tests the axis of the current meter was set at various known angles relative to the towing direction, and the frequency output was measured at known, con- stant velocities. The variation of k as a function of GC, the angle between the axis of the current meter and the towing direction, is shown in figure 6, which indicates that k is given very closely by Ix (&) =K(6) Gs 2 B12 2 Z2ec (5) The largest deviation occurred at values of @ near "7/2 and was probably caused by asymmetry in the mounting arrangement. Since the component of velocity = “ A A q = iu + jv + kw in the x direction (taken along the axis of the current meter) is u = [7 | cos B 5 the current meter is sensitive to the component of velocity along the axis and insensitive to the components perpendicular to the axis. A second calibration of the current meter was obtained using a low speed wind tunnel (appendix A), The calibration curve is shown in figure 7. The slope of the straight line is the same as that obtained from the in-water calibration, but the straight line intercepts the U axis at 10 cm-sec™/ instead of passing through the origin. Since the measurements were performed at relatively low wind tunnel velocities, the difference is attributed to error in measuring the low velocities with a pitot static probe. The correct value of the cali- bration coefficient is assumed to be the in-water value. Response to Accelerated Flow The current meter has been used (Shonting, 8, 9, 15, 16) previously to make measurements of the particle motions in ocean waves. For those measure= ments the mean water velocity was zero or near zero. Under such conditions it was determined through wind tunnel and in-water tests (8, 22) that the response time of the current meter for a step function change in water velocity IMPELLER ANGULAR VELOCITY, § 2 (RPS) Figure 7 e = MEASURED VALUES 7 - - -- = WATER TANK CALIBRATION , 20 40 60 80 100 WATER VELOCITY, U (cm/SEC) Wind Tunnel Calibration Curve for the Current Meter TR No. 120 22 TR No. 22 is of the order of 50-70 milliseconds, In making the turbulence measure- ments reported herein, however, a towing velocity of approximately 400 cm-sec™ was superimposed on the turbulent velocity field. Therefore it was necessary to determine the response of the current meter to a step function change in velocity superimposed on a mean velocity. Wind tunnel measurements of the response time of the current meter are described in appendix A. It was found that the response time for a relatively small step function change in water velocity varies inversely with the mean velocity such that the product of the response time and the mean velocity (the response distance) is a constant with a value of 0.97 cm. The frequency response of the instrument is determined by the response time; the instrument is insensitive to variations in velocity occurring at frequencies greater than ] Ms sisted << Srp re (6) 1 Assuming that Taylor's hypothesis is applicable, that is, aU a+ i rials eae (7) this corresponds to a wave number of | <¢ a K elle ee Peane ies = (8) which, from the previous measurements of response time, is balls mie =| Fe Ae Gua eas icine Thus the current meter hag the capability for measuring turbulence over the constant range of wave numbers from 0 to 0.103 om71, regardless of the mean velocity superimposed on the turbulent field by towing. (Actually the value given for Kay, is optimistic because of the size of the current meter, 15. cm long; a more reasonable value is of the order of 1/150 cm = 0.0068 em~,) Since spectral analysis of turbulence is more correctly performed with respect to wave number than frequency, this is an important result. TR No. 22 Sensitivity The lowest water velocity sufficient to maintain a constant angular velocity of the impeller is of the order of 5 to 7 em-sec™+, No measure-~ ments were made to determine the sensitvity of the current meter as a function of velocity, but typical commercially available turbine flow meters have sensitivities equal to +0.25% or less of the mean velocity. If the performance of the ducted impeller current meter is assumed equal to that of commercial flow meters, it has a sensitivity of f1 cm-sec~+ Output From the calibration coefficient, the distance required for the current meter to advance relative to the water in order for the impeller to complete one rotation is 21K = (6.28)(3.12 cm) = 19.61 cm, The output of the current meter is six pulses per rotation or 6 pulses/19.61 cm = 0.306 pulses per cm advance. In practice the output of the current meter was modified using a Schmidt trigger-binomial counter circuit in a divide-by-six mode to obtain one pulse instead of six per rotation of the impeller. This was found necessary because of the approximately 410% variation in angular spacing between adjacent impeller blades, which otherwise would have resulted in a noise level (measurable) corresponding to variations in velocity t40 cm=sec"+, The practical output of the current meter is 1/19.61 cm = 0.051 pulses per cm advance. The recorded data consists of successive periods per rotation of the impeller; corresponding values of the water velocity can be computed using the calibration coefficient: hi ae Uy = ae Sy ean Ueki eS (10) The term u; is the average value of the instantaneous velocity u(x) over the interval of time T;. Since a mean velocity is superimposed on the turbulent TR No. 22 velocity component, = ! tao U;, +u Multiplying by T;, T= 19/62) eme= Us Ty ul ae The expression U; T; is the distance relative. to. the water which the current meter has advanced in the interval T... Hence if u'; is negligible compared to Uj, the values of u; are obtained at distances of x;, and are approximately equally spaced at intervals of AAx = 19.61 cm, regardless of the mean velocity. The error in assuming that the data are equally spaced is of the order of tu'y/Uj = +10/400 = 42.5% for the measurements reported herein, which is not greater than the existing ambiguity in establishing the correspondence between the values uj and the series of times a4 | + =a J Jeo Such equally spaced data are of the appropriate form for digital spectral analysis with respect to wave number. Aliasing A discussion of the problem of aliasing is given by Blackman and Tukey (17) where it is shown that if there are significant contributions to the energy from velocity variations occuring at wave numbers greater than tne Nyquist wave number given by // a pale Kn a Sow [in interval Re Cad ZL: (11) then the computed ehergy spectrum is in error at all wave number. The Nyquist wave number for the data obtained from the current meter is tr /19.61 cm 0.157 em71 TR No. 22 The equally spaced values of velocity can be considered to result from sampling the average velocity Met (12) at intervals of ZXx. Equation 12 can be written as a centered moving average; Bliotie doh U-x') du! SEO (13) where ih OW Wace Et? Du Vam Te O* otherwise (14) If the Fourier transform of u(x) is dz( K ) and that of @(x) is @(K des é then, applying the convolution theorem, a) Kox) sin (2 ae lk) ( Be ) (15) Siy ca ise %) ISESION eel) A (k) = The quantity is the Fourier transform of h(x) and operates on the energy spectrum as a low pass filter. Variations in velocity occuring at wave numbers greater than around TWHAK = 0.157 cm~! are strongly attenuated. Since this value TR No. 22 is equal to the Nyquist wave number, and since velocity variations at wave numbers greater than about 0.007 cm-l (see section under "Response to Accelerated Flow") can be expected to be attenuated because of the dimensions of the current meter, aliasing is not considered a problem. FIELD OBSERVATIONS Figure 8 is a section of C. & G. S. Chart No. 353 showing the area within which measurements were made. The area is located in the Sakonnet River between the north end of Aquidneck Island and Tiverton, R. I. The area indicated on the chart as Station I is formed from stone breakwaters projecting from the island and the mainland. The tidal current at Station I is given in Table 1 which was constructed from information given in the tide and current tables (20), Table 1. Tidal Current at Station I. Time with respect to high Current at Station I tide at Newport, R. I. ohh ea cs Ree High Tide 1.7 knots South 1 hour(s) after Do oy WW 2 Ww WwW 3.0 Ww ih] 3 Lh] ] Di? w i m1 " a8 1.2 " 1 5 WU u 1.1 knots North 6 i u - see Note 7 Ww wy = ih Ww 8 we we a " Ww 9 W we a Ww ty LO) HS 2.3 knots North Te M 2.0 knots South 12 we in) 1.0 w Ww NOTE: The current during this time interval is unpredictable, can change rapidly from North to South or from South to North, and can be as much as 3.0 knots in either direction. 10 FIXED BRIDGE HOR. CL. 3) FT ne =~ smouth VERT. CL. 12 FT. \ \ OVERHEAD POWER CABLE 0 ;AUTHORIZED CL. 95 FT. \W 4 5 JO. _THE COVE * /,) fale Areal /| oF | YAWN U ( MN \ VA i 1] Wi 4 ‘s \ | Section of C. & G. S. Chart No. 353 Showing the Area Figure 8 Within Which Measurements Were Made TR No, 22 Measurements were made on 4 November 1966 from 1300 hours to 1400 hours, The time of high tide at Newport was given as 1130 hours, and therefore measurements were made during the interval when the current was a maximum of 3.0 knots south. The width of the channel at Station I is approximately 116 meters, and the depth 6.7 meters, North of Station I the depth is 18.6 meters, and in the area from Station I to Station II, 800 meters south of I, the depth varies from around 10 to 20 meters, with a width of about 400 meters. The Reynolds number based on width at Station I is approximately 1.3 x 108, Figures 9, 10, and 11 show the method of mounting the current meter on the bow of the NUWS boat, a 74-foot OAL torpedo retreiver. Brackets were fabricated to support the mount ing strut, an 11 1/2-ft long section of steel pipe approximately 1 1/2" in diameter, to the lower end of which was clamped a 3-ft length of 3/16-in by 3-in steel bar stock, along the bow. When in position the lower end of the strut extended approximately 1 1/2 meters below the surface of the water. The current meter was affixed to the end of the strut in a horizontal position; the clamping arrangement allowed the bar stock to be rotated so that the axis of the current meter could be aligned with the centerline of the boat. The current meter output was recorded on FM magnetic tape at 30 inches/ Sec on a Precision Instrument PI-2100 recorder, It was necessary to include an attenuator in the circuit to reduce the signal level 8 dB to an appropriate level for the recorder, A gasoline engine driven 115 VAC generator followed by a Sorensen voltage regulator was used to supply power to the recorder. The original intention was to proceed against the current from Station II to Station I along the centerline of the channel at as slow a velocity as pos- sible in order to obtain the maximum amount of data with a minimum change in position or downstream distance from the channel buoys, The ideal technique would have been to tow the instrument at a velocity equal to that of the cur- rent. The first run showed that this was impracticable as it was impossible to control the boat in the turbulence at such low velocities, The remaining runs were made at a velocity of 4 meters-sec”+ relative to the water; the engine RPM was maintained constant throughout. A typical run consisted of dial TR No. 22 Figure 9 Lower End of Mounting Strut and Current Meter LO Mounting Strut on Bow of Boat TR No. 22 Figure 11 NUWS Torpedo Retriever TR No. 22 TR No. 22 proceeding against and along the center of the current from the vicinity of Station II to Station I. Four runs were made.proceeding with the current and four against (including the first, the data from which was not analyzed). On each run, the instant when the boat passed between the channel buoys was observed and recorded. A light southerly breeze prevailed during the time measurements were made; surface waves were limited to wave heights. of a few centimeters and therefore no wave particle motions should have. been recorded, although the current meter was only 1 1/2 meters below the water surface. DATA ANALYSIS Analog to Digital Conversion The data analysis follows the procedure given by Blackman and Tukey (17). Figure 12 is a block diagram indicating the process involved in obtaining data in digital form appropriate for computer analysis. The original data was recorded on 1/2 inch magnetic tape at 30 inches-sec”~ and has the waveform shown in figure 3 (top trace). It was reproduced at 30 inches-sec71, amplified 10 dB, and modified using a Schmidt trigger so that the waveform was.as shown in figure 3 (lower trace). A binomial counter was used to divide the original frequency by six thus resulting in the square wave shown in figure 4 (lower trace), where one cycle of the square wave corresponds to one rotation of the impeller or 19.61 cm advance of the current meter through the water. The average frequency of the original data was (at 30 inches-sec7+) 120 Hz and that of the modified data 20 Hz. The modified data were recorded on 1 inch FM magnetic tape at 30 inches-sec”™- on an Ampex FR-1100 recorder. The square wave data were converted, using.a Honeywell analog-to-digital converter, to digital data at a conversion rate of 2500 counts-sec ~ and re- corded on digital magnetic tape. Reproducing speed-was 7 1/2 inches-sec7; as a result the average frequency of the square wave was 5 Hz, and therefore the number of counts per square wave cycle was approximately 500. The maximum error in determining the period of one square wave cycle is *1 count or ap- proximately 40.2%. At an average towing velocity of 400 em-sec7l, this error corresponds to variations in velocity of 0.5 cm-sec7l. 2 TReNOp ee CURRENT METER P1-2100 FM RECORD 30 INCHES/SEC 8 DB ATTENUATOR P1-2100 DYMEC DC FM REPRODUCE AMPLIFIER SCHMIDT 30 INCHES/SEC X 10 TRIGGER BINOMIAL AMPEX FR-11 00 COUNTER; = 6 ATTENUATOR FM RECORD | 4 30 INCHES/SEC HONEYWELL ANALOG TO DIGITAL CONVERTER FM REPRODUCE CDC 3200 7 1/2 INCHES/SEC DIGITAL COMPUTER Block Diagram of Analog to Digital Conversion Process Ipabfenbaee IL) TR No. 22 Computation of Auto Covariance Series and Energy Spectra The data processing was performed on the NUWS CDC 3200 digital computer. The FORTRAN programs are included (appendix B) for reference. The following were determined for each run and for i= 1, 2, 3, ..., N = number of square wave cycles in the run: 1. The time t; from the start of the run (taken to be the start digital recording) to the completion of the ith cycle. 2. The period T; of the ith cycle from West Vedic fon eG (16) 3. The velocity u; for the ith cycle using the calibtation coefficient aot k ? alk (17) The values of u. were assumed equally spaced at intervals of 19.61 cm. Each run was divided into samples of 500 values of welocity per sample; a computer printout of all of the digitized velocity data was obtained. Ex- amination of the data revealed that all except 7 of the 49 samples contained several obviously erroneous points. A section from the printout (run No. 2, sample No. 3) appears in table 2 which shows a typical series of values con- taining indicated erroneous points. The values of erroneous points were replaced with the values of the immediately preceding points. For each sample a straight line was fitted through the data by the least squarés method (18): UO) = a, Pp Ss; (18) 13 22 TR No. G2964° fan E6LTR®SHE BELSOPLHE B82899°ETY BELSOPLHE 60602°SHrE FO0S6L°CHE 9B8990°8FE 2571 7° UKE "B990°BFE Tyl2t°snr ZSyT Hr Ove 254TH 0HE BIOES° ITY BES6E° ESE 0B96T ene 98990°8EFE ZS7Tv OE 27208°904 299E2°6FE 98990°8EFE SS2R°6FE SS728°6EE £9009° THE 90S61° SHE 60602°SrE BIOES6*TI4 90S6L° SHE EBLE6°EHE ZS7T OnE ZSVT HOHE 60S06°9FE ZSyT HOHE =ALIDONSA SALTOOTNIA SALTIOONSA =ALIOONSIA =ALTIONSAA SALTIIONSIA SALIOONSA =ALIOONSZA SALIIONIA =ALIOOTNSIA =ALIDONZA SALIONVSA ZALTIONSA =ALIOONSZA SALIDONIA SALIDONIZA SALIOOVIA SALIOONSA =ALTOONSA =ALIOONISA =ALIOON3A SALIOONIA SALISDONZA =ALTOIONIA SALIOOTNIAN =ALIOONIA SALIOONSA =ALTOONSA =ALIOONIA SALIIDONIA SALIDONIA SALIOONFA =ALIDONZA oezset® 08922° 09S22° o96Rt® 09See° 02l22° ogBed® 00¢EC° Ov0EZ® 00¢E2° O9E6T® Ov0E2® 0v0E2° ov06el® Ov822° 02622° o0¢e2° O0v0Ed® oRdZét® o2lted® o0zEe2° O80Ee° oBs0Eg2® 09622° ORHAZ® Oe Aad 0706T°® oRB2e° 00822? OV0EA® Ov0E2® oRcEe? Nv0E2° =39ONVHO =3ONVHO =JONVHO =39ONVHO =3ONVHD =3ONVHO =39ONVHO =39ONWHO =3ONVHO =SONWHO =S9ONVHO =3ONVHOD =39NVHO =39ONVHD =JONWHD =SONWHD =39NWHOD =39ONVHO =39ONWHO =39ONVHO =JONVHD =39ONWHO =39ONVHO =S9NWHD =3ONWHOD =SONVHD =3ONVHO =3ONVWHO =39ONWHO =39ONWHO =3ONVHO =SONVHO =39NVHO awtl Swot awtd 3wit 3wtt awit awl AWTl 3wrtl AW J. AWTI 3WTl awit AWT I. 3WT1 awit 3wtd qwrt awit AWT1L awit awit dWtl antl awit Swi) awit AWT | SW AaWtd Swit 3WIl awit ZS0TL* oe? ZEGES° HE? 29862 ° vt? Z262ZL0° FE? ZEERB TEE? 2l1/199° FE? Z2SGEH° FE? 2ltu2°eeta €1696°2Ed FE6ELS 2A ECELUS® 2t2] elLElEe°2e2d FEENO°2E?C €62GR° TE? ES299° TE? Elver ted E6v02°TE2 €62L6°NE?2 €S27) °0€2 EL67S° NE? eSAlEe°oe2 £S9n0°0E! ELGSR° 422 £6429°622 LEGOE ° Ae? €S599T°AdZ EEHE6* Re! F6RDL ERC? €102g°Re2 ElzZo2°k22 €L190° RE? FETER SLA? ESROSe 1 e2 =iINIOd SIHI SlNIOd SIH Sl1NIOd SIH SiNIOd SIHI SlLNIOd STH =I1NIOd SIHL =INIOd STH) SINIOd SIH) =LNIOd SIHI =INTIOd SIH) =LNIOd SIHI =INIOd SIRL =!NIOd STHI SINIOd SIH =LNIOd SIHI =LNTOd STHL =INTOd SIHI1 =LNIOd SIHI =1NIOd SIH SINIOd SIH} SlNIOd SIH1L =1NIOd SIHI SiNIOd SIH =INIOd STHI! SLNIOd SIHL SiNIOd SIL =1NIOd SIHI =LNIOd SIHI =INIOd SIHL =LINTIOd SIHI =INIOd SITHI =1NIOd SIHI =SLNIOd SIH1L eqyeq AQTOOTaA PezTITSTd eyy Fo (SUTTOWT] wersorg) qnoqyutTag zeqgnduiog 344 jo UOT}OSS SATISe{USSSAday "2 eTqeL Os 0) oO) (on Ol 0! Ot (on Ot Ot O4 Ol O41 Ot on Ol Ot OL Ol OL OL OL Ol Ol OL Od QJ Ol O41 Ol Ol io 0! Gwil dwtt awit guilt awit Jw Bwtl awit ajwil Swtl awd gwd Gwil ull Iw aw) awit awit qwil jwit Qwilt Bhw1t gwd dwt Qwik dwt awit awit BwIl Bwit awl Iwi wit EEOT ZEOT Teo] oFOT 6c0T KOT Lcot 9dul GduT geil edul eeut Teo Oot 6l0T RloT Ztol Slot SToT Tat Elot 2fol Ito OvoT SUNT HUOT Lv90t SUNT SuOT bU0T F0OT cuUgT tvoT =31VA9 =31YA9 HIWAYI s3qvAU =3a74vAu =31IA9 HS31AS =47~A0 =a1vAS 2390949 = 414A5 =qvAo SIA =314A0 =jnlAu FP ba key We) Se iOS) =3VIA9 S31 A9 =31IA0 SsaqAO =3T9A9 =3I1A9 =3qIA9 =37YA0 HAAG =31VA0 =31YA9 =3N4A9 SAA =IVWAI SIVA =37%A9 JSAuUM SAYIN SAT sAuM AAWM sAyM SavnM dAUM SAVI ANU AAW SAN0M SAM SAUM AAW sAuM SAVR SAUM SAUM AAWM 3AUM SAUs SAUM SAMM JAW SAUM sAvM SAVM SAuM SAUM SAUM SAvM SAWN SHUNOS Anvnos 3x 7n0s AyVnos 3advnos SHvNOS Bxvnos aavnos 346vnos 2HVNOS Aavnios ayvnos AHVNOS 3xVNUS BaHVNOS SHvnos Saxvnos auvnos S3yvnos By8vnos BxHVvneSs axevnos 3yHvNOSs AHxVNOS axvnos ayVNOS SHvnos 35Vnos Syvnos Asvnos aavnos Asvrnios 4uvnos 14, RAN Of 2i2 where U5 and a were computed from £00 00 £00 S00 Dy ne ‘ab a oo XU if, k=l _ke wer KEI D = i La a Oa au S00) A y x,| ie k=| k=) £00 = k ax =\412) x ji Me Vegeee VANS SAS: The mean velocity and the trend in the data were eliminated: Cie ij, =(y Hak 2) {1 A= (Dy, eigaial) , The apparent autocovariance series was computed at lags equally spaced at intervals of AS = Ax = 19.61 cm to a maximum lag of mAx = SOAx = (50) (19.61 ecm) = 980.5 cm using a0-k Ralkasy = == ou laax] u'[ (ark Jor] ul) ; obs. = eos PGR % (22) =f 15 TR No. 22 for k = 0, 1, 2, 3, e+, 50. The apparent autocovariance series was modified according to hannings 5 (I+cos i ) : kK 250 Ru lkos)< Ralkos) 0, otherwise (23) The Fourier transform of the modified autocovariance series was computed at values of wave number K equally spaced at intervals of ZK = 17/50Dx = 0.00320 em? from 24>, (Gok) =2@, & BL>X 61 D kar lad 1 B[2) Balk os) Cos +@,,(0) +2, (PFE) es am | - ata i 51 feo IL) paeierul< ; Values of the computed energy spectrum were obtained for wave numbers up to the Nyquist wave number ent = Ooalay/ emt, the values are referred to positive wave numbers only. The values of the computed energy spectrum function were divided by the sample variance: / Fa, (Fok) Gea (72k) = ; Km CO) (24) Location of Samples From the original data and the computer printout of the digitized velocity data, the following were determined: (S = time from the start of the run to the instant the boat passed between the channel buoys (sec); 16 TR No. 22 ¥\. = the number of impeller rotations from the start of the run to time tos J = time from the start of the run to the start of the kth k sample; NM, = the number of impeller rotations from the start of the s run to time +, . If the average current from ty tot is U (meters-sec”+), then the position of the kth sample relative to the channel buoys is X, (meters) = U(4,-% ) + 0.1461 Cn =Op). Accurate measurements of U, over the distance between Stations I and II were not available. However, a large error in Ue does not result in a corresponding large error in x,; for a le (0. 146!) = pele CC) Thus: x L : e é Xie = (Nip uae) | i+ me xX, ia If a value of 1/2 the current through Station I is used for U., and if this value is in error by 150%, then a> oe = han = OK /4 ( 1008 } = t8.4%, £12.5%. mR pt 08/4 Table 3 gives the positions of the samples relative to the channel buoys as determined from = + x, = 008 (th - t,) 0.1961 (N, - n) and are assumed to be correct to within around 10%. 17 TR No, 22 Table 3, Positions of Samples Run No. Sample No. Downstream distance of Center of Sample from Channel Buoys (meters) -164 - 44 73 181 308 427 544 661 300 305 229 152 75 == 70 56 168 286 4O4 523 -218 =no5 26 146 226 386 443 416 338 260 183 105 MOH FWONKHPANEWNHKRHOAUOFWONFOAFWNHEHDWOWAFOA HF WN EH 18 TR Nos 22 Table 3. Positions of Samples (Con't) Run No. Sample No. Downstream distance of Center of Sample from Channel Buoys (meters) ~-112 “J NAYAMOFWNRP DWN F WN BP w @ TR No. 22 RESULTS AND DISCUSSION Figures 13 through 17 are graphs of the digitized velocity data for several typical samples. The autocovariance series corresponding to the samples are shown in figures 18 through 22. Thirty-seven useful samples were obtained from seven runs. It is not necessary to show the autocovariance series and energy spectra for the individual samples; the autocovariance series shown in figures 18 through 22 and the energy spectra given in figures 23 through 27 are representative of the results. The results from the 37 samples are tabulated numerically in appendix C. The values of the energy spectra have been divided by the corresponding sample variances previous to being plotted. Before proceeding to a discussion of the results it is appropriate to consider the deficiencies in the data and/or measurements which are apparent in the autocovariance series and the energy spectra. Noise The energy spectra do not continue to decrease for wave numbers greater than around K= 0.06 cm71 as expected but approach a constant value of the order of orf K) = 20 cm3-sec72, with considerable variation among samples. This can be shown to result from random error in the digitized velocity data. If, for a sample consisting of N equally spaced values of velocity the ®¥ror which the ith value, u!, is subject ot is ei» then the ee error in the kth value Ore (BS autocovariance series 1s ! aes \ ( Nets NEI fL Peee ll Hel Sa, J | dap ele [-I< N-K = nee uly! Alle WE jg * u! (ee Nea! Jtk Pree J Eee stk J | (25) F Nk J Gj +c ~ N-k4 Uy rk y), N-k JA N-K Je | KEK Ree. | iN y \ ey eee “Si * Wk ed Ak nko I IFK s = 20 22 TR No. Odl Ol! OO! 06 pyoq AyioojaA poezyi6iq jooiddAy (S4afaw) x 08 Ow 09 OS OV OF 02g Ol OOv Olv Ocv | Of OVD OSb O09” OL” (x)n (9as/Wwd) Figure 13 22 TR No. pyog Ayoojaa pazyyiBiq joojd4) (S4asqu) x Odl Ol! OO! O6 qe Ol O9 OS Ov O£ Od O| O O8e O6¢e OOv i Olv Ocv OLD OVD OSY (x)n (2aS/Wd) Figure 14 TR No. Od! 06 pyog AyIn0jaA paziyiByq jooidAy (Sdafaw) x 08 OL 09 OS Ov O€ O2 Ol O6€ O00v Olv OFA 7 Of£v Ove OSb (2aS/W9) (x)n Figure 15 O6 pyoq AyoojaA pazyi6iq joordéy (Sdafaw) Xx Os OL O09 OG Ov Of Og O| O8e O6e OOv Olv O2v OL Ove OSD O9v (Das/wo) (x)n Figure 16 (Sia pow) O06 oy) xX pyog AyoojaA pazi4!6iq joo1dA) Od 09g OS Ov O€ Od O| OLE O8¢e O6E OOv Olt OcdD OL Ovv OS (Das/wo) (x)Nn Figure 17 Rg (19.61 k) (cm? /sec)2 Figure 18 70 60 Run | Sample 2 e, ample 0 200 400 600 800 Lag = 19.61 k (cm) Autocovariance Series Corresponding to Figure 13 AUR INO)q 22 TR No. @ 70 @ @ @ %e e 60 5 *og0 ‘ ® px ®e Run | % 50 Ode Sample 6 aS E a z 5 40 o 5 [-4 (es) oO 20 Lag = 19.61 k (cm) Autocovariance Series Corresponding to Figure 14 Figure 19 22 TR No. 70 60 Run | 50 Sample 7 =) 30 Rg (19.61 k) (cm2/sec2) 20 0 200 400 600 800 1000 Lag = 19.61 k (cm) Autocovariance Series Corresponding to Figure 15 Figure 20 60 nn o Ra (19:61 k) (cm2/sec2) Paynes ZL Run | Sample 8 Lag = 19.61 k (em) Autocovariance Series Corresponding to Figure 16 TR No. 22 TR No. 22 70 60 Run 7 50 Sample 4 R (19.61 k) (cm2/sec2) 0 200 400 600 800 1000 Lag = 19.61 k (cm) Autocovariance Series Corresponding to Figure 17 Figure 22 Figure 23 Run | Sample 2 -2.6 -2.2 -1.8 “1.4 Energy Spectrum Corresponding to Figure 13 TREN ne) ne) Figure 24 3 log D (k) Run | > ® Sample 6 Log k Energy Spectrum Corresponding to Figure 14 TR No. 22 3 Log D am (k) Run | Sample 7 2 -2.6 -2.2 -1 8 -1.4 -1.0 Log k Energy Spectrum Corresponding to Figure 15 awe 25 TR No. 22 3 Log DB om(k) Run | Sample 8 2 e@ @ 1 (:) e t @ ®@ Energy Spectrum Corresponding to Figure 16 Figure 26 TR No. 3 Log @ tk) e Run 7 2 Sample 4 Figure 27 -2.6 -2.2 -1.8 -1.4 Log k Energy Spectrum Corresponding to Figure 17 MUR INO) ine) ine) TR No. 22 Since the e; are assumed random, statistically independent variables , the u' and the e, are uncorrelated, as are the wt and the e,. j +k ja bs J Therefore Nek N-k milk, ‘ | a a | = NK & ay SMe 7 hes e WS ON Uiail is | (27) In addition, the e. are uncorrelated with the e. nes unless k = 0. Then we have J ¥ | N \ 2) ee a Totes ' es an Cy an Rey Nel a Ci+k 7 NL {3 =e o, otherw ‘se IN (28) Nek \ oe beni Ly ‘ KX (kos ) +Rey, = Mi . ™\ ‘e C Sie ai J where eu ©, otherwise This demonstrates that the presence of random error in the digitized velocity data has an effect on only the value of the autocovariance series at k = 0 (the variance). The expected form of the autocovariance function for small values of 5 is (Batchelor, 1) te Comparison of this with the autocovariance series given in figures 18 through 22 indicates that the sample variances are larger than expected by around 3 cm2-sec”2. The Fourier transform of equation (29) is ae IRkes)+ moe di ee Cos KK Os Sana 4s N AS Fie: separ See eh Ss j e us N J=I (31) 1416 om = @(k) + sues [2 omr-see” ) i 2a TR No. 22 The sources of error in the digitized velocity data have been dis-= cussed previously; 1, Sensitivity of the current meter of *0,25% of mean velocity corresponding to an error of 11 cm-sec™1, 2. Analog to digital conversion rate resulting in an error of ti em-sec7l, The total expected error, then, is of the order Orne cm=-sec”, which agrees well with the observed noise levels for the energy spectra. Figure 28 is a plot of the sample variance as a function of the es- timated downstream distance, x', of the sample from the channel buoys. Because of the large amount of variation it was not possible to determine the change in variance with respect to x’. According to Batchelor (1) the change in variance is SU > Re oe i 27 (32) where A is a number of the order cf one and Xp is the wave number at which the maximum in the energy spectrum is located, Applying the Taylor hypothesis, this is 2 2H ls i 1S D x ay PT (33) An order of magnitude estimate of the change in variance with respect to x' can be obtained from this. The average value of the variance for 34 samples is 55.6 cm?-sec~* +25,0 (standard error), (The variances from the third and fourth samples from run No. 4 and the first sample from run No. 7 were not included in the average since the values are excessively large, probably caused by motion of the boat.) The average value of the variance derived from the energy spectra is 3.2 x 1073 or less. Then ay BU LESS oy ayo ax 400 ZoDE = aa —2 s £9 210 Cm-s5ee 22 22 Hust IN), sXong jauubYy*) WOdJ} SDUDISIG WD31JSUMOG SA SIUDIIDA (suajaw) |x Figure 28 TR No. 22 For a change in x’ of 100 meters (the average sample length) the change in variance is about 5,3 cm?=sec™“, which is not significant compared to the statistical variations among successive samples, The large variations are attributed to inhomogeneity of the field of turbulence, short sample lengths, and non-linear variations in the towing velocity. A more precise indication of the accuracy of the results is obtained from the energy spectra. A measure of the accuracy of any computed value of the energy spectrum is the equivalent number of degrees of freedom of the value (Blackman and Tukey, 17). The equivalent number of degrees of freedom is approximately given by 2(sampie length) maximum lag je 8 which for all of the samples is k = 2(500) = 20 degrees of freedom. 50 The distribution of computed values of the energy spectrun@,,A/opta ined from a large number of similar samples having an equivalent number of degrees of freedom, k, is assumed to be equal to a Chi-Square distribution with k degrees of freedom, That is 8 GOS) Bee Uk) (34) where U(X) is the value of the energy spectrum function that would be obtained from a sample of infinite length. Using this assumption, confidence limits can be assigned to the computed values of the energy spectrum function. From the tables in reference 18 values of X* corresponding to the probabilities of occurrence of deviations greater than Yrcan be found, For a probability of 0.10 of a deviation greater than Lae the value of £* for 20 degrees of freedom is 28.412, Similarly, for a probability of 0.90 Z*= 12,443, Thus the prob- ability is 0.80 that the deviation from Z’is within the interval 12.443 to 28.412, or that KP, U0 Lk ) 23 Nyars IG 222, 4 12 Composite Energy Spectrum Figure 29 TR No. 22 TR No. 22 for k = 20. Then we have 80% confidence that the correct value of the energy spectrum function is within the interval Ge. Ue ) Ba 2 Gig) 2 “enk) N42 ZA, 62. or that beh We) Bish SVAN 2 bee ZA. G8) epee The 80% confidence limits are indicated on the energy spectrum given in figure 23. The confidence limits for the other spectra are the same. Examination of the energy spectra indicates that the 80% confidence limits are reasonably correct. The predominant characterisitc of the spectra is the linear range (on a plot of log @/&) as a function of log K ) extending from wave numbers of 0.01 cm7+ to 0,06 cm™+, At larger wave numbers the computed values of are subject to large error because of the relatively high noise level. Since any actual variations among the spectra are considered negligible with respect to statistical variations, a composite spectrum was formed from the individual spectra to determine more certainly the existence of the linear range: Keon (Ue) Kin (2) 685) =) Hb af / / Fn (i= 5) as (k ) ) Giese Cin p= | The composite spectrum is shown in figure 29. The effective sample length is 37 times longer than that of the individual samples, and the equivalent number of degrees of freedom is 740. The 80% confidence limits are indicated on the spectrum, Several of the individual spectra display secondary maxima at wave numbers ranging from 0.02 em~1 to 0.03 cm. This feature, however, is not apparent on the composite spectrum; so no significance is attached to it. If the approximate noise level, as estimated from the composite spectrum, is taken as SOO N61 ca ? a —e f ~ rd We (Golan ~ $6 Cm —See , eal and a noise correction applied to the composite spectrum, the result is as shown in figure 30. Within the range of wave numbers from #= 0.01 cm to [2 = 0.026 om™ >, the composite spectrum is of the expected form, viz: nw Se Gy (ke) OK 24 TR No. Slope = -5/3 Composite Energy Spectrum with Noise Correction Figure 30 TR No. 22 For wave numbers greater than K = 0.026 om~t Bk) decreases more rapidly with increasing wave number than pe 9» Which reflects at- tenuation of the higher wave number variations in velocity because of the size of the current meter. At AK = 0:0353 om7t, As ay) is 3 dB below the =-5/3 log k line. The necessary condition for the existence of the inertial subrange can be stated precisely as (Batchelor, 1) ie % = ) D2? ] (36) where u is the RMS value of the turbulent velocity and R is the length corresponding to the wave number at which the maximum in the energy spec- trum is located. Using the values obtained herein: cm-sec”_ US a AS ees We 0) 15 sap 1 this is i fils) aes gn a value sufficiently large that the condition (12) is probably satisfied. Values of the energy spectrum were not obtained at wave numbers large enough to allow calculation of the dissipation spectrum Kh, RK) > and subsequently the rate of energy dissipation by viscosity Es nop? | ers Pa a oO since dissipation occurs at wave nuinbers of the order of 10 om72 (Grant, Stewart and Moilliet, 2). Regardless, if the Kolmogoroff hypothesis is assumed, an estimate of the average value of € can be obtained from the spectra using 22 Fd BOE, (k) -p, ga eJk ie of (37) ~% 25 TR No. 22 At K= 0.01 cm™+ the average value of the computed energy spectra is P an (kK) = 9,15 x 10° cm°-sec™“, It is necessary to have a value for the universal constant K'. If the value obtained by Grant, et al (2) is used, then the average value of K' is 0.47 10.02 (standard error). Substituting this value along with the average value of @,,, (&) into equation (13), ae 9.15 x 107 | Yes (G10 ene sace (ORE) (OER ES OS) The result is of the same order of magnitude as the values reported in reference 2, No attempt has been made to determine € for the individual spectra because of the statistical variations. The individual spectra would, in general, yield different values of € 3; because of inhomogeneity of the field of turbulence, € is a function of position as well as time. CONCLUSIONS 1. The ducted impeller current meter, with a constant wave number response of from 0 cm ~ to 0.0353 cm, is a practical instrument for measuring oceanographic turbulence. The high wave number response is limited by the dimensions of the current meter instead of the response distance (also constant), measured as 0.75 cm. The data obtained from the instrument are approximately equally spaced at intervals of 19.61 am, resulting in a Nyquist wave number of 0.157 cml; the sampling process further attenuates velocity variations at wave numbers greater than the Nyquist wave number. Since the Nyquist wave number is greater than the highest wave number at which the current meter is responsive to velocity variations by a factor of four, aliasing is negligible. 2. The average sample variance is 55.6 om?-sec72 +25,0 (standard error). Superficial comparison of the distribution of the values of the energy spectra with the expected Chi-Square distribution, however, indicated that the variation is statistical. The variation is attributed primarily to short sample lengths and inhomogeneity of the field of turbulence. 26 TR No, 22 3, The composite energy spectrum is of the form predicted by the Kolmogoroff hypothesis within the range of wave numbers from 0.01 em™! to 0.026 cm™ ; at wave numbers greater than 0,026 cm” the energy spectrum decreases more rapidly than predicted because of at- tenuation of the higher wave number velocity variations, At wave numbers less than 0.01 cm7/ the turbulence is assumed anisotropic and inhomogeneous. The maxima in the individual energy spectra are located at wave numbers less than 0.003 cm. 4, The average rate of energy dissipation by viscosity is estimated =-3 as 0.84 cm*=sec ° 5. The energy spectra are subject to a high noise level -- of the order of 20 cm3-sec™? -- resulting from random error in the digitized velocity data. The sources of error are an insufficiently high analog-to- digital conversion rate and insufficient sensitivity of the current meter combined with a large towing velocity compared to the variations in velocity. PLANNED RESEARCH Two much improved versions of the ducted impeller current meter are presently being considered for making additional turbulence measurements. The first is a Braincon Corporation Type 430 ducted impeller current meter, shown in figures 31 and 32. It is similar to the current meter used herein except that it is manufactured of type 316 stainless steel instead of brass, has a lighter weight impeller resulting in a smaller response distance, and has imporved bearings and hence increased sensitivity. The Type 430 current meter has approximately the same dimensions as the current meter used herein, and thus the high wave number response is similarly limited; the estimated useful wave number range is from 0 cm™~ to 0.04 cm ~, The primary advantage of the Type 430 current meter is its sensitivity, which is expected to result in a very low noise level. The second version is a Cox Instruments Model 12-SCRX turbine flow meter which was modified by machining off the pipe threads from the body (figures 33 and 34). The modified flow meter is 1.8 cm dia and 8.3 cm long. The advantages of the Cox unit are its small size, sensitivity (0.1% of mean flow), and simple disassembly for ball bearing replacement. o ° sll - The estimated wave number response range is 0 cm™~ to 0.1cm . 27 TR No, 22 It is intended to mount the instruments on 2~ft Braincon "V"-Fins and to tow the instruments at different depths in the Cape Cod Canal against the 4-knot tidal current existing there. Measurements are also planned for the open ocean. It is expected that much longer samples can be obtained than for the measurements described herein, 28 TR No. ETO ‘yaenes HUE {iduialimoubaluluhustntoululotuoloubuelsauluuloituddoeausubdoluuluoluubuules Braincon Corp Type 430 Ducted Impeller Current Meter, 3/4 View Figure 31 22 TR No. ; a tp ge ON ART ABO ea aR RRS ! s 2 3 See 4 ’ | TWeHes ao 10 20 30 40 30 ty 10 10 a 100 ie 10 3 Tt) eu i itoulnolmbihimbiiliatialaiioatiliihilindudiiiliabadiatialiadtialidin Braincon Corp Type 430 Ducted Impeller Current Meter, End View Figure 32 22 C2 TR No. lew fied Cox Company Turbine Flow Meter, 3/4 V Modi Figure 33 TR No. 22 Figure 34 Modified Cox Company Turbine Flow Meter, End View 1. 10. 11. TR No, 22 REFERENCES Batchelor, G.K., 1960, The Theory of Homogeneous Turbulence, Cambridge, The University Press Grant, HoL., Stewart, R.W., and Moilliet, A., 1962, Turbulence Spectra from a Tidal Channel, Journal of Fluid Mechanics, Vol. 12, Part 2, 24a Grant, H.L., and Moilliet, A., 1962, The Spectrum of a Cross-Stream Component of Turbulence in a Tidal Stream, Journal of Fluid Mechanics, Vol. 13, Part 2, 237 Bowden, K.F., and Howe, M.R., 1963 Observations of Turbulence in a Tidal Current, Journal of Fluid Mechanics, Vol. 17, Part 2, 271 Stewart, RoW., and Grant, H.L., 1962, Determination of the Rate of Dissipation of Turbulent Energy near the Sea Surface in the Presence of Waves, Journal of Geophysical Research, Vol. 67, No. 8, 3177 Bowden, K.F., 1962, Measurements of Turbulence near the Sea Bed ina Tidal Current, Journal of Geophysical Research, Vol. 67, No. 8, 3181 Lumley, J.L., and Panofsky, H.A., 1964, The Structure of Atmospheric Turbulence, New York, London, and Sydney, John Wiley and Sons Shonting, D.H., 1967, Measurements of Particle Motions in Ocean Waves, Journal of Marine Research, Vol. 25, No. 2, 162 Shonting, D.H., 1964, A Preliminary Investigation of Momentum Flux in Ocean Waves, Pure and Applied Geophysics, Vol. 57, 149 Shafter, M.R., 1961, Performance Characteristics of Turbine Flowmeters, The American Society of Mechanical Engineers Paper No. 61-WA=25 Rubin, M., Miller, R.W., and Fox, W.G., 1964, Driving Torques in a Theoretical Modei of a Turbine Meter, Fhe American Society of Mechanical Engineers Paper No. 64-WA/FM=2 29 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. TR No. 22 Grey, J., 1956, Transient Response of the Turbine Flowmeter, Jet Propulsion, Journal of the American Rocket Society, Vol. 26, No. 2, 98 Lang, T.G., 1956, Windmilling Characterisitcs of Propellers, NOTS 1455, NAVORD Report 5252 Frenkiel, F. N., and Klebanoff, P.S., 1967, Higher-Order Correlations in a Turbulent Field, The Physics of Fluids, Vol. 10, No. 3, 507 Shonting, D.H., 1963, A Proposed Study of Turbulent Transports in Ocean Waves, U. S. Naval Underwater Ordnance Station Internal Technical Note No. 14-63 Shonting, D.H., 1965, Preliminary Studies on the Turbulent Characteris- tics of Ocean Waves, U. S. Naval Underwater Ordnance Station Technical Memorandum No, 342 Blackman, R. B., and Tukey, J.W., 1958, The Measurement of Power Spectra, New York, Dover Publications, Inc. Kenney, J.F., and Keeping, E.S., 1951, Mathematics of Statistics, Part 2, Toronto, New York, and London, D. Van Nostrand Co., Inc. Coburn, 1955, Vector and Tensor Analysis, New York, Macmillan The Eldridge Tide and Pilot Book, 1966, Boston, Robert Eldridge White Schlichting, 1960, Boundary Layer Theory, New York, Toronto, London, McGraw-Hill Book Co., Inc. Massey, A.T., 1965, Response Times of an Orthogonally Mounted Ducted Current Meter, U. S. Naval Underwater Ordnance Station Internal Technical Note No, 124-65 Cardin, D.J. and Rooney, J., Calibration of an Eckman-Marz Current Meter in the NAV UNDERWATER ORDSTA Wind Tunnel, U. S. Naval Underwater Ordnance Station Internal Technical Note No. 30-62 30 TR No. 22 Appendix A RESPONSE OF CURRENT METER TO ACCELERATED FLOW Expressions for the resultant driving torque on the impeller of a current meter as a function of the geometry of the current meter, impeller angular velocity, and the velocity of water through the cur- rent meter are given by Rubin, Miller and Fox (11), and by Grey (12). Similar expressions are given by Lang (13) for the resultant driving torque on a windmilling propeller, If bearing friction and other torques are assumed negligible, the resultant driving torque is of the form 2 k =cu f(J), (1) where J li uf D) (2) and c is a constant of proportionality and is a function only of the geometry of the current meter. When the water velocity and the corresponding angular velocity of the impeller are constant, the driving torque is zero. Therefore £(J) = 03; J’ = Jo = constant - (3) Hence VA (4) which gives the calibration coefficient for the current meter. If the water velocity through the current meter consists of a time varying component superimposed on a constant component u=U+rtu'’, (5) where u’ is assumed small with respect to U so that the lift and drag forces on the impeller blades are approximately linear, then the equation of motion of the impeller can be written as 1=k jw) seu £ (J). (6) Aol TR No. 22 The angular velocity of the impeller also consists of a constant plus a time varying component: / By Si Za), (7) / Since u' is assumed small with respect to U,@ can also be assumed small with respect to S23; and K (u, &’) can therefore be expanded in a Taylor series about the equilibrium value, zero: " IK Ki os) = 1K (aw) en ie we 22k iw! ee lbh i ZAMS) Bak 12 , O2K Free eK ay yl ele acre Syl eso U i) BIEN 15, The coefficients of the linear and second order terms in the series are 1g (U, Ww) | mek, sp. (9) Seg = oeU fer) + an i ES SNe. L282 o \eyice se (10) C O a) Z ey =) T 6 OK ae 2 Golo oe eu = Coy Caine uy (11) A2K (y OAs) (12) ee) DEH)| LA we, =e out Sy To ae ee sar A=2 0 ) DP Kl4je0) eee 7 SECT. TR No. 22 2 Suaw oir Sy 2 SVD) bo 2 - ee oe =o ) = € Qt Be 4+ ) J, (13) a K (4,w) = Sea =) £(5) 6 aw * L4Sv Sas Gy, ee a7) a =} tala op aS a é oT oP 58 (14) 6 Substituting equations (8) through (14) into equation (6) gives I w'. c, Uu' = c, UW +e ate tec, uli cp te eyo it 1 2 3 4 5 (15) If U (and therefore S2. ) is zero, then equation (15) becomes / dao" _ 12 ’ ’ 2, eaten FRC WCU) cri 5: (16) whereas if u! an SS ly then / and equation (15) becomes daw‘ tee = Gy UO = a U w', (17) neglecting second order and smaller terms. Equation (17), which pertains to the method in which the current meter was used, is a linear first order A=3 TR No. 22 equation for the time varying component of the impeller angular velocity as a function of the time varying component of the water velocity. The general solution is is US qe Ge! Ge) a DA zt / L (18) 0 q/ Ct) = From equation (18) the theoretical response time of the current meter can be determined. The response time is defined, for a step function change in water velocity, as the time required for the change in angular velocity of the impeller to achieve 1 -l/e of its final value. If the step function change in water velocity is Ont. G0 uf (t) = u' = constant, t > 0 (19) f : LE then the corresponding motion of the impeller is, from equation (18), OF tio / Piel CV COE) Se G1 me =p Wes (20) From equations (10) and (11) F(T) Gy st 2p Je Z biles th tice Cs DATES a0 LATS ay ee Za Cp J, ae D) ° G23) Therefore Gv ee = 2! | EE / tu (+t) = ae le Examination of this result shows that the response time is given by Ta encad \ peaR ee AON: C= Cy 2 (23) Thus the response time of the current meter is not a constant but is inversely proportional to the mean water velocity. The quantity defined by nae rey ir (24) is however a constant for the current meter and is referred to as the response distance, The response distance in air is considerably larger than in water and consequently more easily measured. The value obtained can be converted to what it should be if it were measured in water. The procedure is similar to that used in calibrating ocean current meters in the wind tunnel (23). The dimensions of each term in equation (17) are ML tT; and since the dimensions of ( and u are T7+ and tee respectively, the dimensions of the constant cy are ML. Constant rm) is necessarily of the form es A B Cc co = 2 P WA ih (25) TR No. 22 where c} is a dimensionless constant and A, B, and C are to be determined. Substituting the preceding dimensions into this equation, we obtain = ase Cc cm?y4 unten 28 = ML, from which NS al ) B=0 7 @ Ss ih (26) y so that G. 8 el (27) 2 a “ From equations (23) and (24), we get Assuming that I, L and C4 have the same values in air and in water, J air ( air = DM eecess ( water. (28) Therefore air -3 )] water = /lair alg aly o2 ALO) ) air. (oes (29) The virtual moments of inertia in air and in water have been neglected in the foregoing analysis. The current meter was mounted in the test section of a closed circuit, single return, low speed wind tunnel (figures A-land A-2). A step function change in air velocity was simulated by suspending a small section of screen A-6 TR No. Current Meter Mounted in Wind Tunnel for Measurements of Response Time Figure A-1 22 Figure A-2 Instrumentation for Measurements of Response Time TR No. 22 TReNo 22 immediately in front of the current meter so that it blocked some of the air flowing through the current meter, When the impeller had achieved a constant angular velocity, the screen was quickly removed and the output of the current meter measured as the angular velocity of the impeller increased from its original value to its final value. Initially, the period between pulses was measured at intervals of approximately 0.2 sec with an @lectronic counter connected to a paper tape digital recorder. The interval was determined by the maximum printing rate of the recorder-5 lines/sec, The results, however, were subject to a large amount of scatter, which was found to be caused by the variation in angular spacing between adjacent impeller blades 110%. To eliminate this the output of the current meter was modified using a Schmidt trigger=binomial counter circuit so that the period per rotation of the impeller could be measured instead of the period between pulses. Measurements were made as described at six different wind tunnel velocities. The velocity was determined from measurements of dynamic pressure, wet and dry bulb temperatures, and barometric pressure; the dynamic pressure was measured with a pitot static probe connected to a differential micro-manometer, A calibration of the current meter was also performed in the wind tunnel by measuring the output frequency at various known wind tunnel velocities and using the method described in reference 23 to convert the values measured in air to in=water values. From equation (22), we get _F- / / 3 Coe Wy. Shane (30) | S ~N Xan iT This can be written as Al = es Pes c an TR No. 22 using | TGs CHES) J Dey dais eel 2a; y) Tyee ae yy (32) Swim For each wind tunnel velocity the quantity |= eee N= (Mey yee) was calculated from the recorded data and plotted as a function of time; figure A-3 is representative of the results. The response time in air was determined from the slope of the straight line fitted through the points using the least squares method: lv ab slope ain The reciprocal of the response time in air was plotted as a function of air velocity (figure A+), and the response distance in air was determined from the slope of the straight line through the points. The response distance in water was computed according to equation (29), a value of 0.97 cm resulting. A=8 TR No. 4.0 1 - Té/T (t) 7 Slope = |/ Tair = 0.840/ sec T (0) = 0.03014 sec Tf = 0.01887 sec U = 545 cm/sec 0 ] 2 3 4 5 Time, t (sec) Response of Current Meter as a Function of Time for Step Function Change in Wind Tunnel Velocity Figure A-3 22 TR No. / Tair (I/sec) 1.0 0.8 0.6 Slope = VA air = 1.2 X 1079 /em 0.4 0.2 U (cm/sec) Response Time as Function of Mean Velocity Figure A-4 22 TR No, 22 APPENDIX B Computer Programs Bel aa TR No.22 @SEQUENCE:0 8 @JOB26/7sBBELS3602ND @FORTRAN 9L 9X 120 40 PROGRAM TIMELINE DIMENSION A%84H3J%2500031B%/7n0 CHARACTER AoIB EQUIVALENCE %JsAqu READ%6051200NR 9NT FORMAT%214un NOTC#1 ML#¥1 READ%60240n0 IB%MLO FORMAT%O12 NBIGSAMP#0 NSWP# N#3 CHAN# BIGCHAN#O. TIME# SW#HOe SAMP# . BUFFER IN %3910%J%102J%250000 GO TO %19253s4nUNITSTF%30 K#LENGTHF %3o PRINT 109 K FORMAT%1Xe17H EOF ON LV3 AFTER2I5:s6H WORDS GO 10 YY K#LENGTHF%3ao PRINT 205 K . FORMAT%1Xs26H PARITY ERROR ON LV3 AFTER:I5296H WORDS&B G@ WO ial K#LENGTHF%3q0 IF%A%40-eEQeIB%MLO0O51:6 DO 7 I#NeK IFSI eLE «30958 IF%IeGEeKH9218 IF%J%IoeLEe-80007199 Di Fecoe) Soe ee Ere — 8 OlO END) a0l/2 TF%IJ%IG1O5«eLEe—-800H1499 TR No.22 9 SAMP#SAMPE1. TIME#TIMEG1¢/25006¢ GO TO 7 14 SAMP#SAMPE&1. TIME#TIMEG1¢/25006 CHAN#T IME-CHAN SWHSW le VEL#4 .2/%5e10*CHANH WRITE%619300SWsTIMEs CHANs VEL WRITE%2 5 3000CHANs VEL» TIMEs SW 300 FORMAT%SF12¢59Fl1l0e59F1l2e52F5.00 30 FORMAT%1Xs19HSQUARE WAVE CYCLE# »F5e022Xs20HTIME TO THIS POINT# oF 1120¢552X513HTIME CHANGE# 3F12-522Xs10HVELOCITY# »F10-5n CHAN#TIME NSWP#NSWPG61 IFSNSWPeEQe500H6627 66 NRIGSAMP#NBIGSAMPE1 WRITE%612808 80 FORMAT%1X9///2100%1H*oOn RIGCHAN#TIME-BIGCHAN WRITE%612s1O00HNBIGSAMP:sTIME»BIGCHAN 100 FORMAT%1X2/s1Xs20HLARGE SAMPLE NUMBER 2®12919Xs10H AT TIME# sF12.53 18H SECONDS3/230X925H TIME SINCE LAST SAMPLE# »F12e¢5:s8H SECONDS 9/291 2Xe100%1H*os///u NSWP# BIGCHAN#TIME 7 CONTINUE GO TO i 6 WRITE%59210000H%A%lOs1#128n 1009 FORMAT%1X»6HCODE# »801n PAUSE 12345 GO) lO SSeS on SSWil Giileode B35) Mbeki IF %ML eGTeNRO42 941 41 READ%60»4001B%MLU NSWP# BIGCHAN#O.e CHAN# TIME# . SWHO e B-3 TR No.22 SAMP# . END fFUILie 2 N#¥3 NBIGSAMP#O WRITE%61»2000ML 200 FORMAT%1H1260Xs9H RUN NOe 2118 GOR TONS 99 REWIND 3 WRITE%61s/700NOTC 70 FORMAT%IXs19HEND OF TAPE NUMBER »I1la NOTCHNOTCE1 IFS%NOTCeLEeNTH919999 91 WRITE%595600 60 FORMAT%1Xs20HUNLOAD LV3. AND SAVEe2/928HMOUNT NEXT TAPE ON SAME UNI 1Ts/s1l?HHIT GO WHEN READYu PAUSE 1 GO) lo) aLal 999 REWIND 3 2 lelNipy Fluke 2 REWIND 2 END FINIS @EQUIPs2#MTCOEOQU02 @EQUIP s3#MTCOEQUO3 @LOADs56 @®RUN 210 nw FWNrF @UNLOAD 9293 2@ B- TR No. 22 a@ @®SEQUENCEs0 8 @®JOB267sTC21202ND @EQUIPs1#MTCOEOU0] @EQUIPs2#MTCOEOQUO02 @FORTRAN »L 9X PROGRAM FITNSUB DIMENSION V%452097%452n DIMENSION TIM%5000sVEL%5008 DIMENSION ZA%80n COMMON VEL%50002TIM%500H VSUM# . YO4#19.261 SUESIO CODE# . READ%60.30%ZA%IlOs1#19800 FORMAT%80R140 IF%ZA%20eEQe00H80281 81 M1#50 READ%60»130DMIN»sDMAX 13 FORMAT%2F10.5H SXFO 0 SY#06 SXX#Q 6 SXY#0 © 100 FORMAT%1H12 PRINT LOG WRITES61240%ZA%INoI#12800 4 FORMAT%25Xs80R14a DO le elo SOO READ%1s2000VEL%IO»TIM%I4u 200 FORMAT%12X3F1l0.529F12e5n COP Or lew Gia BORG Risin 16 CONTINUE DO 76 J#225C0 IFYVEL%JOeoLT eDMING22 523 ZZ NEE SUE EN eo) ver G@ 1O. 76 23 ITF SVEL%IJOeGTeDMAXH24 976 24 VELSIJOFV ELS J= 15 Wr Ik 301 18 80 iat DYE CONTINUE DO 17 I#1:2500 SY#SY VEL%IO SX#SX TIM%IQ SXY#SXYS6“VEL%IlOXTIM%Ion SXX#SXXG%TIMSIO*TIM%IoOn SLOPERS%JIJ*SXYO-%SX*SYOOH/%%IIS*SXXO-%SX*SXOO YINT#HS%SSXY*¥SXO-%SY*¥SXXOO/%%SX*¥SXO-%IIJ*SXXOO WRITE%619301HSLOPE sYINT FORMAT%1Xs8HSLOPE # »F60e322Xes12HINTERCEPT # »F8-4n DO 18 I#1+500 VEL%SIO#VEL%IH-%“SLOPEXTIM%SIOSYINTO CALL SPECTRA %JJ»CODE»M1:sYO4u GOP TOMS END SUBROUTINE SPECTRA%N:»CODEsM1sYO4u DIMENSION A%10202B%10202C%10202D%102H2E%10202F%102n COMMON X%50002Y%5U00 Phe Sho baal) SUMX#0.0 SUMY#0.0 ETC ODE HI eal Zr Ie DOM Sa walaesiN SUMX#SUMXEX%I14 SUMY#SUMY&Y%I148 EN#N SUMY#SUMY/EN SUMX#SUMX/EN WRITE %6126068 MlsN»xYO4 WRITE%6196080 SUMX»SUMY WRITE%61s6090 DO 973 I#l»N X%1O#X% I G-SUMX Y%IToO#Y%IO-SUMY GO TO 16 DO 4 I#1>N SUMX#SUMX6X%1Io EN#N SUMX#SUMX/EN TR No.22 TR No. 22 WRITE%619s6060 MlsN2»YO4 WRITE%6196070SUMX WRITE%61260340 DO 913 I#1>5N 913 X%1lo#xX%IO-SUMX 16 M#M1-1 M2#M161 DO 22 L#l»M2 SUM1# 0 SUM2#0.0 SUM3 #00 DO 23 ILO LZ#I-L&1 SUM1L#SUMIEX%LZO*X%IO SUM2#SUM26EX%LZuU 23 SUM3#SUM3&EX%10 ZZ#N-LE1 CORR RI 6/44 GOERZHECOBRR72 A%LU#COEF*SUM1—-COEF 2*SUM2* SUM3 IF%CODED 25224925 25 SUM4#0.0 SUM5#0.0 SUM6#0.20 SUM7#0.0 SUM8#0.0 DO 26 I#L»N LZ#I-L6&1 SUM4#SUM4EY%LZO*Y%IO SUM5#SUM5&Y%LZuo SUM6#SUM66Y%Iu SUM7#SUM7EX%LZoO*Y%IoO 26 SUMB#SUM8EY%LZuU*xX*#@1oO B%SYLOXHCOEF*SUM4—COEF 2*SUM5*SUM6 C%LOHCOEF*SUM/-COEF 2*SUM2*SUM6 %®LOF#COEF*SUM8—COEF 2*SUM5*SUM3 E%LO#%DSLO&C%LOO/2. FSLuU#¥%D%LO-C%¥LOO/2. 24 CONTINUE 22 CONTINUE NM (os) BS) Bi DO 27 K#1ls»M2 IF%K-lo 285928529 ZM1#M1 DELT#1le/%2e*ZM10 (GO) 7O) 372 IFSK—-M2031228928 ZM1L#M1 DELT#H1.e/Z2M1 SUM1# 0 SUM2#0.0 SUM3 #020 SUM4#0.0 EM1L#¥M1 CAY#K—-1 DO BB) (Ls 2 OM EL#¥L-1 GUT#%1-eGCOSFSPI*EL/EM1LOO*COSFSPI*CAY*EL/EMI14 SUMI#SUMI1&EGUT*A%LO PF MCODEm 25533 03:5 SUM2#SUM26GUT*B%LE SUM3 #SUM36GUT*E%LO TR No. SUM4#5UM46%1 ¢GCOSFSPIXEL/EM1OO*SINFSPI*CAY*EL/EM1O*F%LO CONTINUE X1L#DELT*%SUM1&EA%1500 IF%CODED37 936937 YI#DELT*%SUM2&B%1lqo0 ZH¥DELT*%SUM3&6E%1u00 WHDELT*SUM4 R¥SQRT%%Z**2EW*X* 20/%X1*Y 100 THATANF&W/Z40 T#T/ 20174533 P#Z/SQRT%X1*Y10 Q#W/SQRTSX1*Y10 KK#K=—1 XLQ#M1 XLQP#KK FXLP#%2e¢*XLQ*YO4H/ XLQP WRITE%61 26020KK sAMKOSBS¥KOSESKOsFYKGsX1l9Y1lsZeWsFXLPoReT WRITE%02 s602H0KK sASKOSBOKOSESKOsFYKOSX1l9Y19ZeWsFXLPoRsT GO 1 27 22 36 2U 39) 38 609 608 607 602 KK#K-1 XLQ#M1 XLQ@ FXL PHKK PH%2 e¥XLQ*YO40/ XLO@P FREQ#1e¢/FXLP WRI WRI CON END IF % CC# WRI CON FOR 1QUA FOR FOR FOR FOR FOR FOR TE®6196020KK sAKOeX1lsFXLPsFREQ TE%0296020KK sA*®KOsX1sFXLPsFREQ TINUE Filia 2 CODEH39 » 38939 E%loO/SQRT%A%1lO*B% loo TE%61930CC TINUE AT%1X944HK ACOV U ACOV W COV IN COVOUT SP U SP W PER R PHIa MAT%1X»98HMEAN U #oF6e1l98Xs8HMEAN W #5F6010 AT%1Xs8HMEAN U #9F10-5n AT%1323F 9° 3 2F Be 625 F6e29F4e25F6e20 AT%1Xs5HLAGS#2s I1394H Ni#o15s5Xs3HDT#sF60e2233HSECO MAT%36H K ACOV Sie PERIOD F o MAT%1Xs23HCORRELATION COEFFICIENT sF10.340 RETURN END FINIS B=9 TR No. CO» 22 23\nl TR No.22 @®SEQUENCE:0 8 @JOB2673sTC31209ND ®EQUIPs2#MTCOEOU02 ®EQUIPs3#MTCOEOU03 @®FORTRANsL 2X PROGRAM MOD DIMENSION KK%70H2A%7002X%700O2FXLP%¥/70HsFREQ%/00»ZA%80H»SPK%700 DIMENSION SPN% 700 READ%60 5 LONF 1 FORMAT%1I5a NFC#O Seal READ%S60920%ZA%KOs K#¥128C0 2 FORMAT®%80RI14Q WRITE%612920%ZA%KO» K#1l»s800 WRITE%612110 11 FORMAT%1X»54H K ACOV SIP PERIOD FREQ SPK SF INa READ%3 s160KK%Ilo2A%IlOoXHI1OsFXLPHeIo 16 FORMAT%1393F9~3n l#2 3 READ%3 »40KK%IHsA%lO»sX%IOsFXLP%IOsFREQ*I4O 4 FORMAT%1353F9e32F8.6n GO, TO; Sb 6E BORCKR%3 5 6 1#161 GO, oO) 3 SV RRIE@ Soll atte 999999 DOW Vs elton SPK% JO#312.102*X%Ju SPN%JH#SPK%JB/A%14O WRITE%61s105KK%JOsA%®IJB»X%¥IOeFXLP%¥IOsFREQ%IJHsSPK%IO»SPN%JO 7 WRITE%2s100KK%JO »A%JO2X%JO oFXLP%JOsFREQ%IJO»SPK%IO»SPN%JIO 10 FORMAT%1X21323F9e39F8e6:s2F10.3n ENDER Tet 2 NFC#NFCE&1 WRITE%615150 15 FORMAT%IH1a TFSNFCeEQeNFO8 39 8 REWIND -3 REWIND 2 B-10 Nomenclature ACOV ~ PERIOD = FREQ = SPK = SPN = APPENDIX C Numerical Tabulation of Results lag number, k Ra(k OE ) (em@=sec™*) WE i ame =2 mOE 22. (La &) (em“=sec™*) Secale, 19.61 kK (cm) 1/2TT (wavenumber) ; oth (em=1) 20G,, (PAR) (cm3=sec72) on (40K) = af! (berg) (em) Ral(0 Ke TR No. 22 TR No. 22 GOUNTMP WIN OK RUN 1 CHANNEL 7 ACOV Sh PERIOD FREQ SPK SPN F 300.525 1230074 0 .999999 38411.642 127.815 275.056 1354528 1961.000 2.000510 42298.560 140.749 2702672 130171 980,500 2.001020 4110,695 13.678 274.44) 106928 653.667 2001530 601.733 2.002 274.580 10693 490.250 2.002040 52A.389 Lo) 266.900 126995 392.200 .002550 341.752 ALS 265.260 10144 326.833 2.003060 357.045 1.188 263.554 10969 280.143 003570 333.637 1.110 261.599 0832 245,125 2004080 259.669 . 864 259.949 0521 217-889 2004589 162.605 541 258.247 e398 196,100 .005099 Wilerlss 5S) (2 256,538 0336 178.273 2005609 104.866 349 254.150 0385 163.417 2006119 120.159 4.00 252.837 0327 ©6150-8846 2006629 102.057 . 340 250.637 0289 140.971 2007139 90.197 300 248,305 ©2788 130.733 0007649 860764 .289 245.97] 0296 122.563 2008159 92.382 SOT 243.215 0349 115.353 008669 108.924 . 362 240,199 e430 108.944 .009179 13402204 eli, 237.002 e521 103-211 2009689 162.605 541 234.364 0561 $8.050 2010199 175.089 583 231.972 0594 93.381 .010709 185.389 .617 229.746 0692 89.136 2.011219 215-975 ra Ale) 226.727 e767 85.261 .011729 239.382 . 797 224,725 2785 812708 012239 245.000 .815 2222213 e799 78.440 2012749 249.369 .830 2702043 2805 750423 2013259 2512242 .836 216.901 20833 72.630 2013768 259.981 865 214.231 0868 702936 2014278 2702905 -901 2112388 0831 67.621 2014788 259.357 863 208,350 wns 65.367 615298 241.567 . 804 206.169 0727 63.258 2015808 226.898 ~755 293.066 0656 61.281 -016318 204.739 .681 200.353 0574 59.424 .016828 179,147 .596 196.975 0507 57.676 2.017338 158,236 527 194,937 0464 56.029 2017848 144,815 482 191,556 0426 54.472 .018358 132.955 4he 188,789 0398 53.000 2.018868 124.217 413 185.401 0372 51.605 2.019378 116.102 . 386 183,535 e333 50.282 2.019888 103.930 346 180.909 0303 49,025 2.020398 94,567 315 176.143 0328 462.690 2021418 1022349 5 hak 173,567 0342 45,605 .021928 106.739 £355 170.339 0361 44.568 2022438 1122669 .375 167,264 0436 43.578 2022947 1362076 2453 164.609 0477 42.630 2023457 148,873 495 151.081 0436 41.723 2023967 136.076 2453. 159,044 0446 40.854 2024477 139.197 4.63 155.679 0472 40.020 2024987 147.312 .490 153.159 023) 39.220 2.025497 72.096 .240 0 0 1) 0 0 0 -— OoDrItIovwFr WN DA 11 ACOV 57,033 53.860, §3.519 52.497 51.520 50.831 49,97] 49,332 48,802 48.309 476443 46,857 46.0460 45.016 44,535 43.851 43,286 420407 41,831 41.519 40,589 40.065 39,086 38.814 37,607 37.287 36.467 35.751 35.308 34,774 34.694 34,049 33.372 32.937 32.283 31.613 30.825 36.270 29,556 78.593 28.329 27.2466 26,855 76.254 25.797 24.919 24.534 73-856 232393 22.798 71.778 (a) SP 22.153 25.526 3.910 0975 059A 0355 0324 2199 0167 e207 2192 0135 elll 099A 0064 0949 0953 0049 0144 661 0074 2059 0942 014) 0944 e052 0070 0066 2032 0023 0937 0045 0057 0057 e060 0073 e014 0064 0156 0063 0058 0043 007? 01495 0085 0949 0143 RUN 1 PERTOU G 1961.000 980.500 653,667 490,250 392.200 326,833 280.143 245.125 217,889 196.100 178.273 163,417 150,846 140.07] 130.733 122.563 115.353 108.944 103.211 98,050 93.381 B9.136 85.261 81.708 78.440 75.423 72.630 702036 67,621 65,367 63.258 61.281 59.424 57.676 56.029 54.472 53,000 51.605 50.282 49.025 47.829 46,690 45,605 44,568 43.578 42.630 41.723 40.854 40.020 39.220 0 FREQ 0999999 0000510 0001020 0001530 2002040 2002550 20003060 0903570 2004080 0004589 0005099 2005609 0006119 2006629 0007139 0007649 2008159 2008669 0009179 0009689 0010199 °010709 0011219 e011729 2012239 0012749 0013259 0013768 2014278 2014788 0015298 6015808 °016318 2016828 0017338 2017848 0018358 0018868 0019378 0019888 2020398 0020908 2921418 0021928 0022438 00229467 0023457 0023967 0024477 0024987 0025497 0 C-3 SPK 6913.996 7966.,716 1220.319 304.299 184,764 110.796 1012121 62.108 52.121 642605 59.924 420134 34.643 28.713 19,975 152293 16.541 15.293 13.732 19.938 23.096 18.414 13-108 12.796 13.732 162229 210847 20.599 9.987 72.178 11.548 140045 17.790 172790 18.726 220783 232096 19.975 17.478 19.662 18.2102 13.420 220471 32.771 26.529 15.293 132470 210847 24,656 170478 6,866 0 SPN 121,228 139,686 21.397 5.335 3.240 1.943 le?73 1.089 0914 1.133 1.05] 0139 e607 e503 2350 2268 e290 2268 0241 e334 0405 0323 e230 0224 024) 2285 e383 e361 0175 e126 e202 0246 e312 e3ie2 2328 0399 0405 e350 e306 0 345 aroha e239 0 394 4357/5 e465 2268 e235 TR No. 22 CHANNEL 7 OONDMNUFWNROA ER No. 22 RUN ji CHANNEL 7 AcOV SP PERIOD FREQ SPK SPN 94,965 362966 0 2.999999 11537.163 121,489 91.629 422411 1961.9000 2000510 13236.558 139,384 90.403 6.820 980,500 .001020 2128,536 220414 89,044 20579 653.667 ~001530 804,911 8.476 87,114 16418 490,250 002040 442,561 4,660 85,955 0542 392.200 .002550 169.159 1.781 84,375 0485 326,833 003060 151,369 1,594 82.669 0346 280.143 .003570 107.987 Way lesie 81,231 0293 ©245.,125 ~004080 91.446 0963 79.410 e210 217,889 .004589 65.541] 2690 EGET 0198 196.100 .005099 61.4796 2651 77.082 0173 «178.273 .005609 53,994 »569 75.574 el2i 163,417 .006119 37,764 398 74,056 0975 150,846 .006629 23.408 0246 Tegoe 0074 140.071 007139 23,096 0243 Wiese 0097 130,733 2.007649 30.274 e319 70,168 el@2 122.563 .008159 31.834 2335 69.441 ellM 115.353 .008669 34,331 » 362 67,984 0123 © 108.944 .009179 38.389 0404 66,9R9 e100 103.211 .009689 31.210 0329 66.211 2067 98.950 2010199 20.911 e220 65,287 e038 93.381 010709 11.860 el25 64.479 0025 89.136 .011219 7.803 «982 63.572 0047 85.261 011729 14,669 2154 62,993 2065 81.708 ~012239 20.287 0214 62,617 0947 78.440 012749 14.669 2154 62.017 0036 75.423 .013259 11.236 2118 61.462 0053 72.630 013768 16.541 elT4 60,843 2063 70.036 2014278 19,662 207 60.146 0066 67,621 014788 20.599 e2l? 59.573 0974 65.367 015298 23.096 0243 58,524 0054 63.258 2015808 16,854 enlaval, 57.968 0943 61.281 .016318 13.420 2141 57,310 205? 59.424 2.016828 16.229 Sale 56,516 0053 57.676 017338 16.541 e174 55.166 0073 56.029 2.017848 2207R3 2240 54,299 e086 54.472 .018358 26,841 e283 53.346 2978 53,000 .018868 24,344 0256 §1,813 0076 51.695 .019378 23.720 2250 50.819 e080 50.282 .019888 24.968 0263 49,225 0094 49.025 020398 29,338 0309 47,222 2087 47,829 .020908 218153 2286 45.733 2952- 46,690 ,021418 16.229 onload 43,885 e035 45,695 .021928 10.924 Gis 42,048 0027 44,568 ,022438 8.427 2089 40,351 e026 43.578 022947 8.115 2085 38.6n2 0044 42.630 2023457 13.732 2145 37.929 e957 41.723 2.023967 172790 2187 34,997 005) 40,854 ,024477 15.917 » 168 33.185 0048 40,020 .024987 14,981 2158 31.481 0026 39.220 ,025497 8.115 2085 i) iy) 0 0 0 0 c-) OUBUNDMF WDNR DA AcOv 92.103 88.326 87.197 85.488 83,581 81,378 79.317 77,268 75,103 73,346 71.629 69,959 67.702 66.009 63,975 62.338 60,418 58,754 57.203 55.268 53.882 52.329 50.562 49.084 47.651 45,818 44,571 43.201 41.490 39.794 38.054 36.305 34,562 32.533 30,599 28,825 27.748 26.201 24,978 23.6A4 22.596 21.360 202076 19.247 172¢746 17.015 15.667 14.725 132686 12.648 11.593 0 SP 31.822 40.2558 10.125 20524 1.675 0832 0529 0465 0334 0225 e212 0083 0073 2065 0065 0073 0075 0193 e097 e071 e066 e070 0950 0047 0063 063 0067 008? 0090 0085 06059 2950 0072 0078 057 0045 0059 6077 0077 0062 0054 0154 0153 0076 009) 0090 RUN 1] PERIOD 0 1961.000 980.500 653.667 490.250 392.200 326,833 280.143 245.125 217,889 196.100 178,273 163.417 150,846 140,971 130.733 122,563 115.353 108,944 103.211 98,050 93.381 89.136 85.26) 81.708 78.440 75.423 72,630 70.036 67.621 65.367 63.258 61.281 59.424 57.676 56.029 54.472 53.000 51,605 50.282 49.025 47.829 46.690 45.605 44,568 43.578 42.630 41.723 40,854 40.020 39.220 0 FREQ 0999999 2000510 20001020 2001530 0002040 0002550 2003060 203570 2004080 0004589 20905099 6005609 0006119 0006629 0007139 0907649 2008159 2008669 0909179 0009689 29010199 2010709 e011219 0011729 e912239 e012749 0013259 2013768 2014278 2014788 2015298 6015808 0016318 ©016828 0017338 0017848 0018358 6018868 2019378 0019888 2020398 2020908 2021418 2021928 0022438 0022947 0023457 0023967 0024477 0024987 0025497 0 C-5 SPK 9931.710 12658.233 3160,033 787.745 522.771 259,669 165.102 145.127 104.242 70.223 662166 44,006 25.904 22.783 20.-2A7 20.2a7 22.783 230408 29.0295 30.274 222159 202599 212847 15.605 14.669 19-662 19.662 20.911 25.592 28.089 26.529 18.414 15.2605 222471 240344 17.790 142045 18.414 24.032 24.032 19.350 16.854 16,854 16.541 23-720 28.401 28.089 25.592 19.2038 17.166 9.363 0 SPN 107,833 137.436 34.310 8,553 5.676 2.819 1.793 1,576 1,132 e162 0718 0478 2281 024! 0220 0220 0247 0254 0315 0329 024] 0224 0237 0169 0159 e213 e213 o2el 0278 e305 0288 2200 0169 0244 0264 0193 0152 ©200 026] 0261 0210 0183 e183 e180 0258 0308 0305 0278 e2ot 2186 0102 0 TR No. 22 CHANNEL 7 CMWADMEWNH OK TR No. 22 RUN 1 CHANNEL 7 PERIOD FREQ SPK SPN 0 2999999 1237,4R4 65.451 1961,.000 2.000510 1802.3R9 95.329 980,500 .001020 796.796 he 13 653.667 .001530 412.911 21.839 490,250 .002040 269,656 14.262 392.200 .002550 157.612 8.336 326,833 .003060 94.255 4.985 280.143 2003570 74,592 3.945 245,125 2.004080 102,057 5.398 217.889 2004589 87.076 4.606 196.100 .005099 54,306 PSGie 178.273 2005609 44,318 2.344 1632417 .006119 39,325 2.080 150.846 2006629 25.592 1.354 140,071 .007139 21.223 eee 130.733 2007649 19,662 1.040 122.563 .908159 18.414 974 115.353 .008669 19.662 1.040 108,944 .009179 21.847 Tel56 98.950 .010199 18.414 2974 93,381 ,010709 8.4277 446 89.136 ,011219 8.739 462 85,261 2011729 18.414 974 81,708 2012239 25-280 1.33% 78.440 ,012749 27.465 1.453 75,423 .013259 222159 tL all 72,630 .013768 13,470 Ryalle 70.936 2014278 16,541 .875 67.621 2014788 20.599 1.089 65,367 015298 16,229 858 63.258 .015R08 13.732 a726 61.281 2.016318 16.854 .891 59.424 .016828 22.159 aly 57.676 2017338 22047) 1.189 56,029 .017848 17.790 O41 54.472 018358 15.91)7 B42 53,000 .018868 17.166 .908 51.605 .019378 16.541 6875 50,282 .019888 16.854 891 49.925 .020398 19.350 1/023 47,829 .020908 18.102 ~957 46,690 .021418 21.223 jee? 45.605 .021928 28.713 1.519 44,568 022438 24,032 cle s7all 43,578 022947 222.471 UL aliele) 42.630 2023457 26.217 1.387 41,723 .023967 18.726 .990 40,854 .024477 13.420 SAO) 40,020 ,024987 19.038 TOO 39.220 .025497 11.860 .627 0 0 0 @) C-6 ACOV 82.157 71.276 69.293 67.173 65,625 64.305 632415 62.543 61.377 59.522 57.7n5 56.976 56,537 56.945 56,438 54.9A6 54.161 53.102 52.394 51.401 51,235 50.952 48.772 47,848 45.810 44,375 44,238 42,933 42.108 41,991 40.037 38.812 38.519 38.04) 38.061 372454 36.376 36.345 33.960 32.9A4 31.976 31.773 31.448 31.030 29.782 78.377 28,838 28.194 272184 76.785 270415 (a) SP 2701736 32.661 5.769 12.547 12301 10225 0258 0535 0443 0420 0332 e3en 0314 0418 2584 048? 020) 0186 0189 e166 019A 0237 2268 0265 0215 e189 0199 020? 0228 0240 0188 0155 017? e2\7 0224 0173 0195 e25N 0221 0166 0146 e1lT4 0238 0224 0187 e210 0210 0202 0204 0099 9 RUN 1 PERIOD 0 1961.0900 980,500 653.667 490.250 392.200 326.833 280.143 245.125 217,889 196.100 178.273 163,417 150,846 140.071 130.733 122.943 115,353 108.944 103.211 98.050 93.381 B9.136 85.261 81.708 78.440 78.423 72.630 70-036 67.621 65,367 63.258 61.281 592424 572676 56.029 54.472 53.000 51.605 50.282 49,025 47.829 46,490 45.605 44,568 43.578 42.630 41.723 40,854 40.020 39.220 0 FREQ 0999999 6000510 0001020 0001530 0002040 0002550 0003060 0903570 2004080 0004589 2005099 0005609 2006119 0006629 0007139 0007649 0008159 2008669 0009179 0009689 2010199 0010709 0011219 0011729 0012239 0012749 0013259 2013768 0014278 0014788 0015298 0015808 0016318 2016828 0017338 0017848 0018358 0018868 0019378 2019888 0920398 0020908 2021418 2021928 0022438 0022947 0023457 0023967 0024477 0024987 0025497 0 C1 SPK 8656.461 10193.563 1800.516 482.822 406.045 382.325 298.994 166.975 138.261 131.083 103.618 99.873 98.000 1302459 182.268 150.433 89.261 626733 58.051 58.9R7 51.809 59.924 73.968 83.6463 82.707 65,54] 58.987 62.108 632045 71.2159 74.2904 58.675 48,376 53.682 67 e726 69.911 53.994 60.860 78.025 68.975 51.809 45.567 54,306 74.280 69.911 58.363 65.541 65.541 63.045 63-669 30.898 0 TR No. 22 SPN 105,365 124.074 21.916 5.877 4.942 4,654 3.639 2.032 1,683 1.596 1.6261 1.216 1.193 1,588 2.219 1,831 1.086 0 164 ef0? 0718 0631 0129 0900 1.018 1.007 2798 0/18 e156 2/67 e866 0912 0714 0589 2653 0824 0851 2657 0741 0950 840 0631 0555 °661 0904 °851 0710 CHANNEL 7 DNDUMNPFUWNR DA o£ TR No. 22 RUN 1 CHANNEL 7 ACOV SP PERIOD FREQ SPK SPN 402603 100224 9 2999999 3190.93] 78,589 36.194 14.6701 1961.000 .000510 4588.2)2 113.902 35,308 5.928 960,500 .0019020 1850,141 45,567 33.344 2eetr .653.667 «01015310 710,656 bielos 31.735 16382 490,250 .002040 431.325 10.623 30.203 0901 392.290 .002550 2812204 6.976 28.727 0542 326.833 2.003060 169.159 4,166 27.524 038M) =6©780,143 20035706 118.2599 2.921 26,564 0286) 6©7245.175 004086 &9,7261 2.198 24,383 0191 217.889 2004589 59,611 1.468 73,59) 0228 196.190 .005099 HG WES) 1.753 21.816 2265 178,273 2095609 82.707 2.037 20,878 0184 163.417 2006119 57.427 1,414 19.929 0141 150,846 2006629 44,006 1.084 19.001 0!6? 140,971 007139 50.561] 1.245 18.092 215? 130.733 2007649 47.440 1,168 17.185 2129 122,963 2.008159 37.452 2922 16.458 0966 115,353 .00K8669 20.599 2507 15.795 0941 108,944 .009179 12.796 eas ore S 0954 103.211 2009689 16.854 2415 14,377 2068 98.950 .910199 21le223 ww23 13,373 207? 93.381 .010709 22.471 2553 12.524 0 166 89.136 2011219 20,599 A Bila) ?/ 11,646 AW IT 85.261 2.011729 24,032 2292 11.938 2079 41.708 2012239 24,656 2607 19,753 2065 78.440 2.012749 20e2R7 2500 19,96) 2979 75.423 .0132759 24.656 2607 9,808 2088 72.630 2013768 27.465 2676 8.516 2075 70.036 .014278 232408 ASIA 8.274 0070 67.621 2014788 21.847 9938 UAC, 2078 65.367 .015298 24,344 ~©00 6,329 2068 63,758 ,015898 21.223 apes 5,930 2 04R 61.281 .016318 14,981 » 369 5.283 2045 59.424 ,016828 14,045 2 346 5.165 2045 57 6170 «07338 14,045 2 346 4.907 0049 56.029 .01/7848 15.293 ASU 4.56" 0064 54.472 .018358 19.975 0492 4.879 2198 53.900 .018868 30,586 2753 4.10] eelelen 51,605 .019378 34,331 846 3.947 2097 50.282 .019888 30.274 146 3,233 2126 49.025 .020398 39.325 2969 2.886 21A5 47,829 .020908 39.013 2961 4.104 0067 46,690 .0214)8 20.911 Abilis) 2.787 2053 45,605 2.021928 16.541 2407 2.370 2063 44.568 2.022438 19,662 0484 2.148 057 43.578 .022947 17.790 438 1.705 2958 42,630 2023457 18.102 2446 1.24) 0 RY 41.773 .023967 25-22A0 .o23). 271 0118 40,854 2.024477 36.828 0907 2245 2128 40.9070 .024987 39,949 2984 -().27) 2059 39.220 .025497 18.414 0454 0) ) 0 0 0 0 c-8 OONCUMFEFWNR DSA ACOV 15.693 13.229 Wsiecsiz 2: 12.730 11.912 11.666 NO renrarcs 10,284 9.2669 9.156 B26R5 8.029 72654 7.114 6.2483 6.134 52518 5.279 4.904 42354 3.98) 32657 32179 3.925 22619 22300 2223) 1.679 1.528 1.198 1.037 2836 0495 6495 el49 007] =0,070 “U2e2N4 =0el0)] 02252 =0.364 02244 =0.264 =) 0304 =()¢286 =(), 361 =(.005 = 2295 23) 0138 0126 9) SP 30496 52504 20675 0946 r) 464 0285 0181 0143 ello 0985 eN71 206) 20049 0034 026 0135 0945 004) 0035 0131 0028 013] 037 ef41 0033 0A) 0074 0027 e026 e028 203? 0035 0035 0046 0057 005] 040 e039 e060 2087 079 e068 e074 2967 0148 0148 e056 005? 045 0039 0019 (a) RUN 1] PERTOD 0 1961.000 980.500 653,667 490,250 392.200 326,833 780.143 245,125 2172889 196.100 178.273 163.417 150.846 140.07] 130,733 122.563 115.353 108.944 103.21) 98.50 93.381 89.136 85.261 81.708 78.440 75.423 72.630 70.2036 67.621 65.367 63.258 61.281 59.424 57.2676 56.029 54.472 53.000 51.2695 502282 49.025 47.829 46.690 45.605 44,568 43.578 42.4630 41.723 40,854 40.920 39.220 0 FREQ 0999999 6000510 0001020 2001530 ©002040 0002550 2003060 2003570 0004080 2004589 20005099 2005609 2006119 2006629 0007139 2007649 2008159 2008669 0109179 2009689 0010199 e010709 2011219 0011729 2012239 2012749 0013259 0013768 2014278 2014788 2015298 2015808 016318 0016828 0017338 0017848 0018358 2918868 0019378 2019888 2020398 2020908 0021418 2021928 0022438 0022947 0023457 0023967 20024477 20024987 e0I25497 0 C-9 SPK 1091.109 1717.809 834,873 295.248 144,815 88,949 56.490 44,631] 34.331 262529 220159 19,038 15.293 10,611 8.115 10.924 14.045 12-796 10.2924 92679 8.739 9.675 11.548 12.796 1927299 62554 7.490 8o427 8.1195 8.739 9.9e87 19.924 10.924 14.357 17.799 15-917 1206484 12.172 18.726 27.153 24,656 212223 232096 20.911 14.9R] 14.981 172478 16.229 14.2045 12e172 5.930 0 TR No. 22 CHANNEL 7 K ACOV 073025.710 1 -110.084 2 =122,883 3 -173,876 4 =246,.009 5 -255,.962 6 =266,275 7 #-273,635 B 295,602 9 2©174,188 10 146,869 Wi <137,320 12 -118,374 13 -192,134 14 ==86,637 15 990.47] 16 =87,159 17 =64,043 18 -75,621 19 =91,444 20 =101,077 21 78.139 22 275.292 23 -61,925 24 52,427 25 49.473 26 ~46.074 27 48,309 28 =30.975 29°) =72.414 30 =75.144 31 -78,2765 32 =56,057 33 =46,627 34 -49,576 35 =39.403 36 =*57,083 37 =66,496 38 -71.197 39 «6=55,295 40 =86,081 4) =80,498 42 63.788 43 =-85.487 44 =75.124 45 -=65.006 46 54,906 47 =58,946 48 =62,037 49 =80,379 50 -87.018 =() 1) RUN 2 SP PERIOD 168.668 0 375.62? 1961.000 425,686 980,500 448.754 653.667 464.773 490,250 4732296 392,200 479.996 326,833 483.976 280,143 483.831 245,125 477¢43? 217,889 4712169 196,100 471,080 178,273 469.499 163,417 464.373 150,846 4612621 140,07) 460.554 130,733 6590275 122.563 460.526 115,353 461.943 108,944 460,609 103,211 4602299 98,0950 462.49] 93.381 463,797 89,136 463.25) 85,261 462.132 81,708 460,871 78,440 459,48] 75.423 459.376 72,630 461.443 70,036 461.876 67,621 460.781 65,367 461.165 63.258 461,86) 61,281 463.024 59,424 4632809 57.676 464.298 56.029 464.922 54,472 464,304 53,000 463,859 51,605 463-859 50,282 4636404 49,025 462,658 47.829 462.702 46.690 462,892 45,605 6612059 44,568 460.438 43.578 4626337 42,630 463,128 41,723 462,896 40,854 463.05) 40,020 2312614 29,220 0 0 FREQ SPK 0999999 52641.620 0000510117232.377 6001020132857,.452 2001530140057.021 2002040145056,583 0002550147716.628 2003060149807,.712 2003570151049,878 2904080151004,623 2004589149007,482 0005099147052,787 2005609147025,010 0006119146531.577 2006629144931,742 2007139144072,837 0 007649143739.875 0008159143340.646 0 008669143731.086 © 009179144173,334 2009689143756,990 2010199143660,238 2010709144344, 366 0011219144751.971 0011729144581 ,564 ©012239144232.321 0012749143838,761 2013259143404,939 2013768143356,.563 0014278144017.283 0014788144152.423 0015298143810.672 2 015808143930,.519 20163) 8144147,742 2016828144510,716 2017336144755.717 0017848144908,334 0 018358145103.086 0018868144910,207 0019378144771,.322 2019888144771,322 0020398144629,315 2020908144396,4A7 0021418144410,2206 2021928144469,519 2 022438143897 .436 2 022947143703.621 0023457144296,302 2023967144543.175 0 024477144470.767 ©024987144519.143 0025497 722872193 0 0 C-10 ~ a WDDDAADNAAADADADAADAADAAAAAAVAAAADAANAAAADAADAADAADAADANNANANNANAAN ADNAN AAD ON WD WON DWW .286 .O91 .083 . 300 415 .506 22 sill. 2243 »239 .264 .ou7 .226 -259 246 popu .287 1295) 302 -293 peo satel ON MUR NOs 22 CHANNEL 7 OCOOENPTUFWNH BK Acov 60.956 58.142 56.2146 520403 48.811 44.797 41.2268 28,434 35,917 34,035 32.581 31.60) 31.321) 31.21 31.967 B2./13 33.879 35-176 36.443 37.72% 34.842 39.65% 39,975 39,854 39.266 34.8145 37,556 36.632 34,7294 33,543 312489 79,988 28.377 272.422 76374 262017 25.599 252294 24.9270 P% e258 232.459 2243R2 21,127 19,968 16,853 Ivo we 16,696 16.214 15,374 15.227 14.752 (9) SP 19.264] 21.911 30370 32085 4.586 32376 1.480 2649 0597 o 388 e311 0733 012? olf} 0S94 06) 031 0022 030 e037 6036 0029 00P9 0037 0039 034 0032 0940 0138 e030 0029 0028 224 e026 e032 e0AT 0925 0027 ef20 002) 0039 0053 0055 0054 00645 0062 0030 0038 0079 0070 002? 9) RUN @ PERIOD 0 1961.000 980,500 653.667 490.250 392.200 326,833 280.143 245.125 217.889 196,100 178.273 163,417 150.846 140,971 130.733 122.563 115.353 108,944 103.211 98,050 93,381 59,136 85.261 81.798 78.440 75.423 72.630 70.036 67.621 65.367 63.258 61.281 59.424 57,676 56.0209 54.472 53.000 51.605 500282 49.025 47,879 46,690 45.605 44.568 43.578 42,630 41.723 40.854 40.920 39.220 FREQ 2999999 2000510 0901020 2001530 20002040 0002550 0003060 2003570 0104080 2004589 0095099 2005609 2006]]9 20060629 0907139 0007649 2008159 2008669 0009)79 2009689 0010199 e010709 0011719 ©0011729 012239 0012749 2013759 2013768 0014278 2014788 20015298 0015808 00163)8 0016828 2017338 0017848 2018358 2018868 2019378 20019888 2020398 2020908 2021418 20219278 0022438 2022947 0023457 0023967 0024477 2024987 2025497 SPK 60112397 6838.467 1051.784 962.835 1431.300 1053.656 461«911 2152038 186.325 121.096 97.064 72.770 38.076 31.522 29.338 19.038 9.6795 6.866 $2363 11.548 112236 9.051 G05] 112548 12.172 10.611 9.9RT 12¢4R4 11.860 9.363 9.051 8.739 70490 8e115 Ga9RT 7.803 8.427 60242 6.554 12.172 162541 172166 16.854 29.599 LOo SSO 9.363 11-2860 24.6056 219847 62866 0 TReNO wee SPN 98.619 112.187 17.255 15.796 23048) 17.286 oeyve 3.528 5 OS 1/ 1.987 1,592 1.193 2625 Aen 2481 woe 2159 ois) 0154 2189 184 2148 2148 2189 2200 olT74 0164 2205 e195 0154 0148 2143 e123 0133 2164 0138 0128 2138 elte 2108 2200 eel e282 e216 ° 338 e317 0154 0195 2404 2358 lS 0) CHANNEL 7 OONDMNFWNMODA ACOV 672445 63,328 59.762 55.636 51.969 48,356 45.296 42,673 40.2692 38.192 35,756 322950 30.153 282056 252683 P4,.4R5 232715 23.755 24.28] 25295¢ 25.4AaN 75647) 24,797 24.454 24,108 723.838 23,589 23.623 723-2895 23.75) 232521 222.5950) 21.602 20.251 19,498 18,586 18.861 18.901 19.204 19,419 19.616 19.134 16,206 17.922 ios) 16.736 16.4092 17-06) tiers )sis 17.637 IPG VAS) 0 SP 172370 220607 8455 5./32 3.970 22018 0833 0954 0548 0139 0904 0569 0249 0208 0185 2168 0149 016 078 0095 ele? ell7 0096 0087 0094 0090 006) 0054 0057 006] 0063 e053 0955 2052 oe OSI, 034 004] 0954 0168 e071 0156 004) 003? 0935 0045 0043 0067 2088 0066 e049 eI026 0 RUN 2 PERIOD 0 19461.000 980.590 653.667 490.250 392.200 326,833 7802143 245.125 217.889 196.190 178.273 163.417 150,846 140.297] 130.733 122.563 WIS.3'53 108,944 193.211 98.050 93.3A1 89,136 85.261 81-708 78.440 752423 72.630 70.936 67.621 65.367 63,258 61.281 59.424 57.676 56.029 54.472 53.000 51,605 50.282 49.025 47.829 46.690 45,605 44,568 43,578 42,630 41.723 40.854 40.920 39.220 FREQ 2999999 eC00510 0101020 0901530 0002040 2002550 2003060 0003570 2004080 0004589 0005099 2005609 0006119 2006629 2007139 20007649 2008159 0008669 20009179 2009689 2019199 20010709 0611219 2011729 2012239 0012749 0013259 2013768 2014278 2014788 0015298 2015808 0016318 0016828 0017338 2017848 0018356 2018868 0019378 2019888 2020398 2020908 2021418 2021928 0022438 0022947 0923457 0023967 oN24a77 2024987 0025497 Q SPK 5421.212 7055.699 72638.872 1788.969 1239-045 629.822 259.98] 172.905 171.2032 230.643 282.0140 177.586 Ualgentals 64,917 57,739 52.433 66.503 33.083 24.344 29.650 38.076 36.516 292962 27.153 29.338 28.089 19.038 16.854 176790 19.038 19.662 16.54] 17.166 16.229 11.548 19-611 12.796 16.854 2le223 220159 176478 12.796 9.9R7 10.924 14.045 136420 19.350 272469 202599 8e115 G TR No. 22 CHANNEL 7 SMONDMNF WN OR RUN 2 PERIOD 0 1961,000 980,500 653,667 490.250 392.200 326,833 280.143 245,125 217.889 196,100 Sires 163.417 150,846 140.07] 130.733 122,563 115,353 108,944 103,211 98.950 93,381 89,136 85.2461 81,708 78,440 75.423 72,630 70,0936 67,621 65,367 63,258 61.281 59,424 57,676 56.929 54.472 53.000 51,605 50.282 49,925 47,829 46,690 45,605 44,568 43,578 42,630 41,723 40.854 40,020 39.220 0 FREQ 0999999 0900510 0901020 2001530 0002040 6002550 2003060 2003570 6904080 2004589 2905099 2005609 0006119 2006629 2007139 2007649 0008159 2008669 6909179 2009689 2010199 2010709 2011219 0011729 0012239 2012749 2013259 e0O13748 2014278 0014788 2015298 2015808 2016318 2016828 2017338 0017848 2018358 2018868 2019378 2019888 2020398 2920908 09021418 2021928 0922438 0022947 2023457 2023967 024477 2024987 0025497 0 (a3) SPK 5222.715 7658.047 2906,.606 821.452 630,134 535.879 354,236 229.395 302.739 3216465 219.096 123.280 94,879 65.229 42.134 31.834 32.459 34.331 75.592 25.592 31.210 22.159 14,045 17.790 19.975 19.350 17,790 19,350 21.203 18,192 22.159 29,338 26,529 16,229 152293 21,847 19,662 ses 14,981 19.038 17.478 15.605 17.166 16,854 15.605 21.535 32.459 33,083 26.217 18,414 6,866 0) TREN ee CHANNEL 7 ODNPAMNFEWNMR DA SF 172139 21.416 5.33? 1.559 072) 0956 e775 ose 0510 0410 0300 0218 0194 0161 ea? elll 0989 0062 006) 0975 0067 2048 2958 0076 0077 2079 0993 2093 0073 2069 2057 0043 0052 0955 060 0061 0951 0056 0972 0966 2048 2049 2069 2083 e065 0940 049 0062 0966 2067 0031 0) RUN @ PERIOD 0 1961,000 980.500 653,667 490,250 392.200 326,833 280.143 245,125 217.889 196,100 178.273 163.417 150,846 140.071 NEKO EIS) 122.563 115,353 108,944 103,211 98,950 93,381 89,136 85.261 81,708 78.440 75.423 72,630 70,936 67.621 65,367 63.258 61.281 59.424 57.676 56.029 54.472 53,000 51,605 50,282 49.025 47,829 46.690 45,6095 44,568 43.578 42,630 41.723 40,854 40,020 39.220 0 FREQ 0999999 0900510 e001020 2001530 20002040 2002550 2003060 2003570 2004080 0004589 2005099 0005609 2006119 0006629 2007139 0907649 2008159 2008669 0009179 20094689 0010199 0010709 2011219 0011729 0912239 0012749 0913259 2013768 2014278 2014788 2015298 0015808 0016318 0016828 0017338 0017848 0018358 2018868 0019378 0919888 2020398 2020908 0021418 2021928 2022438 0022947 0023457 2023967 0024477 0024987 2025497 0 C-1), TR NO nee CHANNEL 7 ACOV 303.990 221.302 214,516 207.931 203-815 197.667 192.792 188,031 182.003 177.707 172.43] 167.305 161.846 157.930 152.772 148,466 145,645 141.891 138,502 135.271 132.738 129.567 127.243 125.384 121.781 118.657 114.540 112.508 109,229 107.416 103.740 100.923 972408 96.033 93.782 91.570 89.209 86.945 932946 806770 79.220 76,317 732526 71.2153 69.192 67.916 67.131 66.045 65.040 622478 61.056 () RUN 3 PERYTOD 0 1961.000 960,500 653.667 490.250 392.200 326,833 2802143 245.125 217.889 196.100 178.273 163.417 150,846 140.071 130.733 122.563 115,353 108.944 103,211 98.050 93.381 89,136 85.261 81.708 78.%40 75.423 72.630 70.036 67.621 65,367 63.258 61.281 59.424 57.676 56.029 54.472 53.000 51.605 50.282 49.925 47.829 46,690 45.605 44,568 43.578 42.630 41.723 40,854 40.020 39.220 0 FREQ 0999999 0000510 0001020 0001530 00020490 0002550 0003060 0003570 0004080 0004589 0005099 0005609 0006119 2006629 2007139 0007649 0008159 0008669 0009179 0909689 0016199 0010709 0011219 0011729 0012239 0012749 0013259 0013768 2014278 0014788 2015298 0015808 0016318 0016828 0017338 0017848 0018358 2018868 0019378 2019888 0020398 2020908 0921418 0021928 0022438 3022947 0023457 0023967 0024477 0024987 0025497 0 SPK 248322084 30884,053 7847.18) 3086.689 2054,255 1318.007 944.733 7772758 788.058 759.968 711.2280 684.128 655.414 638.269 603.917 553.981 558.975 597.987 581-758 5512484 554.9\7 554.293 534,631 5200274 526.828 526.828 520.898 515.593 506.854 519.338 531.510 515.280 499.051 487.503 482.2510 485.631 482.198 475.956 4702650 4732459 480.325 483,758 491.561 504.045 524.331 525.580 494,994 491.561] 514.656 506.854 245.312 0 eae eae TOIT F— In) NoW PREP RPRPRP RPP PREP RPRPRPBPEP PER RPE RP RP BPP RP BPP BP PREP EP HEED ND DYDD DW TR No. 22 CHANNEL 7 TR No. 22 DBNAOMNEWNRM DA oO RUN 3 CHANNEL 7 ACOV SP PERIOD FREQ SPK SPN 45,924 152403 0 2999999 4807.307 104,543 43.379 202068 1961-000 .000510 6263.263 136.205 42,742 5.239 980.500 .001020 1635,.,102 35,558 41,905 10074 653.667 2001530 335.198 7,289 40,648 0676 490,250 ,002040 210,9A1 4,588 39.9A0 0358 392,200 ,002550 Wlpiven3S 2.430 38,693 0368 376,833 ,003060 114,854 2,498 37.864 0328 280.143 2003570 102.369 2.226 36,790 e216 245,125 .004080 672414 1.466 36.102 013? 217,889 .004589 41.197 2896 35.445 0199 196,100 005099 34,019 0740 34.339 2099 178,273 2005609 30.898 2672 33.684 0089 163,417 .006119 27.771 2004 32,814 2062 150,846 .006629 19,350 421 31,704 0035 140,971 .007139 10.924 2238 30.726 0039 «130,733 .007649 12.172 ~265 29,992 0964 122,563 ,008159 19,975 2434 29.087 e072 «115,353 .008669 22.471 2» 489 27.767 0066 108,944 ,009179 20,599 3448 26.874 0954 103,211 .009689 16,854 2367 25,617 047 98.050 .010199 14,669 2319 24,683 0049 93,38] .010709 15,293 2333 23,708 0047 89,136 ,911219 14,669 0319 22.953 0953 85.261 .011729 16,541 . 360 22,124 0054 81,708 .012239 16,854 2367 21.314 0043 78.440 2012749 13.420 2c92 20,513 2028 75.423 2013259 8.739 2190 19,54) 2018 72,630 2013768 5.618 ol22 18,800 0029 70,036 ,.014278 9,05) 2197 18.967 004? 67,621 .014788 13.108 2285 16.966 0956 65.367 2015298 17475 » 380 16.274 0072 63.258 015808 220471 0489 15,229 060 61.281 2.016318 18,726 0407 14.302 2036 59.424 016828 11.236 0244 13.169 0037 57.676 2.017338 11.548 0251 12.346 004) 56.029 .017848 12.796 2278 11,333 0 044 54.472 018358 13.732 2299 10,270 0054 53.000 ,018868 16,854 e367 9.825 2058 51.605 ,019378 18,102 ~ 394 8.604 2065 50,282 .019888 20.2a7 2441 7.82) 0063 49.925 .020398 19.662 2428 7,036 50771 47,829 .020908 22.159 »482 6,272 2085 46,690 ,021418 26,529 sSu 5.805 0063 45,605 ,021928 19,662 428 4,862 2 04N 44.568 2022438 12.484 eur 4,103 0036 43.578 2.022947 11.236 0244 3.856 2031 42,630 2.023457 9,675 2210 3.2909 037 41.723 2023967 11,548 2251 2.915 2040 40,854 .024477 12.484 ern 2.482 2026 40,020 ,024987 8.115 ale 2.049 2009 39.220 .025497 2.809 061 1) ny) 0 0. 0 0 C-16 RUN 3 PERIOU 0 1961.000 980,500 653.667 490.250 392,200 326.833 280.143 245.125 217.889 196,100 178.273 163.417 150,846 140.971 130.733 122,563 115,353 108,944 103.211 98,050 93.381 89.136 85.261 81.708 78.440 75.423 72,630 70.036 67.621 65,367 63.258 61,281 59,424 57,676 56.029 54.472 53.900 51,605 50.282 49.025 47,829 46,690 45,605 44,568 43.578 42,630 41.723 40,854 40,020 39.220 0 FREQ 2999999 2000510 0901020 2001530 0002040 2002550 2903060 2003570 2004080 0904589 2005099 2005609 2006119 2006629 0007139 2007649 2008159 2008669 2009179 2009689 2010199 e910709 0011219 2911729 2012239 0012749 2013259 2013768 2014278 2014788 2015298 2015808 e016318 2016828 2017338 2017848 20018358 0018868 2019378 2019888 2020398 2020908 2021928 2022438 0022947 0023457 2023967 6024477 2024987 2025497 0 GILT ( SPK 25896510 3642.230 1497.,777 590.497 2494369 184,764 120,783 77.089 66.166 60.548 Selo 472440 38.701 26.529 16.541 15.917 19,975 19,038 15,605 12484 14,981 19,350 18,726 16,854 14,357 15.917 15.605 10,924 10.299 12.484 15.293 18,102 168,414 15,605 10,611 9,363 10,299 13,108 20.287 23,720 19,662 11,860 12.172 25.280 29,650 22.471 21.847 22.471 17.478 15.293 8.115 0 TR No. 22 CHANNEL 7 OTCANDUFWN- OK RUN 3 SP PERIOD 10216) 0 12.594 1961,000 32.316 980,500 16486 653.667 098) 490,250 0646 8 6392,200 0384 326.833 2018) 280.143 0198 245.125 ol?76 217,889 e182 196,100 eel? Slingers e185 163.417 0136 150,846 ell7 140.071 0098 130,733 e085 122,563 0973)» «=115,353 0063 108,944 e050 193,211 04) 98.950 e081 93,381 0067 89,136 0958 85,261 0949 81,708 0064 78,440 2059 75,423 0040 72,630 0040 70,036 20068 67,621 e084 65,367 0054 63.258 0035 61.281 0045 59.424 0047 57.676 0052 56.029 0089 54.472 0094 53.000 0050 51.605 0056 50.282 2086 49,025 0095 47,829 2108 46.690 0993 45.605 0070 44,568 0064 43,578 0059 42,630 2058 41,723 2049 40,854 2039 40,020 0919 39,220 (a) 0 FREQ 0999999 2000510 2001020 0901530 20002040 2002550 2003060 2003570 2004080 2004589 29005099 2005609 09006119 0006629 20007139 0007649 2008159 2008669 2909179 2009689 2010199 20010709 2911219 2011729 0012239 0012749 0013259 2013768 2014278 2014788 2015298 0015808 0016318 2016828 0017338 0017848 2018358 2018868 2019378 0019888 2020398 2020908 2021418 921928 2022438 2022947 2023457 2023967 0024477 0024987 20025497 0 c-18 SPK 3171-268 3930.613 1034,930 463.784 306.172 2012618 119.847 56.490 49,312 54.930 56.803 66.166 SO Ve 42.446 362516 30.586 26,529 22.783 19,662 15,605 12.796 15,917 20,911 18,102 15,293 19,975 18.414 12.484 12.484 21.223 26.217 16,854 10.924 14,045 14,669 16.229 27.777 29.338 15605 17.478 26.841 29.650 33.707 29.025 21.847 19,975 18,414 18.102 15.293 12.172 5.930 0 i TR No. 22 CHANNEL 7 ACOV 38,695 34,35A 31.996 29,091 26,110 23.607 71.282 18,639 16,505 14,805 12,486 12.144 9,672 7,691 6.2762 5.442 4,450 3.960 3.122 2.510 2.546 26473 2.118 2,924 2,998 2.178 2,946 3.407 3,890 4,200 4,719 5,194 5,743 6,037 5,963 6,251] 6,626 6,660 6.262 OG TT 3,513 5,0a9 4,342 3.306 2.002 1.085 ,023 =],058 -1,278 -1,6°98 =2,137 0 SP 60316 10.05] 6,857 4,978 26953 1.308 0958 0668 .562 0447 0355 0263 0225 e202 e165 014) 2142 0137 0128 0116 6085 2078 2078 0065 6080 0086 2057 0044 e056 e063 2058 0043 0046 0093 0128 0126 e095 0054 0038 0945 0051 0055 007) 0992 0085 0962 2058 2065 007) 0066 2028 0 RUN 3 PERIOD 0 Bal .000 980,500 653,667 490,250 392,200 326,833 280.143 245,125 217,889 196,100 178,273 163,417 150,846 140,071 130,733 122,563 115.353 108,944 103.211 98,950 93.381 89,136 85.261 81,708 78.440 75,423 72,630 70,036 67,621 65,367 63,258 61,281 59.424 57,676 56,029 54,472 53.000 51.605 50,282 49,025 47.829 46,690 45.605 44,568 43,578 42,630 41,723 40,854 40,020 39.220 0 FREQ 0999999 0900510 0001020 2001530 0902040 2002550 0903060 2003570 6904080 0004589 2005099 0905609 2006119 0006629 0007139 0007649 0008159 0908669 2009179 2009689 0910199 0010709 e011219 0011729 2012239 0012749 0913259 2013768 0914278 0014788 2015298 2015808 2016318 «016828 0017338 2017848 0018358 2018868 2019378 2019888 2020398 2020908 2021418 0921928 0022438 0022947 2023457 0023967 0024477 0024987 0025497 0 C-19 SPK 1971 .236 3136.937 2140,083 1553,644 796.796 408,229 298,994 208,484 175,401 139,510 110,796 82.083 70.223 63,045 51.497 44,006 44,318 42,758 39.949 36.204 26,529 24.344 24,344 20.287 24,968 26,841 17.790 13,732 17.478 19,662 18,102 13,420 14,357 29,025 39,949 39,325 29,650 16,854 11.860 14,045 15.917 17.166 22.159 28.713 26,529 19,350 18.192 20.287 22.2159 20.599 8.739 0 TRE NOR eae CHANNEL 7 RUN 3 PERIOD 0 1961.000 980,500 653,667 490,250 392.200 326,833 280.143 245.125 217.889 196,100 178.273 163.417 150,846 140.071 130,733 122,563 115,353 108,944 103.211 98,050 93,381 89,136 85.261 81,708 78,440 75.423 72,630 70.936 67,621 65,367 63.258 61.281 59.424 57.676 56,029 54.472 53.000 51,605 50.282 49.025 47,829 46,690 45,605 44,568 43.578 42,630 41.723 40,854 40.920 39.220 0 FREQ 0999999 6000510 0001020 2001530 2002040 2002550 2003060 «003570 2004080 2004589 2905099 2005609 006119 0006629 2007139 2007649 0908159 2008669 e909)79 2009689 2010199 2010709 0011219 2011729 °012239 0012749 2013259 0913768 2014278 0014788 0015298 2015808 0916318 2016828 2017338 2017848 0918358 2018868 0919378 0019888 2020398 2020908 0021418 2021928 0022438 0022947 0023457 0023967 0024477 0024987 0025497 0 C-20 SPK 3101.358 4991447 2105.128 427,268 308.669 175.401 155.739 140.446 94,879 53.994 36.516 30.898 39.949 472440 52.121 49.000 31.834 21.223 21.535 19,038 172478 14.0495 19,350 24,656 24,656 22.783 19.662 16,854 14.669 11.860 12.172 18.414 24.656 21.535 14,669 14,981 24,344 28.089 19.662 15,293 16.541] 17,166 18,726 21.223 23.2096 24.656 24,656 16.541 10.924 5.930 0 TR No. 22 CHANNEL 7 OBNTMFWN— COA ACOV 580.722 425.453 417,278 397.437 336,383 382.037 371,823 368.276 349.748 339,557 327.577 317.346 3052108 291.994 280.112 267.800 255,765 242,141 229.762 2176116 209.4468 194,945 186.104 174.723 180.388 168,875 160.672 152.115 128.755 124.792 117.235 129,854 124.780 122.588 118.739 114.898 112.554 109.362 195.294 194.349 98.096 95.887 92.577 89,880 85.553 82.557 78.106 77.195 712679 70.243 67.778 0 RUN 4 PERIOD 0 1961.000 980,500 653.667 490,250 392.200 326.833 280.143 245.125 217.889 196.100 178.273 163.417 150.846 140.071 130.733 122.563 115,353 108,944 103.211 98,050 93,381 89,136 85.261 81.708 78.440 750423 72.630 70.036 67-621 65.367 63.258 61.281 59.424 57.676 56.029 54.472 53.000 51.605 50.282 49.025 47.829 46.690 45.605 44,568 43.578 42.630 41,723 40.854 40,020 39.220 0 FREQ 2999999 2000510 2001020 0001530 2002040 e0902550 6003060 2003570 2004080 2004589 2005099 2005609 0006119 0006629 0007139 0007649 °008159 0008669 2009179 2009689 2010199 0010709 0011219 2011729 0012239 0012749 2013259 0013768 09014278 20014788 2015298 2015808 2016318 0016828 0017338 2017848 0018358 0018868 0019378 2019888 0020398 0020908 2021418 0021928 0022438 0022947 0023457 0023967 0024477 0024987 0025497 0 C=21 SPK 43899.955 59420.476 20281 .948 6384,359 2554-243 1931.91] 1659446 1462.198 17172497 1511.822 1068.013 1284.612 16250115 1300.841 1052.096 1365.446 1420.688 1038-988 973134 1135.739 1015.580 822.3R9 804.287 806.472 8230329 926.631 9192140 817.395 879,503 9872179 928.816 827-695 849,230 911.2650 883.873 8260446 834,873 915.395 963.147 886.994 933.497 1147.911 1124.191 951.599 1047.414 1192.854 1033.370 836.433 886.994 929.440 443.1895 0 PRE RPNFPRPRPEPRPRPRBRPRPRPRBEPRPRP RPP RPBPBPEPEP RP PRP EPEPE ENDED UNDE NYNYNY NW TR No. 22 CHANNEL 10 OONMNDMNEWNRK OA TR No. 22 RUN 4 CHANNEL 10 ACOV SP PERIOD FREQ SPK SPN 132724 42053 0 2.999999 1264,949 92.171 11,609 4.908 1961-000 -000510 1531.797 111.614 11,388 094] 980.500 ,901020 293.688 21.400 10.814 0515 653.667 .001530 160,733 Pl aelhe 10.384 0706 490,250 .002040 220.344 16,055 9.830 0394 392.200 .002550 122.968 8.960 9,369 0185 326,833 .003N60 57.739 4,207 8.922 0124 280.143 .003570 38.701 2.820 8.513 0098 245,125 004080 30,586 2.229 8.317 0086 217,889 .004589 262.84) 1,956 7.937 0093 196,100 .005099 29,025 Bayne 7,659 0978 178,273 2005609 24.344 1.774 72.590 0044 163.417 .2006119 13.732 1,001 Vashi 0039 150,846 006629 12.172 ~887 72266 0046 «140,071 .007139 14.357 1.046 Vos 0047 130,733 007649 14,669 1,069 7.158 0945 122,563 .008159 14,045 023 7.415 0039 115,353 2008669 12.172 2887 7.309 e025 108,944 ,.009179 7.803 2569 7.705 0936 103,211 2009689 11.236 2819 7.664 2057 98,050 ,019199 17.790 296 7,632 0043 93,381 ,0107N9 13,420 2978 7,542 2033 89,136 .011219 10.299 2750 7.465 2039 85,261 011729 12.172 ~887 7.473 2039 81.708 012239 12.172 887 7,365 2940 78,440 ,012749 12,484 2910 7,234 2040 75,423 ,013759 12,484 2910 6.963 0936 72,630 ,013768 11,236 819 6,736 2027 70,036 .014278 8.427 2614 6.499 2028 67,621 2014788 8.739 2637 6.288 2037 65,367 .015298 11.2548 5.748 0037 63.258 .015808 11,548 5.225 004) 61,281 2016318 12.796 2932 4.785 0946 59,424 .016828 14.357 1,046 4,653 0043 57,676 .017338 13.420 2978 4.152 0044 56.079 ,017848 13,732 3.961 0139 54.472 2.018358 12.172 2887 3.508 0027 53.000 2.018868 8.427 0614 3,079 0022 51,605 .019378 6866 2500 2.990 0025 50,282 .019888 7.803 2569 2,672 2037 49,025 .020398 11.548 2.373 2057 47,829 020908 17.790 1,296 1,845 0056 46.690 021418 176478 1.274% 1.805 0043 45.605 .021928 13.420 .978 1.699 0935 44,568 .022438 10.924 0796 1.510 003? 43,578 022947 9,987 2728 1.613 2050 42,630 .023457 15.605 137 1,187 006) 41.723 .023967 19.038 1,462 2050 40,854 ,024477 15.605 1,249 2939 40,020 .024987 Veale 1.216 0019 39.220 2025497 5.930 0 fy) 0 0 0 C-22 OBrADNHAF WY DHA acov 247.24) 241.4461 235.473 278 -2A4 AP) cave) 2150016 209,574 204.154 199,733 195.424 191.259 186.218 181.669 177.183 1732014 169.116 165.696 141.975 158,45] 194.993 151.614 14He477 144,990 141.012 Waieclns 1326797. 124,854 174.342 120.914 117.2849 116.182 114.263 112.494 1112244 199.832 1972474 195.619 192.728 99,779 76.933 93,304 29.674 R659? 23,437 79,914 760.535 7326?) 702153 66,146 622979 59,848 0 RUN 4 PERTOD 0 1961.0090 980.500 653.667 490,250 392.200 326,833 280.143 245.125 217.889 196.100 asians 163e4)7 150.846 140.971 LIS 4OS) 122.5953 115.353 108,944 103.211 98.950 93.381 89,136 85.76] 81.708 78.440 75.423 72.030 70.936 67.521 65.367 63.758 61.281 592424 57.676 56.029 54.472 53.000 51.605 50.282 49,025 47.829 46,690 45.505 44,568 43.578 42.639 41.723 40,854 40.920 39,220 0 FREQ SPK 0999999 273792460 2000510 33467.910 2091020 0001530 0002040 HOOAS 50 0003060 2003570 2004080 2004589 2005099 2005609 2906119 2006629 000/139 0074849 HOON SS 2008669 2009179 2009689 0010199 0010709 0011219 SON ree 0012239 0012749 09132759 0913768 00142778 2014788 2015798 2015808 20163138 0016828 0017338 2017848 2018358 2018868 0919378 e0149888 0029398 2020908 021418 0121928 0022438 0022947 0023457 0023947 0024477 2024987 0025497 0 C23 7582, 766 24092427 1423.809 1050223 741.242 379.516 404.4R4 400.739 279ee7% 2030178 184.764 141.382 91.758 66.478 620108 Sol te) 56.178 55,554 47.752 37.459 Pulalu tl 34.331 PUSH 19.350 24.2032 28.089 Wot U 292029 34.331 3025R6 27.469 242968 12el72 B.4,f 12 o4h4 12-172 17.790 210223 16.854 20.599 Ao 26e2\! 20.911 18el02 212¢84/ 212539 17.2166 24.968 16.85% 0 TR No. 22 CHANNEL 10 BDBNMNDANPF WNP DA oO ACOV 295.575 289.760 252.63) 275.6A3 268,278 261.091 254.968 248.465 242.246 DADo6 VAS 229,647 224,35? 218.352 211.558 294,404 WOR 217 0 190,031 183,699 178,525 172,544 166.639 160,730 154,44] 148,664 143.088 136,195 134.156 179,056 123.766 119.090 WS Sse LNB OS 1o2,7a7 97.696 94,319 90.515 87.615 Q5.174 82.665 20.256 78,304 76.202 73,488 A Ae 69,900 64.379 67.31] 67,197 66,718 66,873 65.786 () SP 19012045 130.28? 35.287 8,839 4.693 22756 1.873 1./87 1.466 12035 0938 266) 0c k9 07 48 e390 0446 AS e260 e159 018 GAUSS e039 el 4 0128 el05 0095 0141 2167 el2n 0984 0079 e077 0092? elOA 2133 ell} 0958 0067 e100 0076 0043 0043 004) 0044 0066 0164 0967 0369 0963 2068 0938 fy) RUN 4 PERIOD 0 1961.,000 980,500 653 16617 490,250 392,200 326.833 280,143 245.125 217,889 196.100 178.273 163.417 150,846 140,071 WoO. 733 122.563 115,353 198.944 MOS Reel 98,050 93,38) 89.136 85.261 B1.708 78,440 orcs 72.630 70.036 67.621 65.367 63,258 61.281 59.474 57,676 56.929 54,472 53.000 51.605 50.282 49.025 47.829 46.690 45,605 44,568 43.578 42,630 41.723 40.854 40,920 39,220 0 FREQ SPK 0999999 31536.34/ 0000510 40661.273 2001020 11013.143 2091530 2002040 2002550 e00306U 6003570 2004080 0004589 2005099 2005609 0006119 29956429 0007139 0007649 2008159 20086469 2009179 2009689 6010199 2010709 0011219 0911729 2012239 0017749 2013259 0913768 09142778 0014788 2015298 0015808 20916318 0016828 201/338 2917848 e01H358 018868 2019378 2019888 2020398 2020908 2021418 2921928 0022436 20022947 0023457 0 0239Hh7 0024477 0024987 0025497 0 C-2), 2774.275 1436.606 860.153 584,567 557.726 457,542 373.026 292.2752 206,299 90.197 77.401 121.720 139,197 117.662 41.147 49,624 39,949 35,892 2UoUTt 32.459 39.949 33,083 29.650 44,006 52.121 37,452 CO.217 24.656 24,032 28.713 33.707 41,510 35,268 18.102 20.911 31.210 23,7270 13.470 13.420 12.796 Sense 20,599 19,975 19,350 iG Syal5) 19,662 2126223 0 SPN 106.695 137.567 37,260 9,386 4,460 2.910 1,978 1.887 1,548 1.993 2990 2698 0262 TR No. 22 CHANNEL 10 CONPFMNFWNRK DA ACOV 44.424 40.9}0 36.744 35,74) 32.9A89 31.003 79.35) 27,880 26,845 25,997 25,109 74.246 23.159 22.094 20.946 19.715 18.779 Wieeses 16,4829 15,402 14.50] 13.807 NierenSirak 12.946 10,990 10.369 9,608 9,5)6 9,396 9.7646 9.9)4 9.75] 9.3A6 9,068 8,675 8.486 7.906 7,338 6,736 6,341 6.046 6,0)9 Soe) 6,053 6,000 5.955 2.478 4.747 41a? Joos ) SP 11.009 15.520 6.346 22688 126293 0973 10054 084) 0620 0604 0478 0288 02l? ofl? 0185 elN9 0113 o1ll4 2092 0982 e079 0056 0949 0052 0043 OE: 0 V4N 04) 0038 0 04) 0049 0055 2057 0053 e047 0056 0971 2 f69 0961 0951 0038 0 M4) 0963 20075 062 0942 042 006) 2062 0926 (9) RUN & PERTOD 0 1961.0900 980,500 653.667 490,250 392.200 326.833 280.143 245.125 217,889 196.100 178,273 163.417 150.846 140,071 130,733 122,563 115,353 108,944 103,211 98,050 93,381 89,136 85,261 81,708 78,440 75,423 72.630 70.036 67.621 65,367 63.258 61.281 59,424 57,576 56,029 54.472 53,000 51,605 50.282 49,925 47,829 46.690 45,605 44,568 43,578 42,630 41,723 40,854 40,020 39,220 0 FRE 0999999 2000519 2001020 2001530 0002040 #002550 2003060 2003570 0004080 2004589 2005099 0005609 0906119 0006629 0007139 0907649 0008159 2008669 2009179 2009689 0910199 e010709 20112719 0011729 0012239 0012749 2013259 0013768 0014278 0014788 2015298 2015808 0016318 2016828 0017338 ©017848 0018358 oV18868 2019378 0019888 0020398 2920908 2021418 2021928 2022438 0022947 0023457 0023967 aN24477 0924987 2025497 0 C-25 SPK 3435,931 4B843.823 1980,599 838.930 403.548 303,675 328.956 262.478 193.503 188.510 149,185 89,885 66,166 67.726 57.739 34,019 32.147 35.580 28.7)3 25,592 24,656 17.478 15,293 16,229 13.429 11.548 12,484 12.796 11.860 11.236 12.796 15.293 17.166 17.790 16.541 14,669 17.478 22.159 21.535 19,038 15.917 11.860 12.796 19,662 23,408 19,350 13,108 13,108 19.038 19,350 8.115 0 TR None Ze CHANNEL 10 x fiw N —- > TNMDWV ACcCOV 43.487 40.995 3.219) 35.054 322635 30.441) P4.9RYD 28207? 27.569 76.95) 262459 762 3R) 25.809 25.2566 25.216" 24,694 P4&.NRS Bae Nae 2 OAT 21.2095 20254) 19.796 19.451 19,147 13.78% 14.637 17.618 16-747 Weal il 14,38) 122868 11.806 11.659 11,834 L265) 1°?.752 12.947 12.871 12.145 11.872 11.7466 11.878 VW) s619 11,386 Olea 0) TOeo75 9.668 9.165 8.65? 8.544 8.457 ty) RUN 4 PERIODUD 0 1961.900 980.500 653.667 490.250 392.200 326.833 740.143 245.125 217.889 196.190 178.273 163.417 150,846 140.97] VSIGG 7s) Weenoes US sss 108,944 103.211 98.050 93.381 69,136 85.261 81.708 78.440 75.423 722630 70.036 65.367 63.258 61.281 59.2424 57,676 56.029 54.472 53.900 S605 50.282 49.925 47.829 46.690 45.605 44,568 43,578 42.630 41.723 60,854 40.020 39.220 0 FREQ 0999999 00005] 0 e0V1020 0001530 2002040 0$07550 00903060 0003570 e0U40R0 2004589 0005999 2005609 0006119 0006629 0007)39 0007649 2008159 2008669 0009179 0009689 20019199 01709 00112719 e011729 0012239 0012749 0913259 0013768 0014278 0014788 0015298 0015808 0016318 0016828 6017338 0017848 0018358 -018868 0019378 0019888 0020398 2020908 0021418 021928 2022438 oV22947 0023457 023967 0024477 0024987 0025497 0 C-26 SPK 3904.084 4990.823 1381.343 466.280) 3R9,8}5 398,554 300.866 287.1 3% 285.573 LS Syenlno 79.274 112298] 100.497 57.739 53.369 2029) 1 26.217 22073 17.478 17.790 16.229 112860 12.484 20.911 20e2R7 14.357 17.790 18.102 13.420 10.299 10.299 10.611 9.051 19.924 162.854 17.790 15.9) 7 15.605 15.917 16.541 12¢4R4 72.490 14.045 24.032 232.720 202599 19.038 19.975 20.599 9.675 0 TR No. 22 CHANNEL 10 OBNO*MEFWNRK DA ACOV 129.340 60.022 59.730 57.518 56.099 55.386 54,228 52,697 51,876 49,618 48,082 47.110 45,592 44,597 44,034 42,657 42,434 40.453 39,319 37,825 36.902 36,611 36,039 35,526 35.660 35,055 34,409 31.731 312317 31,139 32.710 33,750 32,536 32,511 31.112 31,643 32.463 32,381 30.821 30,784 30,74) 30,125 28,669 27,610 27,421 26,282 25,131 24,880 24,351 24,419 23,297 19) RUN §& PERIOD 0 1961.000 980.500 653,667 490,250 392,200 326,833 280.143 245.125 217.889 196,100 178,273 163,417 150,846 146.07) 130,733 122.563 115,353 108.944 163,211 98.050 93,381 89,136 85,261 81,708 78.440 75.423 72,630 70,936 67,621 65,367 63,258 61,281 59,424 57,676 56.029 34,472 53,000 51,605 50,282 49,025 47,829 46.690 45,605 44,568 43,578 42,630 41.723 40,854 40,020 39.220 0 FREQ 0999999 900510 0001020 2001530 2902040 2002550 «003060 2003570 2004080 2004589 2005099 2005609 0906119 2006629 2007139 0007649 2008159 0008669 2009179 20009689 2010199 0010709 0911219 e011729 6912239 0012749 0013259 2013768 0014278 2014788 2015298 2015808 2016318 e016828 2017338 2017848 2018358 2918868 2019378 2019888 2020398 2920908 2021418 2021928 2022438 0022947 2923457 0023967 0024477 2024987 0925497 0) C-27 SPK 7228.594 8802.213 2322.039 1182,554 714,089 593.618 554,293 484,382 488,128 465.656 416.032 421.338 501,548 515,593 439,440 425.707 466.280 437.567 408,854 4464306 439.128 397,306 411,663 428.516 426,331 421.962 416.032 425.395 419.777 411.663 415,096 410.414 413.223 419.465 418,841 431,325 447,242 447,242 450.675 446,306 420.089 412.911 436,319 445,057 431,325 435.070 438,503 425,083 431,325 450,987 228,771 0 FWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWwWwwwwwwwnwuww Fru 888 -055 15 143 521 .590 286 745 600 217 5259) TR No. 22 CHANNEL 10 DBNDMNFWN MK DA Ne} ACOV 52,790 49,278 48.008 46.117 44,558 42.685 41,390 39,724 36,950 37.533 362481 35,49) 33.202 32.099 31.083 302217 29.130 PeaeTth& 27.524 27-908 75-861 252223 24,396 23.623 23.182 22.792 22.648 212-974 21.175 200146 202056 19.337 15.556 18.1273 17,669 17.100 17.017 16,624 1256778) 152450 14.9n2 15.968 15,152 15.035 15.474 15,045 14,810 14.059 14,228 a) SP 1626356 2leli2 5.598 22249 1.29? 0/57 058? 0508 0378 e291 e2Td 0221 0116 0196 0116 016 e086 0065 0080 0188 0164 0054 016) 0163 268 008? ol9)] 0059 032 046 2052 048 0955 0953 0058 0 D7) 0973 N67 0 J5) e050 0 IAG 0047 0029 0038 0950 060 0 058 0064 0080 0 I9R 0057 9) RUN 5 PERTOD 0 1961.000 980,590 653.667 490.250 392.200 326,833 280.143 245.125 217.889 196.100 178.273 163.417 150.846 146.071 130.733 122.963 PSs s 108,944 103.211 98.050 93.361 89.136 85.261 81.708 78.440 75.423 722630 702936 67.621 65,367 63.758 61.291 59.424 57.676 56.029 54.472 53.090 51.605 50.282 49.925 47.829 46.690 45.695 44,568 43.578 42.630 41.723 40.854 40.920 39,220 0 FREQ 0999999 2000510 0901020 2001530 002040 2002550 2003060 0003570 2004080 0004589 0005099 2005609 0006119 2006629 0007139 0007649 2008)59 0008669 2009)\79 2009689 eQ010N)99 2010709 0911219 0011729 0012239 0012749 0013259 2013768 0014778 0014788 20015798 0015808 2916318 0016828 0017338 0017848 0918358 0918868 9019378 0019888 0020398 0020908 0021418 0021928 0022438 eN2294T 0023457 0023967 0924477 2024987 0125497 0 C-28 SPK 5192.129 6589.097 1840,778 VOM GOT 403.236 236.261 181,643 158.548 117.975 90.822 84.268 68.975 36.20% 292962 36.204 33.083 26.841 2Ne2R7 24.968 272465 19.975 16-854 19.038 19.662 2@le223 250592 280401 18.414 9.987 14,357 16.229 14.9R] 17.2166 16.54] 18.]92 222159 22.783 20.91) 15.9)7 152605 19.975 14.2669 9-051 11-860 15.695 18,726 18.102 19.975 24.968 30.5R6 17.790 0 TR Nog 22 CHANNEL 10 ry POeOADUF WN SA ee a BANDMEUNeE: 19 RUN 5 PERTOD 0 1961,000 980,500 653,667 490.250 392,200 326,833 280.143 245.125 217,889 196.100 178.273 163,417 150.846 140.07) USO 39. 122,563 115,353 108,944 103.211 98,050 93,381 89,136 85,261] 81,708 78.440 75,423 72,630 70.036 67,621 65,367 63,258 61,241 59.424 57.676 56.029 54.472 53,000 51,605 50,282 49.025 47,829 46.690 45,605 44,568 43.578 42,630 41,723 40.854 40,920 39,220 0 FREQ 2999999 0900510 »901020 2001530 2902040 0002550 °003060 6003570 2004080 0004589 0905099 2005609 2006119 -006629 0007139 e007649 20008159 2008669 2009179 2009689 2019199 2010709 2011219 0011729 0012239 20912749 3013259 013768 2014278 2014788 2015298 2015808 0916318 2016828 0017338 2017848 0918358 2018868 2019378 2019888 2020398 2020908 2921418 2021928 3922438 eN22947 0023457 0023967 024477 2024987 2025497 0 C-29 SPK 7395,8R1 9031.920 1906.319 468,153 295,873 191,006 187,885 182.892 159.172 125.153 125.153 132,331 76.777 272465 252904 390.586 37,764 44,318 54,618 80,522 95.191 88.013 78.029 59.611 44,318 39,949 33,707 22.783 12.796 13.108 17.478 22.471 33.707 49,312 58.675 53.057 45,879 44,006 39,325 37.764 33.707 26,841] 23.408 21,847 30.274 37.452 36,204 46,503 59,924 60,860 29,650 0 Te Nonwee CHANNEL 10 => x ODN DAF WN- a) ACOV aah) 722146 70.755 68.991 67,187 64,850 42.970 6) .569 59.229 57.588 55.809 53,96) 51,854 50.745 48.,4)0 46.588 44.767 42.1767 41.209 39.837 39.047 37.8)7 37.456 36.357 2537.8 34.293 33.2449 32.812 31.575 31.221 30.190 29.2\7 28.208 27,152 25.945 24,725 234239 21.839 20.2379 19.9606 17.9690 16.46] Wee Sv7S 14,991 13.221 12.484 11.418 10.768 10.247 9.946 9.349 0 SP 242753 31.878 9.000 3.235 1.688 056? 0460 0434 0403 0336 0197 e108 e129 el6? 0144 0084 0948 0067 2076 0075 2073 0965 006] 0056 0959 006) 2 086 0995 0184 0987 elN4 097 0963 0046 004A 0037 0037 047 046 0038 0074 0957 0155 0087 011? 098) 048 0049 0054 0028 0) RUN 5 PERTOV 0 1961.000 980.500 653.667 490.250 392.200 326,833 2802143 245.125 217.889 196.100 178.273 163.417 150.846 140.97] 130.733 122.963 115.353 168.944 103.211 98.950 93.38) 89,136 85.261 81,708 78.440 15.423 722630 70.936 67.621 65.367 63.258 61.281 57,676 56.929 54.472 53.000 51,605 50.282 49.925 47.829 46,690 45.605 44,568 43.578 42.630 41.723 40.854 40.020 39.220 0 FREQ 2999999 20005)90 2001020 2001530 2002040 2002550 2003060 20034570 0004080 20004589 0005099 2005609 00046119 0006629 2007139 000/649 «008j}59 2008669 0009179 0009689 0019199 0010709 0011219 0011729 2012239 0012749 0013259 0013768 2014278 ©014788 2015298 0915808 2016318 0016828 0017338 2017848 2918358 2018868 2019378 2019888 2020398 2020908 2021418 0021928 0022438 0022947 0023457 2023967 0024477 0024987 0025497 0 C-30 SPK 77252461 9949.188 2808.9]A 1009,650 526.8248 175.2401 143.567 135.452 N2WS VEU 104.866 610484 33.707 49.261 50.561 44,943 260217 14.981 19.350 23.720 232408 22.783 20.28! 19.038 17.478 15.605 19.038 26.841 29.650 260217 27.153 322459 30.274 19.662 14.357 132108 11.548 11.548 14,669 14.357 11-860 19.350 23296 17.790 172166 270153 34.955 2522AR0 14.981 15.293 16.854 8e739 0 TR Nor 22 CHANNEL 10 OBNONEFWN-H OK acoV 108,676 99,369 96.879 94.075 91.707 89,242 86.961 85.2)2 82.996 R2.248 BU 9228 78.433 76.66() 74,945 73,054 71.038 69.042 67.562 66.236 65.094 632507 61.2391 $9.2n7 57.382 55.124 53.926 51.945 50.077 47.2486 45.285 42,689 41.312 40.726 39,727 38,688 37.678 36.159 35.247 S35 20.966 28.396 256779 23,633 212643 200759 18.809 17.601 152522 11.873 9.969 8,374 1) SP 366081 452764 19.6519 22489 1.821 10415 12022 0630 0/8) 0667 0512 0503 0327 0192 0 34) e267 e179 e205 e228 023? 0252 0234 019) e179 0168 0153 0159 014? e158 0174 0193 e180 e152 el69 e160 0129 e113 e112 0116 0145 0157 0149 0178 0192 el77 0153 el49 6155 0118 0042 9 RUN 5 PERTOD 0 1961,.900 980.500 653.667 490,250 392.200 326.833 280.143 245.125 217.889 196.190 178.273 163.417 150,846 140.971 S07 SS 122.563 115.353 108,944 103.211 98.050 93.381 89.136 85.261 81.708 73.440 75.423 72.630 706036 67,621 65.367 63.258 61.281 592424 57.2676 56.029 54.472 53.000 51.605 50.282 49,025 47.829 46.690 45,605 44,568 43.578 42.630 41.723 40.854 40.920 39,220 0 FREQ 2999999 20005]0 6001020 0091530 0002040 2002550 2003060 0003570 2004080 0904589 00050999 2005609 2006119 0906629 0007139 2007649 2008159 »908669 2009179 0009689 2019199 0010709 °011219 0911729 0012239 0012749 2013259 0013768 20014278 2014788 2015298 0015808 °016318 0016828 0017338 2017848 20158358 0018868 0919378 2019888 2020398 2020908 0021418 0021928 0022438 2022947 0023457 0023967 e024477 0024987 0025497 0 C=31 SPK 11269.952 14126.985 3280.192 7762822 563.338 441.624 318.968 196.624 243.752 159.796 156,987 192.057 59.974 81.147 196.427 83.331 53.057 63.981 716159 722408 78.650 732032 59.611 55,866 522433 47.752 49.674 50.561 49.312 54,306 60.2236 56.178 47.440 49.936 49.936 40.261 35.2684 34.955 36.204 45.255 49.000 46,503 55,554 59.974 55.242 47.752 46.503 48.376 36.828 13.108 0 TRENOp ee CHANNEL 10 oA ODMOANAU FWY SP 192248 33.828 18.137 5.87} 4.212 20610 1.207 1.101 1.25] 1.033 062) 059) 0725 054) 0292 2755 0246 019) 0149 0109 °080 0078 2095 0118 0098 0956 0948 2052 0044 042 RUN 5 PERIOD 0 1961.000 980,500 653,667 490.250 392.200 326.833 280.143 245.125 217.889 196,100 178,273 163,417 150,846 140,071 130,733 122,563 115,353 108,944 103.211 98,050 93,381 89.136 85,261 81.708 78.440 75.423 72,630 70.036 67,621 65,367 63,258 61,281 59,424 57.676 56.029 54,472 53,900 51605 50.282 49,025 47,829 46,690 45.605 44,568 43,578 42.630 41.723 40,854 40,020 39,220 0 FREQ 06999999 0000510 2001020 0001530 2002040 2002550 0903060 2003570 20004080 2004589 2005099 2005609 2006119 0006629 0007139 2007649 ~008159 2008669 2009179 2009689 0010199 2010709 2011219 2011729 2012239 0012749 e913259 2013768 2014278 0014788 2015298 2015808 2016318 2016828 2017338 2017848 2018358 2018868 29019378 e019888 2020398 2020908 0021418 2021928 2022438 2022947 2023457 2023967 0024477 2024987 2025497 0 C=-32 SPK 6007-339 105572786 5660.594 1832.351 1314.574 814.586 376.707 343.674 390.440 322.401 193.815 184,452 226.274 168.847 912134 79,586 76,777 59.611 46,503 34,019 24.968 24,344 29,650 36,828 30.586 17.478 14,981 16.229 13.732 13,108 11.548 9,9A7 14,669 21,847 24,032 21.847 15.917 10,611 11.860 16.229 18.726 16.854 17.2166 18.414 19,662 25.280 26,841 24,656 27.153 32,459 17.790 0 SPN Pela (/S1/ 112.052 60.077 192447 13.952 8,645 3,998 3,647 4.144 3.422 2,057 1.958 2.401 1,792 2967 845 815 2633 0494 2361 2265 TR No. 22 CHANNEL 10 = L_ OBDANPrPUFWN COA ACOV VSTi Test. 225.899 221,217 220.191 212.092 209,635 2oT.oTT 204,8A9 197.752 194.185 187.790 184.036 178.290 174.605 168,594 165,184 159.270 153.068 152.540 146.681 140.670 134,873 131.2341 125.234 122.121 118,996 116.068 107.216 110.377 101.665 99.047 97.881 89,122 92.736 81.190 83.501 81.120 85.801 84,319 83.199 85,415 82.337 85.174 90,097 90,608 95.426 90.539 96.243 94.176 95,831 94,093 0 SP 99.2790 1370462 58,839 38.526 35.182 34.550 33264) 33.717 33.34) 33.187 33.493 33.521 330321 330327 336229 33031] 336396 33.048 32.894 32.878 322890 33.007 32.923 322799 32.866 32916 322974 33.217 33-23) 33.022 322986 332155 33.395 33.297 33.005 33.059 33.122 32.956 32.998 33.273 33.087 32.705 33.050 33.150 32.852 33.2131 33.210 32.728 322617 322743 16.351 0 RUN 6 PERIOD 0 1961.000 980,500 653,667 490.250 392.200 326,833 280.143 245.125 217.889 196.100 178.273 163.417 150.846 140.07] 130.733 122,563 115.353 108,944 103.211 98.050 93.381 89.136 85.26] 81.708 78.440 75.423 72.630 702036 67.621 65.367 63.258 61.281] 59.424 57.676 56.029 54.472 53.000 51,605 50.282 49.025 47.829 46,690 45.605 44,568 43.578 42,630 41,723 40,854 40.020 39.220 0 FREQ 0999999 0000510 0001020 2001530 0002040 0002550 2003060 0003570 6094080 0004589 2005099 2005609 2006119 6006629 0007139 0007649 0008159 0008669 ©009)179 2009689 0010199 2010709 0011219 ©011729 0012239 0012749 0013259 0013768 0014278 0014788 0015298 2015808 6016318 2016828 0017338 0017848 0018358 0018868 2019378 2019888 2020398 0020908 2021418 2021928 2022438 0022947 0023457 0023967 0024477 0024987 0025497 0 C=33 SPK 31144,.659 429022165 18363.770 12024.042 10980.373 10783.124 10499.423 105232143 10405.793 10357.729 10453.232 10461.971 10399,551 10401.423 10370.837 10396.430 10422.958 10314.347 10266.283 10261.290 10265.035 10301.551 10275.334% 10236.633 10257.544 102732149 10291.251 10367.092 103712462 103062232 10294.997 10347.742 10422.646 10392.060 10300.927 10317.780 10337442 10285.634 10298.742 10384.570 103262519 10207.296 10314.971 10346.181 102532175 10340.251 10364.907 102142474 10179.831 10219.156 51032180 0 mb Not DO 07 0 0 0 0 8 8 80 8 1 0 FT 8 8 8 8 8 8 0 8 8 8 0 8 8 8 8 8 1 8 8 8 8 8 0 0 0 0 0 I 7 TT NNO TR No. 22 CHANNEL 10 ODMDATOMNEFWNMNKrOA 10 ACOV 116.506 112.403 109.672 105.794 100,887 96,105 91,298 87.161 84,028 81,291 79.321 77.780 U5 Viel 76.518 76,643 77,158 78,370 79,240 81.331 83,037 84,057 84.260 84,448 83,528 82.097 79,387 76,545 73,639 69,839 66,330 63,216 60.482 58.44) 56.262 54,588 53,514 52.536 51.652 51.224 50,749 50.282 49,593 49,400 48,848 47,973 46,829 45.655 44,195 42,130 49.232 37.931 0 SP 41.715 47.768 62615 3.235 5.882 4.623 1.641 098) e719 2628 0376 e202 e124 2068 0966 2982 0971 0040 2052 0072 0102 2095 2932 0075 0092 2061 2945 2045 060 012 0969 0067 0956 0045 0070 0104 094 0967 0966 0963 205) 2053 0168 ©9072 0052 RUN 6 PERIOD 0 1961.000 980,500 653,667 490,250 392,200 326,833 280.143 245.125 217.889 196.100 178,273 163,417 150,846 140,071 130,733 122.563 115,353 108,944 103,211 98.050 93,381 89,136 85,261 81,708 75.423 72,630 70,036 67,621 65,367 63.258 61.2481 59.424 57,476 56.029 54.472 53.000 51,605 50.282 49,025 47.829 46.690 45,605 44,568 43.578 42,630 41,723 40,854 40.020 39,220 0 FREQ 0999999 2000510 0901020 2001530 6002040 2002550 2003060 6003570 2004080 2004589 2005099 2005609 2006119 2006629 2007139 2007649 2008159 008669 2009179 2909689 2010199 2010709 2011219 2011729 2012239 0012749 2013259 2013768 2014278 2014788 2015298 2015808 2016318 2016828 2017338 2017848 0018358 2018868 2019378 0019888 2020398 o020908 2021418 2021928 2022438 2022947 2023457 0023967 2024477 2024987 2025497 0 C-3h SPK 13019,335 14908.488 2064,555 1009.650 1835.,784 1442,.848 512,159 181.331 224.401 196,000 117.350 63,045 38.701 21.223 20.599 25,592 22.159 12.172 12,484 16.229 22.471 31,834 29,650 14,981 9,987 23,408 28,713 19,038 14,045 14,045 18.726 220.471 212539 20-911 17.478 14.045 21.847 32.459 29,338 20.911 20.599 19.662 15.917 16,541 21.223 22.471 16.229 10.924 12,484 20.599 13.420 0 TR No.22 SPN 111,748 1272963 17.721 8,666 15,757 12,384 4,396 1,556 1,926 1,682 1,007 2541 2332 182 aaLarall 220 2190 0104 elo? 2139 2193 e273 2254 2le9 086 2201 2246 2163 el2i el2l e161 0193 0185 Bie 2150 el2l 188 0279 2252 Gye ol7T 169 SHS 0142 CHANNEL 10 ODADMNEWN— DSA ACOV 52.140 46,234 41.731 35.583 30,254 254737 21-9A7 18,944 16.757 14,879 12.981 12.283 12,325 13.263 14,786 16.806 18,339 19.407 19.793 19,598 19,588 18.507 16.871 14,644 12.02) 9.211 6.906 4.408 3.379 2,668 3.281 2,947 2,796 2.206 1,593 1.377 1.900 2.492 3.168 2.792 2.123 1,538 2606 -1,.280 =2,696 =4,518 =6,152 =7,568 =8,262 =8,841 =8,371 0 SP 92304 13.723 52619 2.697 32939 4o715 3.24) 1.295 0686 01/43 e758 053? 0551 0586 035] 0199 e174 0125 e125 0159 0128 0094 099] elll 2118 0090 0077 0966 0148 0054 006) © 960 0058 0978 0998 0092 0984 2068 0068 2099 0988 0968 e072 2089 0089 0096 e115 e105 0970 0982 2055 f) RUN 6 PERIOD 0 1961,000 980,500 653.667 490.250 392,200 326,833 280.143 245.125 217,889 196,100 178.273 163,417 150,846 140,071 130.733 122,563 115.353 108,944 103.211 98,050 93.381 89.136 85,261 81.708 78.440 75.423 72.630 70.036 67,62) 65,367 63.258 61,281 59,424 57,676 96,029 54,472 53,000 51.605 50.282 49.025 47,829 46,690 45,605 44,568 43.578 42,630 41,723 40,854 40.020 39.220 i) FREQ 0999999 2000510 2001020 0001530 2002040 2002550 2993060 2903570 0004080 2094589 6905099 2005609 0006119 ©006629 0007139 0007649 2008159 2008669 0009179 2009689 2910199 2010709 0011219 0011729 2012239 0012749 2013259 2013768 2014278 2014788 2915298 2015808 0016318 2016828 2017338 0017848 2018358 2918868 0919378 2019888 2020398 0020908 °021418 2021928 0022438 2022947 2023457 0023967 0024477 0024987 0025497 0 C-35 SPK 2903-797 4282,976 1753.701 841.739 12292370 1490.287 1011.523 404,172 214.102 231.892 236.573 166.038 171.968 182,892 109.548 59.299 54.306 39.013 39.013 49.624 39.949 29.338 28.401 34.643 36.828 28.089 24.032 20.599 14,981 16,854 19,038 18,726 18,102 24,344 39.586 28.713 26.217 21.223 21.223 28.089 270469 21,223 22.471 27.777 27.777 29.962 35.892 32.771 21,847 25.59¢ 17.166 0 TR No. 22 CHANNEL 10 OBNDMNFWNR DK ACOV 37,038 32.442 30,662 28,038 25.398 23.364 21.492 20.5935 19.370 18,866 18.120 WIG WIE 16.369 HIG UNE) Wsverane 12.484 Less 9.769 8,799 8.363 7.555 6.630 5.713 Seon! 5.326 5.299 5,305 5.422 5.164 5.494 5.022 4.909 4,660 4.364 4,204 3.525 3,486 3.031 2.710 3.143 2,833 2.9R5 2.855 3.065 2.622 2.606 SP 72614 Le S51 5.854 22830 1.295 e132 2839 0918 e73) Cair/al 0459 e315 2195 0129 ell 0156 e120 e075 0057 0074 el05 e097 0064 0054 0971 e088 ~ 082 0064 052 2057 2988 2096 208) - 080 0074 0067 0956 0059 008) 0982 2082 0109 2108 0I95 e100 0079 2063 0073 208? 2068 0025 0 RUN 6 PERIOD 0 1961.000 980.500 653,667 490.250 392.200 326,833 280.143 245,125 217.889 196,100 178.273 163.417 150.846 140,071 130.733 122,563 115,353 108.944 103.211 98.050 93.381 89,136 85.261 81.708 78.440 75,423 72,630 70.036 67.621 65,367 63.258 61,281 59.424 57,676 56.029 54.472 53.000 51,605 50,282 49,025 47.829 46-690 45.605 44,568 43.578 42,630 41.723 40,854 40,020 39.220 0 FREQ 2999999 2000510 2001020 2091530 0002040 00902550 2003060 0003570 2004080 2004589 0005099 2005609 2006119 ©006629 2©007139 2007649 2008159 2008669 2009179 2009689 2010199 2010709 2011219 2011729 2012239 0012749 0013259 2013768 2014278 2014788 2015298 2015808 0016318 2016828 2017338 0017848 2018358 2018868 2019378 2019888 2020398 0020908 2021418 2921928 2022438 2022947 0023457 2023967 0024477 0024987 2025497 0 SPK 2376.345 3605.090 1827,045 883.249 404,172 228.459 261.854 286.510 228.147 178.210 143,255 98,312 60.860 40,261 44,006 48,688 37.452 232408 17.790 23.096 32.771 30,274 19,975 16,854 22.159 27,465 25,592 19,975 16,229 17.790 27.465 29.962 25.280 24,968 23.096 20.911 17.478 18.414 25.280 25.592 25.592 34,019 33,707 29,650 31.210 24,656 19.662 22.783 25.592 21.223 7,803 0 TR No. 22 CHANNEL 10 Cty D MOF WN OA Aacov 292185 25.956 23.900 Billo 19,4R7 17.639 16.275 15.7458 Noe aS 16578 16.779 16.961 WhOvercurall 15.215 13,682 12.107 10,319 9.128 7.988 7,134 Oo iV 6.209 5,733 5.307 4,749 4,306 32464 2.919 2e1lBS 1.623 STS 2423 2009 =), 394 -0,661 =0,942 =ji,37/7 = | 2288 -1.585 2,160 =2.561 =2.950 =3,4A9 =4,280 =4,676 4,989 =5,.117 =5,2A7 5,427 =-5,547 -5,168 0 RUN 6 PERTOD 0 1961,900 980.500 653.667 490.250 392.200 326,833 280.143 245.125 217,889 196.100 178.273 163.417 150,846 149,971 VEO 5 7S) L225 96! IRS 5 SBS 198,944 103,211 98,050 93.381 89.136 85.261 31.708 738,440 75.423 72,630 70,036 67.621 65,367 63,258 61,281 59.424 57,676 56.929 54,472 53.000 51,605 50.782 49,025 47.829 46,690 45,605 44,568 43.578 42.630 41,723 40.854 40.920 39.220 0 FREQ 2999999 20000510 2001020 0901530 20002040 2002550 2003060 2003570 2094080 0904589 2005099 0906119 2006629 2007139 09DTH4Y9 2908159 0008669 -009179 2009689 e019}99 eVL0709 20011219 2011729 20012239 2012749 0913259 2013768 00142786 0014786 2015798 -015808 2015318 20116828 0017338 2017848 0918358 o 014868 2019378 0919888 2020398 2020908 0021414 -02)928 022438 0022947 023457 2023967 a024+477 0025497 Q CoS SPK 1922.460 3080.447 1438.,478 3R9,815 156.051 121,096 183.516 280.264 330.516 261,854 158.548 79,274 36.204 23.720 No Ss 220/83 21.535 20.28! 20,911 22.471 232.408 24.650 22.67) 220471 25.592 22-471 19,350 18.102 17,166 17,790 13.108 10,924 12,796 14,669 19,662 22.159 19,038 16,229 14,669 14,9A1 17,790 14.669 9.363 10,299 14,669 17.166 15.917 15,293 15.293 10.924 3.745 0 TR No. 22 CHANNEL 10 COUN TUF WN HDA ACOV 42.185 38.261 360,272 33.877 Silay 390,257 A oe 24,501 Co ses 27,542 76.7152 26.961 26,354 25.739 24,388 23.449 22,562 21.669 21,099 BOS (al 19.995 19,742 19,480 18.8273 18,2274 17,198 16,573 16.061 Sve Ourar, 15.382 SAT 14,692 14.198 13.708 13,678 13.463 13.032 12.578 12-014 11.896 11,481 10.833 10,320 VO GwilS 9.665 9,559 9,498 9.472 9,022 8,555 R940 ra) SP 122354 MaGays! 4.288 1,565 0990 0/9) e728 oN A 4 al & 263) 043? 0245 alten e190 2 l9N eho5 0150 e158 2106 0055 e950 0951 0066 2 OT 0970 208) 0086 0967 2059 043 20148 0059 0076 0074 059 0959 2966 077 0973 0 N48 0037 0049 06? 0067 0176 009) 09S 0077 0150 e033 e913 A RUN 6 PERIOD 0 1961,000 980,500 653,667 490,250 392,200 326,833 280,143 AOS) MEE) 217,889 196,100 178.273 163.417 150,846 140.071 NSO G'S 122,563 I Ses53 108,944 103.211 98.950 93,381 89,136 85.261 61.708 78.440 75.423 72,630 70.036 67.621 65,367 63,258 61.281 59.424 57.676 36.029 54.472 53.000 51.605 50.282 49,025 47,829 46,690 45,605 44.568 43.578 42,630 41.723 40,854 40,020 39.220 0 FREQ 0999999 20005) 0 2901020 0001530 2002040 2002550 2003060 2003570 0004080 2004589 2005099 2005609 2096119 2006629 2007139 2007649 2008159 2008669 0009179 20909689 2010199 2010709 2911219 2011729 2012239 2012749 2913259 2013768 °©014278 0014788 20015298 2915808 0916318 0916828 2017338 0017848 6018358 5018868 0019378 2019888 2029398 2020908 2021418 2021928 0022438 0027947 0023457 2023967 ~V2447T 0024987 2025497 Q) C-38 Wt NOs 22 CHANNEL 10 IA OrTWDMNPFwWN— ACOV 338.5648 332.549 327.417 3700714 314,339 307.956 371.2303 29350412 229.034 283.30 277.8094 272.710 2662242 261,082 255.2159 249.783 244.417 238,817 2342448 229.262 224,731 219-138 213.590 2082144 2032395 198.442 193.985 189.678 185.193 180,854 176.779 172.834 169.076 165.543 162.2392 159.867 157.416 154.751 152,562 149.061 146.886 144,279 141,552 138.269 135.033 132.145 129.343 126,823 123.87) 120.2969 117.571 0 SP 1276427 153-046 31.154 8349 45499 32040 22044 12334 1.97) 0833 0 144 0544 e396 023? e219 028) 024) 2181 el6) 0193 0175 0131 0995 0065 0075 0094 e103 097 0109 2108 083 0058 ©9050 e050 0054 004) 0153 0092 0196 0106 0086 e952 0953 0074 e1l2) 0153 212) 0078 0149 0052 0035 is) RUN 7 PERTOD 0 1961.900 980.500 653,667 490,250 392.200 326.833 280.143 245,125 2172889 196,100 178.273 163.417 150,846 140.071 130.733 122.563 NUS GS ISE) 108.944 193.211 98.050 93.381 49.136 85.261 81.708 78.440 75.423 72.630 70.036 67.621 65.367 63-258 61.281 59,424 57.676 56.929 54,472 53.000 51.605 50.282 49.925 47,829 46.490 45.605 44,568 43.578 42.630 41.723 40,854 40.020 39.220 0 FREQ 2999999 6006510 eQUL020 001530 2002040 6002550 ° 0030460 0003570 0004080 20004589 2005099 ©905609 2006119 »006629 0907139 0007649 2008159 2008669 0009179 2099689 2010199 0019709 2011219 6011729 2012239 2012749 0013259 20013768 2014278 2014788 2015298 2015608 2016318 0016828 0017338 6017848 °018358 0018868 2019378 0019888 2020398 -020908 09214)]8 0021928 2022438 2022947 0023457 2023967 0024477 2924987 0025497 0 C-39 SPK 3977 0ecee 47765.963 9723.226 26056740 140414 948.790 637.936 416.344 334.261 2596981 2320204 169.783 95.503 72.408 B7.076 87.701 750217 56.490 50.248 600236 54.618 40.885 292650 20.287 232408 294338 32.147 300274 31.210 33-707 252904 18.102 156605 15.695 16.854 122796 16.541 28.713 33.083 33.083 260841 16.229 16254] 232096 37.764 47.752 37.764 242344 15.293 166229 10.924 0 TR No. 22 SPN 117.466 141,082 28.719 1,696 4.1417 2.802 1.884 1.230 2987 2/68 e686 050] e282 02) 5ESY 0259 0e2e e167 2148 2178 e161 ol2l 2088 2060 0069 2087 2095 2089 2092 2190 e077 0053 2046 2046 0050 2038 e049 0185 2098 2098 e079 0048 2049 2068 elle 014] elle 072 0045 2048 0032 9) CHANNEL 10 2 A DNSTOUFWNY G ACOV 232076 20.518 20.080 19.222 18.344 17.598 16,939 16,379 15.748 14,917 14.148 13.334 12,690 11,895 11,354 19,440 WOR Shs! 9.496 9,088 8,592 8,154 (ea Siaie 1,268 6,556 6,234 Dees Syele70 4,649 4,188 3.792 3,2A1 22679 2.010 1.595 Wersiral 20876 » 411 =0.,040 @(),3348 -0,932 -1.172 =-1.,/748 =2.222 =2,456 =2,713 =2.933 =-3,514 =3.400 =4,032 =4,536 -4,777 {) RUN 7 PERTOD 0 1961.000 980,500 653,667 490,250 392.200 326,833 280,143 245.125 217,889 196.100 TER 2 US) 163.417 150,846 140,971 130.733 122,563 WN SBS) 108,944 OL Gass 98.050 93.381 49,136 85,261 81,708 78,440 75,423 tee O10 70,936 67,621 65,367 63.258 61,2A1 594424 57.676 26.0929 94,472 53.000 51,605 50,282 49,025 47.829 46,690 45,605 44,568 43.578 42,630 41.723 40.854 40.920 39,220 0 FREQ 2999999 2000510 0001020 2001530 0002940 «6002550 2093060 2003570 eNU40RD0 2004589 2005099 2005609 2006119 ~006629 2007139 0007649 2008159 2008669 0009179 2009689 2010199 2010709 2011219 2011729 2012239 2013259 2013768 2014278 2014788 015298 2015808 2016318 0916828 2917338 7017848 2018358 0018868 2019378 2019888 0920398 2020908 2021418 2021928 2922438 2022947 0235457 2023967 0024477 0024987 2025497 0 C-O SPK 18192243 C727 TTI 1107,.026 341,127 212.229 112,981 67.102 46.191 43,070 42,758 45.255 49.261 29.650 28s 27,465 18,726 14,357 16,854 14,357 8,739 9.363 9.9R7 11.548 14,669 14,0945 14,669 16,854 13,420 9,051 13.2108 17,166 15.917 13,732 11.860 11,548 13,108 15,695 19.975 19,034 12.484 9,987 15.293 20.287 17,478 16.229 17,790 13.420 72490 8.4Af 20,599 14.669 0 TR No. 22 CHANNEL 10 ( CEONTDTMNPFVDNeK BA ACOV 49,560 46.092 45,649 44,563 43.275 41.474 40,510 39.802 38.981 34.4R9 37,623 37.020 362684 36.078 35.773 35.168 342409 33.2918 330477 33.089 33.000 320407 32.35? 31,800 31.545 312416 30,915 30-487 30.108 29.821 2922A9 29.4258 294138 29.072 29.381 28.618 24,646 262239 27,842 27,839 27.194 27.282 27.542 26.953 26.637 26.063 25,573 242996 24,665 232943 0 RUN 7 PERIOU 0 1961.000 989.500 653,667 490.250 392.200 326,833 280.143 245.2125 217.889 196,100 178.273 163.417 150.846 140.97] 130.733 122.563 115.353 108.944 103.211 98.050 93.381 89.136 85.261 61./08 78.440 75.423 72.630 70,036 67.262] 65.367 63.258 61.281 592424 57.676 56.029 54.472 53.000 51.605 50.282 49.025 47.829 46.690 45.605 44,568 43.578 42,630 41.723 40.854 40.020 39.220 0 FREQ 0999999 2000510 e001020 0001530 0002040 2002550 0003060 20903570 0004080 0004589 2005099 0005609 0006119 °006629 2007139 2907649 2008159 2008669 0009179 2009689 0010199 0010709 e011219 0911729 0012239 0012749 0013259 0013768 0014278 2014788 0015298 2015808 26016318 2616828 0017338 0017848 0018358 0018868 0019378 0019888 0025398 e02)908 00214168 0021928 2022438 0022947 0023457 0023967 0024477 0024987 0025497 0 C-41 SPK 5770.766 6541.970 1048,975 445.057 267.784 177.56 123.592 93.943 84,580 55.242 29265") SGU 34.955 30.898 33.707 23-720 13.732 14.35! 200287 23.720 242656 19.975 15.9)/ 170478 14.045 122484 14.9A)] 14.357 1324270 142045 18.414 20.599 19.038 18.414 210223 19.350 14.98] 242656 31.2210 302898 292029 19.662 19.975 24.2656 18.726 15.2293 192350 220159 22073 19.662 B8.4eaT 0 SPN 116,440 132,001 21.166 6,980 5,403 3,583 20494 1,896 A 0) t/ NG as) 2598 0689 AWA tke) 2623 2680 0479 OY 0290 0409 0479 6497 0403 e321 0 353 0283 0252 0302 2290 e271 0283 e372 0416 e384 e3ale2 2428 e390 e302 497 2630 sO23 2586 e397 0403 e497 2378 2309 2390 a44/ 0460 0397 0170 0 TR No. 22 CHANNEL 10 OBADMNMEWNH OA 10 AcOV 49.294 45,658 45,165 43,5A4 42,177 41,330 39,811 39,020 36,737 35,523 34.703 33,474 32,365 31.493 30,894 29,753 28.951 2a S 27.012 25,875 24,5R2 23,604 22.809 22,051 Ave tor 70,642 WO el 18.292 l7os3 16,897 16.494 15.866 15.6R1 15.360 14,570 14.011 WSAWICTE 12.057 10,973 10,108 9.180 8.463 7.556 6,653 5.726 4,61] 4,057 3.591 3.180 2.642 19] SP 15.756 20,532 52749 1258) 0859 061) e520 e272 0225 2180 e139 2196 2196 014 007) 0 085 20095 0974 2050 2058 0068 CENTS 004? 0944 0047 GE) 0073 008? 0952 0029 0930 0929 0030 6 044 0067 20079 0064 0058 2087 2097 0082 0087 2097 e080 2073 0091 0094 0076 0953 005) 0929 0 RUN 7 PERIGD 0 1961,000 980.500 653.667 490.250 392,200 326,833 280.143 245.125 217.889 196,100 178.273 163.417 150,846 140.071 130.733 122,563 115,353 108,944 103,211 98,050 93,381 89,136 85,261 81,708 78.440 75.423 72.630 70.936 67.621 65,367 63,258 61,281 59.424 57.676 56.029 54.472 53.0900 51.605 50.282 47.829 46,690 45,605 44,568 43.578 42.630 41,723 40,854 40.020 39.220 0 FREQ 0999999 2000510 2001020 2001530 2002040 0992550 2003060 2903570 2004080 2004589 2005099 2005609 2006119 2006629 2007139 2007649 2008)59 2008669 2009179 2009689 2019199 2910709 2911219 2011729 2012239 2012749 20913259 2013768 0014278 0014788 2015298 0015808 2016318 0016828 001/338 0017848 2018358 2018868 06019378 2019888 0020398 2020908 2021418 2021928 0022438 2022947 2023457 -023967 0024477 0024987 0025497 0 C-4o TRE NO ee CHANNEL 10 ¢ CMONTMNF WN CA ACOV 40.218 36,378 SE O75 Mp 110) t/ 30,736 28.922 26,933 25.35) 23.436 21,857 20,402 19,022 Wg Sie) 15.378 11.154 10,290 9.487 9,093 8,315 8,385 7,480 6.555 5.441 4,694 4,493 4,174 4,032 3.092 22638 1,918 1,787 Ladys) 2577 =-0,208 -1,014 =-1.422 =1,350 =1,530 -1.750 =2,059 =-2,682 =2,990 =3,538 =4,161 5,031 =5,066 =4,954 =4,660 =4,759 0) SP 8.378 13.955 7022) 30271 1.832 0920 0512 238) 0367 0427 0398 0212 e103 2089 0126 0125 e058 0077 0140 0196 0042 2050 2062 0965 0063 RUN 7 PERIOD 0 1961,000 980,500 653,667 490,250 392,200 326,832 280.143 245.125 217,889 196.100 178,273 163,417 150,846 140,071 NSO 6 73S 122,563 115.353 108,944 103,211 98,0950 93,381 89,136 85,261 81,708 78.440 75.423 72,630 70,936 67,621 65.367 63,258 61,281 59,424 57,676 56.929 54.472 53.900 51,605 50.282 49,025 47,829 46,690 45,605 44,568 43,578 42,630 41,723 40,854 40,020 39.220 0 FREQ 6999999 eV00510 0001020 6001530 2002040 2002550 2003060 2003570 2004080 2004589 2005099 29005609 2006119 0006629 200/139 0007649 0008)59 2008669 2909179 2009689 2010199 2010709 2011219 2911729 0012239 2012749 2013259 2013768 20142778 2014788 0015298 0015808 2016318 2016828 0017338 2017848 2018358 018868 0019378 0019888 2020398 0020908 2021418 0021928 2022438 2022947 0023457 2023967 0024477 2024987 025497 0 c-h3 SPK 2614-791 4230.543 2253.69 1020,886 ST len 287.134 159.796 118.911 114,541 133.268 124,217 66.166 32.147 27.777 39,325 39.013 18.192 24.032 43,694 29.962 13,108 15.605 19,350 20.2eR7 19,662 19,975 22.47) 25.2k0 24,032 18.414 120484 11.236 11.548 11.548 10.611 9.363 14,669 21.223 22-783 24.344 23.408 24.032 32.771 36.20% 26,841 19,9795 25,592 28.401 19,662 12.172 5,306 0 TR No. SPN 65.015 105,190 56,037 25,384 14.217 7,139 3.973 2.957 2,848 3,314 3,089 1,645 2/99 2691 2978 2970 2450 2598 1,066 AVE) 2388 481 2504 2489 2497 2559 629 0298 2458 e310 e279? east e287 0264 e233 e365 228 2266 2605 2282 2598 2815 e900 ~66T 2497 636 2/06 489 e303 engi 0 Ce CHANNEL 10 OONOMFWNRDA SP 122569 19.922 9.416 2.18? 12054 2569 0453 0363 0260 023? e215 0164 0143 eo 1l47 e1ll4 0104 elie 2085 oVNT1 0969 0949 0945 0055 0057 052 044 0042 0040 0036 0050 OS 2040 0042 0944 0951 0067 0983 0039 0062 0964 2069 0963 0968 0056 2065 0104 RUN 7 PERIOD 0 1961.000 980,500 653,667 490,250 392,200 326,833 280,143 245.125 217,889 196,100 Steen 163.417 150,846 140.071 WSO 7c) 122,563 VS .353 108.944 103.211 98.950 93,381 89.136 85.261 81.708 78.440 75.423 72.630 70.936 67.621 65,367 63,258 61,281 59,424 St oe) Fe) 56.929 54.472 53.000 51,605 59.282 49.025 47.829 46,690 45,6095 44,568 43.578 42.630 41.723 40,854 40.920 39.220 0 FREQ 2999999 000510 2001020 2001530 002040 2002550 2003060 »0U03570 2904080 0004589 005099 2005609 2006119 006629 20007139 0997649 2008159 2008669 0009179 2 009689 2010199 20010709 0011219 0911729 0912239 0012749 2013259 2013768 0014278 0014788 2015298 0015808 2016318 2016828 2017338 2017848 2012358 2018868 2019378 0019888 0020398 2020908 2021418 2021928 0922438 2022947 023457 2023967 0024477 0024987 0025497 0 c=. SPK 3922.810 6217.696 2938.752 868,268 328.956 177.586 141,382 113,293 81.147 72.408 67.10¢e 51.1895 44,631 45,879 35.580 32.459 34,955 26.529 22.159 21.535 15.293 14.045 172166 17.790 16.229 13.732 13,108 12.484 11.236 15.605 15.91f 12.484 13,108 13.732 WEG Sil 19.975 20.911 25.914 BAU GUT 19.350 19,975 21535 19.662 21.223 17.478 20.2R7 32.459 32.771 20.911 13.420 5.939 0 IWR INO, 22 SPN Tice Siral 122,402 58,041 17.149 6,497 3.507 2.792 CHANNEL 10 OGBnNDMNFPwWN-—-SssZ ACOV 7R.3286 74,422 72.158 69.486 66.705 64,506 62,187 60,125 58.496 56.6948 Seq Shi) (7 53.667 522318 50.172 47,779 45.799 43.746 41.586 39.043 36.835 34,567 31,893 29.2112 272943 25,629 23,774 22,82) 21.235 19,688 17.894 15.687 13.809 11,970 9,939 B,736 {.516 6.96] 6.394 5.707 5.149 5.091 4,098 3,381 Io 2.837 2.873 2.607 2.476 2,578 2.105 2.418 () SP 22.6496 322.64? 11.567 22465 16297 297386 e937 097? 0645 0 343 0 385 0390 0165 095 ole ol67 2160 0125 ella en? 085 e4 049 ewan 009? 0113 0UT?2 2935 0134 0 f56 5 (770) 2158 2056 062 e270 0069 0048 0163 289 e080 e073 0 084 298) 2048 0929 0937 995 06] 2050 0962 0049 Q RUN 7 PERIOD 0 1961.900 980.500 653.667 490,250 392,200 326.833 280.143 245.125 217.889 196,100 178.273 163.417 150.846 140.071 130.733 122,563 ISS os 108.944 LOS G2 Wu 98.050 93)38) 89.136 85.261 B1.708 78.440 75.423 72.630 10), O36 67.621 65.367 63,258 61.281 59.424 57.676 56.929 54,472 53,900 51,605 50.282 49,925 47,829 46,690 45.695 44.568 43,578 42,630 41./23 40,854 40,020 39,220 0 FREQ 2999999 9V00510 2001020 0001530 2092040 2002550 2003060 2003570 099408U 0094589 2005099 2005609 20006119 2006629 2007139 2007649 2008159 2008669 2009179 2009689 26019199 0019709 0011219 0011729 0012239 0012749 2013759 2513768 2014278 2014788 0015298 2015808 20915318 2016828 0917338 017848 2018358 2918868 00149378 2919888 0020398 2920908 2021418 0021928 2022438 2922947 2023457 2023967 2024477 024987 0925497 0 Cak5 SPK 7145.8R7 10167.633 3610,0R4 769,331 376.707 307,733 2922440 303.363 2012396 M75 West! 120,159 199,236 51.497 29,650 39,637 52.121 49,936 39.013 34.331 33,399 262529 16,854 15,293 18.726 28.7)3 35,268 Pee47l 10,924 10,611 17.478 21.847 18,12 17.478 19,350 21,84/ 21.2535 14,9R] 19,662 eTet7l 24.968 22.783 26.21¢ 252280 14.981 9,051 11.548 17,166 19.038 15.605 LO esi50 12.484 0 TRONOn ee. SPN 91.163 129,968 46,955 9,415 4,806 3.926 esi 3.870 2.948 1.366 1,533 1.394 2657 CHANNEL 10 a a re DISTRIBUTION Addressee Director of Defense Research and Engineering Office of the Secretary of Defense Washington, D. C. 20301 ttn: Office, Assistant Director (Research) Office of Naval Research Ocean Science & Technology Group Department of the Navy Washington, D. C. 20360 Attn: Surface & Amphibious Programs (Code 463) Attn: Undersea Programs (Code 66) Attn: Field Projects (Code 418) Attn: Geography Branch (Code 414) Attn: Ocean Science Programs (N61S) Commanding Officer Office of Naval Research Branch Office 495 Summer Street Boston, Massachusetts 02210 Commanding Officer Office of Naval Research Branch Office 219 South Dearborn Street Chicago, Illinois 6060} Commanding Officer Office of Naval Research Branch Office 1030 East Green Street Pasadena, California 91101 Commander Naval Undersea Warfare Center 3202 Kast Foothill Blvd. Pasadena, California 91107 Commanding Officer Naval Torvedo Station Keyport, Washington 98345 Chief of Naval Overations (Op03EG) Naval Oceanographic Office Liaison Officer (Code 332) Anti-Submarine Warfare Force U. S. Atlantic Fleet Norfolk, Virginia 23511 TR No. 22 No. of Copies aL PRPRPEP TR No. 22 DISTRIBUTION (2) ( Addressee No. of Copies al Director al Naval Research Laboratory Washington, D. C. 80390 Atta: Code 5500 Commander IL Naval Oceanographic Office Washington, D. Ce 20390 Attn: Code 1640 (Library) Attn: Code 031 Attn: Code 70 Attn: Code 90 Attn: Mr. Pat DeLeonibus PRRPPR West Coast Support Group aL Naval Oceanographic Office c/o Naval Command Control Communications Laboratory Center San Diego, California 92152 Naval Oceanographic Office Liaison Officer (Code 332) 1. Anti-Submarine Warfare Force Pacific Fleet Post Office San Francisco, California 96610 Commanding Officer Al Naval Torpedo Station Keyport, Washington 98345 (QEL Technical Library) Commanding Officer and Director aL Naval Ship Research and Development Center Washington, De. C. 20007 Attn: F. N. Frenkiel Al, Commander Submarine Force Pacific Fleet Fleet Post Office San Francisco, California 96610 Commander=in=-Chief alk Pacific Fleet Fleet Post Office San Francisco, California 96610 Commander 2 Naval Ordnance Systems Command (ORD-9132) Department of the Navy Washington, D. 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Addressee Director Hudson Laboratories 145 Palisade Street Dobbs Ferry, New York 10522 Director Seripps Institution of Oceanography La Jolla, California 92038 Applies Physics Laboratory University of Washington 1013 N. E. Fortieth Street Seattle, Washington 98105 Director Ordnance Research Laboratory Penn State University University Park, Pa. 16801 NAVY-1ND, DPPO, Newport, R. I. DISTRIBUTION (8) TR No. 22 No. of Copies all UNCLASSIFIED Security, Classification DOCUMENT CONTROL DATA-R&D Security classification of tithe, body of abstract and indexing: annotation must be entered when the overall report is classified) 1 ORIGINATING ACTIVITY (Corporate author) 2a. REPORT SECURITY CLASSIFICATION UNCLASSIFIED 2b, GROUP Naval Underwater Weapons Research and Engineering Station, Newport, R. I. 7 REPORT TITLE Turbulence Measurements in a Tidal Current 4, DESCRIPTIVE NOTES (Type of report and,inclusive dates) 5. AUTHOR(S) (First name, middle initial, last name) Massey, Alan T. 6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b, NO. OF REFS August 1968 143 23 8a. CONTRACT OR GRANT NO 9a. ORIGINATOR’S REPORT NUMBER(S) . PROJECT NO. TR No. 22 ib Task Assignment No re 9b. OTHER REPORT NO(S) (Any other numbers that may be assigned R360-FR-107/219 1/Ro11-01-01 this report) . DISTRIBUTION STATEMENT This document has been approved for public release and sale; its distribution is unlimited SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY NUWS - NOSC - ABSTRACT Measurements were made of the component of turbulent velocity along the axis of a 3-knot tidal current 1.5 meters below the water surface using a ducted impeller current meter. Values of the one- dimensional energy spectra were computed on a digital computer at wave numbers from 0 cm-l to 0.157 cm-l. The composite energy Spectrum obtained from the individual spectra was of the -5/3 power law form predicted by the Kolmogoroff hypothesis for wave numbers from 0.01 ecm-! to 0.026 cm-l. At higher wave numbers the energy spectrum decreased more rapidly than predicted because of attenuation of the turbulent velocity variations caused by the relatively large size of the current meter. The average variance for the field of turbulence was 55.6 cm2 - sec7-2 +25.0 (standard error), and the average rate of energy dissipation by viscosity was estimated using the Kolmogoroff hypothesis as 0.84 cm2 - sec73. D)D) Oe als) (PRE 1) UNCLASSIFIED S/N 0101-807-6811 Security Classification heahaos UNCLASSIFIED Security Classification OCEAN CURRENTS TURBULENCE (OCEAN) TIDAL CURRENTS AIR - SEA INTERACTION CURRENT METERS DD uneicel Aig oS. 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