DISTRIBUTED BY: Ritional Technical Information Service U. S. … · 2011. 5. 14. · SECURITY CLASSIFICATION OF INHIS PAGE (1 4 7%en Dile EuF4.-,rod) REPORT DOCUMENTATION PAGE BEORE

AD-AO10 868

AN ANALYSIS OF A RAY TRACE EXPE-RIMENT ONTHE UNDERWATER RANGE AT DABOB BAY

Victor Joseph Bankston

Naval Postgraduate SchoolMonterey, California

March 1975

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NTONALTCN!AA THE U~~NFORMATION RANERVTICEBBUSct Dog)Ir~ m J o fe colstortpmid V~A.c 21975

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1. r-PORT NUMBER 12. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

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An Analysis of a Ray Trace Experiment on the Master't. Thesis; March 1.975

Underwater Range at Dabob Bay• ~6. PERFORMING ORG. REPOk(T NUMSER

7. AUTHOR(#) 8. CONTRACT OR GPANT NUMBER(s)

Victor Joseph Banks'ton

9. PERFORMING ORGANIZATION NAME AND ADDPESS 10.- PROGRAM ELEMENT. PROJECT. T..,SK

AREA 6 WORK UNIT NUIAUERS

"Naval Postgraduate SchoolMonterey, California 93940

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Naval Postgraduate School March 1975Monterey, California 93940 13. NUMBER OF PAGES

86

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Approved for public release; distribution unlimited.

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It. SUPPLEMENTARY NOTES

1I. KEY WORDS (Continue on teo verse sid i nsceceary and Identity by block uumber)

Ray-Tracing.Underwater RangeDabob BayKeyport, Washington

20. ABSTRACT (Contincle on reve.re ld2 It necesstary and Iden fly by block nunmber)

An analysis of an experiment t.o determine the precision, the effects of

varying amounts of environmenLal data, %nd tlhe feasibiliLy of the use of hs.8-torical environmental data at the NAVTORPSTA, Keyport, Washington, Dabob Bay,facility is presented. The analy•;is verifies and extends the result.s of apreliminary investigation of the experimental data. T'he experiment (on1sis Lcd

of tracking a 75-kllz source at six depths at each of six horizonta] range:.r ho data were anallyzed utilizing 3111 isograI-diellt ray-Lia,icng progBraii. Tho

FORM

DD JAN7 1473 r.,ITION OF I NOV 6,5 IS OBSOLETE UNCIASS IVT El)(P g J.•0 ) S/N (1102-014.6601 JSECURITY CLAtSItriCATION Or TIllS PAG•. (h.'n :)at* Cnltr*d)

PRPCES SUIJ. QI 10 CHM"GE

(it.IJ41TY CLASSIFICATIONI Or THIS PAGE(4',1'- -),r £nA.j.

20. results showed that the '.recision of the range position as determined

by the ranging system is depor.dent only on the rise-time of the 75k11z signal;

,that the use of less environmlental data and historical data as the environmen-tal input for position calc-'"ations have been shown to cause only a minordegradation in the accuracy, of the ranging system.

DD Form 1,473 (BACK)I Jan 71 -1MCASSTF],I)

S/N 0102-014.-6601 SF.CU ,ITY CLASSi IC ATI•, or 'r,,IS p .It-. ,' ,^ I,'Mrtd.•

An Analysis of a Ray Trace Experimenton

The Underwater Range at Dabob Bay

by

Victor Joseph BankstonLieutenant, United States Navy

B.S., Louisiana State University, 1968

Submitted in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN SYSTDIS TECHNOLOGY

from the

NAVAL POSTGRADUATE SCHOOLMarch 1975

Author

Approved by: _ .___________, __

"Thesis Advisor

Second Reader

- Chai rman, AS,9 Academic Group

- Academic Dean

3

ABSTRACT

An analysis of an experiment to determine the precision, the effects

of varying amounts of environmental data, and the feasibility of the use

of historical environmental data at the NAVTORPSTA, Keyport, Washington,

Dabob Bay facility is presented. The analysis verifies and extends the

results of a preliminary investigation of the experimental data. The ex-

periment consisted of tracking a 75-klIz source at six depths at each of

six horizontal ranges. The data were analyzed utilizing an isogradient

ray-tracing program. The results showed that the precision of the range

position as determined by the ranging system is dependent only on the

rise-time of the 75kHz signal; that the use of less environmental data

and historical data as the environmental input for position calculations

have been shown to cause only a minor degradation in the accuracy of the

ranging system.

TABLE OF CONTEiTS

1. INTRODUCTION ----------------------------------------------- 8

II. DABOB BAY TRACKING FACILITY --------------------------------- 9

A. DABOB BAY FACILITY ------------------------------------- 9

B. RANGE DESCRIPTION ------------------------------------- 10

III. EXPERIMENTAL PROCEDURE ------------------------------------- 12

IV. RANGE DETERMINATION TECHNIQUES ------------------------------ 14

V. PRELIMINARY ANALYSIS --------------------------------------- 18

A. ANALYSIS ---------------------------------------------- 18.

B. RESULTS ----------------------------------------------- 18

C. CONCLUSIONS ------------------------------------------- 19

VI. PRECISION OF DATA ------------------------------------------ 20

VII. ENVIRONMENTAL EFFECTS ON RANGE PRECISION --------------------- 22

VIII. HISTORICAL ENVIRONiENTAL ANALYSIS 26

IX. CONCLUSIONS ----------------------------------------------- 29

X. COM"INTS AND RECONMENDATIONS -------------------------------- 31

FIGURES --------------------------------------------------------- 32

TABLES ---------------------------------------------------------- 54

APPENDIX A. ISOGRAD --------------------------------------------- 64

APPENDIX B. ISOVEL ------------------------------ 67

APPENDIX C. ANCOAL ---------------------------------------------- 71

APPENDIX D. STUTRACK I ------------------------------------------ 76

BIBLIOGRAPY ----------------------------------------------------- 85

INITIAL DISTRIBUTION LIST ------------------- ------------- 86

LIST OF ILLUSTRATIONS

1. DABOB BAY RANGE --------------------------------------------- 32

2. EXPERIMENTAL AREA ------------------------------------------- 33

3. HYDROPHONE ARRAY -------------------------------------------- 34

4. TILT CORRECTION ------------------------ 35

5. RAY PATH REFRACTION----------------------------------------- 36

6. PHI versus THETA, by Stition --------------------------------- 37

7. PHI versus THETA, by Depth ----------------------------------- 38

8. COMPARISON OF SOUND VELOCITY PROFILES, as derived by the

Equal-Changz-in-Velocity Method ------------------------------ 39

9. COIMPA1RISON OF SOUND VELOCITY FROFILES, as derived by tbG

Equal-Change-in-Gradient Method ------------------------------ 40

10. COMPARISON OF SOUND VELOCITY PROFILES, as derived by the

"Eyeball" Method -------------------------------------------- 41

11. DABOB BAY SOUND VELOCITY PROFILE, TYPE 1 ---------------------- 42

12. DABOB BAY SOUND VELOCITY PROFILE, TYPE 2 ------------------- 43





17. DABOB BAY SOUND VELOCITY PROFILE, TYPE 7 --------------------- 48



20. DABOB BAY SOUND VELOCITY PROFILE, TYPE 10 ---------------------

21. DIABOB BAY SOUND VELOCITY PROFILE, TYPE 11 ---------- 52

22. DABOB BAY SOUND VELOCITY P1OIFILE:, TYPE 12 --------------------- 53

6

LIST OF TABLES

I. STANDARD ERROR OF ESTIMATE, THETA -------------------------- 54

II. STANDARD ERROR OF ESTIMATE, PHI ---------------------------- 55

III. STANDARD ERROR OF ESTIMIATE, R ----------------------- 56

IV. STANDARD ERROR OF ESTIMATE, caused by Environmental

Description by Velocimeter -------------------------------- 57

V. STANDARD ERROR OF ESTIIMATE, caused by Environmental

Description by the Equal-Change-in-Velocity Method --------- 58

VI. STANDARD ERROR OF ESTIMATE, caused by Environmental

Description by the Equal-Change-in-Gradient Method --------- 59

VII. STANDARD ERROR OF ESTIMhATE, caused by Environmental

Description by the "Eyeball" Method ------------------------ 60

VIII. STANDARD ERRORS OF ESTIMATE OF APPROXINLATED PROFILES,

as derived from Historical Profile It between the

Surface and 200 feet -- ----------------------------------- $61

IX. STANDARD ERRORS OF ESTI1MATE OF APPROXIMATED PROFILES,

as derived from HIistorical Profile 4 between 100

and 300 feet --------------------------------------------- 62

X. COIMPARISON OF STANDARD ERRORS, caused by the Approximtation

of Sound Velocity Profiles by the Equal-Change-in-Ve.ociý:y

Method ------------------------------------------------- 6

7

I. INTRODUCTION

An acoustic experiment was conducted to provide a basis for the

comparison of various ray-tracing techniques which can be utilized to.

determine the three-dimensional position of a source with respect to a

fixed receikver. The experiment was conducted at the .t0abob Bay facility

of the Naval Torpedo Station (NAVTORPSTA), Keyport, Unodhington on 23

March 1974 by members of the Ray Trace Committee of the Range Study

Group at the Naval Postgraduate School, Monterey, Ca~lifornia.

The purpose of tile experiment was to determine what factors,, both.

instrumental and environmental, influence range accuracy and precision.

A preliminary investigatioa of two of the fifty-seven sets Of data

collected [Ref. |.] led to thcse tentative conclusions:

(,) The precision of the position location is essentially independent

of the range from the array and depends only on the rise-time of the

|75-kliz signal.

(2) There is no significant difference in the accuracy of results ub-

tained by either isovelocity or isogredient ray-tracing i.echniques.

(3) The isogradient method appeared Lo need less environmental data

to obtain a given precision.

This thesl.• wns undertaken to verify and to extend the results of

this pre].imi4ry Lnvestigation by testing the isogradient method of

ray-tracing at 1ll statioiis and depths studied and by determining the

amount of env.ronmenLtai dad l-eqtire" to iaintain accuracy and by ascer-

taining if histodical d•,ta , than real time data may he urilized.

8

I1. DABOB BAY TRACKING RANGE

A. -DABO,3 BAY iFAciiLrY

A facility for the three-dlmensional tracking of surfAce ships,

Ssubmarines, and torpedoes is located at the Dabob Bay facility of the

Naval Torpedo Station, Keyport, Washington. Chosen because of its

favorable oceanogpraphic features and its proximity to the NAVTORI'STA,

Keyport, Dabob Bay has been used for torpedo testing since 1949. It

consists of a 75-kllz primary tracking system enveloping nearly the

entire bay providing for underwater tracking in a volume approximately

-30,000 feet by 4,500 feet by 600 feet deep.

Dabob 13ay, a branch of the Hood Canal, is in a deep depression ad-

jac!ent to the Olympic .,,rountains. The Quilcene River flows into I"he

northernmost part and the Dosewallips River intoL. the southernmost. The

sides of the bay are precipitou3 and predominately roely, while the

bottom is mud. Annual precipitation averages about 15 inches and the

average snowfall is about 1.3 inches. Winds generally blow along Lhe

length of Dabob Bay in a North-South directi.on. Normal wind velocities

tare 5 to J5 mil]es per hour. Tide. levels in Dabob Bay rnge from about

-5 to +15 feet referenced to mean lov-Iow wa.er (iLLW).

Water temperatures chanteo markedly from scason to ;.eason and even

from day to (lay. Sallnity varies considerably with Aepth as fresher

surface water from terrestr'•al runciff overlies more .,JiJne water. The

variation in salinity is also quit{e seasonal, reaching a maximum il, the

spring. The main contributor to sound velocity changes i., water tem-

perature variatitn and r0o rosu]tli ag sound velocity psrofile is

rei•|o..entt. a~ of the L,,1'c)jerature bradie-hL.

B. RANG. DESCRIPTION

The basic underwater tracking system is comprised of three compo-

pents: Ihydrophone array, computer system, and vehicular instrumentation.

The shifkboard transducek° emits a 75-kflz acoustic pulse in synchronism

with a master clock at the/,computer site. This pulse is detected by

each of the four hydrophones in. the array and mixed with a local oscil-

lator havIng a frequency unique to that hyIrophone.

'The outputs of these oscillators are preamplified and fed to a

multiplexer, which sums the signals and transmits -the composite signal

via underwatev cable to the computer site, where it is processed to de-

termine the ih-water transit time to each hydrophone (Tx, Ty, Tz, Tc).

1. llvdrovhone Array Configuration

The hydrophones in the NAVTORPSTA Range are arranged in a

short-base line system in groups of four, each one located on one of

four adjacent corners in an imaginary 30-foot cube, thereby defining

the orthogonal coordinate system in which the measurements were made.

These hydrophone arrays use buLvant spheres which exert an upward force

in excess of two thousand pounds to keep them upright. The array is

not free to rotate about the Z-axis, but may tilt as much as two degrees

from the horizontal in strong currents. This Lilt is measured by servo-

pendulum transducers whose specified resolution is 0.00833 degrees,

accuracy 0.025 degrees, and linearity 0.05 par cent over the full scale.

The range consists of six arrays (Fig. 1) aligned along a line

450 feet east and parallel to the range axis, spaced at 6000-foot in-

tervals, with the 00 array being the farthest north. The range axis is

1910 18' 14" T.

I0

2. Computer System

The computer system, a Scientific Data Systems (SDS) Model 920,

is installed on Zelatched Point and consists of three main subsystems:

the signal-processing subsystem, the data-collection subsystem, and the

computer tubsystem. The sighal-processing subsystem, the link between

the hv. iphones and the data-collection subsystem, processes the multi-

plexed signal received from the arrays, discriminates against unwanted

signals,, and determines the in-water transit time to each hydrophone.

The data-collection subsystem establishes the master clock timing by

which all timing is computed. It also prepares all the array signals

for the computer subsystem, which calculates the position of the tracked

object, prints the tracking data, and records the data on magnetic tape.

For the real-time examination, the data were plotted on X-Y plotters.

1]

III. EXPERIMENTAL PROCEDURE

A 92.5-dB (re !,sibar) acoustic source with approximately ten pounds

of ballast was suspended from the stern of a sound boat to depths of 25,

50, 75, 100, 150, and 200 feet at six horizontal ranges (stations) from

900 feet to 4700 feet from the 02 hydrophone (Fig. 2). The first sta-

tion was located approximately 900 feet north of the array, and 250 feet

east of the range axis. Successive stations were located parallel to

the range axis;, the second being directly over the array, the third 600

feet past it, and then at about 1500-foot intervals to about 4500 feet,

beyond which signal-to-noise problems made further examination impossi-

ble. The source emitted one 1.3 millisecond 75 kHz pulse per second for

sixty to ninety seconds at each depth at each station.

The horizontal position of the boat on the range was found from the

range's Autotape system, a portable commercial microwave system used

exclusively for ship tracking that yields accuracies of + 3 feet. The

*.j position if the acoustic source with respect to the Autotape antenna was

determined from the length of cable let out, the horizontal distance

from the antenna to the stern of the boat, and the ship's heading.

Tidal data were i Žcorded and used for correcting depth coordinates to

MLLW. The array U: khaown to be 585 feet below MLLW, so that the depth

of the source below tile su,.face and the tide measurement allows calcula-

tion of the vertical distance between the source and the array. All

measurements were made with respect to the array's coordinate system,

although the array's orientation and location on the range were known,

making it possible to transform this data to a true position on the

range. The X-axis of the 02 array was 250 24' 36.0" 1'.

1.2

A NAVTORPSTA digital velocimeter that has an accuracy to +1.0 ft/sec

and resolution of + 0.7 ft/sec-was used to measure the sound-velocity

profile at each station. NAVTORPSTA instrument-t.ion at Dabob Bay meas-

ured and recorded the acoustic travel times from the source to each of

ithe four hydrophones in the array to six decimal places for every source

depth at ,each station. The three-dimensional position of tbh source

with respect to the array was calculated by the NAVTORPSTA NUTRAK III

computer program.

The data were gathered on 2.1 March 1974 during a neap tidal period

and while the bay surface was smooth and glassy, although there had been

ripples earlier in the day. The day was bright and sunny with scattered,

thin, high overcast, the temperature was 55'F, and no noticeable wind was

present. The shiny stainless steel transducer disappeared from view when

about eight feet deep, indicative of thick biological concentrations in

the water. Rudimentary drift measurements of boat movement relative to

the surface water were taken by throwing paper into the water and watch-

ing its relati7e motion with respect to the boat, which indicated a value

of approximately 0.3 ft/sec.

13

IV. RANGE DETERMINATION TECHNIQUES,

PA. TEC~hNIQUES

The three-dimensional position of an acoustic su:'rce with respect to

a receiver may be readily d3etermined by computer analysis. Two ray-

tracing techniques which a'ie easily adaptable for high-speed digital

computation are: (1) an isovelocity aechnique in which the water mass is

divided into layers of isovelocity wacer; and, (2) an isogradient tech-

nique in which the water is divided into isogradient layers. Both

techniques utilize Snell's law, which describes the refraction of sound

rays in a medium of variable velocity.

The isovelocity metý.- is .rrently utilized in the NAVTORPSTA pro-

cedure NUTRAK III. STUTRACK I was developed in the preliminary

experimental analysis. It consists of both an isovelocity and an iso-

gradient method to be utilized as comparators with NUTPAK II1. Both

programs require as inputs the velocity profile, the transit time and

angle of arrival of the acoustic wave at the geometrical center of the

array.

B. PREPARATION OF DATA

The required inputs for the computer analysis must be derived fromthe information available at the array, w1ich is the transit times of the

acoustic pulse from the tracked source to the four hydrophones of the

receiving array. The geometry involved in the calculation of the raw

array coordinates is shown in Figure 3. The expressions for the raw

array coordinates are:

14

-RAW c2 (Tc + Tx) (Tc Tx) (1)

2d2

RAWYI - (T + T) (T -T) (2)2d c y c .y

andi. c2

2d- (Tc + Tz ( c - Tz (3)

where

c = the average sound velocity, ft/sec;

A = the distance between hydrophones, 30 ft;

Tx, Ty, T z, Tc = travel times to respective hydrophones, sec.

A correction factor must be applied to correct for the array receiver

integration time (pulse width discrimination), 800.0s. The relations now

become:

2RA4X = -7 - (T' + T' - 1) (T' - ') (4)

2dW c c x c (4

C2

RAINY -C- (T' + T'- K) (T I - T') (5)S2d c y c y

and2

RAcZ (V_ + T' (T'I - T) (6)2d c z -K) z

where

K = twice the integration time, 1.6 x 10- 3s.

CI, TIy, T'z, T' = the measured transit time, sec.

These raw coordinates are referenced to a non-horizontal reference

plane due to the 4rray's freedom to tilt in the horizontal. The arcay is

instrumented to sense the angles the array axis makes with the horizontal,

XTILT and YTILT.

The correction of the RAW coordinates is a matter of geometry, as

shown in Figure 4. The corrected coord(Iiates become:

15

CORX = RUNWX - RAWZ [SIN (XTILT)] (7)

CORY = RAWY - RAWZ [SIN(YTILT)] (8)

CORZ = RAhWZ + RAVX [SIN(XTILT)] 4- RANY [SIN(YTILT)] (9)

In a homogeneous body of water, the minimum time path between an output:

transducer and a receiving hydrophone is a straight line. When the speed

of propagation is spatially varying due to temperature and salinity vari-

ations, refraction occurs and the minimum time path is no longer a straight

line (Figure 5). Corrections must therefore be made to determine the true

position of the source.

From Sne ll's law, a minimum time path is computed, working back in

time from the array center in the direction of the "apparent" position and

tracing the acoustic ray through each velocity layer until the measured

"time is consumed. The vertical angle of entry at the array, computed from

the tilt-corrected array coordinates is

A =SIN 1 CORZ 2 1/2 (10)0 L CORX2 + CORY 2 + CORZ2J

This entry angle is assumed to be equal. to the entry angle for the

minimum time path. This assumption is good if the source is far enough

so that the wave fronts are planar over the dimensions of tite array, and

the speed of sound is constant over the dimensions of the array.

The travel time, T, to the origin is computed from

ST S.- = -- (11)c c

where

S = [(CORX) 2 + (CORY) 2 (CORZ) 2] 1/2 (12)

and

16

= )2 152 152 1/(3Re [((CORX + 15) + (CORY + 15) + (CORZ + 15) 1/2 (13)

where R is the slant range to the array center hydrophone, and S is theC

slarx range to the array center.

The entry angle, A0 , the travel time, T, along with velocimeter data

describing the sound velocity profile may now be utilized as inputs to

the computer program. The outputs will provide the three-dimensional

position of the source with respect to the - iver.

37

I

V. PRELIMINARY ANALYSIS

A. ANALYSIS

The analysis of the experimental data was to have determined the

adcuracy- of NUTRAK III as compared with both modes of STUTRACK I. The

Autotape system was to foi.a the reference for this determination, but its

precision was much less than expected. The analysis was, therefore, pri-

marily devoted to the determination of the precision of the various

methods of ray-tracing. Stations 1-25 and 6-50 were chosen for prelimi-

nary investigation since station 1 was closest to the array and station

6 was farthest. The effects of varying the amount of environmental data

was also investigated.

B. RESULTS

NUTRAK III showed good point to point continuity at station 1 for all

coordinates, while the coordinates at station 6 were very erratic. A

transformation of the coordinates to a spherical coordinate system showed

that the variations of phi versus theta to be approximately the same at

both stations.

Both modes of STUTRACK I were compared to NUTRAK III and in both

cases no significant differences wer-, noted when the most structured

sound ve]ocity profile was utilized. As the number of linear segments

defining the sound velocity profil.e was decreased, the isovelocity toch-

nique provided consistently poorer results. Using the isogradient

technique to compute the source's position resulted in only a slight

degradation as the number of segments in the profile was decreased and was

considered adequate in precision.

38

.4

C. CONCLUSIONS

Comparison of the two stations investigated showsd station 6-50 to

have greater spatial variability. The transformation to spherical co-

ordinates shows the difference is not present in the angular display as

would be expected if the time errors were the important source of vari-

ability. Improved range accuracy can only be obtained by improving the

accuracy of the time measurements or increasing the baseline of the

hydrophone array. The isogradient method of STUTFACK I provides greater

precision than the two isovelocity techniques when less environmental

data was utilized.

f.

p].

Ia..

- --- ------------ -

V1. PRECISION OF DATA

The data collected at Dabob Baywere tested at all stations to verify

that the results of the preliminary analysis were generally appli~cable.

If the precision was independent of range and depth the standard, devia-

tion of the source coordinates as calculated from the transit times at

the array- should be zero with a small standard deviation about the mean.

-Factors which could cause variation are the rise-time ef the 75-kHz source

(as discussed in the preliminary analysis), and the actual drift of the

source transducer caused by the currents which exist in the experimental

area.

Analysis of the precision of the ranging system must remove the ef-

fects of drift from the calculations. Regression analysis on the

components of the calculated horizontal. position of the source provided

an equation for the displacement of the transducer as a function of time.

A second-order regression equation was considered to adequately describe

this displacement as it accounts for the velocity and acceleration com-

ponents of the drift.

Each set of data was processed to determine the calculated components

of the source position. Each horizontal component was fitted to a simple

second-order curvilinear regression equation with time being the indepen-

dent variable and the corresponding component as the depend-nt variable.

The value of the component evaluated from the regression equation for each

time was taken as the estimated value at that time. By taking the dif-

ference between the estimated ard the corresponding calculated values the

effects of drift are removed from the comiputations. The mean depth was

taken to be the simple arithmeLic mean. The StandOrd deviation, standarl

20

error of estimation, of these differences between the estimated and cal-

culated coordinates is a measure of the precision of the ranging system.

Tables I-III show the standard errors for the theta, phi, and radius

components of the source position for .all stations and depths. Figures

6 and 7 are scatter diagrams of the standard errors of phi versus theta

by station in Figure 6 and by depth in Figure 7. Both Figures show that

the standard errors with the drift effect- removed are essentially random

with no dependence on station or depth.

21

VII. 'ENVIRONMENTAL EFFECTS ON RANGE PRECISION

The effect on range position accuracy and precision due to varying

the amount of environmental information was investigated by varying the

number of linear segments which were used to describe the sound velocity

profile. Decreasing tlhe: number of segments which describe a particular

'profl32e while maintaining the required precision would result in faster

p~ro.essing time for the ranging data.

Three methods of decreasing the number of segments in a profile were

studied: (1) equal changes in gradient; (2) equal coianges irn velocity;

and (3) "eyeball" fitting. All three methods were compared to determine

which would suffer the least degradation in accuracy and precision as

the profile was simplified. In the experiment, environmental data was

provided by a velocimeter which described the existing sound velocity

profile in 64 to 67 dizcrete points in 600 feet. Any profile described

adequately with fewer points would significantly reduce data processing

time. The equal-change-in-gradient and velocity methods utilized in this

investigation were developed by the author for this analysis.

The equal-change-in-gradient method det.rmines a set of linear seg-

ments by locating the depth and velocity points which, if connected by

straight lines, would cause a givei, percentage change in the gradient.

The first three points from the bottom of the most detailed sound velo-

city profile are fitted with a straight line by the method of least

squares. The slope of this line is used as the initial. reference gradient.

The gradient of the linear segment in the original profile between the

first point used to determine the referetice gradient and the next poin't

22

in the profile is computed. This. ,radient is conmpared with a Eeist value

given by the reference gradient plus a designated change from 5 to 30%.

When the computed gradient exceeds the test value, the prior point in

the profile is considered as the end point in that segment. The points

thereby included in this segment are fitted by the. method of least squares.

The end point of the segment which has been processed is now the first

point used in the determination of a new reference gradient as described

above and the next linear segment is deLermined by repeating the process.

The velocity at the highest depth of the initial segment does not equal

the velocity at the lowest point of the second segment after processing;

thereforL, an adjustment must be made to cause the two segments to inter-

cept at this mutual depth. This adjustment consists of making the sound

velocity of both profiles the mid-point of the calculated velocities at

that depth. This process is continued until the surface is reached.

Appendix A is a listing of the computed program which utilizes this

method for decreasing the number of segments which describes a s-und

velocity profile.

The equal-change-in-velocity method utilizes a constant percentage

change in velocity between the minimum and maximum velocities in the pro-

file and tihe minimum and maximum velocities to decrease the number of

segments in the profile. The m,.nimum and maximum sound velocities of the

original profile are located; a fixed percentage (5 to 30%) of the dif-

ference between them is used to determine the velocity at each point in

the new profile. The surface sound velocity is incremented by the given

change in velocity and the original profile is searched until the depth

of the incremented velocity is located or the minimuan or maximum velo-

cities occur. The method determines the diroL:tion of tho change in

23

velocity from the oziginjl ;profile. Once, the riiw point in the profile is

deteimined, its veloci' 1., incremented, and the sequence, as described

above, continues until tIW.-bottom of the original ,profile -is reached.

The original sound velocity p*r.i'ie "now described by a, lesser niumber

of linear segments. Appendix B 4i, .A listing of the dumlputer program

which utilizes this method.

The "eyeball" method is simply the avthor's estimate of tha best-

,fitted segments which describe a sound veloc:.ty ,prot.ie. It is derived-

by estimating, the segments which provide the best &!scription of the

original profile in the minimum number of segments. Then by decreasing

the niumber of possible segments, estimates are made of the. best-fitted

profile with the decreased number of segments.

Thirteen curves describing the sound velocity profiles at both sta-

tions I and 6 were deQtermined using the above methods, six by the equal-

change-in-velocity method, three by the equal-change-in-gradient method,

2 and four by the "eyeball" method. Figures 8-10 show the change in the

characteristics of the profile at station 1 due to its description by

each of these methods. These p•rofiles were used to study ae effect on

source position due to varying the amount. of environmental data. The

position of the source at each depth I.or stations 1 and 6 was calculated

for each profile. Tables IV-VII show the resultant standard errors of

estimate from these calculations. At both stations the standard etror

uf the theta and p.hi components remained constant as the amount of envi-

ronmental data was var .cd. The standard error of the slant range changed

with each profile. Excluding the, results for tl-- "eyeball" method at

station 6, the average standard error for all methods was 0.181 feet at

station I and 0.317 feet at station 6. The average standard errors by

I 24

method for stations I and 6 were: (1) equal-change-in-velocity, 0.160

and 0.343 feet; (2) equal-change-in-gradient, 0.220 and 0.318 fcet; and

(3) "eyeball", 0.172 and 1.586 feet. The equal-change-in-velocity method

appears to cause the least degradation in positional precision with the

least environmental data at these two stations.

25

VIII. HISTORICAL ENVIRONMENTAL ANALYSIS

The possibility of using historical environmental information rather

than real-time information as the sound velocity input for computing

position has as its *:•jor advantage the lessening of the cost and time

required prioz to performing any range operation. Historical information

along with its reduction by the methods discussed in Chapter VII would

decrease total processing time and, thereby, increase the efficiency of

the ranging system. This hypothesis is only valid if the use of this in-

formation does ihot degrade the accuracy of the positional calculations.

The objective of this section, therefore, is to analyze the feasibility

of utilizing historical environmental information in computing position

with precision as the measure of effectiveness.

Figures 11 thru 22 show the twelve sound velocity profiles which de-

scribe the environmental conditions which exist at Dabob Bay. The

"profiles were based on three years (1971-1973) of environmental informa-

tion collected at the facility [Ref. 2]. Each profile type shows the

minimum, maximum, and median (mid) profiles which are charal,.teristic of

the particular type. These historical sound velocity profiles were used

*i in this analysis.

In order to perform the analysis, the inputs for the range positioning

algorithm, STUTRACK I, had to be deLermined based on the historical pro-

files. A simulation was developed to generate the transit time of an

acoustic pulse from a source to the array, the angle of entry of the

acoustic wave with respect to the center of the array, and the apparent

horizontal distance of the source from the array. The simulation

26

generates these parameters by searching for the entry angle in which a

ray would enter the array from a known position cf-a. qource. Once the

entry angle is located, the transit time for that angle is determined.

This simulation, as with STUTRACK I, utilizes Snell's law as its basis

and performs the same calculations as STUTRACK I, but in reverse order.

Appendix C is the computer listing, of the subroutine, ANGCAL, developed

for the simulation.

The simulation computes the input data for STUTRACK I at a fixed

horizontal position from the array. This position was chosen to provide

a horizontal range from the a, ay similar to that of station 6 in the

experiment. Fifty vertical points at four-foot intervals from the sur-

face to 200 feet were used as the vertical component of the source

position. The use of this scenario was chosen to provide data for the

analysis under the conditions that were found to cause the least preci-

sion of source position in the experiment, station 6.

Each of the historical profiles was first described in 60 ten-foot

layers from the surface to 600 feet, and this descriptic, was used as the

environmental input for the simulation. The transit time, entry angle,

and apparent horizontal range for the 50 positions were used to compute

the three-dimensional position of the source with STUTRACK I. Each

historical profile was then reduced using the equal-chang,:-in-velocity

method at five to thirty percent change intervals, providing approxi-

mations to the original profile. Each of these simplified profiles was

used as the environinental input to STUTRACK I and the source position

was calculated with the transit times, entry angles, and horizontal

ranges from the original profile.

27

The position of the source as calculated from the reduced profiles

was compared to that of the original profile. The standard error of es-

timate for each of the reduced profiles was determined for the 36

profiles describing the twelve historical profiles at Dabob Bay. A

comparison of the minimum and maximum profiles of a particular type with

the mid profile was also performed. This comparison was designed to show

the effects of using a single profile to describe the environment when

the actual profile existing at that time is withip. the range of a parti-

cular sound velocity type. Table VIII shows the results of these

comparisons for Profile Type Four. All profile types showed simila"

results.

In conducting the above comparisons, it was noticed that much larger

errors occurred at shallower depths. Each profile type shows its great-

est varitation near the surface due to water runoff, solar insolation,

and seasonal temperature variation. Therefore, it was decided to perform

the same analysis as above, but with the data points below the point

where large variations in the gradients of the minimum and maximum pro-

files of a sound velocity type occurred. The calculations were performed

between 100 and 300 feet. Table IX shows the results of these calcula-

tions for Profile Type Four as before. The values, as calculated from

data points between 100 and 300 feet, generally, showed less standard

error than the values calculated using the same number of points between

.2 the surface and 200 feet. Table X shows this comparison.

28

IX. CONCLUSIONS

A. PRECISION OF DATA

"The analysis of the experiment showed conclusively that although the

magnitude of the spatial variation grows as the source's range from the

array increases, the variation in the angular description of source

position is independent of range. This is consiLtent with the results

of the preliminary investigation. It is concluded that the increase in

the spatial variation of the range position discrimination of the 2.5-MHz

clock in measuring the arrival time of the 75-kHz source signal used in

the experiment. This uncertainty can cause a maximum error of 3.3,Msec

in the arrival time which is one-fourth of the period of the 75--kllz sig-

nal, causing an error of approximately one foot at station I and 4.5

feet at station 6.

SB. ENVlROM!ENTAL EFFECTS ON RANGE PRECISION

The investigation of precision of range position due to the amount of

environmental information used in the calculations has shown that the

method of dLscribing the existing profile is not critical.. Of the three

methods of reducing the number of segments describing the exicting sound

velocity profile, the equal-change-in-velocity method appears to produce

results with more precision than either the equal-change-iin-gradient or

"eyeball" fit methods. Describing a profile in terms of a 20 percent

equal change in velocity between segmenLs, usually six or seven segments,

produces the best precision with the minimum amount of environmental

information required for calculations. This result is independent of

depth and horizontal range.

29

C. IIISTORICAL ENVIRONMENTAL ANALYSIS

The analysis of the twelve profile types which describe the acoustic

environment at Dabob Bay show that the use of historical information

rather than real-!tme environmental data is indeed feasible. The use

of a profile which has been reduced by a 20 percent change in velocity

in the equal-change-in-velocity method provides the most precision for

all velocity profile types studied. The use of the mid profile to de-

scribe any profile falling within the range of a particular type causes

very little degradation in precision. Therefore, it is concluded that

the use of historical data is feasible in the determination of the source

position and only a small number of segments are required to describe the

existing sound velocity profile.

30

X. CO,2MENTS AMD RECOMMENDATIONS

This thesis has verified the preliminary conclusions reached in

Reference 1, that the precision of the range position in calculations as

a function of thp rise-time of the 75-kllz acoustic signal used in the

experiment. The angle of entry of the signal to the array is thus the

critical factor in range-precision. Increasing the accuracy of time

measurement and decreasing the error due to rise-time (increasing the

array baseline) will improve precision.

The historical profiles may be segmented as described in this thesis

and catalogued. The sound velocity profile which actually exists on the

range could be sampled daily with a velocimeter. This profile can then

be fitted to an historical profile type which describes it and the ap--

propriate catalogued sound velocity profile used as the environmental

input for any range positioning calculations to be performed that day.

As noted in the preliminary investigation, the sum of the source

depth and the individual calculated Z component at each time differed

from the known array depth. The range of this difference was +4.8 to

-18.8 feet with the average being 3.1 feet less than the array depth.

Verification of the recorded tidal levels with the predicted. tides at

the time the experiment w Ls conducted showed no discrepancies of this

magnitude.

Further study should be conducted to determine the accuracy c~f the

rangi.'g system at Dabob Bay and Nanoose and to provide a greater con-

fidence level in the use of less envirornental data in rnnge position

calculations. The apparent inaccuracy in the Z component should

receive special attention.

31

N ~ ~ JSPIT *

THQ2t'DIKE0AY

LaK 47 0A8*N-- -

- BOLORIGIN,P S Z 000 YDS

o qANGE C

•-ý 91018,14.1,

LOW ( / 000 L

\VHITNY/.' /A 0/ 01 0

SOUTH5000 YD z

S, __'z:0 PTI E"- - <- ~' 02 _

03 •.SERVA f PIN E

- ~PT.K

10,00 YDS~-L-- 0 4LAT(FRO,- ," SCALE: YDS(xlOO-

0 1 2-- '- ~ ~~~---470 42'NI -',--

$KUTSKC~~

CN~ 01c**q

VPCGUHE 1. DA13013 BAY RANGE

32

MA13GE CL 1910 13' 14.1" TRUE

SCALE: V" 1000 YA\DS

1000 0 1000 12000

PO.I I~*f_/sI E/WI ___ 3-D TflNSDUC.F.? DWPTIERr

5&000 15o 25 50 75 1 1 2,5800 15013 25 50 10 r5

____ 750 100 . 1200

3 6200 150o 25 50 75 100 150 2CCo__ _ - -_._ _ -

4 6700 150E 25 50 75 100 150 12"0

x 5 72001 15o ,. 25 50 75 100 150 120o

6 7700 -15 0 25 50 75 100 150

__7 8200 250E 5 50 75 100 150 J2CO

S.. •T&"fespondc-r 1y 02 .

\ v2

RANGEAX IS

04 .900T To Responder 2-____ _..

FIGURE 2. EX PERIMENTAL AREA

33

SYNCHRONOUS

CLOCK

cT, cTy

Z AXIS

1 -°

op 7 ///

R / I d -- Y AXISI "" Ry---. I /

I /

X AXIS

FIGURE 3. }YDROPIHONE ARRAY

14/

IXTILT

RAWZ

pI

XT 1 LTICORX

RAWZ SIN(XTILT)

The SIN(xTILT) is positive when the X transducer is

above the horizontal plane passing through tho C

transducer, and negative whan the X transducer is

boJlow the horizontal plane passing through C.

FIGURE I1. TILT CORRECTION

35

Tr'ue •

4855'/see Position Poset

Position

4850'/sec

./

4865'Iseo/

Layer 3

4860 ,'see A 2Layer 3

6z22

jAZZ

4870 '/sec N

LAs1 laziLayer I

(Not To Scale)

FIGURE 5, RAY PATH REFRACTION

36

Fi I

PH VE:. 1.__ " I " I ?HI S THETH ,

L Y STNTION x . -________" , _____6 0-_"_________ I "-"

II0

S. . . .. ., . . •i I .I , I •iL -i - T .; -. i : ___! .,___, + f I ! ! I I j '+.. . ........ .. . . 1 .f. . . . . .. .. .

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: _2 . " a.I . • : ., i. .j- • I i: ! ;- , "

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DR0 9HYSOUND~ VFILLITY PRtIFIVF'

TYPEF IMOND~ VELOCITYrFT/SECM

IMi

SOIUND VELOICITY PERIFILE

"TYFPE 2,WUNI> VEL:flCYFT/SEi

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ld

I~i1

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SO1UND VELLCITY PRO~FILE

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44

4/6

I>RiiE3 BRY

OUJND VELOCIJC:TY PROFILE

TYPE H

I1L

5

FIUR Ili

:•. BDRE03 BRY

SOUND VELOCITY PROIFILE

TYPE ES 1N YlCTYYT'/•ECI

w

ILI-

FIGURE 1.5

4 6

SOUND VELOCITY PtRIOFILE

TYPE E

,°-I

Ia!

II

FIGIGURE 16

47

DR303 ERY

13OUND~ VELOCITY PROFILE

TYPE 7

FIGURE, 17

418

DR3i-3 BFIY

SOUND VELOCITY PRIOFILE

TYPE AS•lN VE'CI.~TYIEFT/SEM

15M

IL

u 3w

I-.I.

FIGRllE" 18

49

SOUND~ VELOICITY PROFILE

TYPE 9SWJND VmnltCTYrnT/sEc!

1450

ILI

W

PIIGURE 19

50

S:SQULND VELI:CF::IY FPROFILE

TYPE 1I0

* 15

I~l

w $l

F IGURE' 20

51

DbRE9J6 EIHY

SO2UND VELU:CITY PROIF!LETYPE 1I

I,

FI 'b' GUREI, 21

5 2

MUM~t VEIA2CIT1Y PROFILETYPE 12

SMUJNý VELnCfTyrFT/.lCE4

______R 22i

~153

COMPONENT

THETA

STANDARD ERROR OF ESTIMATE(DEGREES)

•0 00 00 o • o •••0•0 " e• • • 0 o *0 0• ••o0 0 00 *0 0000 •• 00S 00 0•0• o0

:. . . . DEPTH(FEET) 0........ ......... o •..o ..... •00 . .o . 0.00 . o.S• . • 0.

O . 250 50. 75 .100 150 200 •

S 0 0 0 0 00 0 0

O • I • .006 .070 . .060 o.090 .074 . .078 .• •0 • e 0 0 go••0 • 0 • o 5••• •• 4 •• o0 0 0•0 4 0• •

• 0 2 o •070 o .086 ..098 • • •• ••6• 0~.0 .. 0•• 0S•• • o • o •D .o .00 0 0 s 0 •..o a o .o ..., • .•o • •• o

• S •3 ..059 o •099 o.112 • •065 .087 o .102

O • -4 • 131 . .035 • .059 • .053 .049 . .028* A ... .•00... •o ........... o ...... ,....o ... o ........ o ......

• T * 5 o 6146 * .157 ..038 ..042 .028 * .037• 1 •o• • •• e • o••o• • • •o0 • , o • 0•o •o 0 • ••

• 6 * .092 • .092 ..143 ..078 .104 .095 o• 0 0 0 0. • o 0

O N . 5P • .124 o •042 .054 • .051 .058 o.041O s0000000*9000 0a 0 0 0 0 0a

* . 4P .122 : .069 * .042 : .026 * .039 . .069 .0 6 • • 0•• 0• • o•o6 o••••., , 0 0 0.go••o, 0 ,•••q

* . 3P • .045 o •030 * .031 • .027 . .061 . .046 .a 0 a• *0 a* 46 0 •a*8 0 • • • * 0 0 a • 6 0 0 a 5 0 * o 0 • 0 0 a 0 It • • 0 6

IP • .055 *.0460 .052 ..05, o.066 .•079 aS 00 0 0 0 0.0 05 0 0o a •a& 00 00 0 0 o a0 0 1. 0 00 •,•0 0 6 a 5 00a•0 4 0 0 00

TABLE I

S~54

COM PONENT

PHI

STANDARD ERROR OF ESTIMATE(DEGRUES)

* a* 60a00 00000 6 *@ eae e a~OB *as 5 05 aB, a Sa Se...... 0 0 *Se a B 0 680

sess• .DEPTH(FEET)

. • 25 . 50 . 75 1 100 * 150 • 200

1 . 0 •028 .03 .020 . .021 .030 .030 :a eeeoeo••••• e••o segee•e•ooe eoe~oeoooeso oeoseoo • • o o~ e •.e

• • *2 • .065 • .204 • .199 • a

. S • 3 .038 • .042 ..036 * .035 • .049 ..032

* A .4 . 031 ..034 . .037 .034 • .034 ..035

. T * 5 • .037 ..034 • .025 * .048 * .034 • .042

0 6 o .062 • .055 * .078 * .080 ..096 * .080* 0 *..• .... o....... .•• sc•aB•e S•. *s•••e•••• ••c••55•B•• •5

N . 5P .•039 . .037 .035 .037 • .036 . .044

a 4P * .038 s .033 .037 .035 ..052 . .032

3P • .032 * .032 * .030 ..033 • .049 • .043S~~~ 6 a 5 :

S• •IP . .028 .027 • .033 .•048 • .030 . 0.56

TABLE II

i55

COMPONENT

R

STANDARD ERROR OF ESTIMATE(FEET)

* . DEPTHt(FEET)

* . 25 * 50 * 75 100: 150 • 200.*0S*** *o **O* .... 0o wO.... e00 ... 00 0 .e•..... 0a0 0.. e. e... 0.0

* I • .186 * .112 * .178 o •192 * .249 * .171.0. ...... * .eew.c 0..0..... eoC.ee... .e~..e

* . 2 • 1.330 * 2.505 * 1.700

6 0 " 0 * " 0 0 0 "0: '

o S o 3 ".151 o212 .172 " .199 o.o269 o154• T . .I I t •I . • 0 0

o 19Y 2 .239 .238 o .248 o 296 o .269

T *5 *.273 o 269 *.194 lq.12 *.337 *.286 *:,C :eewew * ... w :.. ... e :.e..w wew 8 we*.• . e . . e w .

• 6 o .409 o .316 o .366 ..486 .414 o .3730 0 •• 01•@ ° o 0 • 0 0•o• e • • • l• @ • i • a • o

a N • 5P o .314 . .258 * .232 * .277 .375 . .338 o

.4P 251 .231 .230 228 .280. .199

00 C e e e .l ci . C e

o .3P * 145 * 195 *.178 * 165 * 202 * 166

0IP o o190 i .55 *.167 *.253 *.211 *.284

TABLE III

56

STANDARD ERROR OF ESTIMATECAUSED 3Y ENVIRONMENTAL DESCKIPTION

BY VELOCIMETER

* . D • COMPONENT* S E .....

* T * P ..

.A. T THETA. PHI • R0 . H .'(DEG) (DEG) . (FT)

25 * .067 e .0-9 * .187

• . 50 * .073 . .033 * .114.* 6• ap • g • • •o0 5 0 0•• • •

• . 75 * .062 * .020 , .175... .................... e....e....• •ao •• 0 • C•q~ • 0 •5•••

S • 100 ..094 * .022 • .199

150 • .076 • p030 • .248

S. .200 .082 .. 031 .•175o

25 .095 .055 • .283 .

* • 50 .•095 • .056 , .319C, 0. 6 • C J 0 • 4 • l C o • •

75 .i45 * .079 .36L.6

100 • .081 * .076 ..422SC.... *Og.oe .ee e... olcOOS S1 ,0 01 0 * 0 0

150 *.108 *.098 *.415

0 a 1 0 0 0

2. ,200 .098 .081 .37-

TABLE IV

)5

STANDARD ERROR OF ESTIMATE OF RCAUSED BY ENVIRONMENTAL DESCRIPTION

BY THE EQUAL CHANGE IN VELOCITY METHOD

0*0e 000ee••,d•••..••. 000 SeO 08 0 00•• 06• 0000.0 OO • 0• •• •••* 0 0

* . D • PERCENTAGE CHANGE* S • E * IN VELOCITY

A T T . • ....* • H • 5 1 10 • 15 * 20 25 30

* • 25 , .153 • .166 ' .157 * .165 . .135 . .158

* • 50 o .142 , .151 * .149 . .129 . ,214 .223.. ...... 0 O 0 0 . ....... .0.•.•.

* . 75 * .215 • .140 .157 ..154 • .142 . .155* 0.Oe••0,••O•0• ,m••O•••9 0 0 • 0,•, •0 U 0 64, ,

, • 100 • .156 .,174 . .165 • .13 .1 .54 .14).O 0 • • 4,• oo••4• 00 0 40 O• 8•9 909 •Oq 04 • 0•

O • 150 ..195 ..157 • .162 • .172 o.172 • .158

O 200 4 .145 • .1o3 I/.163 .130, .146 . o169

4. .0.. • 0 00. 00. •0 o. 0 • 0e 00 00 ... •. 0. 0 .. • 0• 0 .. .0 . •0 ...

o 0 0 0 • 0 0 0 •

* . 25 . .269 . .268 * .252 . .194 . .258 • .252

• . 50 2 ,Z70 .•241 • .242" .267 • .Z20 . .246

. 4, 075 4, .268 • .2570 • .314 0 .580 . .019 00.417 •

......... 0 .. . .. . . .. . .

1, 100 -.31t4 • .246 • .592 , .214 . .834 o .383

S •150 • .415 = .478 * .274 * .314 ..319 * .308

. 200 , ,377 • .315 , .319 o .289 ..242 , .984 o

TABLFE V

S58

STANDARD ERROR OF ESTIMATE OF RCAUSED BY ENVIRONMENTAL DESCRIPTION

BY THE EQUAL CHANGE IN GRADIENT METHOD

0 0 0* . D• PERCENTAGE CHANGE* S . E • IN GRADIENT* T . P ......* A o. T o . ,• . H o 5 0 150• ...... 0 ......... ... .. .

• . 25 . .170 . .168 . .637 •• .o • a oo • a• • 6••• 0 o •

* 50 .139 o .151 .637

• . 75 ..146 o .103 ..209

* . 100 * .201 * .157 .,169

. . 150 * .218 o .187 ..189

• & 200 • .162 o .138 • .177• •••..,0. ..•• .. *... S O D.0aOo0 .500a ,

0 0 * o . o •.• 0 • . o . 0.

25 o 4413 o .428 • .435 .

0 0 • p , .

50 . .247 ..259 o .271

o 6 75 .259 .284." .295

100 • .330 4 .310 * .318

150 .310 0 .305 .299.. o. 0•o 0 .04 0 • 4 ... to

• " 200 .334 .31.4 .305

TABLE VI

59

STANDARD ERROR OF ESTIMATE OF RCAUSED BY ENVIRCNMENTAL DESCRIPTION

BY THE 'EYE13ALL' METHOD

* . 0 * NUMBER OF• S * E • SEGMENTS* T * P .......o ..•.oo ...•• .o .••Oa.••

* A * T . . • .* . H * 5 * 3 * 2 1 1 .

• . 25 * .176 • .350 • .172 * .196* 5• • • 0 *o• • •0 o . •o • 0 • 00

• . 50 . .198 .167 ..172 • .204• ao a eeo so 0 0• oo 9 • o • 0 00 ••c • •• ••0 • ae •

75 .. 16 .144 o130 • o192

... 00. .. .

0 . 100 o .134 • .148 ..132 • .165

. . 150 ..177 • .167 • .172 .199

a 200 ..200 o .140 • .168 ..161 •

0 1

• . • NUMBER OF SEGMENTS• o*o ••• • •0 o• 0 S ••d

* . . 6 s 4 * 3 o I1

25 . .241 , .240 * .210 *

• 50 o .239 ..187 * .267 * .

0 1 : 06, % * * *P

• * *7 .1 o18 1 .I79 * .179 o **6•

* . i00 . .229 * .277 • .235 : .245................. •0 • 006 .... o. e. 0--.0--o-

• . 1.50 .0298 * .230 * .209 * .408• S• q • Sd • C oo • Co o l lae•

* • 200 . .441 .207 • * .210

* g INDIICATES SIANDARfD ERRORGRhAFrER THAN 1.000

TABLE VII

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CO4PARISON OF STANDARD ERRORS

CAUSED BY THE

APPROXIMATION OF SOUND VELOCITY PROFILES

BY THE EQUAL CHANGE IN VELOCITY METHOD

. . STANDARD ERROR

S * RANGE OF CLCULATIONS

*•0 - 200 FT 1 100- 300 FT."* PER"* CENT . • •" CHANGE . PHI . R PHI R• CAG (DEG) * (FT) .(DEG) (FT)

oii•fl p L l.l •• 1 . oi . . ..o.. o . ••i . i........

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S 10 O 0.031. 1.988. 0.031. . 1.844.0.. 05•• . 0 o5 •. . 5 0. • • e 5. •

S .15 " 0.016: 3.306: 0.011: 1.451:

* 20 . 0.041. 5.179: 0.037. 1.681.S.S .. 00.0.0.. 5 • S@0 .... * * *.8.0...,S5 *00•

* 25 * 0.04a: 6.o086: 0.0o4, 1.961:.O S ...060. e 0 .. O..S..O•O e.. *0SS •o..S e~O .. ***o

: 30 . 0.023: 6.213: 0.012. 2 2.04-8:

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SiBIBLIOGRAPHY

1. Karon, S. C., Ray Trace Experiment on the Underwater Range at DabobBa, Masters Thesis, Naval Postgradiuate School, Monterey, 1974.

2. Naval Torpedo Station, Keyport, Memorandum from Mr. Bob Helton, Code7023, to Dr. Carl Menneken, Naval Postgraduate School, Monterey,Subject: Sound Velocity Profiles, 27 March 1974.

3. Kinsler, L. Eý and Frey, A. R., Fundamentals of Acoustics, 2d ed.,Wiley, 1968.

4. Urick, R. J., Principles of Underwater Sound for Engineers, McGraw -

Hill, 1967.

5. Research and Engineering Department, Instrumentation Division, RangeSystems Branch, Mathematics of Acoustic 3-D Tracking (NUTRACK III),

by J. W. E. Edmonson and D. L. Pearson, p. 15, 24 November 1969.

6. Naval Torpedo Station Report 1030, NAVTORPSTA Range Users Manual, byA. E. Anunson, p. 125, 20 April 2.971.

7. Naval Ordnance Systems Command, Description and Operation, 3-D RangeEquipment, by J. E. Udd, p. 36, 15 February 1973.

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