Estimating the depth of neutrally buoyant floats

Deep-Sea Research, Vol. 27A, pp. 293 to 296 ~3 Pergamon Press Ltd 1980. Printed in Great Britain

0011-7471/80/0401-0293 $02.00/0

INSTRUMENTS

AND

METHODS

Estimating the depth of neutrally buoyant floats BRUCE V. HAMON*

(Received 19 October 1979, aecepted 30 November 1979) Abstract--Equations are given for calculating the depth of a neutrally buoyant float from measurements made on the chart record obtained during a position fix on the float. The method is independent of errors in ship navigation. The accuracy is probably 10 to 15~o.

INTRODUCTION

IN USINGexpendable neutrally buoyant floats (see e.g. SWALLOWand WORTHINGTON, 1961) to measure ocean currents, it is desirable to estimate the depth of each float, because an error might have been made in the ballasting or a slight leak might alter buoyancy and therefore operating depth. The possibility of a slight leak suggests that many depth estimates should be made during the life of each float. This note gives details of a method based on the recorded signals from the towed hydrophone array now usually used (M. J. TUCKER, personal communication) in getting fixes on the floats. It can be used each time a position fix on a float is obtained with only minimal alteration to normal operating procedure. The equations look complex but are easily dealt with on even a small programmable calculator. Unlike the method of depth estimation given by SWALLOWand WORTHINGTON(1961 ), the present method is independent of errors in ship's navigation. METHODS

We assume that the floats have crystal-controlled pulse repetition rates with period T(s). Each float will usually have a different period, for identification, in a narrow range near 1 s. Signals from a rectangular hydrophone array towed behind the ship are recorded on a facsimile recorder (e.g. Mufax, Raytheon), which has been modified to be driven by an external variable-frequency oscillator (VFO) that can be adjusted to suit the values of T for individual floats. The hydrophone array consists of a 'near' and a 'far' hydrophone, spaced 2 m (2 ~ 100 m) on one cable towed from the port side of the ship and an identical pair towed from the starboard side. A fix is obtained by using the timing of signals from port and starboard hydrophones to decide course alterations so that the ship steams directly over the float. The ship's position when signals from near and far hydrophones on the one cable arrive simultaneously then defines the fix. If the VFO (variable-frequency oscillator) is adjusted so that the recorder stylus sweep * CSIRO Division of Fisheries and Oceanography, P.O. Box 21, Cronulla NSW 2230, Australia.

293

294

BRUCEV. HAMON

rate exactly matches T, the record from one h y d r o p h o n e is a hyperbola. In principle, the float depth (d, m ) can be estimated from m e a s u r e m e n t s on this hyperbola, provided relative horizontal velocity between ship and float (v, m s - 1 ) is k n o w n or can also be estimated from the record. This m e t h o d gives p o o r results in practice because d depends on t,z. Better estimates can be obtained by m e a s u r e m e n t s based on the separation between signals from near and far h y d r o p h o n e s , a m e t h o d originally suggested by R. DE SZOEKE (personal communication). In this m e t h o d , v must still be estimated but d depends on v, not o n /22. Figure 1 shows the basic set of four quantities that must be measured from the record near a fix. M e a s u r e m e n t is m u c h easier if the V F O is adjusted intermittently during the pass to reduce the slopes of the records to the time axis. Such adjustments are indicated at A, B, C in Fig. 1. The m e a s u r e m e n t s from the record are an angle of slope of the record (01 ) at a time tl before the cross-over or fix and the spacing between near and far h y d r o p h o n e signals (z) at a time t before the fix. In addition, the V F O frequency fl at the time 01 is m e a s u r e d must be known. Introduce recorder scale factors S r (cm s - 1) for stylus m o v e m e n t , and (cm s - 1) for paper drive, both for T -- 1 s. Let C (m s - 1) equal sound velocity and assume t, t 1, and z of Fig. 1 are m e a s u r e d in centimetres. Then the basic equation for float depth d (actually m i n i m u m slant r a n g e - - s e e b e l o w ) i s

S,

d-(l+~2)St [

ct + \ ~cT~z2

1

,

~'LUS

,A

Fig. 1. Part of record, showing the four measurements required for estimation of depth and relative velocity. Curve 1 : trace from 'near' hydrophone. Curve 2 : trace from 'far' hydrophone. The variable-frequency oscillator that drives the recorder has been reset at A, B, C. Note the sign convention for 01.

(1)

Estimating the depth of neutrally buoyant floats

295

where ct = droop of far hydrophone below near hydrophone, as a fraction of their spacing (2) and ~: = constant for each pinger = TC/Sy2. [If t is regarded as positive when approaching a fix, as in Fig. l, the + sign is used in the last term of (1).] The relative horizontal velocity v is given by vwhere k =

tan0[ I ( x~

l+

1+

kto~an ~

t t?

(2)

CSJSy and 0 and to are related to the measured quantities 01 and t~ of Fig. 1 by tan 0 = tan 01 "~ ( f o - f t ) Sy fo S, S~

(2a)

to = tl +_~ (ctd-2/2)/v.

and

(2b)

[In (2a),fo is the VFO frequency for which stylus sweep rate equals float pulse repetition rate. 0 is then the slope that would have been measured with ft = fo. In (2b), the + sign is used when approaching a fix, as in Fig. 1. The - sign within the bracket assumes that 01 is measured on the trace from the near hydrophone, as in Fig. 1. Nominal values of d and v can be used in (2b).] Equations (1) and (2) can be solved iteratively for v and d. Alternatively, an analytic solution for d is with

d = kl(k2+2/kl) ½ kl=[ktanO tT

and

k2 =

~ -

{ _ ~ d _ {1 d-~2 (1 +~2)S, _ \ K2z~

ktotanO

"

(3) )½}]2 1

(3a) (3b)

PRACTICAL CONSIDERATIONS

As a float is approached, z (Fig. 1) decreases from a maximum (Zmax = 2Sy/CT) to zero at the fix. In our tests, Zmax was 3.05 cm for T = 1 s. Equation (1) is least sensitive to errors in measuring z when 0.5 < Z/Zma, < 0.7. In this range, an error of 0.3 mm in z introduced about 2.5~o error in d. The slope 0 or 01 is the basic measurement that leads to an estimate of v. Equation (2) shows v is independent o f d or to, provided to is large e n o u g h - - u n d e r these conditions one is measuring the slope of the asymptotes of the hyperbola. This suggests that tl in Fig. 1 should be as large as possible, but constant v over the time t is assumed, so there appears to be little point in taking tl too large. Actual fluctuations in v, particularly if the ship is encountering head seas, are believed to be the main source of error in the method. An overall accuracy of 10 to 15~o seems to be attainable. The quantity d in the above discussion is actually 'minimum slant range' from hydrophone to float. If the ship does not pass directly over the float an offset (x) should be

296

BRUCE V. HAMON

measured between signals from a port hydrophone and the corresponding starboard one immediately after the fix, and a corrected float depth dc should be calculated from dc ~ d( 1 - tx/xm)21 ~,

t4)

where xm is the maximum possible offset, xm Should be measured directly, (e.g., by steaming past a float soon after launching), rather than being calculated from the athwartship spacing between hydrophone cable attachments, because the cables are drawn together in the ship's wake. The VFO should be stable, preferably to ~ 1 in 10 5, once it has been set, and provision should be made to monitor its frequency to that accuracy to giver1. It is not necessary that the VFO be adjustable to better than 1 in 104. f0 needs to be known to the same accuracy as fl. f0 is best calculated from the frequency of the crystal in each float and the design parameters of the recorder.

REFERENCE SWALLOW J. C. and L. V. WORTHINGTON (1961) An observation of a deep counter-current. 1 19.

Deep-Sea Research, 8,