Langevin, M.

English

University of New Brunswick: Centre for Digital Scholarship Journals

ON THE ULTRA-SONIC MIRAGEbyM. L A N G E V IN , P r o f e s s o r  a t  t h e  C o l l e g e  d e  F r a n c e .The problem which I  have had the occasion to solve and about which I  would like  to say a few words, concerns one particular case of detection by echo by means of u ltra­sonic waves. The greater part of its interest lies in  the circum stances under which it came to m y notice.The particular case is that of the effects of mirage which occur during the propa­gation, in sea water, of sonic or ultra-sonic waves. You are aware that we use the echo method to detect the presence of obtacles and in  order to fix their positions. We emit, by means of a piezo-electric projector, a pencil of ultra-sonic waves which is nom inally rectilinear and which can be made as narrow as desired. The reflection of these waves by an obstacle gives rise to an echo which can be received by the em itting appliance acting as a receiver. The direction in  which this appliance is set determines the direc­tion of propagation of the pencil and, thus, gives the direction in  which the obstacle lies and, further, the time taken by the waves to go to the obstacle and return deter­mines the distance thereof. The very first trials and, moreover, other experiments in  submarine acoustics, show that serious error m ay be made if  the pencil be assumed to be projected in  a straight line. As a m atter of fact mirage effects come into action and thus deflect the general direction of the p e n cil; they are due to variations in  velocity of propagation in  the water from  one point to another. The velocity depends, in  fact, on temperature, salin ity and pressure and is particu larly affected by differences in  tempera­ture. In  pure water, at temperatures ranging from o° to 30° C. (32° to 8 i° F.), it  varies from 1400 to 1500 metres (4593 to 4921 feet) per second, and the variation per degree near o° C. (320 F .) is 1/300. These effects are such that the pencil, particularly  when its direction is near the horizontal, undergoes considerable deflection.As we go down from the surface, velocity of propagation is first reduced on account of the fact that the temperature of the medium is dim inishing with the depth, and velo­city varies with temperature. In  greater depths the influence of the increase of pressure, which dim inishes com pressibility and consequently increases the velocity, commences to take effect. The result is that, in  depths varying from 1000 to 2000 metres (3280 to 6560 feet) depending on local conditions, a minimum velocity is experienced. Down to 1000 metres there is usually a decrease in  velocity as the depth increases. This gives a downward deflection of sonic and ultra-sonic rays and this is due to an action the prin­ciple of which I  venture to recall to your memory, taking the particular case of a ray  or pencil which was originally horizontal.The waves corresponding to the ray or pencil m ay be considered as plane, w ithin  an area which is sm all with reference to their distance from the source, and these planes are vertical at the outset. As the upper part of these waves is propagated more rapidly  than the lower part, owing to the manner in  which velocity varies with depth, the direc­tion of the planes of the waves inclines gradually during the propagation, hence there is a downward deflection of the rays which represent the orthogonal trajectories of these wave planes.A  pencil, in  the form of a narrow cone, emitted horizontally thus gradually goes towards the bottom instead of running along parallel to the surface and, when the varia­tions of the temperature are somewhat rapid, some inconvenience results, as we have noted ever since we began experiments for the detection of an obstacle lying near the surface. The range obtained by the echo method varies according to circum stances and is greater in  the northern seas and in  the ocean, where there is a gentle gradient in  the temperature, than in  seas which have a higher surface temperature, such as the M editer­ranean.I  was led to examine the question more deeply and in  a more quantitative manner in  connection with the trials undertaken by M r. Georges C l a u d e  to determine the pro­file of the bottom in  the vicin ity  of H avana where he is now setting up a tube for the purpose of bringing cold water up from great depths.Mirage effects are not experienced when we are m aking a section of the bottom in  the usual manner by means of soundings obtained with vertical ultra-sonic pencils. The velocity of propagation, which is generally but a function of the depth, is  alw ays the same throughout the plane of the horizontal waves which occur in  a vertical pencil and thus, being sym etrically affected, this pencil is not deflected*The making of a series of vertical soundings along the line for which the profile of the bottom is required is done somewhat after the fashion of cartesian coordinates, i.e. the movement of the sounding vessel gives the abscissa and the observed depth gives the ordinate (see fig. 1).But this method is not suitable in  the case of a profile such as is shown in  fig. 2, which M r. C l a u d e  hoped to find in order to set up his tube in a boring through the earth into the sea, thus avoiding the movement near the surface of the water. Such profiles may be obtained, by a process which I  call that of “Polar Coordinates”, from  a fixed station of the vessel (0, fig. 2) by em itting an ultra-sonic pencil in  various direc­tions in  a vertical plane, beginning with the horizontal, and determ ining the radius vector OA  for each direction by the echo method, the vertical angle <p0 being given by  the inclination of the em itting appliance.We have constructed an apparatus which enables us to make the necessary changes in  inclination about a horizontal axis, but it is  necessary to go into the question of how  far the effects of mirage and of deflection of the pencil affect the application of this method, and as to how the necessary corrections can be applied in  the sim plest manner.The pencil being emitted in  an in itia l direction which lies at an angle <p0 to the horizontal and the observed interval until the echo returns being t and, further, the velocity of propagation at the surface, deduced from local temperature and salinity con­ditions, being represented by V0 the apparent distance I  to the point on the bottom  reached by the pencil is  :—2and the apparent position of this point is B  which lies in  the direction <p0 and at a distance OB =  I.The real trajectory of the pencil is, in  fact, a curve OA  deflected towards the bot­tom and tangent to the direction O B  at O. The fact that the velocity of propagation depends on depth only gives the result that the trajectory OA  of the pencil is a plane curve lying in the vertical plane which passes through OB. This plane is that of figure 3 which see.The problem consists in • determ ining the position of the true point of m pact A  from the apparent position B ,  taking into account the fact, which is evident from  the principle of the inverse return of rays, that the echo returns from A  to O along the curvilinear trajectory of the outgoing pencil but, of course, in  the opposite direction. It  w ill be seen that the mirage correction, which w ill give the true point of im pact A  fromthe apparent point of im pact B, m ay become very great under the ordinary conditions which are met with in . the ocean, p articularly when the pencil lies in  a direction which is not far from the horizontal or, in  other words, when the value of the angle q>0 is small.A fter various trials and some fa irly  complicated calculations I  have succeeded in  putting these corrections into the following form :—It  is essential that, in  the first place, the observers should ascertain the manner in  which the velocity, at the place where they are to work, varies as a function of the depth. They must take a series of soundings (in the case of M. C l a u d e ’s  experiments up to iooo or even 1500 metres) to determine how temperature and salinity vary with depth.A  form ula established by M r. E k m a n , the results of which are given in  num erical tables published by the B ritish Adm iralty, gives the variation in velocity V  as a func­tion of the depth z. The value of the index n — — ~  , of water of depth z in  ratio to sur­face water and then the value of the quantity e =  m2 —  1 as a function of z can be deduced therefrom for given serial values of z.This quantity e, which would be o if  the velocity were everywhere the same as at the surface, reached values which attained 0.1 in  the conditions under which the expe rim ents had to be made. In  fig. 3 erect the perpendiculars A P  and B Q  to the surface from the true and apparent points of im pact respectively. The perpendicular A P  cuts the apparent trajectory O B  at D . The position of point A  w ill be fixed if  we know the abscissa O P  =  x  and its ordinate P A  =  z. These quantities may be ascertained easily by means of the following form ulas :—(1 +  s) dz e +  sin* 90/dz. - _ = = .O y  e +  <Poto which the following may be added :—/e dz° y  s +  sm 2 <p0O Bv/OD  =D B- f ' w_  r* — _________J  0 \ /  6 +  sin2 <Poe -f- sin 2 <p0 e dzWhen e has been determined as a function of z these integrations m ay be carried  out ; however, the calculation m ay be replaced by a graphic method which is well-known,using, to calculate the quantity ------- , ., :... t a curve which applies to a ll cases, andy  e +  sin 2 <p0whose ordinate is equal to j L ' j ' as a function of the abscissa x .V  *It  is easy to obtain for the value 90, which corresponds to each experiment, the values of , 1 . which correspond to the various depths z for which the valuey  e|  sin2 <p0c is known by means of this curve.This makes the construction of the two curves (figs. 4 and 5) which give O B  / and O P  =■ x  as functions of z respectively, quite easy.In  the first curve the point on the ordinate I  w ill give the true depth z, and on the second curve the ordinate of the point on the abscissa z w ill be the true value of the horizontal distance x  at which the point A  lies.The application of this process consists, therefore :—1. In  determining, at the point selected as origin for the curves b y means of soun­dings, the value of e for the values of z at 100 metres apart, for example using tables sim ilar to those of the B ritish  A dm iralty ;2. In  utilizing the curve o f— , which applies to a ll cases, for carrying out theV *calculation (if desired graphically) of the integrals, which give I  and x  as functions of z for the values of <p0 at which the polar ordinates are to be found (e.g. every 50);3. As each echo experiment at a given angle <p0 results in  the determ ination of anapparent distance I —  —-— , in  deducing therefrom  the value of z by means of the curvewhich gives / as a function of z, and from this last quantity in  determ ining x  by means of the second series of curves.The application of these form ulas to the particular conditions which exist in  the v icin ity  of H avana showed me that, for distances of about I  =  1000 metres and with angles of from 50 to io°, the true depth m ight be doubled, by the m irage effect, in  relation to the apparent depth.It  is possible that these results m ay never be used, but I  thought it advisable  ^to point them out to you, first, in  order that the somewhat extensive calculations whichI  have made should not be done a ll over again, should such a case arise, and also because this work, which I  carried out owing to my friendship for M r. Georges^ C l a u d e , has given me the opportunity to be associated with you in  your work, for which I  am very pleased.B O B S

On the Ultra-Sonic Mirage

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On the Ultra-Sonic Mirage

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