`
`
`Ex. PGS 1032
`
`
`
`EX. PGS 1032
`
`
`
`
`
`

`

`United States Patent £19J
`Waters
`
`[ 11 1
`
`[451
`
`4,033,278
`July 5, 1977
`
`[75)
`
`(56]
`
`(54] APPARATUS FOR CONTROLLING
`LATERAL POSITIONING OF A MARINE
`SEISMIC CABLE
`Inventor: Ketllleth H. W•ten, Ponca City,
`Okla.
`·
`(73) Asaignee: CODthleai8J OU Compaay, Ponca
`City, Okla.
`Feb. 25, 1976
`[22] Filed:
`(21 1 Appl. No.: 661,065 ·
`[S2) U.S. Cl ............................. ... 114/245; 114/281;
`340/3 T; 340/7 PC
`lat. Ct.t ................... 8(;38 ll/56; 8638 17/00
`( 5 I ]
`[S8] Field of Seuch .......... 114/66.5 H, 121 , 235 8,
`114/236; 244/44, 123; 340/3 T, 7 PC
`Refereaces Cited
`UNITED STATES PATENTS
`4/ 1968
`3,375,800
`3/1969
`3,434,446
`3,611,975 10/1 971
`
`3,753,41 S
`
`8/1973 Burtis ................................ 114/1 26
`
`Primory Examiner-Stephen G. Kunin
`Attorney, Agent, or Firm-William J. Miller
`
`ABSTRACT
`(57)
`Apparatus for controlling the lateral position of a ma(cid:173)
`rine seismic cable relative to water current which is
`effective through utilization of one or more cable para(cid:173)
`vanes having a thrust adjustable hydrofoil and/or stabi(cid:173)
`lizer elements. The hydrofoil is constructed as a pivot(cid:173)
`ally supportable frame having an elastomeric skin
`which is supported on the sides of the hydrofoil by
`movable support members, and a servo-controlled re(cid:173)
`versible motor is controlled to reciprocate the opposite
`side support members relative to the hydrofoil longitu-
`. dinaJ center line. One or more hydrofoils may then be
`controlled as to angle of attack and camber from the
`towing ship by means of acoustic energy transmission
`and reception at the paravane.
`
`5 Ct.lms, 9 DnwiDa Flcures
`
`Cole et a1 ...................... 114/ 235 B
`Cole ............................... 114/235 B
`Ashbrook ...................... 114/235 B
`
`Ex. PGS 1032
`
`

`

`U.S. Patent
`
`July 5, 1977
`
`Sheet 1 of 4
`
`4,033,278
`
`----c: 18
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`
`Ex. PGS 1032
`
`

`

`U.S. Patent
`
`Julys, 1977
`
`Sheet 2 of 4
`
`4,033,278
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`Ex. PGS 1032
`
`

`

`U.S. Patent
`
`July 5, 1977
`
`Sheet 3 of 4
`
`4,033,278
`
`
`
`Ex. PGS 1032
`
`

`

`PULSE
`GEM€-RATOR
`
`132
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`DRIVE-R
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`DRIVE
`MOTOR
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`176
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`174
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`AMPL/r/1:-R
`
`DRIVE
`MOTOR
`
`Ex. PGS 1032
`
`

`

`2
`FIG. 5 is a top plan view of the para vane illusrated in
`FIG. 4;
`FIG. 6 is a vertical cross-section through a hydrofoil
`constructed in accordance with the present invention;
`FIG. 7 is a cross-sectional view through a hydrofoil
`constructed in accordance with the present invention;
`FIG. 8 is a partial section of the paravane frame of
`FIG. 4 showing a hydrofoil rotating control assembly;
`and
`FIG. 9 is a block diagram of one form of remote
`control circuitry which may be utilized in the present
`invention.
`
`I
`
`4,033,278
`
`APPARATUS FOR CONTROLLING LATERAL
`POSITIONING OF A MARINE SEISMIC CABLE
`
`5
`
`BACKGROUND OF THE INVENTION
`1. Field of the Invention
`The invention relates generally to marine seismic
`cable control practice and, more particularly, but not
`by way of limitation, it relates .to improved para vane
`and hydrofoil apparatus which is remotely controllable I 0
`as to lateral thrust.
`2. Description of the Prior Art
`The prior art now includes numerous types of seismic
`cable para vanes which are utilized for controlling cable
`depth and such paravanes are particularly character- 15
`ized by the teachings of U.S. Pat. Nos. 3,434,446;
`3,531,761 and 3,531,762. Still other depth-controlling
`paravanes are existent in the prior art and in large part
`these teachings depend upon particular guidance and
`control structure for their novelty. Lateral cable guid- 20
`ance by paravanes in the old and well-known mine
`sweeping tradition is also utilized in seismic practice
`and this method is particularly shown in U.S. Pat. No.
`3,581 ,273. Actual guidance both vertically and hori(cid:173)
`zontally is taught in U.S. Pat. No. 3,605,674 wherein 25
`remotely controllable D-C motors are utilized to rotate
`guidance vanes to control paravane and cable attitude
`both laterally and vertically.
`
`DETAILED DESCRIPTION OF THE INVENTION
`FIG. 1 illustrates the problem encountered with tow(cid:173)
`ing a marine seismic cable in cross currents of any
`magnitude. Thus, a tow vessel 10 towing streamer or
`cable 12 along the designated course 14 is very much
`hampered by a cross current 16. The cross current 16
`tends to carry cable 12 to a considerable starboard
`quarter angle and, in turn, causes tow vessel 10 to crab
`to a bow angle oriented along line 18. Vessel 10, in
`attempting to proceed along designated course 14,
`must proceed with increased resistance under rudder
`strain, and it is difficult to chart received seismic data
`which must be correlated and recorded with respect to
`designated course line 14.
`FIG. 2 then illustrates the manner in which a plurality
`of para vanes 20, as constructed in accordance with the
`30 present invention, function to maintain cable 12 in
`proper alignment along the survey line or designated
`course 14 despite the cross current 16. As depicted,
`each of the paravanes 20 are illustrated as a single
`hydrofoil having greater camber placed on the port
`35 surface thereby to exert portside thrust and to maintain
`cable 12 linearly along the designated course 14. As
`will be further discussed below, the amount and direc(cid:173)
`tion of camber of the hydrofoil elements of each para(cid:173)
`vane are remotely controllable such that amount and
`40 direction of sideward thrust may be continually con(cid:173)
`trolled from aboard the tow vessel 10.
`FIG. 3 illustrates in schematic form one scheme
`wherein paravane 20 may be controlled from the two
`vessel 10. This is simply a scheme whereby two ship-
`45 board energy transmitters 22 and 24 are controlled to
`transmit energy patterns having the requisite control
`modulations but which energy enjoys diversity and
`dependence through frequency differentiation, pulse
`modulation techniques, timed firing, or such other
`50 modes as are generally recognized as providing multi(cid:173)
`ple operation transmission differentiation. It is pres(cid:173)
`ently proposed that sonar energy transmission of two
`different frequencies be utilized with dual frequency
`magnetostrictive or piezoelectric reception at the para-
`55 vane 20. The dual frequency transmissions are alter(cid:173)
`nately emitted to enable parallactic control, and the
`transmission frequencies fa and f2 should be selected in
`approximate frequency range and frequency difference
`such that there will be no harmonic interference as
`60 between frequencies fa and f2 , and little or no effect
`relative to the hydrophone reception of desirable seis(cid:173)
`mic energy reflection signals. Thus, selected frequen(cid:173)
`cies in the range between 25 and 30 kilocycles will
`provide good paravane control transmission.
`FIG. 4 illustrates a paravane 20 in greater detail as it
`is shown supporting cable 12 within a body of water 26.
`Paravane 20 is attached to cable 12 by means of a pair
`of spaced cable clamps 28 which are securely affixed in
`
`SUMMARY OF THE INVENTION
`The present invention contemplates a marine seismic
`cable control system wherein signals transmitted from
`the towing ship are received and utilized at one or more
`cable-controlling paravanes to effect variation of the
`attack angle and lift thrust of the paravane hydrofoils
`thereby to vary and control lateral positioning of the
`towed cable. The hydrofoils are constructed for pivotal
`support and are controllably pivotable and deformable
`in their transverse dimension so that the arcuate side
`surfaces can be reciprocally varied to alter the camber
`and lift thrust.
`Therefore, it is an object of the present invention to
`provide an improved method for lateral positioning of a
`seismic cable under tow.
`It is also an object of the invention to provide a para(cid:173)
`vane apparatus having remotely controlled hydrofoil
`elements with variable angle of attack and lift thrust to
`effect lateral positioning.
`Finally, it is an object of the present invention to
`provide a remotely controllable hydrofoil element
`which is readily variable as to its horizontal cross-sec(cid:173)
`tional configuration thereby to vary the lift thrust force
`exertion upon movement through water.
`Other objects and advantages of the invention will be
`evident from the following detailed description when
`read in conjunction with the accompanying drawings
`which illustrate the invention.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`FIG. 1 is a schematic representation of a seismic
`cable under tow and the effects of lateral current;
`FIG. 2 illustrates the present invention while effect(cid:173)
`ing desirable correction to the two attitude of the seis(cid:173)
`mic cable;
`FIG. 3 is a schematic showing of one form of control 65
`method of the present invention;
`FIG. 4 is an elevational showing of a para vane con(cid:173)
`structed in accordance with the present invention;
`
`
`
`Ex. PGS 1032
`
`

`

`30
`
`3
`Jsition on cable 12 and detached to elastomeric sup(cid:173)
`ort cables 30 and 32 which attach to a securing eye 34
`s integrally formed with lower hydrofoil 36 of para(cid:173)
`ane 20. An upper hydrofoil 38 also includes an inte(cid:173)
`rally formed securing eye 40 for attachment to a lead 5
`ne 42 which, in turn, is secured to a float indicator 44
`t the surface ofthe body of water 26. The float indica-
`)f 44 constitutes a surface buoy which functions not
`nly to suspend cable 12 from the surface of water 26
`ut also to provide visual indication of the cable posi- 10
`.on for shipboard observance. Adjustment of the
`mgth of lead line 42 in accordance with proposed ship
`~eed will then provide control of the depth of cable 12
`uring sounding operations.
`The paravane 20 is comprised of a central body or 15
`rame member 46 which may be planar in character
`1hile providing interior space for storage and dispo(cid:173)
`ition of electronic circuitry and other auxiliary devices
`.swill be further described. The remainder of the inter-
`Jr is filled with non-conductive fluid medium which is 20
`,djusted in well-known manner to achieve requisite
`tUoyancy characteristics. The upper and lower hydro(cid:173)
`oils 38 and 36 are each attached to a shaft 48 which is
`otatably supported through the center of frame 46 at
`ts forward end, as will be further described below. The 25
`.haft 48 is constructed to have a central bore through
`vhich wiring can be run as between hydrofoils 36 and
`~8 and frame 46. Upper and lower stabilizers 50 and 52
`tre supported on a shaft 54 which may be secured in
`'ixed position through the center of frame 46 at its
`:railing end.
`FIG. 5 illustrates the para vane 20 in top view with
`lydrofoi138 shown in the position of starboard camber,
`lS will be further described. Referring again to FIG. 4, 35
`.veight such as predetermined amounts of lead ballast-
`tng may be added in lower hydrofoil 36 in the area
`generally shown by dash line 56 and, in like manner as
`frame 46, the interior of all stabilizer and hydrofoil
`elements are filled with a non-conducting fluid to allow 40
`control over buoyancy of paravane 20. Such practice
`also serves to reduce overall impedance contrast of
`paravane 20 such that scattering of reflected seismic
`waves from "bladder effect" is minimized.
`Referring now to FIG. 6, a hydrofoil element, in this 45
`case upper hydrofoil 38, is constructed in a manner
`which allows transverse deformability of the side sur(cid:173)
`faces such that adjustable camber is effected thereby to
`vary the transverse thrust of the hydrofoil upon move(cid:173)
`ment through water. The basic frame of hydrofoil 38 50
`consists of the leading edge circle as formed by an
`arcuate forward frame tube 60, see also FIG. 7 which
`illustrates the approximate degree of arc. A longitudi-
`nal frame 62 having aT-head 64 is secured to the for(cid:173)
`ward frame 60 by affixure of the T-head 64 within the 55
`inner arcuate surface of forward frame 60. The oppo(cid:173)
`site end of frame member 62 is then secured by welding
`or bonding, depending upon structural materials, to the
`trailing edge frame 66, a generally triangular block
`form having the trailing or outer edge conformed for 60
`least water resistance. A generally arcuate frame rib 68
`is then rigidly secured between the upper leading por(cid:173)
`tion of forward frame 60 and the upper leading portion
`of trailing edge frame 66 to complete the structural
`unit. As shown in FIG. 6, forward frame 60, rib frame 65
`68 and trailing edge frame 66, as formed constitute a
`streamlined outline offering optimum hydrofoil advan(cid:173)
`tages.
`
`4,033,278
`
`4
`Yet another T -bar or upper frame 70 having T -head
`72 is utilized to provide structural rigidity. Thus, T(cid:173)
`head 72 is also rigidly secured within the inner circum(cid:173)
`fery offorward frame 60 while the trailing end of upper
`frame 70 is secured as by welding or bonding to the
`upper extremities of trailing edge frames 66. An inter(cid:173)
`mediate support bar 74 is vertically disposed and se(cid:173)
`curely affixed between the upper surface of frame 62
`and the lowr surface of upper frame 70, and support
`bar 74 retains a thrust assembly 76 therein, such thrust
`assembly 76 to be further described in detail.
`The entire outer skin of hydrofoil 38 consists of an
`elastomeric material covering 78, e.g. rubber, which
`serves both to seal the hydrofoil unit and to enable
`deformable changes in transverse cross-section. The
`side surfaces of the resilient covering 78 are strength(cid:173)
`ened by a series of vertically aligned stiffeners or plates
`as bonded or otherwise affixed to the inner surface of
`covering 78. Thus, forward plates 80, middle plates 82
`and rear plates 84 are bonded to the inner surface of
`covering 78 on each side, each plate being shaped for
`optimum hydrofoil configuration, and the stiffening
`plates maintain the transverse cross-section of the hy(cid:173)
`drofoil in a predetermined shape as controlled by the
`screw jack assembly 76.
`Screw jack assembly 76 consists of a thrust screw 86
`which is securely retained by a suitable captive fixture,
`welding or the like between the opposing midplates 82,
`while extending through a drive nut 88 having a drive
`gear 90 integrally formed around one edge thereof. The
`drive nut 88 is then rotatably secured through support
`bar 74 by means of a suitable form of bearing member
`92. The gear 90 is then engaged by a worm gear 92
`which transmits output rotation from a motor 94 to
`rotate drive nut 88 thereby to vary relative positioning
`of side plates 82 with respect to support bar 74. The
`motor 96 is preferably one of the well-known commer(cid:173)
`cially available D-C reversible electric motors having
`selected size and power rating.
`A sonar receiver 100 may be mounted on the T-head
`64 of frame 62 in suitable manner to extend a trans(cid:173)
`ducer 102 for rigid affixure through a front bore 104 in
`forward frame 60 so that the forward surface of trans(cid:173)
`ducer 102 is energy coupled through covering 78 to
`surrounding water. Spaces shown as dash lines 106 may
`be utilized for placement of electronic circuitry and the
`D-C power source, e.g. a conventional form of battery
`having the requisite power rating. Associated wire in(cid:173)
`terconnection as between hydrofoils 36 and 38 and/or
`main frame 46 may be run through a central bore
`formed within shaft 48, and the entire interior of the
`hydrofoil is then filled with a non-conductive fluid for
`purposes of buoyancy regulation; except, in the case of
`the lower hydrofoil 36, a selected amount of ballasting
`weight such as lead will be formed along the rib frame
`68 within the confines of dash-line 58. (See FIG. 4).
`The control circuitry as contained in upper hydrofoil
`38 may also be utilized to effect attack angle and cam(cid:173)
`ber control of lower hydrofoil 36.
`The above-recited hydrofoil structure includes motor
`96 for enabling energization of screw jack assembly 76
`to vary the camber and direction of camber of the
`hydrofoil; however, it is also contemplated that con(cid:173)
`trolled movement of shaft 48 be exercised in order to
`alter the angle of attack of hydrofoils 36 and 38 thereby
`to enable still more rapid change of position of para(cid:173)
`vane 20. As shown in FIG. 8, the drive assembly in(cid:173)
`stalled within the forward end of main frame 46 may be
`
`
`
`Ex. PGS 1032
`
`

`

`4,033,278
`
`5
`6
`conjunction with the respective drive motors 96 and
`utilized to apply controlled rotation to hydrofoil shaft
`122 in response to control input and position reference
`48. The shaft 48 is rotationally disposed through main
`as supplied by links 186 and 188, respectively.
`frame 46 as supported by suitable bearing members
`It is preferable that control amplifier circuits 180 and
`108 and 110. A beveled gear I 12 is then affixed as by
`include pulse
`time discrimination circuitry
`welding or the like to the central portion of shaft 48, 5 182
`and only a sector 114 need be toothed between op-
`whereby control of drive motor 96 is effected in accor-
`posed stops 116 for engagement with a bevel drive gear
`dance with received pulse time differential to maintain
`118. Bevel drive gear 118 is then powered by a shaft
`automatically the trailing position of cable 12 as pre-
`120 and a D-C reversible electric motor 122 as ener-
`designated. That is, if ship board delay networks 138
`gized by leads 124 which lead to a power source, e.g. a 10 and I40 are set equal, with no time delay between pulse
`outputs of sonar transducers 132 and 134, the paravane
`D-C battery in space 106 of hydrofoil38. A small bore
`126 will allow entry of conductors 124 to be led
`receiver circuitry will respond by servo controlling the
`through the inner bore of shaft 48 and to the interior of
`para vanes to maintain the pre-set aft positioning. Like-
`hydrofoils 36 and 38.
`wise, if delay is interposed utilizing delay networks 138
`FIG. 9 illustrates a basic form of electronic control 15 and I40 and cable 12 may be controlled to maintain a
`laterally offset trailing position as might be utilized with
`system which may be utilized in the present invention.
`For example, the system may utilize one or more sonar
`a multicable array trailing from a single vessel. The
`frequency transducers aboard the two vessel; and with
`shipboard control of the paravane 20 would primarily
`reception of one or more differentiated frequency
`consist of coarse and fine control through respective
`acoustic energy signals at the paravane for subsequent 20 hydrofoil rotation drive motor 122 and camber control
`drive motor 96.
`control of hydrofoil rotation and/or hydrofoil camber
`control. Various forms of such control systems have
`It is also contemplated to utilize a transponder type
`been utilized in the past for remote control of para-
`of control circuit aboard the para vane whereby deter-
`minative acoustic signals are either reflected or re-
`vanes and such control circuitry alone constitutes no
`part of the present invention. For example, U.S. Pat. 25 transmitted from the paravane back to the two vessel
`No. 3,412,704 in the name of Buller, et al discloses one
`IO thereby to enable further control and indication.
`form of frequency responsive transmission system for
`That is, such returned signal energy can be processed
`maintaining a cable depth controller. Also. U.S. Pat.
`and utilized aboard the two vessel 10 to provide signal
`No. 3,434,446 in the name of Cole discloses yet an-
`input to an analog or digital computer which will en-
`other form of frequency responsive transmission sys- 30 able calculation and display of the paravane position
`relative to the ship's path. Yet further calculations may
`tern for effecting predetermined paravane control.
`A transmitting system I30 consists of a pair of sonar
`be enabled, e.g., true geographic position of the para-
`transducers 132 and 134 as energized in conventional
`vanes can be made if additional inputs from the ship-
`manner and operated in tandem from each side of the
`board electronic positioning system and attendant
`two vessel IO. The pulse generator 136 provides basic 35 servo compass equipment are provided.
`The foregoing discloses a novel marine seismic cable
`repetition rate control, as further controlled by delay
`control paravane having unique capabilities of auto-
`networks 138 and 140 for input to respective modula-
`tors 142 and 144. Modulator 142 also receives master
`matic lateral positioning control. Such control is en-
`oscillator input at two selected frequencies, e.g. fre-
`abled through utilization of two degrees of variation of
`quencies/1 and/3 from oscillators 146 and 148 where- 40 the vertical hydrofoil elements. That is, the vertical
`upon output from modulator 142 is supplied to a driver
`hydrofoils may be controlled as to angular rotation for
`150 which energizes the sonar transducer 132. In a like
`course control of the paravanes, as operated in tandem
`manner, the oscillators 152 and 154 provide frequen-
`if plural paravanes are utilized, and yet a further mode
`cies / 1 and / 4 as input to modulator I44 which, in tum,
`of position-keeping is enabled by remote adjustment of
`energizes driver 156 and sonar transducer I34. The 45 the camber of the hydrofoil element or elements of one
`or more paravanes. Thus, not only can hydrofoil angle
`sonar transducers I32 and 134 may be any of the con-
`ventional types, i.e., magnetostrictive, piezoelectric or
`of attack be varied, but the amount of lateral thrust can
`the like.
`also be varied for position-keeping. It is contemplated
`Acoustic energy transmitted from transducers 132
`that automatic control be utilized whereby course or
`and 134 is then detected by counterpart, frequency 50 rapid cable positioning can be effected by altering by-
`drofoil angle of attack, and desired position can then be
`selective magnetostrictive or piezoelectric elements at
`a sonar receiver 160 whereupon received energy is
`kept by adjusting the direction and amount of camber
`amplified in conventional manner. Output 162 is then
`of the hydrofoil elements on one or more paravanes.
`applied to a bank of filter-detectors which are charac-
`Changes may be made in the combination and ar-
`teristically designed to fdter their designated frequen- 55 rangement of elements as heretofore set forth in the
`specification and shown in the drawings; it being under-
`cies of electrical energy with subsequent detection for
`stood that changes may be made in the embodiments
`output via respective lines 172, 174, I 76 and 178. The
`output on leads 174 and 178 are then applied in known
`disclosed without departing from the spirit and scope of
`manner to a control amplifier 180 which energizes the
`the invention as defined in the following claims.
`camber control drive motor 96 in accordance with 60 What is claimed is:
`signal input. Detected output on leads I72 and 176 is
`1. A paravane apparatus for controlling depth and
`similarly applied to a control amplifier 182 in order to
`lateral positioning of a marine seismic cable, compris-
`effect control of the hydrofoil rotation drive motor
`ing:
`122. Similar control circuits, motors and transducer
`elongated frame means including a stabilizer element
`response elements may be included on any number of 65
`at one end thereof;
`paravanes that are in operation.
`means resiliently attaching said paravane to said rna-
`rine seismic cable to support said cable at a prese-
`The control amplifiers 180 and 182 may constitute
`any of well-known servo control circuits operating in
`lected depth; at least one hydrofoil means rotatably
`
`
`
`Ex. PGS 1032
`
`

`

`7
`attached to and extending vertically from said
`frame means at the other end thereof; and
`means controllable to vary the camber and direction
`of camber of said hydrofoil means including:
`a first motor and gear linkage actuatable to rotate S
`said hydrofoil means;
`a second motor and gear linkage actuatable to vary
`said camber and direction of camber of said hydro(cid:173)
`foil means; and
`electronic circuit means for selectively engaging said I 0
`first and second motors to effect lateral positioning
`of the seismic cable.
`2. Apparatus as set forth in claim 1 wherein said
`electronic circuit means is a remotely controllable
`transmission and reception device.
`3. In a paravane which includes controllable ele(cid:173)
`ments for maintaining lateral positioning of a marine
`seismic cable, said paravane having a frame portion
`resiliently supporting said cable in water with at least
`one hydrofoil extending from said frame means, an
`improved hydrofoil comprising:
`frame means rigidly defining the peripheral shape of
`said hydrofoil means;
`resilient skin material completely covering said frame
`means;
`
`8
`a plurality of rigid plates bonded to the inside of said
`resilient skin means on each side of the hydrofoil
`means which are independently movable relative to
`said frame means; and
`a screw jack assembly affixed between opposite side
`plates and being movably affixed relative to said
`frame means such that said screw jack assembly
`functions to vary the camber and direction of cam(cid:173)
`ber of said hydrofoil.
`4. An improved hydrofoil as set forth in claim 3
`wherein said frame means comprises:
`a longitudinal base frame affixed to an arcuate for-
`ward support frame defining the leading-edge cir(cid:173)
`cle which, in tum, is secured to an arcuate rib
`frame that is secured to a trailing edge frame mem(cid:173)
`ber as affixed to the remaining end of said longitu-
`dinal base frame thereby to define said peripheral
`shape.
`5. An improved hydrofoil as set forth in claim 3
`20 which is further characterized to include:
`electrical motor means supported by said frame
`means and energizable to actuate said screw jack
`assembly thereby to enable selective variation of
`said hydrofoil camber.
`• • * • •
`
`15
`
`4,033,278
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`
`
`Ex. PGS 1032
`
`