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NAVY DEPARTMENT
THE DAVID W. TAYLOR MODEL BASIN

WASHINGTON 7, D.C.

October 1953 Report 859

AN ELECTRONIC WAVE-HEIGHT MEASURING APPARATUS

W.S. Campbell

October 1953 Report 859

NP21-50845

Wave-Height Measuring Apparatus

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TABLE OF CONTENTS

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APPENDIX
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ERRATA SHEET
for
DAVID TAYLOR MODEL BASIN REPORT 859

In Figure 4, page 7, the three transformers Shown in the semigne ampli-
fier portion of the schematic diagram are identical. Cores should be shown
in all three. They are manufactured by the Audio Bevotopient Company as
their type A-5511.

NOTE: See Figure 4, page 7. In later models of the instrument all the
calibrating capacitors shown as 17, 36, 64 ......-. 114 uufd, were not in-
cluded. Only one, the 106 uufd capacitor was permanently connected to the
calibrating switch, thereby providing an easy means of checking the opera-
tion of the instrument. Calibration is accomplished by actually moving the
transducer up and then down in the water. The extra switch section which
was required for the calibrating capacitors is not used.

In Figure 5, page 8, the rectifier tube is erroneously shown as a type
6AS7; actually, two type 5U4 tubes, each with their plates connected in par- ~
allel, are used.

In Figure 5, both output tubes in the amplifier circuit are type 6V6,
although only one is so indicated.

ABSTRACT

This report describes briefly the salient features of new instrumentation
for measuring and recording the wave amplitudes and wave forms of water waves.
This instrumentation was developed by the Electronic Circuit Development Branch*
of the Electronic Engineering Division of the David Taylor Model Basin, at the re-
quest of the Hydromechanics Laboratory. Because of the increased accuracy and
flexibility afforded by the instrumentation described, it has replaced other tech-
niques which were formerly used.

The gaging element of this system consists of extremely small insulated
wire, suspended rigidly upright in the water. The conductor acts as one plate of
a capacitor and the water in which the gaging element is partially submerged acts
as the other; the insulation material on the wire forms the dielectric of the capac-
itor. The capacity of this ‘‘condenser’’ (measured between the conductor and
water) is directly proportional to the linear length of the submerged portion of
the wire. This capacitor is connected in one arm of a resonant-bridge circuit,
which may be.balanced for the quiescent level of the water. Variations in water
height which occur as waves pass the gaging element produce capacitive unbal-
ance of the a-c bridge in each sense, and the direction of unbalance is recovered
by a more or less conventional phase sensitive demodulator circuit incorporated
in the circuit of the wave-height recorder.

This report includes schematic wiring diagrams of the instrument, its
power supply, and a direct-coupled amplifier suitable for driving the recording

galvanometer in a Sanborn direct-writing recorder.

INTRODUCTION

For the accurate measurement of small amplitude water waves, it is, of course, desir-
able to use a gaging element whose presence will least affect the height or form of the wave;
ideally, measurement of amplitude should be made at one very small point or along an imagi-
nary vertical line, normal to the still surface of the water. One previously used technique
for measuring wave height and profile at the David Taylor Model Basin was to photograph a
grid alongside the basin wall. It was found that small imperfections along the wall or even the
engraved grid lines created a considerable adverse effect on the shape of the wave. Moreover
because of viscosity and surface tension effects in the proximity of the wall, it was found
highly desirable to measure wave profile at some distance from the wall. A further disadvan-
tage of the photographic method is the necessity for development of the film, which requires

considerable time, and, at best, one obtains only the amplitude and profile of one particular

*Now the Metric Systems Branch of the Instrumentation Division.

wave. In the adjustment of water-wave generators it is advantageous to be able to observe
the effect of various adjustments on a direct-writing recorder which is producing a continuing
record of each wave as it passes the measurement point. A still further disadvantage of the
photographic method lies in the relative difficulty of moving the measurement point out near
the center of the basin or to other points along the length of the basin at which measurements
are required.

On 18 January 1952, the Electronics Engineering Division received a request from the
Hydromechanics Laboratory to develop reliable instrumentation of this type which preferably
should possess none of the disadvantages met in the application of photographic methods then
in use. The following performance requirements were stated in lieu of specifications:

The instrumentation should be capable of measuring and recording amplitudes of water
waves in the range of 0 to a maximum of 2 ft; the lengths of the waves to be recorded lie with-
in the range of 2 ft to 30 ft, with corresponding periods of 0.564 to 2.43 sec; frequency re-
sponse should be such as to show no more than +1 percent variation in amplitude from 0 to
at least 2 cps. A maximum error of 1/4 in. in 2 ft of wave height was to be allowable.

A study of various techniques employed at other laboratories engaged in work of the
same general nature was made.!*? All systems investigated by the author were found unsatis-
factory for this particular purpose because of their inability to satisfy the accuracy and fre-
quency-response requirements or their dependence on the chemical composition of the water.
Float systems usually fail to respond rapidly enough to ‘‘follow’’ rise and fall of extremely
short waves due to the inertia of the float or the friction or mass of the pickup unit attached;
moreover it is difficult to design a float which will approach, dimensionally, the requirement
for measuring the wave height at a single point. Systems which depend on the variation of
electrical resistance between two probes immersed in the water approach the dimensional re-
quirement but suffer from their dependence on the mineral content of the water, corrosion, or
oxidation of the probes and cleanliness of the water surface.

The capacitive -wire gage system described herein meets or exceeds all the require-
ments and avoids the difficulties stated in the preceding paragraph; further advantages which
influenced the choice of this system over the many other types of systems in current use
included the fact that there are no critical tolerances or spacing adjustments, it has excellent

linearity characteristics, is easily cleaned or replaced, and is inexpensive.

MEASUREMENT SYSTEM

The measurement system described in this report is known at the Taylor Model Basin
as the type 145-A Dynamic Wave-Height Recorder. For discussion, it may be divided into
three major functional parts--the gaging element, the electronic circuitry, and the direct-

writing recorder. (See the semi-pictorial sketch, Figure 1). The principle of operation may

tReferences are listed on page 13.

DC Amplifier
and
Power Supply

Model 60
Sanborn
Recorder

Figure 1 - Functional Block Diagram of Apparatus

be described briefly as follows:

The rise and fall of the water level in which the gaging element has been immersed
produces very nearly linear changes of electrical capacitance as measured between the two
terminals of the gage; the gage forms a small part of a larger fixed capacitor which is one
arm of a resonant a-c bridge. These relatively small capacitance changes produce output
voltages from the bridge which are proportional in amplitude and phase, to the degree and
sense of the bridge unbalance. These voltages are amplified and demodulated in a linear
phase sensitive detector which produces a d-c voltage proportional to the height of the water
surface as measured from the water level at which the bridge was first balanced (usually the
quiescent water level before waves were generated). This varying d-c voltage is then further
amplified and furnishes the driving power required for the direct-writing recorder. Each of
the three units so briefly referred to above are described in greater details in the following

paragraphs.

GAGING ELEMENT

Probably the most interesting part of the system is the gaging element itself. It con-
sists simply of a length of No, 28 enamel covered copper magnet wire stretched tightly be-
tween two support points, one below the water surface and the other located an equal distance

above the surface on a vertical line running through the lower point. The distance between

== ~— Cable to Instrument these two support points may be about twice
the expected double peak amplitude of the
largest wave to be measured, This wire is
completely insulated from any electrical con-
tact with the water. One type of suitable gage

support bracket is shown on the sketch, Figure

Number 28E

nBer 2. The J-shaped support bracket is fabricated

from a length of 1/4-in. brass rod. The lower
Water Surface Dory Mees pid : :
end of the gaging wire is fitted with an insula-
tor coupling which plugs into a small bayonet-
type socket, an integral part of the lower end
Wave Motion
of the bent brass rod. The upper end of the
wire is fastened, electrically and mechanically,
to a 2-pin cable connector mounted on the upper
Figure 2 - Sketch of Gage and support member. The connecting cable (any
Support Bracket reasonable length of high-quality, low-capacity
cable such as Amphenol RG-62U) is fitted with a connector in such a manner that the “‘high”’

’? shield side makes electrical con-

side contacts the conductor in the gage wire and the “‘low
tact with the water through the upper support arm and the J-shaped brass rod. A tensile pull
of about 3 pounds has been found sufficient to maintain the wire taut and straight under all
conditions encountered in tests so far conducted.

Electrically, the conductor of the gaging element and the water in which it is immersed
form two plates of a coaxial capacitor. Measurements made with the General Radio precision
capacitance bridge indicate that the capacity of this unique condenser varies linearly with the
length of submerged portion of the gage wire. This is not surprising since the wire diameter
is very closely controlled by the manufacturer and the thickness of the enamel insulation is
very nearly uniform. The power factor of the gage in the water is exceptionally good espe-
cially if at least 4 in. of the wire are always wetted. No appreciable difficulty has been ob-
served from meniscus or flowback effects, and static peak-to-peak calibrations obtained by
physically moving the gage element up and down in the water hold equally well for dynamic
conditions.

The choice of gaging wire size was made by use of experimental methods to determine
the degree of error encountered under dynamic conditions; the use of very large wire, rod, or
tubing, which might seem desirable from the support problem viewpoint, is precluded by sur-
face tension and slow flowback effects when the water recedes. The No. 28 enameled copper
wire appeared to be about the optimum since the capacity changes follow wave-height varia-
tions up to at least 4 cps with negligible phase error, and yet it can be put under sufficient

tension to avoid bending by the advancing waves.

ELECTRONIC SYSTEM

The electronic apparatus is required to transform the changes in capacitance which
appear in the gaging element into proportional current or voltage variations to drive the recor-
der. The equipment as designed provides a sensitivity range of 0.60 to 25.0 in. (trough to ©
crest wave amplitude) for full-scale (80-mm) recorder deflection. A precision attenuator is
built in which allows selection of 10 fixed sensitivity positions--0.60, 1.0, 1.5, 2.5, 4.0, 6.0,
10, 15, 25, and 40-in. peak-to-peak amplitude for full-scale recorder deflection. Calibration
is accomplished by switching the calibrating condensors which are chosen by the setting of
the attenuator first to one side of the bridge and then to the other. This simulates equal in-
cremental variations in water level about the zero reference point, i.e., the water level at
which the bridge was initially balanced by the operator.

The circuits employed are a modification and adaptation of those employed in the reso-
nant-bridge carrier system which has been used for some time for the measurement of extreme-
ly small changes in capacitance.* The system consists of a doubly resonant capacitance
bridge which is driven by the output of a 10-ke oscillator-amplifier circuit, an attenuator, a
2-stage voltage amplifier and a dual demodulator, the output of which is a d-c voltage whose
magnitude and polarity are proportional to height of the water surface from any arbitrary zero
point chosen by the operator (usually, but not necessarily, the quiescent water level in the
avsence of waves). A block diagram of the complete system is shown in Figure 3. The 10-kc
oscillator-amplifier circuit (block 1) supplies the excitation to the resonant bridge (block 2)

which incorporates provision for manually balancing out the resistive and reactive components

10 ke

Voltage Null Sanborn
Amplifier Detector Recorder

Oscillator and
Power Amplifier

| 6
: Resonant Direct
ee Capacitive Attenuator Demodulator Coupled
Bridge Amplifier
3 2 4 t 8

Figure 3 - Block Diagram of the Type 145-A Dynamic Wave-Height Recording System

of gaging-element impedance which is connected in parallel with one arm of the bridge. Drive
voltage is applied to the bridge from a balanced source, which permits grounding (earthing)
of one of the bridge terminals which is also connected through a cable (RG-62U) to the ground
side of the gaging element, (see Figure 2). This is a necessary condition since the body of
water in which the gaging element is to be submerged is used as the ground reference potential
point for the entire system. Unbalance voltages arising at the opposite terminal of this bridge,
which is initially manually balanced for still-water conditions, are applied to the attenuator
(block 4) and thence to the voltage amplifier and demodulator circuits (blocks 5 and 7). The
null indicator (block 6) is employed in order to ascertain when bridge balance has veen achiev-
ed. The output of the demodulator circuit is a d-c voltage which varies from 0 to 2 volts in
either polarity as a linear function of water height. The output impedance at this point is
quite high and should not be loaded heavily in the interest of linearity. Since very little
power can be drawn from this circuit, a direct-coupled power amplifier (block 8) is designed
to match the particular recorder chosen (block 9). Any desired recorder could, of course, be
used provided that a suitable power-amplifier circuit is substituted.

Copies of the final schematic wiring diagrams of the gage control unit and the power

supply-amplifier unit are included as Figure 4 and Figure 5, respectively.

RECORDER

The instrument described in this report is designed particularly for use with the San-
born* Model 60 direct-writing electromagnetic recorder. (This model is a two-channel unit,
which is used in those measurements where waves are to be measured at two points simultan-
eously.) This recorder is equipped with heated stylii and records on heat-sensitive paper.
Frequency response is uniform to about 40 cps, which is far more than adequate for this ap-
plication. The galvanometers (pen motors) are rugged and reliable, and, except for some
slight mechanical hysterisis which amounts to approximately 0.25 mm on the record, the re-
corder is quite satisfactory. With the amplifier shown in the schematic diagram, Figure 5,
full-scale deflections of +2 cm from the center can be obtained with good linearity. One
great advantage realized by use of this recorder is the rectilinear recording feature which
facilitates analysis of recorded wave forms. A wide range of paper speeds is made available
by changing gears in the chart drive mechanism; in addition a quick shift ratio of 10 to 1 may

be accomplished by a small lever located on the control panel.

*Manufactured by the Sanborn Company, Cambridge 39, Mass.

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Figure 5 - Schematic Wiring Diagram of the Power Supply-Amplifier Unit
of the Type 145-A Dynamic Wave-Height Recorder

OPERATION

For operation the instrument may be powered from any source of 115-volt, 60-cycle,
single-phase voltage capable of furnishing at least 300 watts of power. The gaging element
should be mounted on a rigid support in such a manner that approximately half the length of
the insulated wire is submerged. One such support designed for use at the Model Basin is
equipped with a fine screw adjustment by which the gaging element can be raised or lowered
in the water. This permits a simple and direct means of calibrating the entire system. After
the instrument has been turned on for about five minutes or more and the gaging wire has been
placed at the desired point, the operator may proceed to balance the bridge by means of the
controls provided for this purpose. Bridge balance is obtained in the usual manner prescribed

for balancing a-c bridges, utilizing the null indicator meter deflections as a guide. Maximum

deflection of this meter obtainable by adjustment of the decade capacitor and resistance bal-
ance controls indicates that the bridge is balanced. If difficulty in arriving at balance is en-
countered with a high-sensitivity setting of the attenuator, this control may be rotated toward
the 25-in. position until a position is reached where the null indicator meter responds to ad-
justment of the balance controls.

After the bridge has been balanced, the operator should select the attenuator position
whose marking most nearly approximates the peak-to-peak amplitude of the expected waves
to be recorded. At this time, calibration may be performed by raising and lowering the gage
element through an accurately measured distance and recording the corresponding deflections

of the recording pen.

PERFORMANCE

A complete wave-height recording system of the type described in this report was in-
stalled in the miniature model basin in late March 1952. After an initial period devoted to
calibration, testing, and minor adjustments to suit the selected operating conditions, the per-

formance characteristics were verified to be as follows:

1. Maximum usable sensitivity was 0.6 in. (double peak amplitude) of wave height which
produced 3 cm deflection of the recording stylus; (the built-in sensitivity control provides

attenuation in 10 fixed steps covering the range from 0.6 to 40 in. of wave height).

2, Linearity of the gaging element and the electronic system is approximately 1 percent
of full scale on any sensitivity range selected. The recorder itself was found accurate to

approximately 2 percent of full scale.

3. Resolution (on the record) on the most sensitive step of the sensitivity control is of

the order of 0.010 in. of change in water level.

4, Frequency response of the system was measured by mounting the gage and its support-
ing bracket on a cam-driven vertical oscillator whose frequency of vibration was adjustable
from 0 to about 5 cps. Response was found to be uniform up to the upper frequency limit of
the mechanical oscillator. There is no reason to believe that the range of uniform response
does not extend considerably above 5 cps, since no measurable amplitude distortion was

evident at this frequency.

Figure 6 is a photographic copy of one continuous record taken in the 140-ft towing
basin by personnel of the Hydromechanics Laboratory using the instrumentation system de-
scribed. The upper trace on each strip shows the record obtained from a gage placed 38 ft
from the wavemaker and the lower trace shows the record from another gage located 22 ft
from the wavemaker.

Early in October 1952, an exact duplicate of this system was constructed and placed
in use along with the original pilot model. The performance characteristics of this system

were found to be identical to the first one, and no adjustments or modifications were required.

5s al il
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La BI |

Wave Length 4 ft
Blower Speed 1940 rpm
Paper Speed 50 mm/sec

Pneumatic Wavemaker Installation
10 ft x 5 ft x 140 ft Basin
Data Obtained 30 January 1953

(Tet Te
Ae Hy

HN | Ate

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EBs

Figure 6 - Record of Wave in the 140-ft Basin

Photographic copy of one continuous record taken in the 140-ft towing basin. The upper trace on each

strip shows the record obtained from a gage placed 38 ft from the wavemaker; the lower trace shows the

record obtained from another gage placed 22 ft from the wavemaker.

Since October 1952, both of these measurement systems have been in continual use on one

or another of the various research programs currently being conducted at the Model Basin.

It is felt that this instrumentation, although simple in principle and design, represents a

forward step in the technique of recording small wave heights and wave forms.

PERSONNEL AND ACKNOWLEDGMENTS

The conception and design of the wave-height measuring system described herein was
the work of the author. The pilot model of this instrument was constructed by other members
of the Instrumentation Division who contributed many valuable suggestions and constructional
““‘know-how.*’ Messrs. Howard Reese and Paul Golovato of the Hydrodynamics Division per-
formed calibration, linearity, and frequency response tests, the results of which are included

as a part of the verified quantitative performance characteristic data in this report.

12
APPENDIX

A. GAGE FACTOR OF WIRE GAGE

The increment in capacitance AC produced by a change in water height Ah may be
computed from the formula,

Tk 0.555 uf per cm [1]

ih
ust

where & is the specific inductive capacity of the dielectric (enamel),
In is the natural logarithm,
is the outer radius of dielectric,

is radius of the conductor, in the same units as 7,, and

Ah is the change in water height in cm.

The total capacitance presented by the gaging element is of secondary interest only,
as this capacitance may be considered as a part of the fixed capacitor in the bridge arm in
which the gage is connected.

Formula [1], although exact, should be used to obtain approximate values only, owing
to the difficulty of accurately measuring the thickness of the insulation on the wire and de-
termining the dielectric constant # of the insulating material. For example, computed values
for AC (uyf per in.) of the No. 28 enameled wire used was 58.5 pyf per in., while the average
experimental value obtained by direct measurement was 56.0 yyf perin. (This value was

used as a basis for selecting the internal calibrating condensers.)

B. LINEARITY CONSIDERATIONS

The degree of linearity obtainable from a conventional four-arm bridge is a function
of the ratio of the maximum change in impedance which will occur in the active bridge arm
and the impedance of the same arm at balance.

The expression for the open circuit output voltage for a capacitive bridge with one

active (variable) arm is

volts [2]

where e is the bridge driving voltage and a is the ratio of the change in capacitance of the
active arm to the capacitance of the arm at balance, i.e., a.

For example, in order to realize a linearity of one percent of full scale, the error
2
+o

factor in Equation [2] must not be numerically less than 0.99. Or stated otherwise, the

ratio AC must not exceed 0.02.

The range of the instrument described extends to 20 in. of water (single peak amplitude),
The ratio 42 for this largest amplitude is approximately 0.012 so that the bridge nonlinearity
does not exceed 0.6 percent of full scale on this sensitivity setting and is considerably less

for the measurement of smaller wave amplitudes.

REFERENCES

>
(2) —>1. ‘‘An Ocean Wave Measuring Instrument,’’ Technical Memorandum No. 6, Beach Erosion
Board, U.S. Army Engineers, Vicksburg, Miss., October 1948.

2. Chinn, A.J., ‘‘Progress Report on Wave Measurements at Apra Harbor, Guam,’’ Univer-
sity of California Department of Engineering Report No. HE-152-2, 5 July 1949.

8. Cook, G.W., ‘‘A Resonant-Bridge Carrier System for the Measurement of Minute Changes
in Capacitance,’’ TMB Report 626, February 1951,

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NAVY-OPPO PRNC, WASH. OC

INITIAL DISTRIBUTION

Chief, Bureau of Ships, Technical Library (Code 327), for distribution:
5 Technical Library
1 Applied Science (Code 370)
2 Electronics Design and Development (Code 810)
1 Civilian Consultant to Chief of the Bureau (Code 106)

Director, U.S. Naval Research Laboratory, Washington 20, D.C.

Commanding Officer and Director, Naval Electronics Laboratory, San Diego 52,
Calif.

Commander, U.S. Naval Ordnance Laboratory, White Oak, Silver Spring 19, Md.

Commanding Officer and Director, U.S. Navy Underwater Sound Laboratory, Fort
Trumbull, New London, Conn., Attn: Mr. Whannel

Commander, Norfolk Naval Shipyard (Code 227), Underwater Explosion Research
Field Unit, Norfolk, Va.

Director, National Bureau of Standards, Wash., D.C., Attn: Office of Basic
Instrumentation, 1 for Dr. T.A. Perls

Director, U.S. Coast and Geodetic Survey, Department of Commerce, Washington,
D.C.

Beach Erosion Board, U.S. Army Engineers, Little Falls Road and MacArthur
Blvd., N.W., Washington, D.C.

Director, Experimental Towing Tank, Stevens Institute of Technology, 711 Hudson
St., Hoboken, N.J.

Director, Woods Hole Oceanographic Institution, Woods Hole, Mass.

Director, St. Anthony Falls Hydraulic Laboratory, University of Minnesota, Minne-
apolis, Minn.

Dr. Dennison Bancroft, Swarthmore College, Swarthmore, Pa.

British Joint Services Mission (Navy Staff), P.O. Box 165, Benjamin Franklin
Station, Washington 25, D.C.

Canadian Joint Staff, 1700 Massachusetts Avenue, N.W., Washington 6, D.C.

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