3 2 4 7 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 been achiev-
ed. The output of the demodulator circuit is a d-c valtage which varies from 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.
The instrum.ent 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 m.echanism; 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.
To 6SJ7 3 amp
To Heaters on both
Ctiassis 10 amp
Figure 5 - Schematic Wiring Diagram of the Power Supply- Amplifier Unit
of the Type 145-A Dynamic Wave-Height Recorder
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.
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 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.
(a) Lower trace shows build-iqj of wave at the 22-ft station.
(b) Upper trace shows build-up of wave at the 38-ft station.
(c) Steady-state conditions at both measurement stations.
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.
A. GAGE FACTOR OF WIRE GAGE
The increment in capacitance AC produced by a change in water height AA may be
computed from the formula,
— =0.555 ^/if per cm 
where k is tlie specific inductive capacity of the dielectric (enamel),
In is the natural logarithm,
r„ is the outer radius of dielectric,
T. is radius of the conductor, in the same units as r^, and
A 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 , 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 k of the insulating material. For example, computed values
for AC (/xfif per in.) of the No. 28 enameled wire used was 53.5 /xfif per in., while the average
experimental value obtained by direct measurement was 56.0 /x^f per in. (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
e„ = volts 
° 4 2+ot
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., .
For example, in order to realize a linearity of one percent of full scale, the error
factor — — in Equation  must not be numerically less than 0.99. Or stated otherwise, the
ratio -^^must not exceed 0.02.
The range of the instrument described extends to 20 in. of water (single peak amplitude).
The ratio -^ 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.
— > 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.
3. Cook, G.W., "A Resonant-Bridge Carrier System for the Measurement of Minute Changes
in Capacitance," TMB Report 626, February 1951.
9 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)
2 Director, U.S. Naval Research Laboratory, Washington 20, D.C.
2 Commanding Officer and Director, Naval Electronics Laboratory, San Diego 52,
1 Commander, U.S. Naval Ordnance Laboratory, White Oak, Silver Spring 19, Md.
1 Commanding Officer and Director, U.S. Navy Underwater Sound Laboratory, Fort
Trumbull, New London, Conn., Attn: Mr. Whannel
1 Commander, Norfolk Naval Shipyard (Code 227), Underwater Explosion Research
Field Unit, Norfolk, Va.
2 Director, National Bureau of Standards, Wash., D.C, Attn: Office of Basic
Instrumentation, 1 for Dr. T.A. Perls •
1 Director, U.S. Coast and Geodetic Survey, Department of Commerce, Washington,
2 Beach Erosion Board, U.S. Army Engineers, Little Falls Road and MacArthur
Blvd., N.W., Washington, D.C.
2 Director, Experimental Towing Tank, Stevens Institute of Technology, 711 Hudson
St., Hoboken, N.J.
1 Director, Woods Hole Oceanographic Institution, Woods Hole, Mass.
1 Director, St. Anthony Falls Hydraulic Laboratory, University of Minnesota, Minne-
1 Dr. Dennison Bancroft, Swarthmore College, Swarthmore, Pa.
9 British Joint Services Mission (Navy Staff), P.O. Box 165, Benjamin Franklin
Station, Washington 25, D.C.
3 Canadian Joint Staff, 1700 Massachusetts Avenue, N.W., Washington 6, D.C.
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