DOC
EPA
Jnited States
Department of
Commerce
st and Evaluation Laboratory
lational Ocean Survey/NOAA
Rockville, MD 20852
United States
Environmental Protection
Agency
Office of Energy, Minerals, and
Industry
Washington DC 20460
EPA-600/7-78-145
July 1978
Research and Development
The Vertical
Planar Motion Mechanism;
A Dynamic Test Apparatus
for Evaluating Current
,
Meters and Other Marine
Instrumentation
Interagency
Energy/Environment
R&D Program
Report
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic
energy supplies in an environmentally compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects; assessments of, and development of, control technologies for energy
systems; and integrated assessments of a wide range of energy-related environ-
mental issues.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/7-78-145
July 1978
THE VERTICAL PLANAR MOTION MECHANISM
A Dynamic Test Apparatus for Evaluating
Current Meters and Other Marine Instrumentation
A. N. Kalvaitis
National Ocean Survey
National Oceanic and Atmospheric Administration
Rockville, Maryland 20852
Interagency Agreement No. D5-E693
Project No. EAP-78-BEA
Program Element No. 1 NE 625C
Project Officer
Gregory D'Allessio
Office of Energy, Minerals, and Industry
U.S. Environmental Protection Agency
Washington, DC 20460
This study was conducted
as part of the Federal
Interagency Energy/Environment
Research and Development Program.
Prepared for
OFFICE OF ENERGY, MINERALS, AND INDUSTRY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, DC 20460
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FOREWORD
Oceanic, estuarine, and limnologic circulation studies are conducted for
many diverse purposes for which high data quality is important: energy
exploration and extraction, development and validation of models, climate
research, and pollution and sediment transport, to name but a few. Specifi-
cally, measurement of water flow is basic to the development of circulation
models which are used to predict transport of energy-related pollutants (oil
spills, offshore drilling wastes, etc.). On a smaller scale, current meters
are utilized to obtain water particle velocity measurements used in petroleum
production platform design.
Most flow measurements are made with current meters, which are instru-
ments that sense and record flow speed and direction as a function of time.
If properly calibrated and functional, nearly all current meters will provide
high quality data in a steady environment. In the real world, however, the
flow sensors are typically exposed to a wide range of time and length scale
dynamics which may cause large measurement uncertainties, with errors higher
than 100 percent not unusual. These uncertainties may be quantified using
several different techniques: (1) mathematical modeling, (2) field inter-
comparison, and (3) laboratory testing. Mathematical modeling and field
intercomparisons must be validated in the laboratory to quantify the
uncertainties inherent to these methodologies. The capability to perform
dynamic testing in a laboratory will greatly assist in defining performance
of currently used sensors and accelerate development of improved current
measurement systems and field standards.
ii
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ABSTRACT
The overall objective was to provide a dynamic test apparatus that can
produce known, controlled high frequency dynamics for the evaluation of
current meters and other marine instrumentation. Of primary interest is the
establishment of flow sensor measurement capabilities to assure data quality
in an unsteady flow environment.
The culmination of this development is a Vertical Planar Motion
Mechanism (VPMM) that generates three major modes of dynamics--vertical-
circular, vertical, and horizontal--at length scales from 0.15 to 1.22 m and
time scales from 5 to 12 s. The VPMM mounts on a tow carriage which provides
the steady velocity while the VPMM superimposes oscillatory motions on full-
size current meters.
The VPMM is instrumented such that the instantaneous velocities of the
test sensors and their outputs may be measured at a 20-Hz sampling rate; an
on-board computer allows for near-real time data analysis. This report
describes the development and wet acceptance testing of the VPMM using
several types of current sensors, including the electromagnetic and the
acoustic variety. Current sensor dynamic response is also documented. No
deleterious interactions were noted between the VPMM and the test instruments;
the VPMM performance was within specifications for all conditions investi-
gated.
This report was submitted to the National Oceanic and Atmospheric
Administration (NOAA) in partial fulfillment of Interagency Agreement number
EPA-IAG-D5-E693-EA (Energy Pass-Through Funds) and under partial sponsorship
of the U.S. Environmental Protection Agency. A substantial amount of the
hardware design and fabrication were conducted by the U.S. Naval Ship Research
and Development Center, Carderock, Maryland. The electronic interfacing,
instrumentation, software, and requirements were generated by the Test and
Evaluation Laboratory, Office of Marine Technology, National Ocean Survey,
NOAA. This report covers the period March 1975 to July 1977.
m
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CONTENTS
Foreword ii
Abstract iii
Figures v
Tables v
Abbreviations and Symbols vi
1. Introduction 1
2. Conclusions 4
3. Theory and Description of Operation 5
4. General Acceptance Methodology 8
In-air demonstration 8
In-water demonstration 9
Facilities and equipment 9
Empirical procedures 13
5. Results 14
6. Error Analysis 18
Systematic errors 18
Random errors 18
Appendices
A. Derivation of oscillatory velocity equations for VPMM. ... 20
B. VPMM oscillatory velocity (normalized) vs. drive shaft
angle, intercomparing the three modes of dynamics 23
C. Sample printout record of a test point 28
D. Examples of computations and assumptions in error analysis
for velocity uncertainties 30
IV
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FIGURES
Number Page
1 DTNSRDC Number 1 Tow Carriage 2
2 Vertical Planar Motion Mechanism 3
3 Velocity Diagram of Tow Vehicle and VPMM 6
4 VPMM Acceptance Test Instrumentation System 10
5 VPMM Acceptance Test Current Meters 12
6 Computed VPMM Oscillatory Velocities 15
7 Incremental Angular Displacement of VPMM Drive Shaft 16
TABLES
Number Page
1 VPMM Operating Requirements 8
2 Current Meter Selection Criteria for Acceptance Tests 13
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LIST OF ABBREVIATIONS AND SYMBOLS
ABBREVIATIONS
BCD
cm
DTNSRDC
9
hp
Hz
in
kg
m
NOAA
s
VPMM
SYMBOLS
1
r
t
u
v_
V
vc
vh
vv
w
X, Y, Z
0)
binary coded decimal
centimeter
David Taylor Naval Ship Research and Development Center
acceleration of gravity
horsepower
Hertz; cycles per second
inch
kilograms
meter
National Oceanic and Atmospheric Administration
second
Vertical Planar Motion Mechanism
Distance between drive system and pinion cluster.
One-half test instrument displacement; crank arm length.
Time _
Fluctuating velocity component, vertically orthogonal to V.
Fluctuating velocity component, col linear with V and x axis.
Mean value of current vector; the measurand; also the tow vehicle
velocity.
Oscillatory velocity: vertical circular mode.
Oscillatory velocity: horizontal mode.
Oscillatory velocity: vertical mode. _
Fluctuating velocity component, horizontally orthogonal to V.
Mutually orthogonal axes; 2 is oriented vertically.
Angular velocity of the drive system.
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SECTION 1
INTRODUCTION
The Vertical Planar Motion Mechanism (VPMM) was developed primarily for
producing known, controlled motions to evaluate flow sensor performance. The
VPMM attaches to a tow vehicle mounted over a water filled channel (Figure 1);
the tow vehicle provides steady velocities while the VPMM superimposes high
frequency dynamics. The tow facility is located at the David Taylor Naval
Ship Research and Development Center (DTNSRDC), Carderock, Maryland. Three
distinct modes of dynamics can be generated—circular, vertical, and horizon-
tal (Figure 2). The test instrument is attached to the base of the drive
beam and submerged below the water line. Although not verified empirically,
other devices can be tested. Objects up to 2.0 m long and weighing 80 kg
have been tested at instantaneous velocities up to 1.5 m/s. The overall
dimensions of the VPMM are 3.4 m high, 1.8 m long, and 0.5 m wide. Con-
structed primarily from aluminum, the apparatus weighs less than 680 kg and
is easily handled with a hoist. The VPMM is designed to also interface with
another tow facility at DTNSRDC which develops various combinations of wave
conditions.
The VPMM can generate peak amplitudes over a range of 0.15 to 1.22 m in
0.15-m increments. A 3-horsepower variable speed electric motor and a 40-to-
1 gearbox allow periods of motion ranging from 5 to 12 s. To maintain a
constant speed, the drive system is controlled by a bidirectional servo
control unit. Oscillatory motions generated by the VPMM are monitored with a
digital timer and an angular position monitor which is attached to the drive
shaft of the motor; these time displacement values are then converted into
velocity units by a computer. (An error analysis is conducted in a later
section of this report.) The VPMM can also rotate the plane of motion from
parallel to the direction of tow (0-degree angle of attack), to normal to the
tow (90 degrees) in 15-degree increments. In summation, the VPMM is capable
of simulating various unsteady flow and dynamics conditions, such as wave
particle fields and instrument motions, within a steady water velocity
environment.
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Figure 1. DTNSRDC #1 Tow Carriage
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DRIVE
SYSTEM
TOW
CARRIAGE
STRUCTURE
ROTATABLE
FRAME
CIRCULAR MODE
VERTICAL MODE
HORIZONTAL MODE
Figure 2. Vertical Planar Motion Mechanism.
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SECTION 2
CONCLUSIONS
Based on observations and measurements derived during the acceptance
testing phase, the VPMM system operated successfully in all three modes of
dynamics. Both the uniformity and repeatibility of the VPMM generated
velocities were excellent. An analysis of the data from the tow facility,
VPMM, and current sensors indicated no major deleterious interactions. No
apparent electromagnetic or acoustic interference was noted. Stray dynamics,
such as vortex shedding induced motions, were not detected even during steady
state tows. A toggling effect—a high frequency, small displacement phenome-
non—was apparent during the vertical-circular mode of operation, but did not
affect the test sensor's signals. Rigging and installation of the VPMM to
the tow carriage was readily accomplished, although the availability of a
suitable staging platform would have simplified the operation. Changes in
oscillatory modes and angles of attack were conducted efficiently.
The VPMM provides a unique capability for testing and evaluating sensors
at various combinations of length and time scale dynamics. A typical mission
scenario would be establishing current meter data quality under dynamic
conditions as follows: (1) define measurement system physical character-
istics, i.e., platform, mooring, etc.; (2) using appropriate models, quantify
the predicted motions of the current meter as a function of anticipated
environmental forcing levels; (3) using the VPMM, duplicate the predicted
dynamics in the laboratory to error bound the current meters' performance.
Other anticipated uses for the VPMM include testing wave measurement systems,
validating dynamic response models, and conducting stability tests on towed
vehicles.
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SECTION 3
THEORY AND DESCRIPTION OF OPERATION
The VPMM (Figure 2) and the tow carriage (Figure 1) may be thought of as
a system for superimposing high frequency oscillatory velocities on a known
mean velocity. This is illustrated vectorially in Figure 3, where the tow
vehicle is represented by V, and the v, w, and u components are generated by
the VPMM. The VPMM can operate in three different modes—vertical -circular,
pure vertical, and pure horizontal, all at various angles of attack. The
oscillatory motion may be described as follows:
Vertical -Circular Mode vc = rusinuit (1)
Pure Horizontal Mode vh = fjg^rlcosut).s (2)
Pure Vertical Mode vv = Urs1nut - jb (3)
r = one-half test instrument displacement;
crank arm length
1 = distance between drive system shaft
and pinion cluster
w = angular velocity of drive
t = time
Derivations of equations (1) through (3) are in Appendix A. Note that
each mode of dynamics will generate a unique set of instantaneous velocities
which result from mechanical arrangements inherent to that mode (Figure 2).
The circular motion mode forms a rotating parallelogram such that the test
instrument undergoes circular velocity, uniform in nature; thus the velocity
projection in the x, y, and z planes is sinusoidal. In the vertical mode,
the test instrument motions are limited to the vertical plane by vertically
oriented guide shafts and bearings. Higher harmonics are superimposed on the
planar sinusoidal velocity because of the ratio of the power transmission
beam (i.e., the connecting rod) to the crank. In the horizontal mode, a pair
of pinion gears and a pair of racks transmit oscillatory motions to the test
instrument. The horizontal rack is attached to a slider-bearing combination
which rides a horizontal guide shaft. The resulting oscillatory velocity is
nearly sinusoidal. Normalized comparisons of the three types of oscillatory
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steady
state
unsteady components
where
V
mean value of current vector, the measurand; also
tow vehicle velocity.
v = fluctuating velocity component, collinear with V.
u = fluctuating velocity component, vertically orthogonal
to V.
w = fluctuating vejpcity component, horizontally
orthogonal to V.
Figure 3. Velocity Diagram of Tow Vehicle and VPMM.
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dynamics are illustrated in Appendix B. As expected, the three curves con-
verge as the crank arm radius (r) is decreased from 0.61 m (24 in) to 0.15 m
(6 in).
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SECTION 4
GENERAL ACCEPTANCE METHODOLOGY
The VPMM development was based on the set of requirements shown in
Table 1. Prior to operation of the dynamic test apparatus in water with
actual current meters, it was demonstrated in-air under simulated weights
and hydrodynamic loads to induce and correct any design deficiencies.
TABLE 1. VPMM OPERATING REQUIREMENTS
Maximum steady state velocity
without dynamics
Maximum steady state velocity
with dynamics
Maximum oscillatory velocity
Period of dynamics
Amplitude, peak-to-peak
increment
Angle of attack
increment
Test instrument loading
(worst case)
200 cm/s
70 cm/s
85 cm/s
5 to 12 s
15 to 122 cm
15 cm
0° to 90°
15°
weight in air 80 kg
length 180 cm
diameter 25 cm
IN-AIR DEMONSTRATION
After the major components of the system were fabricated, the VPMM was
8
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assembled in a laboratory at DTNSRDC for an in-air or "dry" demonstration.
The vertical-circular mode of operation was validated first. For these
experiments, weights up to 45 kg were clamped to the drive and balance arms,
and the system was operated at various speeds. Problems with the mechanical
fit of moving parts, structural stiffness, and inadequate speed control were
noted and subsequently corrected. For the final in-air demonstration, weights
and an elastomeric cord were attached to the drive arm to simultaneously
simulate current meter mass and hydrodynamic loading, respectively.
The load conditions that were simulated were derived from mathematical
predictions and were based on the "worst case" current meter for the severest
combination of circular velocities, superimposed on steady state values.
During this experiment, tachometer output from the drive system was measured
to evaluate the speed control; concurrently, the vertical acceleration of the
drive arm was measured. The initial speed control variations were found to
be satisfactory within 5 percent of the mean value. Acceleration spikes
induced by toggling of the drive crank at top and bottom dead center, repre-
senting small changes in displacement, were noted. All in all, the fixture
performance was deemed acceptable. Since both abnormalities were minor from
the standpoint of current meter evaluations, the wet demonstrations were
begun.
The other two modes of dynamics, vertical and horizontal, were checked
in a similar manner, using weights and elastomeric cords. As in the previous
tests, the fixture was subjected to maximum predicted stresses, with no major
deficiencies uncovered.
IN-WATER DEMONSTRATION
The purpose of the in-water, or "wet," demonstration, with the VPMM
mounted on an DTNSRDC towing carriage, was to evaluate the performance of the
total system over a wide range of conditions which could be expected for
standard current meter evaluations. In other words, anomalous interactions
between the test sensor (current meter), the tow carriage/basin, and the
ancillary equipment would hopefully surface during these in-water demonstra-
tions.
FACILITIES AND EQUIPMENT
The tow vehicle (Figure 1) on which the VPMM (Figure 2) is mounted is an
electrohydraulically powered wheeled platform, weighing 40,000 kg, that rides
on rails mounted atop the channel walls; the vehicle has a velocity range of
2.5 to 600 cm/s. The tow channel itself is 335 m long, 13.5 m wide, with
depths of 3.3 and 6.7 m. The facility is located at the David Taylor Ship
Research and Development Center, Carderock, Maryland. Tow vehicle displace-
ments are monitored with an electronic counter and magnetic pickup which
senses magnetic pulses generated by a steel gear coupled to a precision wheel.
A computer converts the pulses into velocity units, normally centimeters/
second.
Wet acceptance testing of the VPMM involved a complex, interrelated
suite of equipment and instrumentation (Figure 4). For simplicity, this
configuration may be divided into several major sectors—steady state
9
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Magnetic Tape
Recorder
Interface
Electronics
Recorders
3-axis
Accelerometer
Test Instrument
(Current Meter)
I
Programmable
Calculator
Digital
Counter
Carriage
Velocity
Wheel
Line
Printer
Interface
Electronics
Shaft Position
Resolver
r
Drive Shaft
(Rotation)
I
"I
Servo
Control Unit
Figure 4. VPMM Acceptance Test Instrumentation System.
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measurements (carriage velocity), nonsteady state measurements (VPMM gener-
ated dynamics), current meter outputs, and a data collection/analysis system
(programmable.calculator) which serves as the measurement control tool. The
following is a descriptive listing of the ancillary equipment:
Absolute Encoder
Converts shaft input to BCD or binary information corresponding directly
to shaft angle while simultaneously displaying a four-digit display of the
shaft angle. The basic unit consists of an electromagnetic transducer
(resolver) and an electronic converter package. The overall accuracy is 0.1
degree of arc. Sampling intervals of 400 conversions/second are attainable.
Time Interval Meter
Measures time intervals between absolute encoder conversions. The out-
put data are in BCD format, and the meter also features a six-digit display
of the time. The accuracy of the interval time base models is typically 1
part in 106 at 25°C and is insured by the use of a crystal controlled oscil-
lator circuit.
Bidirectional Servo Control Unit
Acts as an electronic flywheel to maintain a constant motor rotation rate
by means of a feedback loop from a tachometer mounted on the motor shaft.
Servo Accelerometer/Amplifier System
Triaxial accelerometers are mounted above the current meters to monitor
the dynamics generated by the VPMM and the current meters themselves. The
accelerometers have an uncertainty of 1 percent of full scale and operate on
the principle of a seismic mass suspended in a magnetic field.
Programmable Calculator
Acts as the data collection and reduction system for the VPMM, tow
carriage., and test sensors. A portable calculator monitors and computes
carriage velocity, instantaneous velocity of the apparatus, and sensor out-
puts, along with the associated statistical manipulations such as mean,
standard deviation, etc. Data are recorded on magnetic tape cartridges.
Four different ocean current meters (Figure 5) were used to certify VPMM
compliance with the design specifications. The rationale for each selection
is shown in Table 2.
The rotor and small vane type used in these empirical investigations
weighed 80 kg in air (35 kg in water) and was approximately 2 m long. By
virtue of the size and mass, it imparted the largest loading on the fixture
of any of the current meters. The rotor with large vane weighed 28 kg in air
and 21 kg in water, with an overall length of 1.4 m including a 1-m long vane
with a height of 0.75 m. The electromagnetic current meter weighed 43 kg in
air and had an overall length of 1.5 m. The acoustic current meter weighed
11
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D
Rotor with small vane
Rotor with large vane
I
2-axi s Electromagneti c
2-axis Acoustic
Figure 5. VPMM Acceptance Test Current Meters.
12
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34 kg and was 1.3 m long, with an overall diameter of 22 cm.
TABLE 2. CURRENT METER SELECTION CRITERIA FOR ACCEPTANCE TESTING
Current Meter
Rationale for Selection
VPMM Mode Validated
Rotor with small vane
Rotor with large vane
2-axis Electromagnetic
2-axis Acoustic
Largest and heaviest
current meter
Most common current meter
Very susceptible to
electronic noise
0.2 second time constant
Horizontal & vertical
Vertical-circular
Vertical-circular
Horizontal & vertical
EMPIRICAL PROCEDURES
The VPMM was mounted on the front of Tow Carriage #1 at DTNSRDC and
configured to operate in the vertical-circular mode with a fixed peak ampli-
tude of 1.22 m. After installing the resolver on the drive arm shaft and
attaching the 3-axis accelerometers, the current meter was affixed and the
data collection system activated. Preliminary calibrations were made on the
system dynamics by measuring the drive arm oscillation period versus motor
speed setting.
Once the fixture calibrations were completed, the in-water dynamics were
initiated with the least severe structural loadings and slowest oscillatory
periods. Oscillatory VPMM dynamics of 5-, 8-, and 12-s periods at 1.22-m
peak amplitudes were superimposed on steady carriage velocities of 0, 10, 35,
and 70 cm/s. Outputs from all instruments and equipment were recorded, most
at a nominal rate of 25 times per oscillatory period. Thus, the sampling
density was constant for all three dynamic time scales of 5, 8, and 12 s.
Each data point consisted of)approximately 250 samples, encompassing 10 total
periods. Averaging bias errors were minimized by initiating and terminating
sampling near the zero-crossing points. Additional real-time data analyses
were conducted for each data point; statistical computations were made of the
mean, standard deviation, minimum, maximum, range, and 95-percent confidence
level in the mean for both the standard (carriage velocity) and the test
instrument (current meter). A sample printout of the statistical computa-
tions is shown in Appendix C. After completing these investigations using
the rotor with large vane-type current meter, the electromagnetic flow sensor
was substituted and similar empirical procedures were followed.
Similar techniques were followed in validating the pure vertical and
pure horizontal modes except that an acoustic current meter and a rotor with
a small vane were used as the test instrument.
13
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SECTION 5
RESULTS
The ultimate purpose of the "wet" acceptance testing was to confirm the
operational capabilities of the VPMM and to identify and quantify any inter-
action between the test instruments (current meters) and the VPMM, and vice
versa. Criteria used to describe the overall performance of the VPMM were:
uniformity of oscillatory motions; degree of high frequency vibrations;
electromagnetic or acoustic interference; ease of handling, installation, and
adjustment; changing modes of dynamics; and overall system reliability and
accuracy.
Uniformity of oscillatory motions was determined using outputs from the
angular position resolver attached to the motor drive shaft which couples to
the drive arm holding the test instrument. For all three modes of operation-
circular, vertical, and horizontal—the standard deviation of the drive shaft
angular velocity averaged less than 4 percent of the mean using the largest
and heaviest test instrument and the most severe unsteady conditions.
Figure 6 illustrates typical instantaneous oscillatory velocities, and
Figure 7 the corresponding drive shaft angular increments as a function of
sample number (time). The oscillatory velocities were computed using incre-
mental shaft position (resolver) measurements as a function of time and equa-
tions (1), (2), or (3).
Fixture installation and integration efforts were minimal. The VPMM was
attached to the front face of the tow carriage with a series of clamps;
mounting and adjustment took approximately two hours. Changing the angle of
attack, relative to the tow direction, involved removing two pins and manually
rotating the superstructure, a several-minute procedure. Changing modes of
operation, i.e., from vertical to horizontal, was also easily accomplished,
normally requiring one hour.
High frequency vibrations and accelerations were monitored using a tri-
axial accelerometer system. Various combinations of simultaneous stresses
were generated to establish the effects of oscillatory period, tow speed,
angle of attack, and various current meters. The most significant accelera-
tion levels (1.6 g in the horizontal plane) were noted in the vertical
orbital mode and have been attributed to a mechanical type toggle. A spectrum
analysis of the corresponding vertical acceleration records revealed the
levels to be less than 0.15 g at between 1 and 10 Hz. Initially, large
accelerations of approximately 2 g at approximately 1 Hz were noted in the
horizontal mode. These were caused by an erratic feedback signal to the
motor speed control which was subsequently repaired. Except for the minor
toggling in the vertical circular mode, the high frequency acceleration levels
were small and seemed unaffected by angle of attack, test instrument
14
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35-r
in
o
DYNAMIC TEST FIXTURE EVALUATION
DTNSRDC 5/31/77
Horizontal Mode
12 s Period
90 Degrees Attack Angle
SAMPLE NUMBER
Figure 6. Computed VPMM Oscillatory Velocities.
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18-r
DYNAMIC TEST FIXTURE EVALUATION
DTNSRDC 5/31/77
CO
O)
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configuration and mass, oscillatory dynamics, and horizontal velocity.
An examination of analog records from the electromagnetic and acoustic
current meter indicated that no apparent stray electromagnetic or acoustic
noise was generated by the VPMM system. Although both current meters exhibit
fast time constants, 0.2 s for the acoustic, and 1.0 s for the electromag-
netic, neither signal was adversely distorted. The uniformity of each record
suggests no apparent deleterious interaction between the VPMM, tow basin, and
tow carriage. ^
Numerous tests, both static and dynamic, were made at various positions
and depths in the tow channel; no significant difference was noted in the
shallow end of the channel. In summation, the empirical results confirmed
that the operational capabilities of the VPMM system meet requirements docu-
mented in Table 1.
17
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SECTION 6
ERROR ANALYSIS
Since the VPMM will be used to generate controlled, known dynamics for
determining current meter performance, it is important to quantify the system
uncertainties in the standards, specifically the tow carriage velocity, stray
water currents, and the VPMM superimposed velocity. The velocity measurement
of the tow vehicle and the VPMM generated dynamics are traceable to the
National Bureau of Standards by the time and distance parameters, which are
primary units of measurement. Thus, the uncertainties in the absolute instan-
taneous velocity of the test instrument over the Earth may be readily com-
puted. The total system error is comprised of several individual components
which may be grouped into two major categories—systematic errors and random
errors. The systematic errors arise from estimated uncertainties of standards
used—i.e., instrumentation to measure carriage velocity and dynamic (VPMM)
velocity—and estimated magnitudes of residual currents and blockage effects.
The random errors are a measure of the scatter of instantaneous velocity
values about the computed mean. The error terms for the VPMM and tow facility
are listed below; except where noted, computation to support the numerical
estimates are shown in Appendix D. It should be noted that error estimates
yielding a percent-of-reading result have been converted to absolute velocity
by using a maximum velocity value.
SYSTEMATIC ERRORS
'Uncertainties in steady state (tow carriage) velocity measurements.
{0.014 cm/sf
'Residual, convection, stray currents in tow basin. , >
(estimate based on prior tests at DTNSRDC) «' cm/s>
'Uncertainties in nonsteady (VPMM) velocity measurements. JO.68 cm/s|
"Velocity blockage induced by test instruments placed in tow basin.
{0.02 cm/s(
"Sampling error—maximum uncertainty in determining peak instantaneous
velocity of VPMM. {0.6 cm/s max.f
RANDOM ERRORS
'Steady state (tow carriage) 95-percent confidence level in mean for
n = 250. {0.04 cm/sf
*Nonsteady state (VPMM) averaging error. {0.1 cm/s}
18
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Note that the largest component in the error budget, 1 cm/s, is due to
residual, convection, and stray currents in the basin. These uncertainties
result largely from circulations established from previous tows. Residual
current errors may be minimized by allowing time between test points for
dissipation.
19
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APPENDIX A
Derivation of oscillatory velocity equations for VPMM.
20
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VERTICAL EQUATION
OF MOTION
cos law a2 = b2 + c2 - 2bc cos A
a=l;b=r;c=x
A = e; e = wt
I2 = x2 + r2 - 2xr cos e
I2 = x2 - 2xr cose + r2cos2e - r2cos2e + r2
I2 = r2 (i-cos2e) + (x-r cose)2
I2 = r2 sin2e + (x-r cos o)2
x-r cos e = (I2 - r2sin2e)1/2 :e = cot
x = (I2 - r2sin2u>t)1/2 + r cosut
\i
V = dt =
cosait
21
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HORIZONTAL EQUATION
OF MOTION
cos law a2 = b2 + c2 - 2bc cos A
2 =
a = x; b = r; c = 1
A = e; e = u>t
COS 8
x = (r2 + I2 - 2rl cos 9)
1/2
V =
dL
dx
12 _ 2rl coso)t)"1/2[-2rl (-
ti VA>\ _ II LLIv I I luu **
2rl cosut)
-1/2
22
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APPENDIX B
VPMM oscillatory velocity (normalized) vs. drive
shaft angle, intercomparing the three modes of dynamics.
23
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NORMALIZED INSTANTANEOUS VPMM
OSCILLATORY VELOCITY VS DRIVE SHAR ANGLE
CRANK ARM RADIUS = 24 INCHES
Circular Mode: -
Vertical Mode: -
Horizontal Mode:
ro
Q
UJ
I I II I I I
SHAFT ANGLE (DEGREES)
-------
NORMALIZED INSTANTANEOUS VPMM
OSCILLATORY VELOCITY VS DRIVE SHAFT ANGLE
CRANK ARM RADIUS = 18 INCHES
1.2-r-
0.8
ro
tn
o
o
Q
UJ
M
0.0
-0.4--
-0.8--
-1.2
Circular Mode: -
Vertical Mode:-
Horizontal Mode:
SHAFT ANGLE (DEGREES)
-------
NORMALIZED INSTANTANEOUS VPMM
OSCILLATORY VELOCITY VS DRIVE SHAFT ANGLE
CRANK ARM RADIUS = 12 INCHES
Circular Mode:—
Vertical Mode: —
Horizontal Mode:
ro
en
o
o
Q
ULl
M
0.0
-0.4
-0.8--
-1.2-1-
SHAFT ANGLE (DEGREES)
-------
1.2-1-
ro
o
o
o
Ul
M
-0.4--
-0.8--
NORMALIZED INSTANTANEOUS VPMM
OSCILLATORY VELOCITY VS DRIVE SHAFT ANGLE
CRANK ARM RADIUS = 6 INCHES
Circular Mode:
Vertical Mode:
Horizontal Mode:
SHAFT ANGLE (DEGREES)
-------
APPENDIX C
Sample printout record of a test point.
28
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Run # 9 Run Id 12.00 Date 527 Time 190639
N = 235 Carriage Speed = 35.8 cm/5
Statistical Analysis
Mean
Std. Dev.
Min
Max
Range
S/N
95% conf.
Fix. Mag
cm/s
3.588E 01
2.328E-01
3.541E 01
3.656E 01
1.153E 00
1.541E 02
2.976E-02
VACM Mag
cm/s
3.272E 01
7.045E 00
2.593E 01
1.354E 02
1.095E 02
4.645E 00
9.008E-01
Delt. Ang
deg.
4.226E 01
4.397E-01
1.130E 01
1.340E 01
2.100E 00
2.789E 01
5.622E-02
VACM Mag. Error = -3.2 cm/s
Run # 10 Run Id 12.00 Date 527 Time 201503
N = 243 Carriage Speed = 72.6 cm/s
Statistical Analysis
Mean
Std. Dev.
Min
Max
Range
S/N
Fix. Mag
cm/s
7.199E 01
4.422E-01
7.044E 01
7.313E 01
2.693E 00
1.628E 02
VACM Mag
cm/s
6.870E 01
3.939E 00
6.014E 01
7.934E 01
1.920E 01
1.744E 01
Delt. Ang
deg.
1.186E 01
3.350E-01
1.120E 01
1.270E 01
1.500E 00
3.540E 01
95% conf. 5.560E-02 4.953E-01 4.212E-02
VACM Mag. Error = -3.3 cm/s
29
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APPENDIX D
Examples of computations and assumptions in
error analysis for velocity uncertainties.
30
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SYSTEMATIC ERROR ASSOCIATED WITH
DYNAMICS GENERATION SYSTEM
vtrue ~ rw
Measured = (r ± er)(u ± eu)
Vtrue - ^measured
where V = circular velocity of VPMM arm.
r = amplitude of dynamics, i.e., radius of crank arm.
a) = angular velocity, radians/second.
ev,r,to = enror terms in fixture velocity, crank arm radius, and
angular velocity respectively.
Measured = ru> ± ^r" ± ewr ± ereu
ev = ra) " ^rai ^ ± £u^' dropping the second order term
If the sign of the errors are unknown, we can use the summation of errors
rule.
ev = [() + (j|) 11/2 substituting worst case values
ev = 0.8% of reading
31
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SYSTEMATIC ERROR ASSOCIATED
WITH CARRIAGE VELOCITY
Vtrue = S/t
vmeasured = (S ± es) / (t ± et)
- ^measured
v " vtrue
where V = linear velocity of carriage
S = circumference of carriage measurement wheel
t = time
ev s t = error terms in carriage velocity, wheel circumference,
and time, respectively.
If the sign of the errors are unknown, we can use the summation of errors
rule.
1 x 10"V , ,1 x 10-6x2]l/2
50.79 } + ( 1 } I
ev = 0.02% of reading
32
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VELOCITY BLOCKAGE
where a = cross sectional area of test instrument
A = cross sectional area of test basin
Va = velocity, actual
_ 1 (.2) (.75)
3 4 (6.7) (15.5) Va
Vb = 0.0004Va or 0.04% of reading
33
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UNCERTAINTIES ASSOCIATED WITH SAMPLING
PEAK INSTANTANEOUS VELOCITY
In the dynamic testing of current sensors, the indicated peak instan-
taneous velocity is often compared to the known value computed from VPMM and
tow carriage velocities to obtain a measure of the sensor's high frequency
response. Since the current sensor output is discretely sampled, there is
some error introduced by the sample missing the peak. The following analysis
evaluates this error with the assumption that the sample occurs between the
true peak and the furthest distance possible from the true peak output.
G = uit
where
co = radians/second
t = time, seconds
vi = Vmaxs1nwt
34
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Total area of cross hatched sections = A-| +
rb
= J Vid(ut) , where a = U/2 - 2ir/2n)
b = IT/2
n = number of samples per cycle
since
vi =
=vmax / sirtot d(wt)
solving:
=vmax I
=vmax [-cos ir/2 + cos(rr/2 - |j)J for n = 25
Al + A2 = Vmax (0.12533)
Height of AT = sin 82.8° = 0.992115
Base of AI = j - [f - ff?^] = f5 = 0.125664
Area of rectangle, A-| = (base)(height) Area of A2 = (Ai +
= 0.992115 (ir/25) = 0.12533 - 0.12467
= 0.12467 = 0.00066
Average ordinate for A2 -
= 0.005252
Total ordinate = height of A] + A2 average ordinate
= 0.005252 + 0.992115
= 0.9974
Average error in peak instantaneous velocity
= (1 -0.9974) Vn,ax
Average error = 0.26% of reading
35
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L
T
Maximum Sampling
Error
The following analysis evaluates the sampling error under maximum condi-
tions, i.e., the sample occurs as far as possible (for a given sample rate)
from the true peak output.
Maximum Error =
for n = 25; i.e, 5 Hz, for T = 5 s, and
at all other periods At/T the same value.
= [l-cos(0. 125664)]
= (1-0.992115)
Maximum error = 0.79% of reading
36
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RANDOM UNCERTAINTY ASSOCIATED
WITH TOW CARRIAGE VELOCITY VARIATIONS
The random error velocity component is determined statistically from
250 carriage velocity measurements per data point and by computing the 95
percent confidence level of the mean. For all data points, including those
during the VPMM operation, the random error component seldom exceded 0.04 cm/s.
This value is computed as follows:
where
X = mean
2 = number from cumulative normal distribution table
a = standard deviation
Random error = 0.04 cm/s
37
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