Basics of Measurement-1
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UNIT ± I
MEASUREMENTS
BASICS
BYJayesh Barve
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An Introduction to Measurement and An Introduction to Measurement and
EvaluationEvaluation
Jayesh Barve
Associate Professor
Mechanical Engineering Department
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Practice, Practice, Practice
Focus
Challenge
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Course Objectives
Students will be able to: organize and describe data using descriptive and simple inferential
statistics for research and evaluation in physical education, sport,and exercise science.
apply measurement theory, i.e., reliability, validity, objectivity, andsensitivity to the subdisciplines of physical education, sport, andexercise science.
appreciate the need for testing and evaluation, and goodassessment practices in physical education and kinesiology.
apply culturally sensitive tools and a sense of social justice in all
measurement and evaluation practices. recognize the varying needs of individuals in movement and the
need to develop effective measurement and evaluation tools for special settings.
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Course Requirements
Examination 1 and Examination 2, 40 points
The first two exams will be held in class during Thursday, June 14afternoon session and Thursday, June 28 afternoon session, asscheduled on the course calendar. Exams will consist of multiplechoice, short answer, and essay type questions. Essay questionswill test mathematical computations. Both tests will be open card (tobe explained in class) and calculators will be allowed.
Examination 3, 25 points
The final exam will be given in the morning of the final Thursday,
June 12. It will be a comprehensive examination consisting of essay questions. Thursday afternoon attendance after the finalexam on the last day of class is required.
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Group Project, 20 points
Each student will be assigned to a small group. This group assignmentrequires the design of a question to be tested, and a process for datacollection and analysis. The design, procedure, analysis, and interpretationof data will culminate in a PowerPoint presentation to the class by all groups
during class on Monday afternoon, July 10, 2007. Group Project Evaluation, 5 points
Each student is required to submit an assessment and a grade (A+ throughF) for each group member. These grades and evaluations will beaccumulated to provide 5% of the final grade.
Quality of Class Participation, 10 points
Students are expected to participate in all aspects of class discussions,including participation in homework review of previously taught concepts.Homework will be given almost every night of class. Students are expectedto complete all homework assignments. Homework assignments willinclude computer analyses and will be collected on occasion for theassignment of this portion of the grade.
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Measurement
Measurement means a characteristic isdefined and an instrument is selected tomeasure it, e.g., height can be measuredwith a tape measure, weight can bemeasured with a weight scale.
Name some other things that we measure
inside and outside of our field of kinesiology.
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Evaluation
Evaluation means that you gather information to draw conclusions and makenew predictions.
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Places where measurement and evaluationare used:
Research
Education
Business Sports
Medicine
Health and Rehabilitation
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Reasons for Measurement and Evaluation
Motivation
Accountability
Equipment Placement
Diagnosis
Evaluation of learning
Prediction
Program Evaluation
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Standards of Measurement and Evaluation--Measurement Theory
Reliability Validity
Objectivity
Sensitivity
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Descriptive Statistics
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Ways of Describing Data
Continuous scores - ³« have a potentiallyinfinite number of values, since they can bemeasured with varying degrees of accuracy´.
Discrete scores - ³« are limited to a specificnumber of values and are usually not expressedas fractions´.
Baumgartner & Jackson
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Levels of Measurement
Nominal
Ordinal
Interval
Ratio
Lowest level
Highest level
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Nominal (categorical) scores - when ascore places people or things into acategory these are called nominal scores.Nominal scores cannot be ranked or ordered along any dimension. Thecategories must be exhaustive and
mutually exclusive.
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Ordinal scores - means people or thingsare rank ordered along some dimension.No common unit of measurement existsbetween rankings in a system of ordinalscores. Comparisons cannot be madeacross different group rankings.
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Interval scores - These scores have acommon unit of measurement betweenadjacent points. No true zero point existson the interval scale.
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Ratio scores - These scores have acommon unit of measurement betweenadjacent scores. Ratio scores have a truezero point.
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You are making a measurement
when you
Check you weight
Read your watchTake your temperature
Weigh a cantaloupe
What kinds of measurements did
you make today?
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When we measure, we use a
measuring tool to compare
some dimension of an objectto a standard.
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Some Tools for
Measurement
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Stating a Measurement
In every measurement there is a
jNumber
f ollowed by a
j Unit from measuring device
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Mechanical Measurements
Act of measurement²the quantitative
comparison between a predefined
standard and a measurand to produce
a measured result
Measurand : physical parameter or
variable to be measured
Standard: basis for comparison of
quantitative value to measurand.
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Standards organizations
SASO² Saudi Arabian Standards
organization
ISO
²InternationalO
rganization for Standardization
Others²ASME, NFPA, ASTM, etc.
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Reliability of Measurements
Measurements must be reliable to be useful
Incorrect information is more damaging than
no information
There is no per f ect measurement
Accuracy of measurements
Precision of measurements
Uncertainty of measurements Do not accept data without questioning the
source and uncertainty of the measurements
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Fundamentals Methods of
Measurements
There are two basic methods of measurement:
Direct com parison: with a primary or
secondary standard
Indirect com parison²conversion of
measurand input into an analogous form
which can be processed and presented as
known function of input
- A transducer is required to convert the
measurand into another form
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Sensors
Use of a mercury thermometer to measure
temperature
Use of a radar signal to measure velocity
Use of a strain gage to measure the strain in
a material
Transducers frequently convert mechanical
measurements into electrical responses(voltage, amperage or resistance)
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Generalized Measurement
System
Sensor or transducer stage to detect
measurand and Convert input to a form
suitable for processing e.g. :
- Temp. to voltage - Force to distance
Signal conditioning stage to modify the
transduced signal e.g. :
Amplification, Attenuation, Filtering, Encoding Terminating readout stage to present desired
output (Analog or Digital form)
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Generalized Measurement
System
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Types of Input Signals
Static
Dynamic (Time dependence)
- Steady periodic, complex periodic
- Nonperiodic: nearly periodic or transient- Single pulse.
- Random
Analog or digital:- Analog; continuous signal,
- Digital; distinct values, step changes.
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Calibration
Calibration involves the determination of therelationship between the input and output of a measurement system
Eliminate Bias error
The proving of a measurement system¶scapability to quantify the input accurately
Calibration is accomplished by applyingknown magnitudes of the input and
observing the measurement system output The indirect measuring system must be
calibrated.
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C ALIBR ATION
Once a measurement device is selected, it mustbe calibrated
± Calibration ±Comparison of instrument¶s reading to acalibration standard
± Calibration standard created from a measurement Inherent error
Basic issue is how do we know that what werecord has any relation to what we wish tomeasure?
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Calibration using Primary
or/andS
econdaryS
tandards Known input signal and find the output.
- To establish the correct output scale.
- To find instrument reliability.
- To eliminate bias error (systematic error)
For linear relation o/ p I / p needs single
point calibration.
For non-linear relation needs multi-pointcalibrations.
Static calibration ± vs ± Dynamic calibration
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Primary Standards For
Comparison and Calibration S I S ystem: Meter ± Kg -- Sec.± Kelvin ± volt -Mole ± Ampere ± Radian
LENGTH (meter): Distance traveled by light
in vacuum during 1 /299792458 of a sec. MASS (Kg.): International prototype ( alloy of
platinum and iridium) kept near Paris.
TIME (Sec.): Duration of 9192631770 periods of
the radiation emitted between two excitationlevels of Cesium-133
TEMPERATURE (Kelvin): K = oC + 273
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Dimensional Analysis
Data presented in dimensionless form.
Reducing No of experimental variables.
N o
of variables - N o
of dims.= N o
of groups Use pi method or by inspection
Basic dimensions: M L T (kg,m,sec,ok)
Saving(time&$)(10 tests ±vs- 10 4 tests for F= f n (L,V,,
))
Force coef. F /v 2 L2 = f n (Reynolds number vL/ )
Helping in exp. Planning, insight, and similitude.
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Uncertainty of Measurements
Measurement error = Measured result - True
value
The true value of a measurand is Unknown
( Error is unknown )
The potential value of error can be estimated
(uncertainty)
Two types of error:
- Systematic errors (bias) and Random errors
( Statistics to estimate random errors)
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BIAS AND R ANDOM ERRORS
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Measurement errors
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Bias and Random Errors
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Resistive Displacement Sensor
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Capacitive Displacement Sensor C= Capacitance, o &r =Permittivity of air and Dielectric
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Linear Variable differential
Transformer ( LVDT )
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Linear Variable differentialTransformer ( LVDT )
Primary coil voltage: VS sin(t)
Secondary coil induced emf:
V1=k1sin(t+) and V2=k2sin(t+)
k1 and k2 proportional to the position of the coil
When the coil is in the central position, k1=k2
VOUT = V1-V2 = 0
When the coil is is displaced , k1 k2
VOUT
=(k1-k2)sin(t+)
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Wheatstone Bridge
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Strain Gage [Gage Factor = (¨R/R)/(¨L/L)
& Young¶s Modulus = (P/ A) / (¨L/L)
]
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Viscosity Measurements
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Fluid Viscosity
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Flow Rate Measurements
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Pitot Tube Traverse Points
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Flow Instrumentation
± Orifice, venturi tube, flow tube, flow nozzles.
± Pitot tubes, elbow-tap meters, target meters.
± Rotameter and Nutating diskTohelp protectyour privacy, PowerPointprevented thisexternalpicture frombeing automatically downloaded.To download anddisplay thispicture,click Optionsin theMessageBar,andthen click Enableexternalcontent.
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Obstruction Flow Meter
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Miscellaneous Flow Meters
Turbine, vortex shedding flow meters. Mass meters include Coriolis and thermal types. Hot-Wire Anemometer: Electrically heated, fine platinum
wire immersed in flow Wire is cooled as flow is
increased Measure either change in wire resistance or heating current to determine flow Electromagnetic Flow meter:Electromotive force induced
in fluid as it flows through magnetic field and measuredwith electrodes which is proportional to flow rate
Ultrasonic Flow equipment: Uses Doppler frequency shiftof ultrasonic signals reflected off discontinuities in fluid
Laser Doppler Anemometer which employ Doppler effectand Hetrodyning of two signals
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Flow Meters
Vortex magnetic Turbine
Coriolis mass flow meter
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Flow velocity measurement
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Rotameter
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MEASUREMENT ST AGES
Primary Sensing (Strain gage, thermometer) ± Retrieves energy from the measured system
± Produces some form of output Variable conversion
± Changes data from one physical form to another Elongation to resistance, temperature to volume change
Variable manipulation ± Performs mathematical operation on data Amplifier, filter
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MEASUREMENT ST AGES
Data transmission
± Gets data between measurement elements ± Wire, speedometer cable, satellite downlink system
Data storage/playback
± Stores data for later retrieval
± Hard drive, R AM
Data presentation ± Indicators, alarms, analog recording, digital recording
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Optical Pyrometer
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Thermocouple
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Thermocouples in Series and in
Parallel
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THERMOCOUPLE TIME CONSTANT
The conservation of energy:
m cp dT / dt = h A (To ± T)m : mass of thermocouple junction, C p: specific heat of thermocouple junction
h : heat transfer coefficient , A : surface area of thermocouple
T : junction temperature , To : environs temperature
=T ± To / Ti - ToTi = initial measurement junction temperature, then the solution is
= e (-t / )
w
herew
e have defined the time constant for this process as = m cp /h A
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Hot Wire
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King¶s Law
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Laser Doppler Anemometer
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Strain Gage
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Periodic Wave and its Spectrum
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Time Domain & Freq. Domain
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frequency spectrum examples
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Square and Hanning window functions
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Periodic Signals
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Sine Wave Digitising
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Periodic Wave and its Spectrum
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Square Wave and its Spectrum
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Analog and Digital Signals
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Analog RC Filtering
Bi ( t ti ) d
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Bias (systematic) andRandom (precise) Errors
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Errors in Measuring a Variable
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Propagation of Errors
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Combination of Errors
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Dimensional Analysis
Data presented in dimensionless form.
Reducing No of experimental variables.
N o
of variables - N o
of dims.= N o
of
groups Use pi method or by inspection
Basic dimensions: M L T (kg,m,sec,ok)
Saving(time&$)(10 tests ±vs- 10 4
tests for F= f n
(L,V,, ))
Force coef. F /v 2 L2 = f n (Reynolds number vL/ )
Helping in exp. Planning, insight, and similitude.
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Application of Mech. Measurements
Monitoring and operation of process. Control of a process ( accurate control f n measurement acc.)
Experimentation:- Testing and performance operation
- Verification of properties or theory
- Information needed for analysis
e.g. Checking or evaluation of:
Oil viscosity variation with temp.
Pump performance curvepiping head loss
Lift and drag of new airfoil shape««.etc.
Objectives of Mechanical
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Objectives of Mechanical
Measurements Measurement of physical variables:
Force vector (N), Velocity vector (m/sec.),T(oC), P (Pascal), Frequency (Hz=cycle/sec)..
Measurement of Mechanical Parameters:R e=vd/, Mach No.= v/c, P D=0.5 V 2
Accurate and Reliable Measurements:
R eal value ± vs ± Measured value
Calibration using Primary
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Calibration using Primary
or/and Secondary Standards Known input signal and find the output.
- To establish the correct output scale.
- To find instrument reliability.
- To eliminate bias error (systematic error)
For linear relation o/ p I / p needs single
point calibration.
For non-linear relation needs multi-pointcalibrations.
Static calibration ± vs ± Dynamic calibration
Primary Standards For
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Primary Standards For
Comparison and Calibration S I S ystem: Meter ± Kg -- Sec.± Kelvin ± volt -
Mole ± Ampere ± Radian
LENGTH (meter): Distance traveled by light
in vacuum during 1 /299792458 of a sec. MASS (Kg.): International prototype ( alloy of
platinum and iridium) kept near Paris.
TIME (Sec.): Duration of 9192631770 periods of
the radiation emitted between two excitationlevels of Cesium-133
TEMPERATURE (Kelvin): K = oC + 273
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Measuring System Stages
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FLOWMETER SELECTION
Flowmeter e
lement Recommended Service Range Pressure
loss Typica
lAccuracy,
%L (Dia.) Cost
Orifice Clean, dirty liquids; some slurries 4 to 1 Medium ±2 to±4 of full scale 10 to 30 Low
Wedge Slurries and Viscous liquids 3 to 1 Low tomedium ±0.5 to±2 of full scale 10 to 30 High
Venturi tube Clean, dirty and viscous liquids; 4 to 1 Low ±1 of full scale 5 to 20 Medium
Flow nozzle Clean and dirty liquids 4 to 1 Medium ±1 to±2 of full scale 10 to 30 Medium
Pitot tube Clean liquids 3 to 1 Very low ±3 to±5 of full scale 20 to 30 Low
Elbowmeter Clean, dirty liquids; some slurries 3 to 1 Very low ±5 to±10 of full scale 30 Low
Target meter Clean, dirty viscous liquids; 10 to 1 Medium ±1 to±5 of full scale 10 to 30 Medium
Variable area Clean, dirty viscous liquids 10 to 1 Medium ±1 to±10 of full scale None Low
Positive Displacement Clean, viscous liquids 10 to 1 High ±0.5 of rate None Medium
Turbine Clean, viscous liquids 20 to 1 High ±0.25 of rate 5 to 10 High
Vortex CLean, dirty liquids 10 to 1 Medium ±1 of rate 10 to 20 High
Electromagnetic Clean, dirty viscous conductive liquids& slurries 40 to 1 None ±0.5 of rate 5 High
Ultrasonic (Doppler) Dirty, viscous liquids and slurries 10 to 1 None ±5 of full scale 5 to 30 High
Ultrasonic(Travel Time) Clean, viscous liquids 20 to 1 None ±1 to±5 of full scale 5 to 30 High
Mass (Coriolis) Clean, dirty viscous liquids; some slurries 10 to 1 Low ±0.4 of rate None High
Mass (Thermal) Clean, dirty viscous liquids; some slurries 10 to 1 Low ±1 of full scale None High
Weir (V-notch) Clean, dirty liquids 100 to 1 Very low ±2 to±5 of full scale None Medium
Flume (Parshall) Clean, dirty liquids 50 to 1 Very low ±2 to±5 of full scale None Medium
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UNCERT AINTY IN PL ANING
During the design of the experiment
Identify all possible sources of error:
± Experiment set up: facility effects, environmental effects, human , «..
± Measurement system: velocity, temperature,...
Estimate possible severity of each source ± Discuss with advisor.
For those that are considered ³important ,́ identify strategies.
± Experimental design and/or test protocols (e.g. repeat tests)
Plan for quantitative analysis of reduced data
± Quantitative analysis relies on math model of the system
± Often good for measurement systems: pitot probe, strain gauge,...
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UNCERT AINTY ST AGES
During the experiment ± Execute experiment with replications
± Record notes in lab notebook
± Check for mistakes and Bias errors During data reduction
± Calculate error bars for measurements
± Check for outlier points
During data interpretation/reporting
± Consider errors when interpreting data 1st order &Nth order Assure findings are beyond uncertainty of experiment
± Display error bars in way that aids in understanding findings
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Dynamic Performance
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Sampling and Aliasing error
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Resolution of an A/D Converter
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Experimental Design and Analysis
Simple Comparative Experiment.
One Factor: t-Test (2-levels or treatments)
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F Tests
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Least Significant Difference
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Factorial Design
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Measurement Basics
Jayesh BarveMechanical Engineering Department
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Books to be Referred
1. Measurement and Control by Nakra &Chowdhry
2. Measurement and Control by
D.S.Kumar 3. Measurement and Control by Backwith
and Buck
4. Measurement and Control by Swahney
Some Tools for
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Some Tools for
Measurement
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Measurement in ChemistryIn chemistry we
jdo experiments
jmeasure quantities
juse numbers to report measurements
Applications of Mechanical
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Applications of MechanicalMeasurements
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Why Measurement
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Measurement System generally
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easu e e t Syste ge e a yconsists of Four Stages
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