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UNIT ± I

MEASUREMENTS

BASICS

BYJayesh Barve

An Introduction to Measurement and An Introduction to Measurement and

EvaluationEvaluation

Jayesh Barve

Associate Professor

Mechanical Engineering Department

Practice, Practice, Practice

Challenge

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.

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.

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.

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.

Evaluation

Evaluation means that you gather information to draw conclusions and makenew predictions.

Places where measurement and evaluationare used:

Research

Education

Business Sports

Medicine

Health and Rehabilitation

Reasons for Measurement and Evaluation

Motivation

Accountability

Equipment Placement

Diagnosis

Evaluation of learning

Prediction

Program Evaluation

Standards of Measurement and Evaluation--Measurement Theory

Reliability Validity

Objectivity

Sensitivity

Descriptive Statistics

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

Levels of Measurement

Nominal

Ordinal

Interval

Lowest level

Highest level

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.

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.

Interval scores - These scores have acommon unit of measurement betweenadjacent points. No true zero point existson the interval scale.

Ratio scores - These scores have acommon unit of measurement betweenadjacent scores. Ratio scores have a truezero point.

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?

When we measure, we use a

measuring tool to compare

some dimension of an objectto a standard.

Some Tools for

Measurement

Stating a Measurement

In every measurement there is a

jNumber

f ollowed by a

j Unit from measuring device

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.

Standards organizations

SASO² Saudi Arabian Standards

organization

²InternationalO

rganization for Standardization

Others²ASME, NFPA, ASTM, etc.

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

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

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)

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)

Generalized Measurement

System

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.

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.

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?

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

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

Dimensional Analysis

Data presented in dimensionless form.

Reducing No of experimental variables.

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.

Uncertainty of Measurements

Measurement error = Measured result - True

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)

BIAS AND R ANDOM ERRORS

Measurement errors

Bias and Random Errors

Resistive Displacement Sensor

Capacitive Displacement Sensor C= Capacitance, o &r =Permittivity of air and Dielectric

Linear Variable differential

Transformer ( LVDT )

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

=(k1-k2)sin(t+)

Wheatstone Bridge

Strain Gage [Gage Factor = (¨R/R)/(¨L/L)

& Young¶s Modulus = (P/ A) / (¨L/L)

Viscosity Measurements

Fluid Viscosity

Flow Rate Measurements

Pitot Tube Traverse Points

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

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

Flow Meters

Vortex magnetic Turbine

Coriolis mass flow meter

Flow velocity measurement

Rotameter

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

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

Optical Pyrometer

Thermocouple

Thermocouples in Series and in

Parallel

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 / )

e have defined the time constant for this process as = m cp /h A

Hot Wire

King¶s Law

Laser Doppler Anemometer

Strain Gage

Periodic Wave and its Spectrum

Time Domain & Freq. Domain

frequency spectrum examples

Square and Hanning window functions

Periodic Signals

Sine Wave Digitising

Periodic Wave and its Spectrum

Square Wave and its Spectrum

Analog and Digital Signals

Analog RC Filtering

Bi ( t ti ) d

Bias (systematic) andRandom (precise) Errors

Errors in Measuring a Variable

Propagation of Errors

Combination of Errors

Dimensional Analysis

Data presented in dimensionless form.

Reducing No of experimental variables.

of variables - N o

of dims.= N o

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.

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

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

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

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

Measuring System Stages

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

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,...

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

Dynamic Performance

Sampling and Aliasing error

Resolution of an A/D Converter

Experimental Design and Analysis

Simple Comparative Experiment.

One Factor: t-Test (2-levels or treatments)

F Tests

Least Significant Difference

Factorial Design

Measurement Basics

Jayesh BarveMechanical Engineering Department

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

Measurement

Measurement in ChemistryIn chemistry we

jdo experiments

jmeasure quantities

juse numbers to report measurements

Applications of Mechanical

Applications of MechanicalMeasurements

Why Measurement

Measurement System generally

easu e e t Syste ge e a yconsists of Four Stages

basics of measurement-1

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