1E11 - Lecture notes All PDF

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Caulifield, Boland, Kennedy...

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Experimental Methods 1. Data  Transportation Engineering -Travel diary- Excel spreadsheet (blackboard)- use numbers (codes)- SPSS -Computer based labs, inputting data Transport Data  Tells us what to spend huge, million-euro budgets on  Proves a mode of transport is unsafe  Transport Safety and efficiency  Calculate the emissions 2. Experimental Measurement  (an Introduction to the Analysis and Presentation of Data by Les Kirkup)  Why do engineers take measurements? -Usability, good output -Aesthetics, doesn’t disrupt the environment - Cost - Efficiency  Quantitative Data: Height, Length, materials used  Qualitative Data: Design comments, opinions -Qualitative data determines what the outcome of the design will be.  Function of an Experiment - Take measurements as accurately as possible - Quantify a measurement of uncertainty  How the measurement uncertainty is quantified - Every measurement taken should be expressed X + or – Y (If not it is implied, if it is implied the uncertainty is negligible) SI Units  ESSENTIAL

Sensors and Transducers  Sensor detects energy, a transducer converts energy from one form to another.

 Actuator is a transducer that only produces an output  No sensor is going to be sensitive to one form of energy (Issue)- this will cause uncertainties  Scientific instruments are high quality measurement systems with high accuracy and low uncertainty  Measurement instrument: Medium measured-primary sensing element-variable conversion element-variable manipulation element Therefore they are extremely expensive, ideal instrument meets all our requirements at low costs  Static and Dynamic are two types of quantities that we may be interested in measuring  Static variables=  Dynamic variables =  Range of an instrument: the min./max. values of input or output variables  Span: The max. variation of input or output variables  Linearity: The extent to which input values and output values lie on (or near) a straight line  Non-linearity: There is a more complex relationship between input and output  Hysteresis: some instruments have different loading and unloading performance (increasing=loading, unloading=decreasing)  Resolution: the smallest change in a variable  Ideal linear behaviour can be accepted as linear behaviour - Eg: pressure gauge  Drift: A change in the graph

Calibration  Calibration: a process of validating a measurement technique or instrument  Standard: tests the performance of a piece of instrument

 Primary standard: State of the art calibration (eg: government calibration)  Secondary standard: Available from national labs  Tertiary: In house calibration 1. Data Significant Figures  Count the digits that come after zero; eg: 0.034, two significant figures  If in the thousands, eg: 64000, count only the numbers before zero, 2 significant figures there  You cannot add or subtract accuracy using maths, therefore the results of the formula must have the same number of digits as the input.  Don’t round until the end of the equation Rounding    

Truncation Round to the nearest even Ceiling Flooring

-Truncation Throw away the numbers after the first ‘x’ amount of significant figures Handy for computer programming -RNE If the number after a 5 is even, round up If it’s odd, round down  Accuracy- describes how well the measurement agrees with a known standard

 Precision- describes the degree of certainty about the measurement  The measured value and its uncertainty must always have the same number of digits after the decimal place  Resolution Uncertainty- limit of accuracy of the equipment used How to calculate the uncertainty in the mean: 1. Calculate the range - Max.-Min= Range 2. Divide the range by the number of measurements  Spread of the data- the difference between the deviations of the results from the mean  Standard deviation can be used to calculate the uncertainty  Using standard deviation doesn’t reduce the uncertainty when the number of experiments are increased (NOT IDEAL)  Therefore, the standard deviation of all means is recorded

 Uncertainty=

standard deviation of the means √n

 This is known as the standard error  More experiments result in a smaller uncertainty Simple maths using uncertainties  Find the area/perimeter of a box: l: (3.04+/- 0.05) w: (1.55+/- 0.02) Perimeter: Add the uncertainties and the normal figures `

P= (3.04+1.55) +/- (0.05+0.02) Subtraction: (3.04-1.55) +/- (0.05+0.02)

0.02 1.55 0.05 ´ ¿ 3.04

+¿

Area= ((3.04)(1.55))x(1+/-(

))

Division: ∆Y Y ∆X ´ ¿ +¿ X 1¿´ x ¿ y +¿

)

Multiplication: ∆Y Y ∆X´ ¿ +¿ X 1¿´ XY ¿ +¿

)

ALWAYS HAVE A GREATER UNCERTAINTY AT THE END OF THE EQUATION  Error Bars -> show the uncertainties on a graph Line Fitting  Line must represent the physics that is happening on a graph  Interpolated Point – values in between our measured values  Extrapolated Point – values beyond our measured range - Both quite risky, but it depends on if the line of the graph matches the physics that is happening ->How to Calculate the line of “best fit” Least Squares Method: - Minimises the sum of the squares of the vertical deviation 1. Use Equation: y ic=mxi + c

2. Convert to simultaneous equation to work out ‘m’ and ‘y’: n

n

n

x i yio =∑ m x i❑2 + ∑ cxi ∑ i=1 i=1 i=1 n

n

y io =∑ m x i+ nc ∑ i=1 i=1

3. This gives us: m=

c=

n ∑ xi y io −∑ x i ∑ y io n ∑ x i2− ( ∑ xi )

2

∑ x i 2 ∑ yio −∑ x i ∑ xi yio 2 2 n ∑ x i −( ∑ x i ) y io =Calculated data, xi =calculated data

 The co-efficient of determination calculates how well the line fits the data Co-efficient of Determination:

2

r=

∑ ( y ic − ´y ) 2 ∑ ( y io − ´y ) 2

- Least squares method only works when there are no error bars in the x axis and it assumes that all the uncertainties in the y axis are equal Best Fit Line  Having calculated the line of best fit you must be able to pinpoint the centroid which lies on the line for the line of best fit to be correct - ´y =m ´x + c - This proves this fact  Uncertainty in the slope:

n

√

σ y=

∑ [ y❑io − y ic❑ ]2 i=1

N−2

n

√

=

[ y io❑−(m xi + c )]2 ∑ i=1 N −2

√

❑

σ y (∑ x i ) σ √N , σ c= σm= y Δ Δ

√

2

2 Δ= [ N ∑ xi❑ −(∑ x i ) ] 2

Gaussian Distribution - Normal Distribution 

−( x− μ ) 2 2σ

2

1 f ( x) = e √2π σ

μ=mean σ=standard deviation

σ2

=variance

Transducer/Sensor  Resistance, Capacitance and Inductance are used to measure physical quantities. Resistance Capacitance Displacement Displacement Temperature Sound pressure Strain  Wheatstone Bridge

Inductance Displacement

Strain Gauge 

Strain=

-

ΔL =ε L

change ∈ length unit length

 Uses resistance to measure the strain:

R=

ρL A

- Wheatstone bridge used - Temperature must be constant for this or temperature change must be recorded and accommodated for - This is known as Temperature Induced Apparent Change:

  -

Its undisguisable from strain This can be calculated and removed Extra strain gauge used to calculate the temperature change This is costly and difficult to calculate The Gauge Factor (GF): determines relative change in resistance with strain. The higher the gauge factor the higher the sensitivity Transverse strain will occur when longitudal strain is being calculated. We use Possion’s ratio to determine what the transverse strain will be

 Possions’s ratio:    • • •

v=

−ε trans ε axial

Disadvantages of resistance foil strain gauges Sensitive to temperature – may need some compensation Low output from Wheatstone Bridge – requires amplification Needs a very well-regulated power supply Advantages Behaviour well understood Reasonable cost Small, flexible – can be installed on curved surfaces Microphones

 Two types: Condenser, Electret  They both work using the electrical property of capacitance.  Dielectric: non-conductive material  In a condenser: - one plate of the capacitor is made from a flexible metal diaphragm. - The other plate is rigid metal with a small air gap between the two plates.

- When sound waves hit the front plate, they cause it to vibrate. This vibration changes the distance between the two plates and hence the capacitance. - To avoid the capacitor being sensitive to atmospheric pressure, a hole is placed in the top of the microphone to regulate its pressure  The natural frequency of a system is given by ω n=

√

k m

Where k is the stiffness and m is the mass.  The microphone diaphragm has a natural frequency and we want this to be very far above any of the frequencies which it will likely be exposed to measuring sound  How do we make the natural frequency very high? We need high stiffness and low mass.  We can increase the stiffness during the manufacturing by pulling the material tight across the opening. - This makes the microphone less sensitive, so we increase the area to compensate for this loss in sensitivity - There is a limit to the size of the area that can be used, because if it is too large it will be affected by both the positive and negative parts of the wave. - Hence, we have multiple microphones - The diaphragm should be less than 1.7cm (perhaps half).  Resistance = impediance  Condenser microphones are very likely to have errors in humid conditions - Because the water vapour in the air giving the electrons a semiconductor to get from one plate in the capacitor to the other  Electret Microphones:

 The electret microphone is a modified version of the condenser where the airgap between the metal plates has been replaced by a polymer. Temperature Sensors  Thermocouples: - Voltage output proportional to (absolute) temperature - Seebeck Effect: the junction of two dissimilar metals (alloys) generates a voltage proportional to temperature - When the circuit is broken the open circuit voltage eAB (Seebeck voltage) depends on the junction temperature and the metals used. - For small temperature changes the Seebeck voltage is linearly proportional to temperature.

-

-

 - Where α is the Seebeck coefficient - At every junction there is a seebeck voltage, therefore, we cannot determine the temperature until we know the seebeck voltage at each junction o This is only an issue when the metals connecting at a junction are different (creating another thermocouple) We can solve this problem by using a reference junction. We can place our reference junction (J2) in an ice bath (0°C) Hence the reference junction is called a cold junction V=α(TUNKNOWN-TREF) α is Seebeck coefficient Obviously, this is not a practical solution in most cases. To do this: Firstly make sure junctions J3 and J4 are at same temperature by mounting them on an isothermal block.

- We can measure the temperature of the isothermal block with a temperature sensor which doesn’t need a reference junction e.g. a thermistor. - Advantages of Thermocouples Mechanically durable – easy to package and transport Wide operating range – from about -100°C to +2500°C Easy to construct

- Disadvantages: Low output voltage – micro-volts per degree (μV/°C) Slow measurements times – typically no more than few hundred readings per second Output is non-linear – requires linearisation somehow Temperature Resistance Detectors  Platinum is used as it is accurate and stable  Wheatstone Bridge  RTD has better linearity than a thermocouple  Resistance of 100ῺῺ - Disadvantages: The slope of 0.385Ὼ/°C is a very small change The resistance value of the sensor is small too only 100 Ὼ The resistance of the lead wires can cause very large errors  3 Wire Bridge: - To do this we match lengths of leads A and B. - They should now have same impedance - We change the connection points to measure the bridge voltage so that the leads A and B are now in opposite arms of the Wheatstone bridge. - This requires us to connect the wire C after lead A but before the RTD and lead B. - Hence we need a third wire running to the sensor.

 In order to convert Resistance value to Temperature we need some form of calibration curve  We can approximate the RTD curve with the Callendar-Van Dusen equation: - R (t ) =R (0) [1+ At +B t 2 ] - ( t )=R ( 0 ) [1+ At + B t 2+ (t −100 ) C t3]  Sources of Error: - Self heating - Thermal shunting - Thermal EMF - These sources of error depend on the size of the RTD

Thermistors    

Material used is a ceramic or polymer The operating range is -90ºC to +130ºC They are more sensitive than RTD but have a smaller range They have a non-linear resistance-temperature curve

 There are two types of thermistor PTC and NTC standing for Positive Temperature Coefficient and Negative Temperature Coefficient.  In NTC thermistor resistance decreases with increasing temperature.

 In order to convert the resistance value to temperature we need an equation for the device. In this case it is the Steinhart-Hart Equation: 1 = A+B × ln R+C × ( ln R ) 3 T

 We can make the response of the thermistor more linear by design a circuit with a parallel (shunt) resistor. - This will linearise the output over a short range at the expense of a reduced sensitivity from the sensor

Disadvantages to all 3 Heat Sensors

 Thermocouple: - Needs another heat sensor to calibrate it  RTD: - Very low sensitivity, increases the experimental error

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 Thermistor: Low range Unsensitive Writing  A technical report should generally include the following sections: Title Abstract Introduction Experimental Method Results Discussion Conclusions References  Abstract: An overview of the experiment and its findings  Intro: An overview of the experiment and its findings  Experiment Method: Observations of what was actually done, including observations of what happened  Results: All figures included should be explained and discussed! Aim for at least one paragraph per figure! It is not necessary to include every calculation or figure but there should be enough to support your discussion and conclusions.  Discussion of Results: You should consider whether or not the results are as might be expected from the theory, if not attempt to explain why not. You will consider possible experimental errors and uncertainty at this stage.  Types of Questionnaires:

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Cordon surveys Travel Diaries Roadside Interviews Panel Survey Cohort Survey  Disadvantages of Surveys Panel surveys may become unrepresentative as individuals age May omit phenomena  Methods of transport planning Traffic Impact assessment Traffic Impact analysis Traffic Impact studies  Traffic Forecasting Congestion is calculated by looking at the volume to capacity ratio. v/c When the ratio is greater than 1 congestion will occur

Human Factors  How humans interact with the environment - Quantitative data and qualitative data are used to calculate this Scientific Experiments  Keep a log book  Test Matrix- Experimental plan  Test Point – unique set of test conditions - Each test point must be carefully analysed and chosen accordingly Data Acquisition  This refers to the gathering of data relating from continuous analogue to discrete data form or vice versa

 Analogue signal: a signal which is continuous function of some variable  Digital Signal: a signal which is quantised and can only have a limited number of values within a given range

Binary Number System   -

Number Systems- Positional NS, Decimal and binary NS Positional: Radix- The base or Foundation of the system (root) Digits- the individual numerical symbols or characters which make up the system Decimal Digits: 0 1 2 3 4 5 6 7 8 9 Binary Digits: 0 1 Binary System Weighting: 2^6 2^5 2^4 2^3 2^2 2^1 2^0 MSB LSB Each weighted position is referred to as a Binate, but this term is not common in practice and usually the term Bit is used The term ‘Bit’ is generally used to refer to either the digits ‘0’ and ‘1’ The value of a number is determined by adding up the weighted values of all of the digits in the number This is done by multiplying the digit at each position by the value of the radix raised to the power of the exponent of the radix at the position in question and then summing the values of all digits.

- Decimal to Binary +

 This is done to convert analogue signal to a digital signal  Resolution- the ability to distinguish two measurements as separate rather than single measurements  A staircase approximation is made of the analogue system, this causes an error - The quantised error

 Quantisation Error = Output voltage – Input Signal Voltage= +/½ Level  Quantum Step Voltage = V Q=2 ∆V Fs  Δ= the percentage change of the voltage ∆=

1 ×100 L V Fs 1 +1= +1 2∆ VQ V ref V Q= L

 Number of levels => L =  Quantisation Step =>

 Vref = The reference voltage of the data acquisition system V_FS => V full scale  V V  Voltage Gain= fs V pk

 Number of Bits =      

Lo g 2 L

V Fs V Fs 1 +1= +1 + 1= 2∆ VQ 2 ∆V Fs 1 Absolute error=± V Q 2 L=

Effects of Quantisation The more bits the better the sound Due to the resolution of the sample The more bits the better quality of picture Fourier Series Deconstructs a periodic function into the sum of sinusoidal functions 10

1 sin( ( 2n+ 1 ) w0 t) (2 n+1) n=0

Square Wave → v ( t) =∑

- This is the approximation of a square wave - A function is periodic, with fundamental period T, if the following is true for all t - F(t+T) = f(t) Signal Sampling  The actual number of samples required to create a theoretically perfect copy are ruled by the Nquist-Shannon theorem

 Aliasing- an effect that causes different signals to become indistinguishable when sampled - Causes pictures to become pixelated and sound to become a buzz  Sampling theorem- All of the information present in a bandlimited , time varying signal is contained within samples of the signal spectrum and images of this spectrum f s≥ 2 f m f s=Sampling frequency

 -

Data Acquisition Time = Sample Time + Encode Time Encode time -> Convert to binary Data Acquisition Time TACQ = TSMP + TENC Data Acquisition Time TACQ = TSMP + THLD 1 Data Acquisition Time 1 DataConversion Rate=f con=f S= sample / sec ( Hz ) T acq Data conversion rate=

Capacitance=20 f s

-

DataConversion Serial Bit Rate=n f con =n f s

Analogue to Digital Conversion

#

Digital to Analogue Conversion  RS. This means that the voltage developed across the load resistance is: V l=I s RL - The voltage developed across the load resistance, RL, is dependent on the value of RL itself and the current IS. It does not, however, depend on the series resistance, RS.  Kirchhoff’s Current Law: This law states that the sum of currents at a node is zero. This is essentially the principle of conservation of electric charge, which can neither be created from nothing nor destroyed into oblivion. - Note that a node is considered to be any point in a circuit at the same potential which can therefore include several connections to the same electrical point but at different physical locations.

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Exam  

Q1: all areas of the course, tutorial questions Chose q...