tw22 university of bolton school of engineering …...>> y([8 2 9 1]) % extracts the elements...

TW22 UNIVERSITY OF BOLTON

SCHOOL OF ENGINEERING

BSC (HONS) IN MOTORSPORT TECHNOLOGY

SEMESTER 2 EXAMINATION 2016/2017

CHASSIS AND ELECTRONIC PRINCIPLES

MODULE NO: MSP4001

Date: Tuesday 16 May 2017 Time: 10.00 – 12.00 INSTRUCTIONS TO CANDIDATES: This paper is split into two parts. Part A

and Part B. Answer BOTH questions from Part A and

BOTH questions from Part B. Marks for parts of questions are shown

in brackets. Electronic calculators may be used

provided that data and program storage memory is cleared prior to the examination.

CANDIDATES REQUIRE: i) Formula Sheet (attached) ii) Matlab Tutorial (booklet) iii) PC, Matlab software

PAST EXAMIN

ATION P

APER

of 7 School of Engineering BSc (Hons) Motorsport Technology Semester 2 Examination 2016/2017 Chassis and Electronic Principles Module No. MSP4001 PART A:

Question 1 Performance tests are carried out on a car weighing 650 kg. a) The car completes 2 timed laps. The first laptime is recorded as 1m23.35s and the second as 1m24.23s. If the lap distance is 3.13 km calculate the average speed of the car in SI units to 2 decimal places for: (i) lap 1, (ii) lap 2 and (iii) laps 1 and 2 combined [6 marks] b) With reference to the above question and using a sketch, explain the difference between the terms ‘distance’ and ‘displacement’. [3 marks] c) Straight line tests are then carried out. The car accelerates uniformly from a speed of 18 ms-1. If it takes 12 seconds for the car to travel 400 m, calculate to 1 decimal place: (i) the final speed of the car, (ii) the acceleration during this period and (iii) the force required to achieve this acceleration [9 marks] d) If the diameter of the tyre of the car is 650 mm calculate its angular velocity at the end of the 12 second period. [3 marks] e) The driver of the car then applies the brakes. It takes 2.3 seconds for the car to come to rest in a uniform way. How many revolutions of the tyre will occur during this time? (give your answer to 2 decimal places) [5 marks] f) Calculate the amount of Kinetic Energy lost by the car during braking. Explain what happens to the Kinetic Energy. [4 marks] [Total: 30 marks]

Please turn the page.

PAST EXAMIN

ATION P

APER

of 7 School of Engineering BSc (Hons) Motorsport Technology Semester 2 Examination 2016/2017 Chassis and Electronic Principles Module No. MSP4001 Question 2 a) Brake discs made from steel and ‘carbon-carbon’ are commonly used in motorsport. State two advantages and two disadvantages associated with the use of each material.

[8 marks] b) Formula 1 cars use ‘carbon-carbon’ brakes, as do Le Mans LMP1 and LMP2 cars. LMP3 cars use steel brakes, suggest two reasons why this is the case.

[3 marks] c) Where else can ‘carbon-carbon’ materials be found in the drivetrain of a vehicle? State two reasons why this material is used for this component.

[4 marks] d) Explain what is meant by the term ‘coefficient of friction’ and comment on the units.

[3 marks] e) Explain why motorsport tyres can have a coefficient of friction which is greater than 1.

[2 marks] [Total Marks: 20]

Please turn the page

PAST EXAMIN

ATION P

APER

of 7 School of Engineering BSc (Hons) Motorsport Technology Semester 2 Examination 2016/2017 Chassis and Electronic Principles Module No. MSP4001 PART B: Question 3 For the circuit below, analytically calculate the total resistance, voltage, current and power quantities of Table 1, in the given units.

Quantity Calculated Value (i) RT (Total resistance) Ohms(ii) VR1 (Voltage across resistor R1) Volts(iii) VR2 (Voltage across resistor R2) Volts(iv) VR3 (Voltage across resistor R3) Volts(v) VR4 (Voltage across resistor R4) Volts(vi) VR5 (Voltage across resistor R5) Volts(vii) IT (Total current) Milliamperes(viii) I1 (Current flowing through resistor R2) Milliamperes(ix) I2 (Current flowing through resistors R3 and R4) Milliamperes(x) PT (Total circuit power) Milliwatts

Table 1: Values of calculated quantities Note: Each question carries 2.5 marks

[Total Marks: 25]

Please turn the page

Figure 1: Electronic circuit

PAST EXAMIN

ATION P

APER

of 7 School of Engineering BSc (Hons) Motorsport Technology Semester 2 Examination 2016/2017 Chassis and Electronic Principles Module No. MSP4001 Question 4 i) If y = [7 -1 2 3 9 5 4 -2 8 1], find a Matlab expression in order to display the following: a) Vector y1 consisting of the seventh up to the last element of vector y. b) Vector y2 consisting of the fourth, second and seventh elements of vector y. c) Vector y3 consisting of the second, fifth and eighth elements of vector y, using the colon operator. Hint: vector (first element: step: last element) [10 marks] ii) Using the linspace command, create a vector starting from zero, ending at 1000 and consisting of 5 elements. [5 marks] iii) Sketch using Matlab a sine wave starting from point zero ending at point 12.57 (4π) consisting of 100 points. In your plot, include the x-label: ‘Independent variable x’, the y-label: ‘Dependent variable y’ and the title: 'Sine curve'. [10 marks] Note that for all the questions above you need to include in your answer both the Matlab code as well as the corresponding output. [Total Marks: 25]

END OF QUESTIONS

PAST EXAMIN

ATION P

APER

of 7 School of Engineering BSc (Hons) Motorsport Technology Semester 2 Examination 2016/2017 Chassis and Electronic Principles Module No. MSP4001

FORMULA SHEET

Friction Equation:

F = μ.N Linear and Angular Motion: F = ma K.E. = ½ mv2

Linear Motion: Angular Motion:

v = u + at ω ω αt ω = θ/ t

s = ½ (u + v)t θ ω ω t s = rθ

s = ut + ½ at2 θ ω t αt v = ω r

s = vt – ½ at2 θ ω t αt at = rα

v2 = u2 + 2as ω ω 2αθ

Ohm’s Law

Power supplied by the Voltage Source

Energy

Kirchoff’s Current Law (KCL) at any node

Kirchoff’s Voltage Law (KVL) in any closed loop

Resistors in Series =

PAST EXAMIN

ATION P

APER

of 7 School of Engineering BSc (Hons) Motorsport Technology Semester 2 Examination 2016/2017 Chassis and Electronic Principles Module No. MSP4001 Resistors in Parallel =

Voltage Divider Rule

Current Divider Rule

Decibel (dB)

Logarithm =

END OF PAPER

PAST EXAMIN

ATION P

APER

Matlab CourseMatlab Course

Ioannis Paraskevas (PhD, CEng)

[email protected]

Array OperationsArray Operations

� Definition - Simple Arrays

� Array Addressing

� Array Construction

� Array Mathematics

� Arrays of Ones or Zeros

Definition Definition -- Simple ArraysSimple Arrays

Operations involving scalars are the basis of mathematics. At the same time, when we wish to perform the same operation on more than one number at a time, repeated scalar operations are time-consuming and cumbersome.To solve this problem, MATLAB defines operations on data arrays.

ExampleExample

� Compute the values of the sine function over one-half of its period, namely y=sin(x), x belongs [0,pi].

Forx = 0, .1pi , .2pi , .3pi , .4pi , .5pi , .6pi , .7pi, .8pi, .9pi,

.pi

y = 0, .31, .59, .81, .95, 1.0, .95, .81, .59, .31, 0

In MATLAB:

>> x=[0 .1*pi .2*pi .3*pi .4*pi .5*pi .6*pi .7*pi .8*pi .9*pi pi] (Enter)

x =

0 0.3142 0.6283 0.9425 1.2566 1.5708 1.8850 2.1991 2.5133 2.8274 3.1416

>> y=sin(x) (Enter)

y =

0 0.3090 0.5878 0.8090 0.9511 1.0000 0.9511 0.8090 0.5878 0.3090 0.0000

Array AddressingArray Addressing

� In MATLAB, individual array elements are accessed using subscripts, e.g.,x(1) is the first element in x, x(2) is the first

element in x etc. For example:>> x(3) % The third element of x

ans = 0.6283

>> y(5) % The fifth element of y

ans = 0.9511

Array AddressingArray Addressing

� To access a block of elements at one time, MATLAB provides colon notation. For example:

>> x(1:5) % start with one and count up to 5

ans = 0 0.3142 0.6283 0.9425 1.2566

>> x(7:end) % starts with the seventh element and continues to the last element

ans = 1.8850 2.1991 2.5133 2.8274 3.1416

>> y(3:-1:1) % start with 3, count down by 1, and stop at 1

ans = 0.5878 0.3090 0

>> x(2:2:7) % start with 2,count up by 2, and stop when you get to 7

ans = 0.3142 0.9425 1.5708

>> y([8 2 9 1]) % extracts the elements of the array y in the order we wish

ans = 0.8090 0.3090 0.5878 0

Array ConstructionArray Construction

The basic array construction features of MATLAB are summarized as follows:Basic Array Construction

x = [2 2*pi sqrt(2) 2-3j] create row vector x containing elements specifiedx = first:last create row vector x starting with first, counting by one, ending at

or before lastx = first:increment:last create row vector x starting with first, counting by

increment, ending at or before lastx = linspace(first,last,n) create row vector x starting with first, ending at last,

having n elementsx = logspace(first,last,n) create logarithmically spaced row vector x starting

with 10^(first), ending at 10^(last), having n elements

ExamplesExamples

>> x=(0:0.1:1)*pi % create row vector x starting with first, counting by increment, ending at or before last

x = 0 0.3142 0.6283 0.9425 1.2566 1.5708 1.8850 2.1991 2.5133 2.8274 3.1416

>> x=linspace(0,pi,11) % create row vector x starting with first, ending at last, having n elements

x = 0 0.3142 0.6283 0.9425 1.2566 1.5708 1.8850 2.1991 2.5133 2.8274 3.1416

>> x=logspace(0,2,11) % create row vector x starting with first, ending at last, having n elements

x = 1.0000 1.5849 2.5119 3.9811 6.3096 10.0000 15.8489 25.1189 39.8107 63.0957 100.0000

Array MathematicsArray Mathematics

The basic array operations are summarized as follows:Element-by-Element Array Mathematics

Illustrative data: a = [a1 a2… an], b = [b1 b2… bn], c = <a scalar>� Scalar addition: a + c = [a1+ c a2+ c… a2+ c ]� Scalar multiplication: a * c = [a1* c a2* c … an* c ]� Array addition: a + b = [a1+ b1 a2+ b2… an+ bn ]� Array multiplication: a .* b = [a1* b1 a2* b2 … an* bn ]� Array division: a ./ b = [a1 / b1 a2 / b2 … an / bn ]� Array powers: a.^c = [a1 ̂ c a2 ̂ c … an ̂ c]

c.^a = [c^ a1 c^ a2 … c^ an]a.^b = [a1 ̂ b1 a2 ̂ b2 … an ̂ bn ]

Arrays of Ones or ZerosArrays of Ones or Zeros

� Because of their general utility, MATLAB provides functions for creating arrays containing either all ones or all zeros

Examples

� >> ones(3) % creates a 3x3 matrix consisted of 1s

ans =

1 1 1

1 1 1

1 1 1

� >> zeros(2,5) % creates a 2x5 matrix consisted of 0s

ans =

0 0 0 0 0

0 0 0 0 0

Relational and Logical Relational and Logical OperationsOperations

Relational operatorsRelational Operator Description

� < less than

� <= less than or equal to

� > greater than

� >= greater than or equal to

� = equal to

� ~= not equal to

ExamplesExamples

>> A=1:9

A =

1 2 3 4 5 6 7 8 9

>> B=9-A

B =

8 7 6 5 4 3 2 1 0

>> tf=A>4 % finds elements of A that are greater than 4.

tf =

0 0 0 0 1 1 1 1 1

>> tf=B-(A>2) % finds where A>2 and subtracts the resulting vector from B

tf =

8 7 5 4 3 2 1 0 -1

Relational and Logical Relational and Logical OperationsOperations

Logical operatorsLogical Operator Description� & AND� | OR� ~ NOT

Example>> A=1:9A =1 2 3 4 5 6 7 8 9>>tf=(A>2)&(A<6) % returns ones where A is greater than 2 AND less than 6tf =0 0 1 1 1 0 0 0 0

Other Relational and Logical Other Relational and Logical FunctionsFunctions

� xor(x,y) Exclusive OR operation. Return ones where either x or y is nonzero (True). Return zeros where both x and y are zero (False) or both are nonzero (True).

� any(x) Return one if any element in a vector x is nonzero. Return one for each column in a matrix that has nonzero elements.

� all(x) Return one if all elements in a vector x are nonzero. Return one for each column in a matrix x that has all nonzero elements.

TwoTwo--Dimensional GraphicsDimensional Graphics

The plot command through examplesx=linspace(0,2*pi,30); % creates row vector x starting with zero, ending at 2*pi, having

30 elements

y=sin(x);

z=cos(x);

plot(x,y,x,z) % plots vector y vs. vector x and vector z vs. vector x

xlabel('Independent Variable X') % labels the x-axis

ylabel('Dependent Variables Y and Z') % labels the y-axis

title('Sine and Cosine Curves') % entitles the figure


x=linspace(0,2*pi,30); % creates row vector x starting with zero, ending at 2*pi, having 30 elements

y=sin(x);

z=cos(x);

plot(x,y,'b:p',x,z,'c-o') % plots vector y vs. vector x and vector z vs. vector x,

b:p and c-o specify colour, line style and marker of the curve

xlabel('Independent Variable X') % labels the x-axis

ylabel('Dependent Variables Y and Z') % labels the y-axis

title('Sine and Cosine Curves') % entitles the figure

grid on % adds grid lines to the current axes

axis off % turns off all axis labeling and background


Symbol Colour Symbol Marker Symbol Line styley yellow . point - solidm magenta o circle : dottedc cyan x x-mark -. dashdot r red + plus -- dashed g green * starb blue s squarew white d diamondk black v triangle (down)

^ triangle (up)< triangle (left)> triangle (right)p pentagramh hexagram


Other two-dimensional plotting features� loglog is the same as plot, except that logarithmic

scales are used for both axes.� semilogx is the same as plot, except that the x-axis

uses a logarithmic scale, and the y-axis uses a linear scale.

� semilogy is the same as plot, except that the y-axis uses a logarithmic scale, and the x-axis uses a linear scale.

ThreeThree--Dimensional GraphicsDimensional Graphics

Line plots

The plot command from the 2-D world can be extended into three dimensions with plot3. The format is the same as the 2-D plot, except the data are in triples rather than in parts.


Line plots

The plot3 command through an examplet=linspace(0,10*pi); % generates a row vector of 100 linearly

equally spaced points between 0 and 10*pi.

plot3(sin(t),cos(t),t) % where sin(t),cos(t) and t are three vectors of the same length, plot3 plots a line in 3-space through the points whose coordinates are the elements of x, y and z.

title('Helix'),xlabel('sin(t)'),ylabel('cos(t)'),zlabel('t') % labels the x,y,z axis and entitles the figure



Mesh and Surface plots

MATLAB defines a mesh surface by the z

coordinates of points above a rectangular grid in the

x-y plane. It forms a plot by joining adjacent points

with straight lines. The result looks like a fishing net with the knots at the data points. Mesh plots are very useful for visualizing large matrices or for plotting functions of two variables.


Mesh and Surface plotsThe first step in generating the mesh plot of a function of two variables, z=f(x,y), is to generate X and Y matrices consisting of repeated rows and columns, respectively, over some range of the variables x and y. MATLAB provides the function meshgrid for this purpose. [X,Y]=meshgrid(x,y) creates a matrix X whose rows are copies of the vector x, and a matrix Y whose columns are copies of the vector y. This pair of matrices may then be used to evaluate functions of the two variables using MATLAB’s array mathematics features


The mesh and meshgrid command through an example

x=-7.5:.5:7.5;

y=1:31;

[X,Y]=meshgrid(x,y); % X and Y arrays for 3-D plots

R=sqrt(X.^2+Y.^2);

mesh(X,Y,R) % 3-D mesh surface



Mesh and Surface plots

A surface plot of the same matrix R looks like the mesh plot previously generated, except that the spaces between the lines are filled in. Plots of this type are generated using the surf function, which has all of the same arguments as the mesh function.


The mesh and meshgrid command through an example

x=-7.5:.5:7.5;

y=1:31;

[X,Y]=meshgrid(x,y); % X and Y arrays for 3-D plots

R=sqrt(X.^2+Y.^2);

surf(X,Y,R) % 3-D coloured surface


tw22 university of bolton school of engineering …...>> y([8 2 9 1]) % extracts the elements...

Documents